Valuation of Equity Securities: History, Theory and Application 9814295388, 9789814295383

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Poitras

Professor Paul Davidson Visiting Scholar Bernard Schwartz Center for Economic Policy Analysis New School for Social Research New York, USA Geoffrey provides an excellent account of the development of equity valuation. The historical description is very interesting while the theoretical analysis is very clear and comprehensive. I would strongly recommend this book to all graduate students. Professor Da-Hsiang Donald Lien Richard S. Liu Distinguished Chair Business College of Business University of Texas San Antonio, Texas, USA A different and novel historical and philosophical approach to ideas and techniques for valuation of equity securities. Covers the technical tool-of- trade in a simple and easy-to-understand way whilst stimulating our thinking about traditional frameworks and focus that may influence use of information and ideas on how value is generated. Includes a new chapter on valuation of Canadian oil sands and resource companies. Trevor Wilkins Associate Professor Department of Accounting, National University of Singapore I strongly recommend this book to everybody who is interested in equity valuation, from practitioner to PhD-student. The coverage of the materials is excellent and fully up-to-date. You will not find a better book on the same topic. Chris Veld Professor of Finance University of Stirling, Scotland

World Scientific

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VALUATION OF EQUITY SECURITIES

The recent financial market collapse that led to the Great Recession of 2007-2009 is evidence that traditional efficient market theory of how markets evaluate equity securities is wrong. In this volume, Geoffrey Poitras explains in understandable detail: (1) the various theories that claim to explain the evaluation of securities, (2) why the conventional view can be incorrect, and (3) what factors must be taken in to account in order to understand how the financial market evaluates equities. This book is a must-read for economists, financial analysts, and individual investors.

Geoffrey Poitras

VALUATION OF EQUITY SECURITIES History, Theory and Application

ISBN-13 978-981-4295-38-3 ISBN-10 981-4295-38-8

World Scientific

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VALUATIQN OF EQUITY SECURITIES History, Theory and Application

VALUATION OF EQUITY SECURITIES History, Theory and Application

Geoffrey Poitras Simon Fraser University, Canada

World Scientific NEW JERSEY

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Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

VALUATION OF EQUITY SECURITIES History, Theory and Application Copyright © 2011 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN-13 978-981-4295-38-3 ISBN-10 981-4295-38-8

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Preface

This book contains many echoes of the project started in Security Analysis and Investment Strategy (Poitras 2005). Even though the road map is similar, Valuation of Equity Securities is a substantive step forward. The main difficulty confronted by Poitras (2005) was the treatment of both equity and fixed income securities under one cover that made it difficult to achieve an intellectually advanced treatment of securities valuation. While there are sound traditional reasons for combining the analysis of debt and equity securities — an approach going back at least to the so-called ‘Bible of security analysis’ (Graham and Dodd 1934) — the additional need for brevity meant valuable material had to be omitted to prevent the end product from resembling a big city phone book. Valuation of Equity Securities partially overcomes these difficulties by dropping the bulk of fixed income security valuation. Only basic theory of interest concepts, sufficient to execute discounted cash flow valuation, is examined. This permits attention to concentrate on the difficulties of estimating the future cash flows to equity, avoiding treatment of the subtleties in stochastic discounting techniques essential to advanced fixed income security valuation. Another contrast between this book and Security Analysis and Investment Strategy is the influence of current events. Equity valuation is ‘real time’ and the method of incorporating changing information is integral to the valuation process. Poitras (2005) was influenced by the financial market debacles associated with the collapse of Enron and subsequent contagion engulfing Arthur Anderson, Worldcom, Adelphia, Global Crossing, and Tyco, to name only a few. Major investment banking institutions, such as Citigroup and JP Morgan Chase, were exposed for participating in the accounting shenanigans that hid the activities of Enron and others from the glare of public disclosure. Just as those events provided a useful backdrop for the arguments advanced in that book, Valuation of Equity Securities has been profoundly impacted by the events that began to unfold in early 2008, culminating into the most significant global financial collapse since v

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the Great Depression. Though the substance of the arguments being made is largely independent of current events, considerable attention is given to grounding the arguments in a ‘real-time’ context. While Poitras (2005) took rhetorical and critical aim at the limitations of the prevailing positivist philosophy that dominates both the instructional and research agenda of modern Finance, this book places emphasis on the implementation of valuation techniques. Instead of critiquing modern Finance, the argument is more focused on viewing Finance as a use-oriented subject, which needs to keep one eye squarely fixed on the needs of practitioners in the securities industry. When the theoretical ideas of modern Finance are explored in detail, the objective is not to demonstrate that the positivist approach is insufficient for dealing with the pervasive uncertainty in securities markets. Rather, the objective is to find the usefulness in the received theories of all components of Finance — old finance, modern Finance, and New Finance — for valuing equity securities. This complements the expanded examination of historical and philosophical aspects of the practical valuation problems encountered in the market for common stocks. Mantras such as ‘stock returns outperform bond returns in the long run’ and investment strategies derived from two-fund separation are examined in detail, with a view to extracting the insights for making equity valuation decisions. Those aiming to use this book as the backbone of an advanced course on equity security analysis may be concerned that the philosophical explorations and some other topics lie too far outside the knowledge base of the typical advanced Finance student. Most such students have never taken a course on, say, the history of science or epistemology. Similarly, some of the mathematical content, such as the discussion of the stochastic differential equations associated with different specifications of the forward equation in Sec. 5.3, will be too technical for the typical Finance student. As a casual inspection of the book will reveal, such subsections form only a fraction of the book’s content. Though this material is essential to developing key themes in the book, such as demonstrating how the ex ante/ex post biases in modern Finance can be theoretically resolved, the informational and practical content contained in the book can be readily digested without giving much consideration to these issues. A useful example of the type of non-philosophical and mathematical material in the book can be found in Part III, which deals with applications. It is difficult to conceive of a more practical application of equity security analysis than the real-time material and analysis contained in these chapters.

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The layering of material by sophistication level and analytical complexity makes the book suitable for a range of course levels and course content. Though there is some foundational material similar to what is contained in an introductory investments text such as Bodie et al.’s Investments, it is not pedagogically sensible to use this book as the core text in an introductory investments course. However, depending on instructor preferences, various chapters or subsections in Parts I and II could be used in such a course making the book suitable as a supplementary text and as a guide to a more advanced treatment of the subject. The practical material in Part III is, hopefully, within the grasp of students taking an introductory investments class. The bulk of advanced material in the book, with the exception of Chapter 5, is targeted at courses in equity security analysis at the senior undergraduate and second year MBA level. If all advanced material is included, and the material in Part III is omitted, this book is also suitable for a PhD level course in equity valuation or financial statement analysis. The wealth of practitioner-oriented material also makes the book useful as, say, a supplementary text in trade courses or as a self-study guide for real-time equity security market combatants. Those familiar with Poitras (2005) and two of my other books, The Early History of Financial Economics, 1478–1776 (2000) and Risk Management, Speculation and Derivative Securities (2002) may be concerned that this effort is, yet again, an example of the creeping incursion of typographical and editing errors in modern academic texts. For the sometimes annoying typos in my previous books, I apologize. Though there are no guarantees in life, rest assured that a herculean effort has been made to keep the bugs out of this effort. As with my previous books, the website at www.sfu.ca/∼poitras will have posted an up-to-date listing of the typos and other errors that have been uncovered in this book. (In addition to containing errata lists for my previous books, the website also has a wealth of material on other subjects.) This book has benefitted considerably from the comments of anonymous and not-so-anonymous reviewers on preliminary drafts of the text. The risk of omission is such that I provide a global thank you to all who have participated in the review process. Feedback and discussion from numerous students over the years has also had a significant impact on the topic coverage. John Heaney contributed essential notions that appear in Chapter 5. At World Scientific Publishing, I would like to give special thanks to Lum Pui Yee and Alisha Nguyen. Without their efforts, this book would not have been produced.

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Acknowledgments Though much of the material used in this book is from public sources, such as SEC filings, the preparation also required permission to reproduce copyright materials from journal articles, websites, newspapers, books, and magazines. The author and publisher gratefully acknowledge the permission from the following:

The American Economic Association (picture of Frank Knight on p.1) The Graham Family (picture of Ben Graham on p.1) The Wall Street Journal (Table 1.5) The New York Stock Exchange Euronext (Fig. 1.2) Journal of Economic Surveys (Tables 1.7–1.9) Amsterdam History Museum (Fig. 2.2) New York Historical Society (Fig. 2.7) Berkshire Hathaway and Warren Buffett (Tables 3.1–3.3; picture on p.327) Canadian Oil Sands Limited (Tables 4.1–4.3, Fig. 8.8) Journal of Financial Economics (Fig. 4.4) www.investorsintelligence.com (Fig. 6.1) National Bureau of Economic Research (Table 7.1) Stern Stewart, www.sternstewart.com (Table 7.8) Professor Edward Altman (Tables 7.18–7.19) British Petroleum (Table 8.1) Graphs were also obtained from the internet financial news service www.globeinvestor.com

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Contents

PART I: Philosophy, History, and Equity Securities 1. The Philosophy of Equity Valuation 1.1 1.2 1.3

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The Equity Security Landscape . . . . . . . . . . . . . . . . . Risk, Return, and Uncertainty . . . . . . . . . . . . . . . . . Fact, Conjecture, and Rhetoric . . . . . . . . . . . . . . . . .

2. History of Equity Securities 2.1 2.2 2.3

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Early History of Equity Security Markets . . . . . . . . . . . 98 Developments to Graham and Dodd (1934) . . . . . . . . . . 145 Derivative Security Renaissance . . . . . . . . . . . . . . . . . 186

3. Modern Equity Security Valuation 3.1 3.2 3.3

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Foundations of Old Finance . . . . . . . . . . . . . . . . . . . 252 Value Stocks and Growth Stocks . . . . . . . . . . . . . . . . 278 Modern Finance and New Finance . . . . . . . . . . . . . . . 301

PART II: Theories of Equity Security Valuation 4. Discounted Cash Flow Models 4.1 4.2 4.3

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History of Equity Valuation Models . . . . . . . . . . . . . . . 330 A Variety of DCF Models . . . . . . . . . . . . . . . . . . . . 342 Basic Theory of Interest . . . . . . . . . . . . . . . . . . . . . 375

5. Stochastic Theories of Equity Value 5.1 Foundations of Modern Finance . . . . 5.2 Ergodicity and Asset Pricing Theories 5.3 Bifurcation and Multimodal Densities Appendix: Preliminaries and Proofs . . . . . ix

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6. Technical Analysis Demystified 6.1 What is Technical Analysis? . . . . . . . . . 6.2 Traditional Technical Analysis . . . . . . . . 6.3 Recent Developments in Technical Modeling Appendix: The Story of Richard Hanks . . . . . .

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PART III: Fundamental Analysis and Equity Valuation 7. Fundamental Analysis for Equity Securities 7.1 7.2 7.3

What is Fundamental Analysis? . . . . . . . . . . . . . . . . . 534 Interpreting Financial Statements . . . . . . . . . . . . . . . . 561 Accounting, Legal, and Other Issues . . . . . . . . . . . . . . 612

8. Resource Companies: Oil Sands Producers 8.1 8.2 8.3

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The Oil Sands and the Syncrude Project . . . . . . . . . . . . 640 Investment in Off-Shore Companies . . . . . . . . . . . . . . . 659 Fundamental Valuation . . . . . . . . . . . . . . . . . . . . . 677

References

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Index

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PART I

Philosophy, History, and Equity Securities

“Ye wise Philosophers explain What Magick makes our Money rise When dropt into the Southern Main Or do these Juglers cheat our Eyes.” SwiftJonathan Swift (1667–1745), First stanza of the poem The Bubble (1721) “Human beings act, not on the basis of fact and reality as such, but on the basis of opinions and beliefs about facts, and what is called knowledge, but which at best falls notoriously short of the implications of that term. From a logical point of view therefore, one who aspires to explain or understand human behavior must be, not finally but first of all, an epistemologist.” Frank Knight (1885–1972), “Economic Psychology and the Value Problem”, QIE (1925) “One thing badly needed by investors — and a quality they rarely seem to have — is a sense of financial history.” Benjamin Graham (1894–1976), The Intelligent Investor (1949)

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CHAPTER 1

The Philosophy of Equity Valuation

1.1

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The Equity Security Landscape 1.1.1 Characteristics of Equity Securities . . . . 1.1.2 Regulation of Equity Securities . . . . . . 1.1.3 Trading of Equity Securities . . . . . . . . Risk, Return, and Uncertainty 1.2.1 Basics of the Risk and Return Tradeoff . 1.2.2 History of Risk and Uncertainty . . . . . 1.2.3 The Efficient Markets Hypothesis . . . . . 1.2.4 Testing the Efficient Markets Hypothesis . Fact, Conjecture, and Rhetoric 1.3.1 The Epistemology of Equity Valuation . . 1.3.2 The Rhetoric of Finance . . . . . . . . . . 1.3.3 Ergodicity and True Uncertainty . . . . .

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What Is Value? Value is a concept with many possible interpretations. Taking the ‘value’ to be equal to the ‘true worth’ is too normative for practical purposes. Some methods of determining true worth are needed. Because ‘value’ for equity securities is an ex ante variable, it is unobserved at the time of valuation. As such, it is difficult to transcend philosophical differences over the definition of value. In one sense, the value of an equity security share is equal to the traded price of the security observed in the securities market. This interpretation of value is consistent with the spirit of the efficient markets hypothesis. In the fundamental analysis of equity securities, it is usually assumed that the market price does not necessarily capture the true worth or ‘intrinsic value’ of a security. At any point in time, the market price may be above or below the intrinsic value. In this sense, value is an economic concept that can be estimated using techniques such as discounted cash flow analysis. This requires forecasts of the key inputs to the model, especially cash flows, capitalization rates, and termination dates, to be accurately assembled and interpreted. A substantial portion of this book is concerned with how this task is executed. 3

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The Equity Security Landscape Characteristics of Equity Securities

This book uses a narrow definition of equity securities. More precisely, an equity security is defined as a tradeable ownership claim in a company, corporation, or real asset. This includes common stock, preferred stock and warrants traded on public securities markets. Also included are ownership claims in real assets or portfolios of financial assets that are tradeable securities, such as Canadian oil and gas royalty trusts, real estate investment trusts, and exchange-traded funds. ‘Free standing’ equity derivative securities, such as exchange-traded equity options and equity futures, and difficult to trade equity claims, such as a share in a private partnership, domicile or business, are only considered in historical perspective. The omission of non-tradeable claims is a significant exclusion, impacting many items on household balance sheets. Explicitly excluded are debt securities of all types. Also excluded are insurance products, such as whole life insurance, and hybrid debt/equity products such as convertible bonds and mortgagebacked securities. This approach to defining an equity security follows the common convention of classifying securities issued by corporations with reference to the ‘right-hand side’ of the balance sheet as either debt or equity securities. Corporate securities differ with respect to priority of claim against both income and assets. Because an equity security is an ownership claim, failure by the corporation to make an income (dividend) payment to holders of equity securities is permissible. In contrast, debt securities have a priority claim over equity securities, with default on the promise to make an income (coupon) payment on a debt security being grounds for initiating a bankruptcy proceeding against the corporation. Such proceedings often have dire consequences for equity investors, making some understanding of debt securities essential to the equity valuation process. The specific contract governing a corporate bond issue is the bond indenture for that issue. The bond indenture is a legal document, monitored and enforced by a trustee, that contains the terms and conditions governing that issue. Where applicable, the indenture contains information about coupon payment schedules, protective provisions and covenants, priority of claim relative to other bond issues, conversion conditions, sinking fund payment schedules, and the like. Due to the difficulty of obtaining and digesting the bond indenture contracts, there are a number of information sources, such as Moody’s Investor Services, that provide summary information about the contents of the bond indenture for specific bond issues.

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The bond indenture typically provides a number of conditions under which the bond holder can initiate a bankruptcy proceeding against the issuing corporation. Where applicable, these conditions include failure to make a scheduled coupon payment or violation of a bond covenant governing, say, the net asset value of the company. In the event that a bankruptcy proceeding is initiated, debt claims are typically paid according to the seniority of the issue, as laid out in the indentures of the different bond issues made by the corporation. Debt issues, which are secured by specific property, such as mortgage bonds, are repaid either by repossessing the asset or from the proceeds of the disposition of the asset. Debentures are unsecured issues that do not have a lien against a specific asset identified in the indenture. When a number of debentures are issued by a corporation, the issues are usually further classified as senior, senior subordinated, and subordinated debentures to reflect the associated priority of claim. In a bankruptcy proceeding, debenture holders have the status of general creditors. Tradeable equity securities typically feature limited liability, meaning that in the event of bankruptcy, shareholders are only liable to the extent of the amount that was paid for the shares. This is a significant restriction on the legal and organizational form used to represent equity ownership. Following Guinnane et al. (2007), possible forms for equity ownership include ordinary partnership, limited partnership, limited partnership with tradeable shares, incorporation, and private limited liability company (PLLC). Of these, only corporations and limited partnerships with tradeable shares fall within the definition of equity securities used in this book. For many small- and medium-sized enterprises, the ordinary partnership or PLLC is the appropriate organizational choice. The historical evolution of limited liability from the unlimited liability of the ordinary partnership and the restricted liability of the joint stock company differs from country to country. As a consequence, the prevalence of businesses with tradeable equity securities also differs, e.g., PLLC is widely used in the United Kingdom for smaller businesses. With appropriate adjustment, the general valuation principles developed in this book for tradeable securities can be extended to other more difficult to transfer forms of equity ownership. Equity securities are composed of common stock, preferred stock, and claims against equity such as warrants and rights issues. For many corporations, the common stock does not pay a regular cash dividend, preferring to spend any free cash flow on accelerated expansion, stock buy back programs, and debt repayments. In such cases, the expectation is that the

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stock price will appreciate by more than the cash per share that would have been paid as a dividend. In addition to regular dividends (usually paid quarterly) that may or may not be on offer, common stock holders may also benefit from irregular events such as distributions of special cash or stock dividends, payment of equity securities in a subsidiary that is being spun-off from the parent corporation, or an issuance of transferable rights to participate in a future equity offering. The use of such irregular distributions differs from country to country. For example, while the use of rights issues to raise additional capital are common in East Asian equity markets, private placements or secondary stock offerings to raise additional capital are common in North American markets, e.g., Poitras (2002). Preferred stock differs from common stock in a number of ways. There are a number of possible variations for preferred stock, e.g., it may be redeemable, convertible, or floating rate. All preferred stock is nonvoting, though minimum voting provisions for preferred stock with suspended and accumulating dividend payments are a requirement for listing on the New York Stock Exchange (NYSE). In most cases, there is a regular (usually quarterly) scheduled dividend payment of a fixed dollar amount. Because the size of the dividend payment is fixed, as the market price of the preferred stock changes, the dividend yield will change. Hence, there is a close connection between the valuation of a preferred share and the associated debt of the corporation. Because of capital requirements detailed in various national and international banking regulations classifying preferred stock as a favorable source of capital compared to the issuance of debt, financial institutions are important issuers of preferred shares. Also of importance are utilities and issuers with credit difficulties needing to recapitalize, e.g., General Electric issued such preference shares to Berkshire Hathaway in 2008. Most preferred share issues have cumulative dividend provisions, meaning that if scheduled preferred dividend payments are not made, all unpaid preferred share dividends have to be made good before any dividend payments can be made to common shareholders. Because preferred stock is an equity claim, the dividend payments are not a taxdeductible expense for the corporation (in contrast to interest payments on corporate debt). The associated negative tax implications are offset by the favorable tax treatment given to inter-corporate dividend payments. Traditionally, the corporate tax advantages for preferred stock meant that preferred shares were priced to be attractive mainly to corporate investors. Changes in the tax code have eroded the corporate tax advantages of

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preferred stock dividends to the point where yields for preferred stock can be attractive relative to comparable yields for both Treasury securities and corporate debt. Common stock stands last in the priority ranking, making common stock the residual claim to income payments. The priority of preferred over common also applies in the event of firm liquidation, recognizing that equity is the residual claim against assets.1 In the typical stylized corporation, each share of common stock is entitled to one vote that can be used in the election of the board of directors held at the annual meeting of the shareholders.2 In turn, the board of directors is responsible for selecting the senior management, e.g., chief executive officer and president, that actually runs the company. Votes may also be held at the annual meeting or at special meetings when substantive initiatives are being undertaken by management, e.g., a merger or takeover. Shareholders not attending a meeting may vote by proxy that allows a named person, usually a member of management, to vote the shares. A proxy fight occurs when a dissident shareholder group solicits proxies to vote against current management. A recent example of a proxy fight occurred in 2002 when a dissident group led by the son of a company founder sought to prevent the merger of HewlettPackard with Compaq. In a sense, the common stockholders are the owners of the firm, though in practice there are considerable impediments to achieving this objective. For example, many companies use a statutory voting procedure, where each individual member of the board of directors is voted on separately. In this model, the group holding the majority of the shares is able to elect the full board. In an attempt to address the problem of under-representation, in some states corporation law requires common stock to have cumulative voting rights where each share is entitled to a number of votes equal to the number of board members being elected, with all board members being elected according to the number of votes cast for each. In this type of 1 Liquidation refers only to the winding up of the firm. It is possible for a firm to be liquidated that has a healthy surplus of marketable assets over liabilities due. In the event of bankruptcy, i.e., a surplus of liabilities over marketable assets, a liquidation means no payments will be available to equity holders, though in some jurisdictions exceptions may be made for small payments to speed up legal proceedings. 2 The corporate governance methods and procedures available to corporations is an issue for corporate securities law. Allowable limits will be determined by the law associated with the jurisdiction of incorporation. The ‘best’ method for achieving effective corporate governance outcomes has attracted considerable attention, especially since passage of the Sarbanes–Oxley Act (2002), e.g., Jiraporn et al. (2009).

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voting, a minority group voting as a block is able to get a voice on the board by electing a member or members to the board. Issues of corporate governance contributed to a number of recent corporate debacles, such as Enron and Worldcom, and are at the core of the legal reforms contained in the Sarbanes–Oxley Act of 2002 (see www.sec.gov/about/laws.shtml). In addition to voting rights, common stockholders have a number of other rights and protections. The extent of these rights depends on the corporation law of the state of incorporation. Preemptive rights allow stockholders to subscribe pro rata to any new issues of stock. This right prevents undesired dilution of ownership. Other rights include protections against stock repurchases or recapitalizations. Though these rights may extend to certain types of non-cash dividends, the size of dividend payments made to the common shares is typically at the discretion of management. Many firms do not make regular dividend payments. There are also numerous firms that have a long unbroken record of regular, quarterly dividend payments that have grown gradually over time. Earnings that are not paid to shareholders as dividends are retained within the firm and, presumably, go to the purchase of assets or reduction in other claims against assets, thereby enhancing the claim of common stock against assets and, hopefully, producing an increased common stock price and a capital gain for stockholders. In the United States, except in a few special cases, e.g., nationally chartered banks, corporations come into being when chartered under a particular state code. Each state has a corporation law outlining rules for incorporation and general rules for operation. As such, the state of incorporation defines the rules governing corporate status. While conducting business in states other than the state of incorporation, the corporation is subject to the commercial laws and taxes of that state. At the time of incorporation, a corporate charter has to be filed which contains the articles of incorporation. The corporate charter provides information about: the methods by which the articles of incorporation can be amended; the classes of stock and the par values; features protecting the preferred stock; voting rights for the stock; powers of the board of directors; rules for retiring common stock, dividend payment provisions, rights of prior security holders in the event of new issues; and merger reorganization procedures. Due to differences in corporation laws across states, many of the largest corporations have opted to incorporate in Delaware. (Why?) The Commerce Clearing House (now a division of Wolters Kluwers) specializes in providing useful

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references on relevant corporation law issues such as The Delaware Law of Corporations & Business Organizations (3rd edn. 2007). In most jurisdictions, the corporation law permits different classes of common stock to be issued, usually differentiated by voting rights. Such types of common stock are referred to as dual-class shares, restricted shares, or classified common stock. While such common stock issues are used by companies in Canada, Europe, Brazil, and China, they are unusual in the / degaard (2007), United States, e.g., Partch (1987), Chen et al. (2002), O Dittmann and Ulbricht (2008). Due to perceived and actual abuses, the NYSE had various degrees of listing restrictions on non-voting common stock from 1924 until 1994 (see Subsection 313 of NYSE Listed Company Manual). Where companies do issue common stock with different voting rights, the different classes trade as separate issues, permitting different prices to be quoted. For example, Canadian Tire Corporation traded on the Toronto Stock Exchange (TSX) has Class A non-voting common stock and regular common stock that does have voting rights. Other than voting rights, both classes of common stock have equal claims, e.g., to common stock dividends. Pressure for listing of dual-class stock on the NYSE was created by the globalization of financial markets. Some important stocks in other jurisdictions had a dual class share structure and flexibility was required in the listing requirements. Because conventions applying to dual class stock do differ from jurisdiction to jurisdiction, there is a lack of clarity in the recognition of dual class status. For example, another Canadian company with dual class common stock, Teck-Cominco, has Class A voting (TCK.A-T) and Class B (TCK.B-T) non-voting. Presumably for reasons of liquidity, it is the non-voting Class B Teck-Cominco shares that are traded on the NYSE (TCK-N). There is a wide variation across countries and across firms in the price differences between voting and non-voting shares. For example, the 18 January 2008 closing price for the non-voting Class A Canadian Tire shares (CTC.A) was C$60.01, up $1.11 on the day, with the regular shares (CTC) trading at $70.05, down $1.45 on the day. Neumann (2003) summarizes results from a number of studies reporting an average price premium for voting over non-voting of 13% in the UK; 20% in Switzerland; and 26% in Germany. The highest dual-class share premiums observed were for Israel at 46% and Italy at 82%. Neumann examines the anomalous case of Denmark where, for reasons of liquidity, voting shares traded at a discount to non-voting shares.

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Relevant Accounting Statements The relationship between the assets, liabilities, and equity of a corporation is illustrated in Table 1.1, which provides the Consolidated Statements of Financial Position, more commonly known as the balance sheet, for Boeing Corporation taken from the 10-K for the 2008 year end results. Boeing is used an illustration and is not intended to represent a best practices model. Since 15 November 2007, certain publicly traded companies in the United States are no longer required to follow Generally Accepted Accounting Principles (GAAP) when preparing accounts and can file using International Financial Reporting Standards (IFRS). As a consequence, there is even more latitude in the detail provided for the various items of interest in the accounts than the considerable variation already permitted under GAAP. In addition, the securities of corporations traded outside the United States, or within the United States as American depository receipts (ADRs)3 , are subject to the securities laws of the relevant home jurisdiction. In general, the detail and clarity of accounts for firms subject to U.S. rules sets a standard for reporting requirements in other jurisdictions.4 In the Boeing balance sheet, traded securities are associated with the line items, ‘Short-term debt and the current portion of long term debt’, ‘Long term debt’, and ‘Shares Issued’. The debt items are further clarified in the notes to the audited financial statements. An additional statement, the ‘Condensed Consolidated Statement of Shareholders’ Equity’ is prepared exclusively for the determining changes in the equity account (see Table 1.2). The information content in this statement is often elusive and not closely examined. However, in this particular instance, the statement is helpful. From Table 1.1, Boeing records a disturbing negative equity value for 2008. This is a dramatic change from 2007 when 3 An American depository receipt (ADR) is a security that represents a claim to shares of a foreign security, almost always a common stock listed and traded on an exchange outside the United States. Conceptually, an ADR can be viewed as an all equity financed closed end fund that holds a foreign security as the sole asset of the fund. While publicly traded on U.S. exchanges, an ADR is only subject to SEC reporting requirements on the receipt. The company associated with the foreign security is subject to reporting requirements imposed by the foreign market in which the security trades. 4 Prior to the November 2007 change by the SEC, a process of convergence in the accounting rules used in most international jurisdictions, set by the International Accounting Standards Board (IASB), and GAAP rules determined by the U.S. Financial Accounting Standards Board (FASB) had commenced in October 2002 and is currently ongoing. More information can be obtained from either the FASB (www.fasb.org) or IASB (www.iasb.org.uk) websites.

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11

Table 1.1 The Boeing Company and Subsidiaries Consolidated Statements of Financial Position. (Dollars in millions, except per share data) 31 December Assets Cash and cash equivalents Short-term investments Accounts receivable, net Current portion of customer financing, net Deferred income taxes Inventories, net of advances and progress billings Total current assets Customer financing, net Property, plant and equipment, net Goodwill Other acquired intangibles, net Deferred income taxes Investments Pension plan assets, net Other assets, net of accumulated amortization of $400 and $385 Total assets Liabilities and shareholders’ equity Accounts payable and other liabilities Advances and billings in excess of related costs Income taxes payable Short-term debt and current portion of longterm debt Total current liabilities Deferred income taxes Accrued retiree health care Accrued pension plan liability, net Non-current income taxes payable Other long-term liabilities Long-term debt Shareholders’ equity Common shares issued, par value $5.00– 1,012,261,159 and 1,012,261,159 shares Additional paid-in capital Treasury shares, at cost Retained earnings Accumulated other comprehensive loss ShareValue Trust shares Total shareholders’ equity Total liabilities and shareholders’ equity

17:50:10.

2008

2007

$3,268 11 5,602 425 1,046 15,612

$7,042 2,266 5,740 328 2,341 9,563

25,964 5,857 8,762 3,647 2,685 4,114 1,328 16 1,406

27,280 6,777 8,265 3,081 2,093 197 4,111 5,924 1,258

$53,779

$58,986

$17,587 12,737

$16,676 13,847

41 560

253 762

30,925 — 7,322 8,383 1,154 337 6,952

31,538 1,190 7,007 1,155 1,121 516 7,455

5,061

5,061

3,456 (17,758) 22,675 (13,525) (1,203) (1,294) $53,779

4,757 (14,842) 21,376 (4,596) (2,752) 9,004 $58,986

The Boeing Company and Subsidiaries Consolidated Statement of Shareholders’ Equity. Additional

(Dollars in millions, except per share data) 17:50:10.

Paid-in capital

Treasury stock

ShareValue Trust

Retained earnings

Accumulated other comprehensive loss

$5,061

$4,371

($11,075)

($2,796)

$17,276 2,215

($1,778)

Total

13

13

(39)

(39)

1,733

1,733

73

73 4,018 (8,242)

(8,242)

345

487 (279) 36 325 294

(493)

270

(223)

(259)

(Continued)

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487 (20) 36 325 (51)

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23

$11,059 2,215 23 Valuation of Equity Securities

Balance 1 January 2006 Net earnings Unrealized gain on derivative instruments, net of tax of $(16) Unrealized gain on certain investments, net of tax of $(7) Reclassification adjustment for gains realized in net earnings, net of tax of $23 Minimum pension liability adjustment, net of tax of $(1,116) Currency translation adjustment Comprehensive income SFAS 158 transition amount, net of tax of $5,195 Share-based compensation ShareValue Trust activity Tax benefit related to share-based plans Excess tax pools Treasury shares issued for stock options exercised, net Treasury shares issued for other share-based plans, net

Common stock

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12

Table 1.2

November 3, 2010 10:47

Table 1.2

(Continued)

Additional (Dollars in millions, except per share data)

Common stock

Paid-in capital

Balance 31 December 2006

$5,061

$4,655

(1,698) (301)

301

($12,459)

($2,754)

Retained earnings

(991) (47) $18,453

(991) (47) ($8,217)

$4,739

97

4,074 97

17

17

(21)

(21)

87 3,441

87 3,441 7,695 287

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2

Total (1,698)

4,074

287 (2) 18 85

Accumulated Other comprehensive loss

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Net earnings Unrealized gain on derivative instruments, net of tax of $(58) Unrealized gain on certain investments, net of tax of $(11) Reclassification adjustment for gains realized in net earnings, net of tax of $13 Currency translation adjustment Postretirement liability adjustment, net of tax of $(1,948) Comprehensive income Share-based compensation ShareValue Trust activity Tax benefit related to share-based plans Excess tax pools

ShareValue Trust

The Philosophy of Equity Valuation

17:50:10.

Treasury shares repurchased Treasury shares transfer Cash dividends declared ($1.25 per share) Dividends related to performance share payout

Treasury stock

18 85 (Continued) 13

(Continued)

Additional (Dollars in millions, except per share data)

Common stock

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(32)

241

209

(254)

$151

(103)

(2,775)

Retained earnings

Accumulated Other comprehensive loss

(2,775) (1,129) (11)

(1,129) (11) (11)

$5,061

$4,757

($14,842)

($2,752)

$21,376 2,672

Total

(11) ($4,596)

$9,004

(159)

2,672 (159)

(121)

(121)

4

4

(180) (8,565)

(180) (8,565) (Continued)

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Net earnings Unrealized loss on derivative instruments, net of tax of $93 Unrealized loss on certain investments, net of tax of $61 Reclassification adjustment for losses realized in net earnings, net of tax of $(2) Currency translation adjustment Postretirement liability adjustment, net of tax of $(4,883)

ShareValue Trust

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Balance 31 December 2007

Treasury stock

Valuation of Equity Securities

Treasury shares issued for stock options exercised, net Treasury shares issued for other share-based plans, net Treasury shares repurchased Cash dividends declared ($1.45 per share) Dividends related to performance share payout FIN 48 transition amount

Paid-in capital

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Table 1.2

November 3, 2010 10:47

Table 1.2

(Continued)

Additional Paid-in capital

Treasury stock

ShareValue Trust

243

Accumulated Other comprehensive loss

Total (6,349) 235

(8)

(1,540) 99 (9)

1,452 53

(88) 99 44

(94)

65

(29)

(2,937) (97)

$3,456

($17,758)

97

($1,203)

(2,937) (1,187) (178)

92

(1,187) (86)

$22,675

($13,525)

($1,294)

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$5,061

Retained earnings

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Comprehensive expense Share-based compensation and related dividend equivalents ShareValue Trust activity Excess tax pools Treasury shares issued for stock options exercised, net Treasury shares issued for other share-based plans, net Treasury shares repurchased Treasury shares transfer Cash dividends declared ($1.62 per share) SFAS 158 transition amount, net of tax of $50 Balance 31 December 2008

Common stock

The Philosophy of Equity Valuation

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(Dollars in millions, except per share data)

15

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equity value for a healthy $9 billion (around $9 per share). The shareholders’ equity statement reveals almost all of this equity has been absorbed by $8.56 billion ‘post retirement liability adjustment’ and almost $3 billion in common share repurchases. From the balance sheet, it is apparent that Boeing has used a significant portion of over $22 billion in accumulated retained earnings in repurchasing over $17 billion in common stock. How to make sense of the negative value of equity for Boeing? Closer examination of the statement of shareholders’ equity provides the not surprising information that the large change was due to adoption of FAS 158 ‘Employers’ accounting for defined benefit pension and other postretirement plans’. In effect, Boeing had not been accurately accounting for generous pension benefits. The common stock traded over $100 in November 2007 and did not trade below $30 during the March 2008 market lows. There is clearly a disconnect between book value and market value of equity. For purposes of determining a market value for the equity account, the ‘Condensed Consolidated Statements of Cash Flows’, commonly known as the cash flow statement is typically most helpful (see Table 1.3). This statement provides in a cash flow format information that is contained in the widely reported ‘Condensed Consolidated Statements of Operations’ (Table 1.4) or earnings statement. The cash flow statement starts with net income and incorporates changes in accruals for individual balance sheet items. The balancing item for the cash flow statement is the change in the cash position between the beginning and end of period. In Table 1.1, observe that the liabilities plus equity side of the balance sheet represent the claims against the assets that generate the earnings and cash flows given in Tables 1.3 and 1.4. Traded debt securities are associated with short-term debt ($560) plus long-term debt ($6,952). The annual 10-K report provides some additional discussion of these debt securities, e.g., the $300 million debenture (unsecured debt issue) due in 2024 is redeemable at the holder’s option in 2012.5 However, sources beyond the financial statements and notes contained in the annual report are needed to get precise information about each debt issue. As for equity, the balance sheet indicates that 1,012,261,159 shares have been issued. Boeing has no outstanding preferred stock. While previously Boeing gave precise numbers of shares held in Treasury stock and held in the Share Value Trust, a trust which holds

5 The 2008 Annual Report by Boeing uses the 10-K filing information to provide financial information. Additional information is also available in the Annual Report about the products Boeing produces and the people involved in making those products. There is also visually appealing summaries of the financial highlights in the 10-K.

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17

Table 1.3 The Boeing Company and Subsidiaries Consolidated Statements of Cash Flows. (Dollars in millions) Years ended 31 December Cash flows — operating activities Net earnings Adjustments to reconcile net earnings to net cash provided by operating activities Non-cash items Share-based plans expense Depreciation Amortization of other acquired intangibles Amortization of debt discount/premium and issuance costs Investment/asset impairment charges, net Customer financing valuation provision/(benefit) Gain on disposal of discontinued operations Gain on dispositions/business shutdown, net Other charges and credits, net Excess tax benefits from share-based payment arrangements Changes in assets and liabilities Accounts receivable Inventories, net of advances and progress billings Accounts payable, and other liabilities Advances and billings in excess of related costs Income taxes receivable, payable, and deferred Other long-term liabilities Pension and other postretirement plans Customer financing, net Other Net cash (used)/provided by operating activities

2008

2007

2006

$2,672

$4,074

$2,215

209

287

743

1,325 166

1,334 152

1,445 100

11

(1)

14

50

51

118

84

(60)

32

(28)

(25)

(14)

(4)

(38)

226

116 (100)

197 (144)

82 (395)

564

(392)

(244)

(6,168)

(1,577)

140

872 (1,120)

928 2,369

(744) 1,739

744

1,290

933

(211) 14

71 (143)

(62) 642

432 (29)

1,458 (247)

718 (189)

(401)

9,584

7,499 (Continued)

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Table 1.3

(Continued)

(Dollars in millions) Years ended 31 December Cash flows — investing activities Property, plant, and equipment additions Property, plant, and equipment reductions Acquisitions, net of cash acquired Proceeds from dispositions Contributions to investments Proceeds from investments Purchase of distribution rights Net cash provided/(used) by investing activities

2008

2007

2006

(1,674)

(1,731)

(1,681)

34

59

225

(964)

(75)

(6,673) 11,343 (178)

(5,710) 3,817 (182)

(1,854) 123 (2,815) 2,850 (34)

1,888

(3,822)

(3,186)

13 (738) (357)

40 (1,406)

1 (1,681)

44 100

209 144

294 395

Cash flows — financing activities New borrowings Debt repayments Repayments of distribution rights financing Stock options exercised, other Excess tax benefits from share-based payment arrangements Employee taxes on certain share-based payment arrangements Common shares repurchased Dividends paid

(2,937) (1,192)

(2,775) (1,096)

(1,698) (956)

Net cash used by financing activities

(5,202)

(4,884)

(3,645)

(59)

46

38

(3,774)

924

706

7,042

6,118

5,412

$3,268

$7,042

$6,118

Effect of exchange rate changes on cash and cash equivalents Net (decrease)/increase in cash and cash equivalents Cash and cash equivalents at beginning of year Cash and cash equivalents at end of year

(135)

Boeing stock for the purpose of making distributions to employees, in this regard, the 2008 statement is less revealing. It is necessary to access Item 3 in the Notes to find 719 million as the ‘weighted average number of shares’ that has been used to calculate the earnings per share (EPS) reported in Table 1.4. Accurate assessment of the financial statements of the firm lies at the heart of the fundamental approach to equity security valuation. In this approach, determining the estimated ‘intrinsic value’ for, say, the common stock of the Boeing Corporation requires information in the financial

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Table 1.4 The Boeing Company and Subsidiaries Consolidated Statements of Operations. (Dollars in millions, except per share data) Years ended 31 December Sales of products Sales of services Total revenues Cost of products Cost of services Boeing Capital Corporation interest expense Total costs and expenses Income from operating investments, net General and administrative expense Research and development expense, net of credits of $50, $130, and $160 Gain/(loss) on dispositions/business shutdown, net Settlement with U.S. Department of Justice, net of accruals Earnings from operations Other income, net Interest and debt expense Earnings before income taxes Income tax expense Net earnings from continuing operations Net gain on disposal of discontinued operations, net of taxes of $10, $9, and $5 Net earnings Basic earnings per share from continuing operations Net gain on disposal of discontinued operations, net of taxes Basic earnings per share Diluted earnings per share from continuing operations Net gain on disposal of discontinued operations, net of taxes Diluted earnings per share

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2008

2007

2006

$50,180 10,729 60,909 (41,662) (8,467) (223)

$57,049 9,338 66,387 (45,375) (7,732) (295)

$52,644 8,886 61,530 (42,490) (7,594) (353)

(50,352) 10,557 241 (3,084) (3,768)

(53,402) 12,985 188 (3,531) (3,850)

(50,437) 11,093 146 (4,171) (3,257)

4

38

(226) (571)

3,950 247 (202) 3,995 (1,341) 2,654 18

5,830 484 (196) 6,118 (2,060) 4,058 16

3,014 420 (240) 3,194 (988) 2,206 9

$2,672 $3.68

$4,074 $5.36

$2,215 $2.88

0.02

0.02

0.01

$3.70 $3.65

$5.38 $5.26

$2.89 $2.84

0.02

0.02

0.01

$3.67

$5.28

$2.85

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statements to be combined with other available information relevant to the business prospects of the company including the state of competition in the industry and the quality of the firm’s products and management. The primary objective of determining an estimate for the intrinsic equity value is to assess the difference between the observed market price and this estimated value. If the estimated value is sufficiently above the market price, then this provides a potentially profitable buying opportunity; or, if the estimated value is sufficiently below the market price, this is a selling opportunity. The success of this approach is predicated on the assumption that the market price and the ‘intrinsic value’ can differ at any point in time but, over time, both will tend to the same correct price. By focusing on the elements of firm-specific risk to determine the ‘value’ of an equity security, the fundamental approach advocated by many practitioners differs markedly from the modern Finance approach advanced by academics which seeks to eliminate firm specific-risk through the application of optimal diversification strategies. This approach is predicated on the assumption that the market price ‘stochastically equals’ the intrinsic value at any point in time, i.e., the efficient markets hypothesis. As such, attempting to use available information to generate abnormally profitable forecasts of future equity security price movements is futile and the expected utility maximizing solution is to optimally diversify. The method of valuing securities used by each approach leads to investment strategies that differ substantively, e.g., Poitras (2005). As it turns out, the rational basis for these differences is philosophical and cannot, on a priori grounds, be resolved. Fundamental empirical questions surrounding the ‘value’ of an equity security involve ex ante variables which are not directly observable.

The Classification of Securities Basic characteristics of equity securities include elements such as priority of claim, limited liability, and other features identified in the corporate charter. The explicit consideration of only equity securities in this book follows the conventional analytical classification of corporate securities into bonds and stocks. This classification scheme conforms to the legal distinction between the equity holders as owners of the firm and the debt holders as creditors with a contractually defined claim against the firm, typically for interest and principal payments. The higher priority of claim suggests that debt securities possess a ‘higher degree of safety’ while equity claims have a ‘lower degree of safety’ that, presumably, is compensated by

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21

a greater potential for gain. While useful, this method of classifying corporate securities has limitations that, in some cases, can lead to confusions and misrepresentations. Graham and Dodd (1934) recognized these problems and suggested an alternative classification scheme for securities that was more in keeping with the theme of investment versus speculation in security valuation and selection decisions. The modern investment landscape has become considerably more complicated than in the days of Graham and Dodd (1934). The division of equity securities into common stocks and preferred stocks has been blurred by the presence of hybrid-preferred issues such as mandatory convertiblepreferred shares, e.g., Battacharya (2001, p. 1138), that are closer to common stocks than the traditional non-convertible fixed coupon-preferred stock. The distinction between debt and common equity is blurred by the widespread use of financial structures such as warrant bond issues. Yet, there is still considerable substance in the ‘new classification’ scheme for securities recommended by Graham and Dodd (1934) and carried forward into Graham et al. (1962, p. 101). In conventional terminology, these three classes can also be stated as Class I. Investment grade bonds and preferred stocks; Class II. Speculative grade bonds and preferred stocks, which can be further divided into: II.A. Hybrid Debt, such as convertible bonds and mortgagebacked securities; II.B. Below investment grade senior notes and preferred shares; Class III. Securities with characteristics of common stocks. The basic idea behind the proposed classification scheme is to emphasize the investment characteristics of a security, as opposed to the ‘type’ of security, i.e., bond vs. preferred vs. common. In particular, securities in class I ‘are bought in the reasonable expectation that the income therefrom will continue unchanged and that their market quotation will not deviate greatly from the purchase price’ (GDC, p. 102). Securities in class I provide safety of principal and a steady income. Securities in class II are subject to significant possibilities about the safety of principal. The division of class II into A and B groups is to recognize the possibility of different factors contributing to price changes. In class A, the price change arises from the security combining a ‘straight investment’ with a conversion right or some other privilege, e.g., prepayment options, that carries the possibility of profit or

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loss. In class B, the possibility of profit or loss is inherent in the ‘straight security’ and not in the attached provision. Securities in class B differ from common stock in two ways: the securities have an ‘effective priority’ over some junior issue, which gives some degree of protection; the possibility for profit is limited in time and amount, in contrast to common stock where the possibility of gain is ‘theoretically or optimistically’ unlimited. As for the specific types of security in each class, ‘all straight bonds and preferred stocks of high quality selling at a normal price’ belong in class I, together with ‘sound convertible issues’, where the conversion option is well out of the money. Just because a bond is rated investment grade does not qualify the security as belonging in class I. If the bond sells at ‘unduly low price’ then the possibility of capital gain puts the bond in class II. Precisely where the dividing line between classes I, II, and III is drawn is difficult to specify. The essence of the classification scheme is to shift the focus onto the price and cash flow characteristics of the security as opposed to more traditional features such as priority of claim. “Any issue which displays the main characteristics of a common stock belongs in Group III, whether it is entitled ‘common stock’, ‘preferred stock’ or even ‘bond’.” This would apply, for example, to a convertible bond, where the conversion right was deep in the money. Another example is a senior bond selling at a price so low that the junior bonds have no value. Such a bond ‘lacks the prime requisite of a senior security, viz., that it should be followed by a junior investment of substantial value’. Preferred Stock Versus Corporate Debt The Graham and Dodd Class I–Class III security classification scheme identifies a closer similarity of preferred stocks to corporate debt than to common stocks. This can create pedagogical confusion in a book concerned about equity securities. As a consequence, common stocks dominate much of the attention in this book given to equity securities. When general reference is made to ‘equity securities’ in this book, it is the Class III security category that is intended. Though preferred stock has played an important role in the history of equity securities, this type of equity security currently has a limited role to play in most corporate financing, with the exception of certain advantages for financial institutions subject capital requirements and those seeking the tax advantages that are present for both borrowers and investors. With this in mind, a brief overview of preferred shares is provided at this stage to offset relative lack of subsequent discussion compared to common stocks.

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23

The origins of preferred shares can be traced to the triple contract used in medieval and Renaissance finance (Poitras 2000, ch. 2). Preferred share arrangements appear in the capital structure of early English joint stock companies and were an important financing feature of the U.S. industrial trusts in the late 19th century. Initially, the basic notion of a preferred share related to the prior claim to dividend payments. Over time, other features have been added, such as the prior claim against assets in the event of a liquidation. In addition to preference over common stock to dividend payments and assets in liquidation, features that apply to all preferred issues, there are a range of other features that may or may not be part of the preferred structure. For example, most preferred shares are ‘cumulative’, i.e., if preferred dividends are not paid then the unpaid amount ‘cumulates’ and all cumulative unpaid preferred dividends have to be settled before any dividend payments can be made to common shareholders. Though preferred shares do not usually have the unrestricted voting rights associated with common stock, contingent voting rights provisions are often included that permit preferred stock to have voting rights when there are unpaid preferred dividends outstanding.6 As an equity claim, failure to make a dividend payment on either preferred or common shares is not sufficient to initiate a bankruptcy proceeding, as in the case of debt issues. The prospectus published at the time a share is issued is an excellent source for finding information about the terms and conditions for a specific issue. For example, the prospectus will specify the various protections afforded the preferred shareholder, such as the cumulative dividend provision and contingent voting rights. Other forms of protection may include restrictions on the ability to make additional issues of more senior securities. Another typical protective feature is a redemption or sinking fund provision that permits the corporation to retire the outstanding preferred shares. Preferred share issues may also be convertible, though preferred shares with this provision appear less frequently than straight (non-convertible)-preferred shares.7 Convertible-preferred stock is often issued to facilitate a merger or takeover or recapitalization. As 6 The NYSE requires contingent voting rights as a provision for listing ‘nonvoting’ preferred shares. In the event of unpaid dividends, a range of possible voting provisions are possible. For example, some preferred shares are restricted to only electing two members to the board of directors while preferred shares of other companies have the same one vote per share rule as common stock. 7 In a large study of 3042 U.S. preferred share issues from 1980–1999, Bajaj et al. (2002) found 682 convertible issues and 2360 non-convertible issues. As a measure of the completeness of this sample, between 1985 and 1999 there were 2,636 total preferred

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with debt issues, preferred shares are rated by the major ratings services, Moody’s, S&P, and Fitch, using the same ratings scheme as for bonds. The ratings agencies are another potential source of information about the terms of a specific equity security issue. Three basic types of preferred share dividend payment provisions are observed in modern financial markets: fixed-rate (fixed-dividend), adjustable rate, and auction/re-marketed rate.8 The fixed rate preferred is the traditional type of dividend payment provision. For this type of preferred, the dividend payment is based on a predetermined rate (percentage) of the par value. This may be expressed as a dollar value per share. For example, if the par value is $50 a 10% dividend preferred would have a $5.00 annual dividend payment. As with common stock dividends, the dividend payment is usually paid quarterly so the 10% dividend preferred ($50 par value) would make a regular payment of $1.25 each quarter. Even though preferred shares have redemption provisions and other features that can impact the yield calculation, e.g., conversion provisions, it is conventional to quote the ‘dividend yield’ (Div/P) for preferred stocks and use this as a method of assessing value much as in traditional yield spread analysis. Given that this measure of the dividend yield is a current yield calculation, this procedure is a theoretically precise measure of the yield only if the preferred is assumed to be a perpetuity. Prior to 1982, all preferred shares traded in U.S. stock markets were of the fixed rate type (Wilson in Fabozzi 2001, p. 338). Following a practice that had started a few years earlier in the private placement market, in 1982 adjustable rate preferred stock issues started to appear, followed two years later by auction rate preferred issues and, the following year, by re-marketed rate preferred issues. All of these types of preferred stock issues have a dividend payment that changes from period to period. Though a

share issues raising $324.63 billion. In comparison, there were 7,017 seasoned equity offerings raising $606 billion. 8 Another form of dividend provision arises with participating preferred stock. This type of preferred stock is rare in modern financial markets, though the provision has appeared in isolated historical instances usually associated with mergers and acquisitions activity. Typically, a participating preferred has a prior claim to the initial round of dividends. After a certain amount of earnings has been paid as dividends to common stock, usually the same per share amount as the preferred dividend, then preferred and common stock share equally in any remaining dividend payments. While such an arrangement may seem disadvantageous to common shareholders, the absence of voting rights for preferred stock combined with a preferred redemption provision may provide sufficient offset in situations involving corporate takeovers.

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25

number of variations are possible, an adjustable rate preferred typically has a quarterly resetting of the dividend rate determined by some spread off the highest of three points on the Treasury yield curve, e.g., using the yields for 3-month, 10-year, and 20-year maturities. This maximum rate may be subject to a floor rate below which the dividend payment rate will not fall, i.e., the adjustable rate preferred has a ‘collar’. The spread off the Treasury yield can be positive or negative. A difficulty with this type of preferred stock design is that the method of adjusting the dividend payment rate is fixed. The spread does not change with market conditions or the risk of the issuer. As such there is some associated principal risk. For a number of reasons, purchasers of variable rate-preferred stock are often corporate cash managers seeking a tax-exempt or tax-advantaged money market security (Wilson in Fabozzi 2001, pp. 343–344). This type of investor is seeking a competitive interest rate without risk of principal. The auction rate-preferred structure addresses the potential problem that the adjustable rate preferred poses for this type of investor. For this type of preferred, the dividend payment rate is set at regular intervals, usually every seven weeks, through auctions involving current holders of these preferred issues and other investors interested in purchasing the shares. In this fashion, the dividend payment rate reflects market conditions and changes in the risk of the issuer. The remarketed rate preferred stock issues are a variation on the auction rate preferred that uses a remarketing agent to reset the dividend payment rate. By avoiding the costs associated with the auction process, the remarketed issue can feature a shorter reset period, usually varying between one week and seven weeks. In this fashion, the auction rate and re-marketed rate preferred issues avoid most of the principal risk associated with adjustable rate preferred stocks. Since the first issues appeared, these variable dividend preferred issues have come to represent about half of new preferred issues, with the split between fixed and variable dividends varying from year to year. These changes in dividend structure were accompanied by a change in the composition of issuers. While the traditional issuer of preferred shares was a utility (i.e., electric, water, gas, and telephone companies). More recently, the financial companies, such as banks, thrifts, and insurance companies, have become significant sources of preferred share issues. These entities are important drivers of the variable rate preferred structures. For example, the first auction rate-preferred stock issue, in 1984, was by American Express. From 1990 to 2003, it is estimated that $332 billion in new preferred stock was issued, much of this by financial companies (Poitras 2005). Combined

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with the approximately $60 billion of preferred issues outstanding in 1990, net of redemptions, the amount of preferred stock outstanding in the United States was about $350 billion. Even with these changes and considerable growth, the size of the outstanding preferred share market can be measured in the hundreds of billions of dollars, compared to the trillions in par value of outstanding issues in the debt market. The preferred share is a hybrid security, sharing some features of debt and some features of common stock. On the issue of whether to purchase a preferred stock or the debt of a company, Graham et al. (1962, p. 382) observe: What yield advantage should the investor demand to compensate him for the contractual weakness of preferred stocks against bonds? We are inclined to think that an individual should not buy any preferred stock unless he is able to obtain both adequate safety and a differential of, say, 1 percent in the yield over that afforded by a bond of similar safety. . . . What of preferred stocks of secondary or inferior grade which can be bought at tempting yields? Our attitude toward them is the same as that toward high-coupon bonds. It is unsound to accept inadequate security to obtain a higher income, unless the buyer obtains also an opportunity for a substantial increase in principal value and unless also he or she is prepared to take the speculative risk of loss involved in the transaction.

In addition to being an excellent illustration of the Graham and Dodd approach to speculation vs. investment in security analysis and selection, preferred shares are also an excellent illustration of the impact that tax treatment and regulations can have on a security. For example, the reason that GDC state individual investors will, typically, not be attracted to preferred stocks is due to the different tax treatment compared to debt. Preferred Stock and Taxes Taxes impact security purchasers and issuers in different ways. For example, a high net worth individual subject to capital gains taxes will have different investment concerns than a tax-exempt charitable institution or pension trust. There are so many possible iterations that it is impractical to consider the different possible tax implications involved in the valuation of common stocks, let alone consider the tax implications of an exotic preferred share. In general, the tax rate of the marginal investor is usually too difficult to identify. Unlike common stocks where the tax motivations of purchasers and issuers are unclear, fixed rate-preferred shares provide a relatively clean

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security structure for examining the impact of tax considerations on the valuation of equity securities. For the issuer, preferred shares have the disadvantage that dividends paid are not a deductible expense like the interest payments on corporate debt.9 In the United States, the Internal Revenue Code (IRC) §243 provides a 70% deduction for dividends received by corporate investors owing less than 20% of the paying corporation. This rises to 80% for ownership shares between 20% and 80% and is 100% for greater than 80% ownership. The valuation of preferred stock depends on the tradeoff between the increase in issuer opportunity cost due to the loss of the interest deductibility foregone by issuing preferred stock instead of debt and the reduction in tax liabilities of corporate preferred share purchasers due to the partial income tax deductibility of dividends paid on preferred shares. The benefits to investors means that the coupons on preferred stock will be lower than on comparable debt issues. This makes preferred stocks an attractive source of financing relative to long-term debt for firms with low expected marginal tax rates, e.g., Ely et al. (2002). In practice, the financing benefits of preferred stocks to issuers are reduced by the generally higher issue costs of preferred stock relative to long-term debt. These additional costs depend on a combination of factors related to the characteristics of the preferred being issued (e.g., convertible preferreds are more expensive to issue than fixed rate preferreds), the size of the issue, the credit risk rating and the type of issuer (e.g., financial company vs. public utility) (Bajaj et al. 2002). Given this, the decision to issue preferred stock versus debt will depend on the tradeoff between the tax benefit to the marginal corporate investor and the incremental tax burden on the issuing corporation. Despite some sweeping tax code changes associated with the Tax Reform Act (1986) and later reforms, little has changed for U.S. individual investors in preferred stocks since GDC (1962, p. 382) wrote: “Under present tax laws high-grade preferred stocks are not logical investments for individuals. They are logical investments for corporations, which can obtain a much higher net return from them than from corporate bonds of comparable 9 There

are exceptions to this rule. For example, IRC §247 provides for a partial dividends paid deduction for ‘old money’ preferred stocks issued by public utilities. In turn, the investors in these old money preferred shares are subject to a reduced dividend received tax credit under IRC §244, e.g., Atwood (2002). Old money preferred stocks include public utility preferreds outstanding on 1 October 1942 and all subsequent preferred issues by that public utility used to replace these issues, including subsequent issues made through a tax-free reorganization.

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quality”. Despite some current proposals to reduce or eliminate the ‘double taxation’ of dividends, U.S. individuals receiving common stock or preferred stock dividends are subject to taxation on that income at their marginal tax rate. In the United States, the coupon rates on preferred shares only make sense for corporate investors able to take advantage of the favorable dividend tax treatment. The United States is unusual in applying the full marginal tax rate to dividend payments made to individuals. In Canada, for example, dividend income from both preferred and common stock is usually taxed at rates well below the marginal tax rate for individuals and not taxed when received by Canadian corporations.10 Unfortunately, the theoretically attractive features of this reduction in ‘double taxation’ of preferred dividends has, in practice, been characterized by numerous tax management schemes by corporations to reduce or eliminate the corporate taxes paid. In addition to tax consequences associated with dividend payments, the issuance of preferred shares can also be motivated by regulatory considerations and other aspects of the tax code, e.g., Callahan (2001). In particular, the Tax Reform Act (1986) limited the deductibility of net operating loss carry forwards after a change in corporate ownership. Under the rules, straight preferred stock does not count toward the ‘change in ownership criteria’ that measures ownership change in terms of holdings of common stock and convertibles. As firms with such loss carry forwards are usually subject to severe restrictions on the issue of debt, preferred shares are an attractive form of financing. A regulatory motivation for the issuance of preferred shares for financial institutions can be found in the capital adequacy requirements that have been introduced since the 1989 Basle accord and continue with the 2004 Basle II agreements, e.g., Kupiec (2007). Because preferred stock is considered to be equity, this provides an added motivation for financial companies subject to the capital adequacy guidelines to issue preferred stock instead of debt. The ongoing trend for financial institutions to create equity/debt hybrids that are booked as equity has been an impetus to the accounting standards FAS 149 and FAS 150 that require corporations to treat equity/debt hybrids issued as ‘preferred shares’ as debt on the balance sheet.

10 Institutional information on Canadian securities markets, including topics such as relevant tax rates on securities, can be obtained from material distributed by the Canadian Securities Institute (www.csi.ca).

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The Philosophy of Equity Valuation

Fig. 1.1

1.1.2

b921-ch01

29

SEC website. (http://www.sec.gov/)

Regulation of Equity Securities

Government Regulation Like it or not, governments are key players in the valuation of equity securities. The scope of government influence is pervasive and systemic. For example, exchange rate and interest rate policy indirectly impact the value of equity by affecting the relative price of debt and securities traded in other currencies. Two key areas where government regulation directly impacts equity security valuation are: tax policy, both corporate and personal, and the legal environment, which includes corporation law and securities regulations, and the scope of enforcement by regulators. It would be presumptuous in the extreme to claim that accurate equity valuation can be conducted without intimate knowledge and understanding of the subjects of taxation, corporate law, and securities law. However, to provide detailed discussion of these subjects in this book is not possible, if only because the relevant rules and laws vary across the jurisdictions. These are subjects that require detailed separate treatment. Numerous useful sources are available. What is provided here is a brief overview combined with a certain perspective.

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Besides restrictions imposed by the corporation law governing the corporate charter, there are a number of other laws that govern the issuance of corporate securities. In the United States, most prominent are the federal regulations administered by the Securities and Exchange Commission (SEC) (www.sec.gov, see Fig. 1.1), especially the Securities Act (1933, most recently amended 2008), the Securities and Exchange Act (1934), the Investment Company Act (1940), the Public Utility Holding Company Act (1935), and the Sarbanes–Oxley Act (2002).11 These regulations cover filing requirements for all firms with publicly traded securities. The most prominent filing requirement is the 10-K form, required under the Securities and Exchange Act (1934), that provides annual financial statements of the corporation, certified by a chartered public accountant. Under the Securities Act (1933), companies issuing publicly traded securities for the first time also must meet SEC filing requirements in the form of a prospectus providing full disclosure of pertinent facts about the issue. The SEC is also responsible for monitoring the regulations governing insider trading. The regular and irregular filings with the SEC are essential sources of information for security analysis of publicly traded companies. The federal rules and regulations administered by the SEC are not the only ones relevant to corporate securities. There are also state regulations — ‘blue-sky laws’ — that can cover the licensing of securities firms, filing information requirements, oversight responsibilities, and penalties relating to violating the statutes. A useful reference on these laws is the Commerce Clearing House Blue Sky Law Reporter. State securities laws can have national significance. For example, blue-sky laws of New York and Massachusetts played an important role in the prosecution of major securities firms such as Merrill Lynch when analysts and investment advisors were found to be unfairly touting stocks such as Worldcom to retail accounts. In addition to state blue sky laws, there are also federal and state laws governing corporate mergers, such as the federal Sherman Anti-Trust Act, and corporate bankruptcies, such as the federal Bankruptcy Reform Act 11 For

up to date changes to relevant U.S. securities laws, see the United States Code Classification Tables published by the Office of the Law Revision Counsel of the House of Representatives at http://uscode.house.gov/uscct.htm. For information on the various forms that are required to be filed with the SEC, see http://www.sec.gov/ info/edgar/forms/edgform.pdf. Most filing requirements mandated for requirements fall under Regulation S-T, General Rules and Regulations for Electronic Filings, which identified which filings are mandated for electronic filing. As a consequence of this regulation, all important SEC filings are available on-line, substantively easing the burden of collecting information required for equity valuation.

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31

of 1978 and Bankruptcy Abuse Prevention and Consumer Protection Act of 2005. The significance of government regulation to equity valuation is aptly framed by events of 2008. The virtual absence of effective regulation and oversight of the hedge fund industry facilitated the spectacular success of the Ponzi scheme run by Bernard Madoff. The collapse of this scheme was precipitated when equity valuations both in the United States and globally were devastated by the spillover from the financial crisis. Arguably, this crisis was generated by yet another instance of lax or ineffective regulatory oversight, in this case, associated with the sub-prime mortgage and credit default swap markets. Historically, the ineffectiveness of government regulatory oversight is usually identified as a prime contributor in widespread financial crisis, certain types of corporate collapses and spectacular investment frauds. From the perspective of equity valuation, the associated public policy debates over the extent of government responsibility is ‘dead letter’ — largely irrelevant to the problem at hand. Such debates are predicated on the assumption that governments are capable of effective oversight. Assuming that government regulators will provide adequate protection can prove to be costly in determining an accurate equity security value. An assessment of potential for future changes in the regulatory and tax framework that could impact the valuation is a useful step to include in the equity valuation process. In turn, the selection of a particular process will depend on perceptions concerning the role and effectiveness of government regulation. One obvious example involves the valuation of ‘sin’ stocks for companies producing alcohol, tobacco, or gambling entertainment. While the government regulatory environment changes so slowly that it is typically taken as given, the environment for sin stocks is decidedly more fluid. In general, it is too much to expect government regulators to prevent debacles such as the sub-prime mortgage driven financial crisis, uncover frauds such as the Madoff Ponzi scheme, or effectively detect and deter hedge funds and other unregulated traders engaging in market manipulations. It is also too much to expect that governments will not arbitrarily change laws or regulations having a material impact on the valuation problem. For equity securities where government regulations play a central role, caveat emptor needs to be ingrained into the valuation process. Industry Self-Regulation Despite the appearance of substantial government control and oversight, equity security markets are largely self-regulatory. While the role of

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government has expanded over time, this expansion has been largely driven by events in securities markets. It was not until the collapse of equity markets during the Great Depression that the Securities Act (1933) and the Securities and Exchange Act (1934) were developed. A more recent example is the Sarbanes–Oxley Act (2002) that emerged following the collapse of the technology stock-led financial market bubble in early 2000. Undoubtedly, the financial crisis that began in 2008 will produce additional future examples. From the beginning of trade in equity securities, self-regulation by market participants has played the key role in determining the milieu for trading with government determining the legal and taxation environment. Self-regulation by those directly involved in the market has the potential to address the problems that cannot be effectively tackled by government regulators. Yet, as has been amply demonstrated, self-regulation is a twoedged sword, e.g., Pirrong (1995) and Markham and Harty (2008). While self-regulation is potentially the best mechanism for identifying and averting market manipulation and fraud, the costs associated with achieving this objective can conflict with the profit seeking motives of market participants. Where self-regulation appears to fail, governments react by introducing regulations that change the rules of the game. Given the costs associated with adhering to government regulations, there is an ongoing incentive for equity market participants to develop new equity products, organizational schemes, or trading techniques that avoid government regulatory oversight. Such innovation eventually produces a sufficiently negative event to generate incremental change in government regulatory oversight. Modern securities laws pertaining to self-regulation cover broker-dealers, exchanges, investment advisors, and the like. The basis for these laws can be traced back to the early 17th century trade in shares of the Dutch East India Company, where market manipulation, fraudulent trading practices, and failures in corporate governance featured prominently, e.g., De Marchi and Harrison (1994). From that time to the present, the history of equity security trading reflects a tension between well-positioned market participants seeking to engage in unfettered activity and regulators attempting to protect unwary investors and to avert the negative systemic spillovers arising from such trade. The same relatively-opaque-value characteristic of equity securities that is so useful to the capital formation process also provides tempting opportunities to less than scrupulous market insiders. Despite an impressive layering of regulations and regulators, modern equity markets are still impacted by the general types of self-regulation problems that have plagued the history of equity markets. The collapse

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of the Madoff hedge fund Ponzi scheme is a particularly apt example of three problems generated by the self-regulatory framework for modern equity markets set out in the Securities Exchange Act (1934) also referenced as U.S. Code Title 15, Chapter 2A. Centerpieces of this selfregulatory framework are the equity securities exchange, the broker-dealer, and the investment advisor (15 USC Chapter 2D). Each has legislatively mandated requirements governing registration, oversight, fiduciary responsibility, and the like. The prolonged success and extent of the Madoff scheme speaks to the inadequacies of the protections provided by the current framework. In 1990, 1991 and 1993, Madoff served as chairman of National Association of Securities Dealers, which runs the NASDAQ over-the-counter exchange, one of the two most important U.S. equity exchanges. Founded in 1960, Bernard L. Madoff Investment Securities LLC was at one time the largest market maker on NASDAQ and, at the end of 2008, was the sixth largest market maker on Wall Street. The broker-dealer is another key element of the self-regulatory framework. The final piece of the puzzle is the hedge fund organizational structure that Madoff employed for the Ponzi scheme, aimed specifically at the avoidance of government reporting requirements set out in 15 U.S.C. 78m or 780(d), which governs investment advisors. The rise of hedge funds in equity securities markets over the past two decades has been dramatic. Recognizing that there are a range of possible legal and operational definitions of a ‘hedge fund’, rough estimates from a variety of sources indicate the hedge fund sector, including funds trading commodities and securities, has grown from approximately $22 billion capital invested in 1987 to over $2.7 trillion in 2007 (Cumming and Johan 2008). Much of this growth has occurred in the last decade, from 3,000 operating hedge funds in 1998 to over 13,000 in 2007 (Wyderko 2007). Despite previous warning signs, such as the collapse of Long Term Capital Management in 1998, the considerable subsequent growth of the hedge fund industry raises fundamental questions about the adequacy of regulatory institutions, both in the United States and internationally. Questions regarding the appropriate path to regulatory reform of hedge funds have been complicated by recent U.S. court decisions restricting SEC administrative authority, e.g., Pekarek (2007). In addition to problems associated with hedge funds, private equity and venture capital funds pose similar self-regulatory difficulties. The regulatory treatment of hedge funds is particularly incoherent, even by historical standards. As the SEC observes, ‘there is no universally

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accepted definition of the term hedge fund’ (SEC 2003, p. 3). Definitions that are provided depend on the perspective taken. Regulatory bodies, such as the SEC, use definitions which emphasize legal characteristics, e.g., a hedge fund is ‘an entity that holds a pool of securities and perhaps other assets, whose interests are not registered as an investment company under the Investment Company Act’ (SEC 2003, p. 3). Such definitions implicitly identify hedge funds as entities structured to operate under exemptions from securities laws. However, hedge funds are not the only capital pools operating in domestic capital markets largely outside the scope of regulatory oversight. Private equity funds and venture capital funds are other forms of unregistered capital pools that are legally similar to hedge funds (SEC 2003, pp. 5–8). Some types of commodity pools are also structured to avoid regulatory oversight. As such, the distinction between hedge funds and other unregistered funds is artificial. From a regulatory perspective, the activities of all unregistered funds operating in domestic capital markets require closer public scrutiny. In contrast to the legal definitions of hedge funds used by regulators, an ‘academic’ definition of hedge funds aims to systematically identify the characteristics that are possessed by all hedge funds, e.g., Atiyah and Walters (2004, p. 173) and van Berkel (2008, p. 198). Unfortunately, the evolution of hedge funds and other alternative asset classes has produced such a wide variation in fund structures that it is difficult to identify the characteristics common to all. For example, van Berkel (2008, p. 198) states that a hedge fund is a pooled investment vehicle that is organized as a private limited partnership or limited liability company, usually domiciled offshore, with legal characteristics sufficient to operate under the exemptions in securities laws in order to permit tax efficiency and minimal regulatory oversight. In the United States and most jurisdictions, such exemptions require shares in the hedge fund not be directly sold to retail investors, restricting available clients to a small number of high net worth individuals and institutional investors. In addition to these general characteristics not being unique to hedge funds, the search for generalities ignores the specifics of the conventional ‘master–feeder’ structure used by many hedge funds. Such structures involve making a jurisdictional choice regarding the domicile of the master fund and feeder fund(s) based on tax and regulatory considerations. In practice, this will result in a part of the fund structure that is domestically domiciled. Both the near collapse of Long Term Capital Management and the collapse of the Madoff scheme speak to the impotence and incoherence of the

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regulatory structure governing the hedge fund industry, specifically, and the equity security markets, in general. At the same time that regulators such as the SEC have made a sequence of more-or-less unsuccessful efforts to bring hedge fund trading activities under public scrutiny, the industry has been able to expand dramatically in size and diversity. In practice, the burden and scope of domestic regulatory oversight are further complicated because, for tax and regulatory avoidance reasons, many hedge funds are domiciled in off-shore locations. Not only have hedge funds flourished, the industry has even been able to achieve significant changes in administrative rulings, e.g., SEC rulings on the ‘up tick’ rule for short sales. The upshot is that accurate equity valuation requires healthy ‘sharks in the water’ skepticism about the effectiveness of regulators in preventing the ‘fleecing of the lambs’. As Fred Schwed asked in 1940: “Where are the customers’ yachts?”.

1.1.3

Trading of Equity Securities

Equity securities are traded in a range of different venues. The method of issue and exchange for securities differs according to whether the security is a primary issue or a secondary issue. A primary issue is a new security that is just coming to market, generating a cash inflow to the issuing entity. Some primary issues are seasoned, i.e., are increases in the outstanding issues for companies which are already publicly traded. For example, if Ford Motor makes a new issue of common stock, this would be a seasoned primary issue. Other primary issues are unseasoned, being made by companies which are making a first issue of publicly traded equity.12 The primary market for equity securities, such as common stock, is the initial public offering (IPO) market. Though some companies do sell primary security issues directly to investors, it is conventional to employ an investment banking firm to market the securities. For historical reasons, this investment banking activity is called underwriting (Poitras 2000, ch. 12). Investment banks also do underwriting of debt issues for both corporations and governments. 12 The

distinction between seasoned and unseasoned issues is blurred in certain cases. For example, consider a company with publicly traded common stock and no debt on the balance sheet. Would a new issue of bonds by this company be a seasoned or unseasoned issue? Because there is no market price available for the bonds, the issue would typically be considered as unseasoned. Now consider a company with outstanding issues of both straight debt and common stock that is seeking to make a new convertible bond issue. Is this a seasoned or unseasoned issue?

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There are a number of variations on underwriting that are used by investment bankers in the distribution of primary issues. The mainstay of the investment banking business involves purchasing–distributing, where a lead investment bank (or banks) will set up a purchase group or syndicate with a number of other investment banks. All the investment banks in the group agree to purchase a specified portion of the new issue for sale and distribution to customer accounts. As such, the ability to evaluate the price and marketability of a new issue is crucial to investment banking as are a substantial sales force and connections to the purchasers of new issues. Because the process of underwriting is risky, e.g., the firm could be left holding a sizable amount of unmarketable issue due to changes in market conditions in the period between the pricing agreement with the issuer and distribution of the issue, sometimes agency marketing or best efforts marketing is used to distribute the issue. In this case, the issuing corporation seeks to reduce the investment banking fees by taking on some or all of the risk that the issue will not be sold. Some types of primary issues, e.g., rights issues that are given directly to shareholders, permit the use of standby underwriting where the firm markets the issue and the investment bank agrees to take up any unsold securities at a given price. In order to attract attention from the financial media, securities usually have to be publicly traded and transferable. The main exception is certain mutual funds (open-end funds), which are issued directly by a fund company and are redeemable instead of transferable.13 The secondary market for publicly traded securities has come to be dominated by a network of exchanges that is gradually converging onto two corporate entities that were initially associated with the New York Stock Exchange, now NYSE Euronext group, and the U.S. over-the-counter (OTC) equity market giant the NASDAQ, now NASDAQ OMX group (see Table 1.5 for examples of quoted prices of common stock). The various stock exchanges also trade other securities than individual stocks, such as corporate debt and closed-end funds. This corporate convergence has engulfed regional exchanges and exchanges specializing in trading options and indexes, such as the AMEX, which merged into NYSE Euronext in 2008, and the PHLX, which is now part of NASDAQ OMX. The evolution and convergence of

13 Open-ended funds are distinguished from the two other types of fund groups specified in the Investment Company Act (1940) which are closed end funds and unit investment trusts (unit trusts). These types of fund are publicly traded on the stock exchanges or OTC.

17:50:10.

Name

Sample of NYSE Stock Exchange Stock Prices (Wednesday, 23 January 2008 5:22 PM).

Symbol Open High

Low Close Net Chg % Chg

Volume

52 Wk High 52 Wk Low Div Yield P/E YTD % Chg

1.36 0.79

4.92 4.2

1,245,200 541,588

39.42 31.2

25.23 18.13

— 0.50f

— 2.5

19 19

−23.7 −3.8

ABN

52.43 53.67 52.26 53.59

0.87

1.65

120,100

56.15

31.43

1.60e

3

—

−0.8

ABD

13.1

14.29 12.88 14.11

0.7

5.22

1,003,334

26.09

12.54

—

—

59

ACE AES AFL AG ATG

56.59 17.19 59.63 57.07 35.63

60.35 18.15 62.66 58.41 37.72

56.23 17.06 58.45 49.8 35.63

59.98 18.12 62.59 56.98 37.69

1.57 0.43 1.28 −2.11 1.31

2.69 2.43 2.09 −3.57 3.6

4,801,863 6,659,171 4,906,740 4,566,298 841,011

64.32 24.24 67 71.95 44.67

52.79 16.63 45.18 32.15 35.24

1.08 — 0.82 — 1.64

1.8 dd — — 4.4

8 — 20 178 15

−2.9 −15.3 −0.1 −16.2 0.1

GRO

9.81

9.96

8.65

9.38

−0.77

−7.59

278,477

—

—

—

−9.7

AKS

38.04 40.84 35.32 39.42

0.13

0.33

7,189,870

53.97

18.26

0.2

—

11

−14.7

AMB

48.12 54.61 47.92 54.15

4.73

9.57

1,744,087

66.86

47.07

2

3.7

21

−5.9

ACO

24.99 26.15 23.6

0.57

2.25

846,850

42.7

23.51

0.64

2.5

14

−28

AMR ATS

12.2 1.6

1.9 —

15.45 —

13,796,771 27,300

39.87 4.95

10.95 1.25

— —

— —

8 —

1.2 −28.4

T AVX AXA

35.34 37.02 33.32 36.69 13.1 13.47 12.68 13.27 31.9 33.59 31.35 33.52

0.73 −0.13 −0.75

2.03 −0.97 −2.19

53,332,340 1,203,600 1,933,950

42.97 18.4 47.1

33.6 12.67 32.68

1.60f 0.16 1.42e

4.4 1.2 4.2

19 15 —

−11.7 −1.1 −15.6

25.94

14.34 11.86 14.2 1.6 1.51 1.54

17

7

−12

37

(Continued)

b921-ch01

26.95 29.39 25.25 29.01 18.8 19.69 18.5 19.61

9in x 6in

AIR ABM

The Philosophy of Equity Valuation

17:50:10.

AAR CORP. ABM INDUSTRIES INC. ABN AMRO HOLDING N.V. ADS ACCO BRANDS CORP. ACE LTD. AES CORP. AFLAC INC. AGCO CORP. AGL RESOURCES INC. AGRIA CORP. ADS AK STEEL HOLDING CORP. AMB PROPERTY CORP. AMCOL INTERNATIONAL CORP. AMR CORP. APT SATELLITE HOLDINGS LTD. ADS AT&T INC. AVX CORP. AXA S.A. ADS

November 3, 2010 10:47

Table 1.5

Symbol Open High

Low Close Net Chg % Chg

17:50:10.

0.91 20

2.89 —

Volume 261,850 6,000

52 Wk High 52 Wk Low Div Yield P/E YTD % Chg 41.58

17.51

—

20.3

19.7

— f

2.05

12.07

947,709

30.72

13.27

0.06

1.25

7.81

2,200

27.52

13.25

0.06f

2.71 0.83

7,686,761 12,001,440

32.08 61.09

15.94 49.58

0.20 1.3

3.79

5.14

3,289,272

85.77

66.05

0.7

−0.81

−4.11

1,478,027

57.62

14.13

0.8

1.3

5.76

389,985

−0.23

−0.69

0.74 −0.72

f

14

14.3

—

—

0

0.3

12

−1

0.3

11

−0.1

— 2.2

22 25

−17 3.2

0.9

16

−3

—

dd

−8.3

3.5

19

−6.8

21.17

0.84

4,529,736

44.03

32

0.42

1.3

16

−8.2

12.33 −9.45

270,700 161,104

16.91 32.33

5.51 6.26

— —

— —

14 —

−14.2 −26

0.49

1.92

779,566

35.12

24.14

0.04

0.2

15

−23.7

3.07

7.92

1,273,164

55.7

33.87

0.52m

1.2

13

−7

1.85

7

265,800

43.66

24.41

0.44

1.6

16

0

−0.08

23,500

41.49

22.9

2.02e

—

—

−1.7

−0.03

(Continued)

b921-ch01

29

9in x 6in

0.63 0.48

e

—

Valuation of Equity Securities

AZZ INCORPOAZZ 30.69 32.61 30.08 32.41 RATED A.H. BELO CORP. — 20 20.3 19.7 20 SERIES A AARON RENTS RNT 16.74 19.49 16.17 19.04 INC. AARON RENTS RNTA 17 17.25 15.5 17.25 INC. CL A ABB LTD. ADS ABB 22.07 23.96 21.69 23.91 ABBOTT LABOABT 57.25 58.16 54.67 57.97 RATORIES ANF 72.26 77.96 71.62 77.58 ABERCROMBIE & FITCH CO. CL A ABITIBIBOWATER ABH 20.37 20.37 17.76 18.89 INC. ACADIA REALTY AKR 21.97 24.16 21.88 23.87 TRUST SBI ACCENTURE ACN 33.33 33.33 31.91 33.07 LTD. CL A ACCURIDE CORP. ACW 5.85 6.78 5.81 6.74 7.62 7.62 6.65 6.9 ACORN INTERNA- ATV TIONAL INC. ADS ACTUANT CORP. ATU 24.99 26.2 24.25 25.96 CL A ACUITY BRANDS AYI 37.71 42.38 37.7 41.84 INC. ADMINISTAFF ASF 25.85 28.85 25.64 28.28 INC. A.F.P. PROVIDA PVD 36.26 36.88 36.26 36.61 S.A. ADS

November 3, 2010 10:47

Name

(Continued)

38

Table 1.5

Name

Symbol Open High AEA

7.48

8.31

(Continued)

Low Close Net Chg % Chg 7.3

8.28

Volume

7.12

705,800

19.05

6.94

0.5

6

12

−18.5

43.62

29.51

0.24

0.7

15

−11.6

44

18.87

—

dd

—

−17.7

AAP

31.46 34.02 31.46 33.6

1.37

4.25

1,699,420

EYE

19.19 20.2

20.19

0.56

2.85

690,745

19

52 Wk High 52 Wk Low Div Yield P/E YTD % Chg

0.55

6.65

7.59

6.6

7.56

0.73

10.69

43,635,502

16.45

5.31

—

dd

—

0.8

ASX

3.97

4.09

3.88

4.03

−0.14

−3.36

1,318,500

6.27

3.92

0.22e

—

—

−19.7

AAV

8.68

8.88

8.45

8.59

−0.16

−1.83

936,907

15.11

8.27

1.44g

—

—

−2.5

23.19 23.84 22.6

23.84

−0.58

−2.38

103,873

51.09

23.77

0.37e

—

—

−15.6

ACM

23.29 24.59 22.6

24.51

0.61

2.55

908,246

38.25

19.96

—

—

—

−14.2

ANW

25.8

24.49 26.95

0.95

3.65

451,050

48.63

13.7

0.04

0.1

39

−29.8

AEG

13.89 14.64 13.68 14.61

−0.26

−1.75

3,553,176

21.91

14.06

0.83e

5.7

7

−16.7

27

39

(Continued)

b921-ch01

ATE

9in x 6in

AMD

The Philosophy of Equity Valuation

17:50:10.

ADVANCE AMERICA CASH ADVANCE CENTERS INC. ADVANCE AUTO PARTS INC. ADVANCED MEDICAL OPTICS INC. ADVANCED MICRO DEVICES INC. ADVANCED SEMICONDUCTOR ENGINEERING INC. ADS ADVANTAGE ENERGY INCOME FUND ADVANTEST CORP. ADS AECOM TECHNOLOGY CORP. AEGEAN MARINE PETROLEUM NETWORK INC. AEGON N.V.

November 3, 2010 10:47

Table 1.5

17:50:10.

Low Close Net Chg % Chg

Volume

52 Wk High 52 Wk Low Div Yield P/E YTD % Chg

10.34

1,212,500

32.82

14.23

—

—

11

−21.2

22.55 26.09 21.94 25.96

2.8

12.09

3,822,294

31.88

18.29

—

—

17

−2

AET ACS

51.76 54.55 50.76 54.11 41.4 45.45 41.4 45.15

0.68 1.79

1.27 4.13

6,422,214 962,746

60 61.67

40.82 39.46

0.04 —

0.1 —

16 18

−6.3 0.1

AMG

91.75 97.8

90.29 96.09

2.09

2.22

1,256,672

136.51

86.02

—

—

23

−18.2

31.69 33.56 31.45 33.43

0.59

1.8

4,504,357

40.42

30.26

—

—

21

−9

−0.41

−0.7

4,389,069

62.96

33.25

0.18f

0.3

65

6

36

27.29

2.00f

6.8

16

−1.7

14.5

ARO

A

16.49 14.22 16.44

56.8

59.93 55.93 57.9

ADC

27.71 29.68 27.56 29.58

1.37

4.86

54,300

AGU AKH

56.42 57.44 50.86 56.51 27 29.1 26.99 28.84

−1.57 0.99

−2.7 3.55

6,046,149 187,800

76.14 52.17

32.61 26.22

0.11 0.64e

0.2 —

37 —

−21.7 −17.3

APD

84.2

87.21 80.73 86.76

2.63

3.13

3,187,654

105.02

71.11

1.52

1.8

18

−12

AYR ARG AAI

21.24 22.17 20.66 21.88 39.59 40.68 37.84 40.24 7.14 8.18 7.14 8

0.47 −0.6 0.7

2.2 −1.47 9.59

448,150 1,929,685 2,319,309

41.31 55.89 12.65

20.5 39 6.01

2.80f 0.36 —

12.8 0.9 —

12 19 16

−16.9 −22.8 11.7

(Continued)

b921-ch01

AEM

9in x 6in

1.54

AER

Valuation of Equity Securities

AERCAP HOLDINGS N.V. AEROPOSTALE INC. AETNA INC. AFFILIATED COMPUTER SERVICES INC. CL A AFFILIATED MANAGERS GROUP INC. AGILENT TECHNOLOGIES INC. AGNICO-EAGLE MINES LTD. AGREE REALTY CORP. AGRIUM INC. AIR FRANCE-KLM ADS AIR PRODUCTS & CHEMICALS INC. AIRCASTLE LTD. AIRGAS INC. AIRTRAN HOLDINGS INC.

Symbol Open High

(Continued)

November 3, 2010 10:47

Name

40

Table 1.5

Name

Low

(Continued)

Close Net Chg % Chg

Volume

52 Wk High 52 Wk Low Div Yield P/E YTD % Chg

0.62

3.42

18,700

28.37

16.77

0.24

1.3

18

3.5

ALK

22.48 24.99 22.45 24.69

1.67

7.25

939,086

44.5

21.11

—

—

9

−1.3

AIN

31.52 33.5

0.97

3

335,900

43.62

31.27

0.44

1.3

62

−10.2

ALB

33.45 34.06 32.38 33.82

−0.4

−1.17

1,164,400

48.84

31.99

0.42

1.2

14

−18

ACV

23.62 24.1

−0.65

−2.69

992,100

26.25

20.92

0.22

0.9

30

−4.2

5.94

−0.13

−2.14

23,267,441

14.57

5.7

.22e

—

—

−18.9

AA 28.44 29.2 26.69 29.19 ACL 137.85 140.85 133.94 139.67 AFN 3.03 3.33 3.01 3.3

0.4 −0.42 0.2

1.39 −0.3 6.45

16,615,925 470,508 776,683

48.77 154.9 11.82

27.12 115 2.61

0.68 2.06e 1.23e

2.3 1.5 37.3

10 27 dd

−20.1 −2.4 0.6

6.44

18,000

471

308.25

—

—

347

−1.8

5.98

6.33

917,800

83.73

3.12f

3.1

40

−1.2

11.07

3.1

330.05

—

—

11

−8.5

1.17

2.15

.15e

—

26

−12.6

ALU

5.73

ALX 317 ARE

Y AYE

5.95

31

33.31

23.36 23.51

5.54

347.5 317

347

92.8 100.49 92.8 100.45

355.57 368

347

368

52.94 55.61 51.43 55.6

21

5,400 2,928,526

116.23

437 65.48

45.31

b921-ch01

17.75 18.75 17.56 18.75

9in x 6in

ALG

The Philosophy of Equity Valuation

17:50:10.

ALAMO GROUP INC. ALASKA AIR GROUP INC. ALBANY INTERNATIONAL CORP. CL A ALBEMARLE CORP. ALBERTOCULVER CO. ALCATEL LUCENT ALCOA INC. ALCON INC. ALESCO FINANCIAL INC. ALEXANDER’S INC. ALEXANDRIA REAL ESTATE EQUITIES INC. ALLEGHANY CORP. ALLEGHENY ENERGY INC.

Symbol Open High

November 3, 2010 10:47

Table 1.5

(Continued)

41

Name

17:50:10.

Volume

ATI

63.25 67.65 59

66.87

−1.22

−1.79

5,922,392

AGN ALE ADS

63.82 65.14 62.48 65.01 34.36 37.31 34.16 37.29 59.06 65.38 58.83 65.21

−0.6 2.29 4.92

−0.91 6.54 8.16

3,031,460 361,000 2,332,603

0.22

2.25

286,200

AIQ

9.53

9.99

9.44

9.98

52 Wk High 52 Wk Low Div Yield P/E YTD % Chg 62.35

0.72f

1.1

9

−22.6

70.4 51.3 80.79

52.9 33.76 47.49

0.2 1.64 —

0.3 4.4 —

42 12 31

1.2 −5.8 −13

10.64

6.6

—

—

26

3.7

119.7

b921-ch01

dividend or extras in addition to the regular dividend. annual rate of the cash dividend and that a stock dividend was paid. dd Loss in the most recent four quarters. e Indicates a dividend was declared in the preceding 12 months, but that there is not a regular dividend rate. Amount shown may have been adjusted to reflect stock split, spinoff, or other distribution. f Annual rate, increased on latest declaration. g Indicates the dividend and earnings are expressed in Canadian currency. The stock trades in U.S. dollars. No yield or P/E ratio is shown. i Indicates amount declared or paid after a stock dividend or split. j Indicates dividend was paid this year, and that at the last dividend meeting a dividend was omitted or deferred. m Annual rate, reduced on latest declaration. p Initial dividend; no yield calculated. r Indicates a cash dividend declared in the preceding 12 months, plus a stock dividend. stk Paid in stock in the last 12 months. Company does not pay cash dividend. x Ex-dividend, ex-distribution, ex-rights, or without warrants. b Indicates

9in x 6in

a Extra

Low Close Net Chg % Chg

Valuation of Equity Securities

ALLEGHENY TECHNOLOGIES INC. ALLERGAN INC. ALLETE INC. ALLIANCE DATA SYSTEMS CORP. ALLIANCE IMAGING INC.

Symbol Open High

(Continued)

November 3, 2010 10:47

42

Table 1.5

November 3, 2010 10:47

9in x 6in

The Philosophy of Equity Valuation

b921-ch01

43

Fig. 1.2 NYSE Euronext History and Organization. (http://www.nyse.com/ pdfs/NYSEEuronextTimeline web.pdf)

one of these major stock exchange groups is given in Fig. 1.2 which illustrates the ongoing global consolidation involving the NYSE, including the 4 April 2007 merger of the NYSE with Euronext — itself the merger of four national European exchanges and the London International Financial Futures Exchange in 2000 and 2002. The NASDAQ has also evolved from the primary U.S. OTC stock market into a global stock market trading platform. 1.2 1.2.1

Risk, Return, and Uncertainty Basics of the Risk and Return Tradeoff

Equity security valuation seeks to determine an estimate for the intrinsic value of the security. In turn, differences between the estimated intrinsic value and the observed market price for the security can be used to guide equity security selection. However, due to the absence of comparable par value, it is not possible to directly compare the prices across securities to assess relative value. For this purpose, the security return is often used

17:50:10.

November 3, 2010 10:47

9in x 6in

44

b921-ch01

Valuation of Equity Securities

to measure the changes in value over time and across securities. The conventional method used for calculating the one-period return on a domestic security, R(1), assumes that at t = 0 the security is purchased at price P (0), held for one period and then sold at price P (1). For simplicity, it is also assumed that any dividend payment (Div.) paid during the holding period is received at the time the security is sold.14 The return can now be calculated as R(1) = (P (1) − P (0) + Div.)/P (0) = [P (1)/P (0)] + [Div./P (0)] − 1 = [(P (1) − P (0))/P (0)] + [Div./P (0)] = Capital gain (loss) + Dividend yield The funds received from the sale of the security are available to be reinvested at t = 1. This same security can now be purchased at price P (1), held for one period and then sold at price P (2), with any dividend payment again assumed to be paid at the time the security is sold. This second, one period return is R(2). And so it goes for R(3), R(4), R(5), . . . until a time series of one period returns is generated. The tradeoff between risk and expected return is the most fundamental notion in modern Finance.15 This result has been approached at a number of levels. At one level, the result is empirical, e.g., Campbell (1996). There are many studies that provide empirical estimates for various types of unconditional mean return and volatility of return measures, e.g., Ibbotson and Sinquefield (1976), Siegel (1998, ch. 2), and Dimson et al. (2002). These empirical results cover a wide range of countries, securities, and time periods. At another level, the tradeoff between risk and expected return is theoretical. Starting with Markowitz (1952) and Roy (1952), the tradeoff has been examined in the context of the optimal selection problem for 14 It is also possible to make other similar assumptions. For example, it can be assumed that there is a dividend reinvestment plan. This requires that shares can be traded in fractional increments. Similarly, it can be assumed that the dividend payment is reinvested in a fixed income security with a time to maturity equal to the holding period for the underlying equity security. This poses problems because the expected return on the stock will depend on an unknown interest rate to be earned on the fixed income security. 15 Various interesting internet searches could be done to show the pervasiveness of risk and return in the teaching of Finance, in general, and investment analysis, in particular. For example, in Yahoo, try the search ‘Bodie, Kane and Marcus & Risk and Return’. This will generate well over 1,000 hits for course outlines and descriptions which use this popular textbook and emphasize risk and return in the course content. The universities involved extend globally and include some of the most prestigious, e.g., Princeton, MIT and Chicago.

17:50:10.

November 3, 2010 10:47

9in x 6in

b921-ch01

The Philosophy of Equity Valuation

45

Table 1.6 Annual Returns for U.S. Stocks, Bonds, Bills and Inflation Over the 1974–1998 Market Cycle.

Year 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 Average Standard dev. Minimum Maximum

Small stocks

Large stocks

−29.74 −26.40 69.54 37.26 54.81 23.98 22.02 −7.26 22.29 6.50 43.99 18.77 35.34 32.48 7.79 −4.98 27.44 22.09 34.49 22.37 −14.02 6.46 28.21 32.00 3.40 18.40 −13.95 5.34 21.72 16.86 8.37 31.34 27.08 −3.20 50.24 30.66 27.84 7.71 20.30 9.87 −3.34 1.29 33.21 37.71 16.50 23.07 22.40 33.17 2.50 28.53 20.737 16.161 4.51 3.247 −29.74 −26.4 69.54 37.71

Long-term T-bonds

Intermediate term T-bonds

T-bills

Inflation

5.53 8.50 11.07 0.90 −4.16 9.02 13.17 3.61 6.52 −0.53 15.29 32.68 23.96 −2.65 8.40 19.49 7.13 18.39 7.79 15.48 −7.18 31.67 −0.81 15.08 13.02 10.055 2.042 −7.18 32.68

6.03 6.79 14.20 1.12 0.32 4.29 0.83 6.09 33.39 5.44 14.46 23.65 17.22 1.68 6.63 14.82 9.05 16.67 7.25 12.02 −4.42 18.07 3.99 7.69 8.62 9.436 1.655 −4.42 33.39

7.93 5.80 5.06 5.10 7.15 10.45 11.57 14.95 10.71 8.85 10.02 7.83 6.18 5.50 6.44 8.32 7.86 5.65 3.54 2.97 3.91 5.58 5.50 5.32 5.11 7.092 0.56 2.97 14.95

12.34 6.94 4.86 6.70 9.02 13.29 12.52 8.92 3.83 3.79 3.95 3.80 1.10 4.43 4.42 4.65 6.11 3.06 2.90 2.75 2.67 2.54 3.32 1.70 1.61 5.2488 0.693 1.1 13.29

a portfolio of securities. Over time, this approach developed into ‘modern portfolio theory.’ At yet another level, the tradeoff between risk and expected return is rhetorical. In the spirit of McCloskey (1994), the tradeoff is an essential component of the arguments that academics and practitioners in Finance use to persuade others. Some basic empirical evidence about risk and return estimates is presented in Table 1.6 for U.S. data. This particular sample is chosen for the purposes of illustration. Various studies going back at least to Fisher and Lorie (1964) extend these results to different sample periods, e.g., Dimson et al. (2002) and explore comparative properties of the returns such as

17:50:10.

November 3, 2010 10:47

9in x 6in

46

b921-ch01

Valuation of Equity Securities

the equity risk premium, e.g., Mehra and Prescott (1985) and Samuelson (1994). The main items of interest are the values for the mean and standard deviation over the full sample. Casual inspection reveals that, for the categories selected, stocks exhibit the highest estimated (arithmetic average) return and highest estimated standard deviation of return, followed by longterm bonds and Treasury bills.16 Also included for comparison is the inflation rate, which has an average rate of increase below that of bills. Only the standard deviation of inflation for the United States, which is above that for bills, is anomalous. Unfortunately, upon closer inspection, the number of questions raised by these empirical results is substantial. The implications for equity security valuation and selection are not as apparent as first appearances indicate. The first type of question that comes to mind concerns the form of the estimators used to compare the performance of the securities selected. In Table 1.6, parameters of the unconditional distribution are evaluated, i.e., the expected return for security i is estimated using the arithmetic average of the time series of the observed returns for security i, Ri (t), risk is estimated using the standard deviation of returns, i.e., the square root of the unbiased estimate of the variance17 :   T T

¯ i )2  (Ri (t) − R Ri (t)  t=1 t=1 ¯i = σ ˆi = R T T −1 The use of the arithmetic mean to estimate the expected return can be justified under the assumption that the returns are independently, identically distributed random variables, i.e., the process is strictly stationary. In this case, the arithmetic mean has the desirable property that it is a best linear unbiased estimate of the return to be obtained in the next period. A similar conclusion applies to the use of the standard deviation to estimate the risk. 16 An excellent source on detailed information about risk and return calculations across every conceivable scenario is Ibbotson and Associates (www.ibbotson.com), a division of Morningstar. As for the precise relationship between risk and return, it is possible to pick specific sample periods where expected results do not apply. For example, taking a 1974–2001 sample for Canadian data, the ranking is reversed to have Government of Canada treasury bills with the highest return, followed by long-term bonds and then common stocks. 17 These estimators for the expected return and standard deviation are a function of the time series sample that is selected. Different samples will likely produce somewhat different results. Because the calculation of returns involves taking a difference of prices at different points in time. The sampling frequency will also be relevant.

17:50:10.

November 3, 2010 10:47

9in x 6in

b921-ch01

The Philosophy of Equity Valuation

47

For statistical purposes, being the best estimator in the class of linear unbiased estimators is a desirable property. Yet, when used in the context of calculating the returns from holding a security, the use of this estimate embeds assumptions about the underlying investment strategy. In particular, it assumes that the security selection process and associated portfolio rebalancing occurs each sampling period (t = 1, 2, 3, . . .). Alternatively, it is also possible to assume that the trader is entering the market for the first time that period and will hold the security for one period. If the objective is to determine the return on a security that was purchased and then held over multiple periods, then the arithmetic average return will give a biased result when compared to the geometric average return. The arithmetic average only gives an unbiased estimate of the return over the next period. It can give misleading results when used to describe the return over more than one period. Similarly, the ‘best’ property of the arithmetic average is achieved by weighting each observation equally by 1/T .18 Best in this context means the mean squared error for the estimator is the smallest. In the class of unbiased estimators this translates into the smallest variance around the true population parameter. Weighted average estimators which, say, give more weight to observations that are more recent and less weight to observations in the more distant past would not be statistically ‘best’, but do have the intuitively appealing property of giving more weight to recent changes in market conditions (ω(t) > ω(t − 1)). When unbiased, such estimators can be specified as T


¯ iw = R

t=1

ω(t)Ri (t) T

where

T 

ω(t) = 1

t=1

18 In numerous applications, such as the dynamic investment strategies (Grauer and Hakanson 1993) and in moving average systems in technical analysis (Poitras 2005, ch. 9), moving average windows are used to generate a time series of estimates for expected returns and standard deviations. In this case, the sample size T is fixed and parameter estimates are updated as every new observation is added. For example, if the sample size is 40 quarters and the total sample is 100 observations then the first mean estimate uses the first 40 quarters (t = 1, 2, . . . , 40) of data. The next mean estimate replaces the oldest (t = 1) observation with the newest (t = 41) and generates the estimate with the (t = 2, 3, . . . , 41) quarters of data. This continues until there is a time series of 60 moving average estimates.

17:50:10.

November 3, 2010 10:47

9in x 6in

48

b921-ch01

Valuation of Equity Securities

However, this requires some method of determining the relationship between the various observations, e.g., Dhrymes (1981). If sufficient information is available to formulate prior distributions, the weights could even be determined in a Bayesian fashion. To better understand the investment strategy implications of basing decisions on arithmetic averages, consider again the method used for calculating the one-period return on a domestic portfolio which holds only one security. To calculate the return on this portfolio, it is assumed that at t = 0 the security is purchased at price P (0), held for one period and then sold at price P (1). For simplicity, it is assumed that any dividend payment (Div.) paid during the holding period is received at the time the security is sold. At this time the portfolio is rebalanced, where the funds received from the sale of the security are reinvested at t = 1 in another (probably different) security, which is purchased at price P (1), held for one period and then sold at price P (2), with any dividend payment again assumed to be paid at the time the security is sold. This second, one period return is R(2). And so it goes for R(3), R(4), R(5). The investment strategy associated with the use of arithmetic averages necessarily involves rebalancing at fixed intervals. For purposes of illustrating the difference between the use of geometric or arithmetic averages, assume that the security does not pay dividends and that P (0) = $100, P (1) = $50 and P (2) = $100. It follows that R(1) = ($50 − $100)/$100 = −50% and R(2) = ($100 − $50)/$50 = 100%. The arithmetic average for this process is (−50% + 100%)/2 = 25%. But the security which was purchased at $100 at t = 0 is only worth $100 at t = 2. The security value is unchanged from t = 0 to t = 2 yet the arithmetic average rate of return is 25%. These same numbers can be used to illustrate the properties of the geometric mean: T 1/T  ¯ iG ) = (1 + Ri (t)) (1 + R t=1

√ The geometric mean can now be calculated as (1 + −0.5)(1 + 1) = 1, implying a geometric mean equal to zero. Hence, if the investor is concerned with the terminal value of the investment, then the geometric average would seem to be more appropriate. The advantages of using the geometric mean to guide investment decisions has been recognized at least since Durand (1957a), Latane (1959), and Brieman (1960). Often being referenced as the ‘growth optimal’ model, early explorations in Finance on the implications of using the geometric mean were developed by Young and Roberts (1969), Hakansson (1971),

17:50:10.

November 3, 2010 10:47

9in x 6in

b921-ch01

The Philosophy of Equity Valuation

p = 0.5

p = 0.5

49

$400

$200

t=0 $100

$100 p = 0.5 $50

p = 0.5 $25

Fig. 1.3

An example of a binomial process for stock price.

Roll (1973), and Elton and Gruber (1974). Proponents of the arithmetic average observe that the illustration used is not a fair example as the probabilities of future movements in rates are not given accurate accounting. Say the probability of the 100% increase is 50% and for the −50% reduction is also 50%. Then there are four possible paths (Fig. 1.3): Given the probabilities the expected terminal value at time t = 2 would be: E[V ] = 0.25(400)+0.5(100)+0.25(25) = $156.25 = $100(1.25)2. Assuming that −50% and +100% are both equally likely then the expected return is 25%, not 0%. As noted, differences between the geometric and arithmetic mean can translate into potential differences in investment strategies. Conventionally, use of the geometric mean has been associated with an investment strategy that maximizes the expected terminal value of a portfolio while the arithmetic average has been associated with maximizing the expected utility of the terminal value, where expected utility is identified with a mean-variance objective function. Considerable effort has been given to identifying cases where these two objectives will produce the same portfolio. Not surprisingly, one case that has been identified occurs when returns are normally distributed. Introductory statistics texts observe that a limitation of the arithmetic mean is that it can give misleading results when there are extreme observations. In practice, differences between the geometric and arithmetic means are only significant when returns are decidedly non-normal, as in the case of small stocks, and are almost identical when returns are approximately normal, as in the case of Treasury bills and inflation.

17:50:10.

November 3, 2010 10:47

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History of Risk and Uncertainty

In the first half of the 20th century, the distinction between risk and uncertainty was a hotly debated subject, which fell well within the confines of active academic discussion, e.g., Greer (2000). More recently, this distinction has been ignored in favor of scientific methodologies that rely on the assumption of ergodicity of the underlying time reversible stochastic processes. Parametric inferences drawn from conditional or unconditional distributions are now the fashion. Analysis of the implications of ‘true uncertainty’ has been relegated to non-mainstream proponents, such as the Post Keynesian economists, e.g., Davidson (1991), Bernstein (1997, 1998), and McGoun (2007). This is unfortunate. Inclusion of uncertainty into the valuation of equity securities and formation of security selection strategies does have profound implications for both the modeling process and the conclusions reached. As argued by J.M. Keynes in The General Theory (1936) and elsewhere, the implications of uncertainty extend well into the realm of public policy about the role of equity securities markets in determining aggregate investment behavior.

John Maynard Keynes (1883–1946)

Modern financial economics is careful to develop logical relationships based on parameters from the conditional (or unconditional) distribution. Typically, attention focuses on the expected value (mean) and variance of the distribution of returns, though attention is sometimes given to higher moments of the distribution such as skewness and kurtosis. Precisely how to model predictions for random variable outcomes using the conditional distribution raises deep philosophical questions, variants of which have been debated for centuries. For example, the problem of determining the inverse probability of an event was introduced by Thomas Bayes (1701– 1761), who demonstrated that the conditional (posterior) distribution can

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be determined by combining prior beliefs with available empirical evidence. In the 20th century, both J.M. Keynes (1883–1946) and Frank Knight (1885–1972) advanced different interpretations of the notion that variation in future outcomes is a combination of a measurable component, risk, and an unmeasurable component, uncertainty. This distinction is effectively muted if time reversible ergodic processes are employed, as in modern Finance. Knight and Keynes were both struggling with different facets of the impact that randomness has on economic activity. When trying to make sense of the difference between ex ante and ex post distributions, their seemingly arcane ideas still have considerable relevance. Knight worked within the tradition of neoclassical economics, seeking to explain how economic profits can arise from uncertainty in the process of production and distribution. Neoclassical economic theory depends on the assumption that outcomes are certain, if there is randomness then the probabilities of the possible outcomes are known with certainty. Issues associated with cases where the probabilities are uncertain treat all relevant outcomes as equally likely. In the absence of market imperfections, such as monopoly, neoclassical economic theory argues that economic profits will dissipate to zero and each of the factors of production will earn their value of marginal product. Knight questioned this ex post view, arguing that economic profits could still arise from the ability of entrepreneurs to resolve the ex ante uncertainty facing factors of production. Frank Knight still has relevance, not because of his theoretical musings, but because of his interpretation of the randomness arising from commercial risks. Part Three of Risk, Uncertainty and Profit (1921), especially the chapters on ‘The Meaning of Risk and Uncertainty’ and ‘Structures and Methods for Meeting Uncertainty’, contain many insights. For example, Knight discusses the application of ‘the principle of insurance’ to ‘business hazards’. After recognizing the wide divergence of insurable risks, from life to fire to marine to theft and burglary, Knight concludes (p. 252): “The possibility of . . . reducing uncertainty by transforming it into a measurable risk . . . constitutes a strong incentive to extend the scale of operations of a business establishment. This fact must constitute one of the important causes of the phenomenal growth in the average size of industrial establishments which is a familiar characteristic of modern life”. Knight also clearly recognizes ‘specialization’ in activities which isolate the ‘true uncertainty’ in business risk including ‘organized speculation as carried on in connection with produce and security exchanges’ (p. 257).

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From the perspective of equity security valuation, it is possible to extend Knight’s interpretation of commercial risks (e.g., p. 226) to read like the following: ‘An investor is considering the advisability of increasing the percentage of the portfolio allocated to a certain common stock. He figures more or less on the proposition, taking account as well as possible the various factors impacting the stock price that are more or less susceptible to measurement, but the final result is an ‘estimate’ of the probable outcome of the future common stock price. What is the ‘probability’ or error in the judgment? It is manifestly meaningless to speak of either calculating such a probability a priori or of determining it empirically by studying a large number of instances. The essential and outstanding fact is that the instance in question is so entirely unique that there are no others or not a sufficient number to make it possible to tabulate enough like it to form a basis for any inference of value about any real probability of the case we are interested in’. Keynes, Uncertainty and the Stock Market19 Following Knight, risk is associated with objectively measured probabilities. This applies to cases where the ex post sample path for the random variable provides an accurate estimate of the parameters of the ex ante distribution. Being associated with cases where the ex post and ex ante distributions differ, uncertainty requires subjective probability assessments. The economic rents to business ownership arise from correctly anticipating uncertain outcomes. While Knight struggled with the notion of ‘true uncertainty’, he is clear that ‘risk’ which is objectively measurable is also insurable and, as such, cannot be a source of economic profit. Growth in markets and firm size will foster the transformation of uncertainty into risk, providing for a reduction in true uncertainty over time. This vision based on the production of goods contrasts markedly with the vision of J.M. Keynes, where the increased liquidity provided by the growth in equity markets will exacerbate the impact of uncertainty on equity security valuation and, as a consequence, hinder economic growth. “For it is not sensible to pay 25 for an investment of which you believe the prospective yield to justify a value of 30, if you also believe that the market will value it at 20 three months hence” (Keynes 1936, p. 155). Seeming conflict between Knight and Keynes on the correct interpretation of risk and uncertainty can be traced to the context used to capture the basic notions. Knight was 19 This

subsection is based on Poitras (2002a).

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concerned about the role of the entrepreneur in resolving the uncertainty in commercial ventures. In this case, the growth in goods markets will temper uncertainty. In contrast, Keynes was concerned about the implications of uncertainty in the equity valuation process, where the enhanced liquidity associated with the growth of equity markets will increase market instability. The General Theory of Employment, Interest and Money (1936) is a difficult book to read, quite untidy, and poorly written. Keynes proposes “not one, or two, but three or four ‘models’ of the workings of a modern economy” (Blaug 1978, p. 682). Of particular interest to the history of equity security valuation is chapter 12 of The General Theory, a largely self-contained essay on ‘The State of Long Term Expectation’. In this chapter, Keynes is concerned with the social consequences of instability in stock markets, arguing for government intervention to offset inherent deficiencies. The core of the argument revolves around an examination of the process by which expectations are formed in financial markets. Due to an excess bias toward maintaining liquidity, expectations in financial markets are focused on near-term prospects (p. 157): “Investment based on genuine long-term expectation is so difficult today as to be scarcely practicable”. The importance of the book lies in the substance of certain arguments, who was making those arguments and when the book was presented, i.e., during the stagnation following the economic collapse of the early 1930s. Many ideas are presented in The General Theory, some seemingly offthe-cuff. Such is the case with chapter 12. Some of the observations are insightful, for example (pp. 154, 155): It might be supposed that competition between expert professionals, possessing judgment and knowledge beyond that of the average private investor, would correct the vagaries of the ignorant individual left to himself. It happens, however, that the energies and skill of the professional investor and speculator are mainly occupied otherwise. For most of those persons are, in fact, largely concerned, not with making superior long-term forecasts of the probable yield of an investment over its whole life, but with forecasting changes in the conventional basis of valuation a short time ahead of the general public. They are concerned, not with what an investment is really worth to a man who buys it “for keeps”, but with what the market will value it at, under the influence of mass psychology, three months or a year hence. Moreover, this behaviour is not the outcome of a wrong-headed propensity. It is an inevitable result of an investment market organized [to concentrate resources upon the holding of “liquid” securities]. For it is not sensible to pay 25 for an

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investment of which you believe the prospective yield to justify a value of 30, if you also believe that the market will value it at 20 three months hence.

In true Keynesian fashion, this is shortly followed with the rhetorical statement (p. 155): “The social objective of skilled investment should be to defeat the dark forces of time and ignorance which envelop our future”. The source of these ‘dark forces’ is the uncertainty confronting players in the equity security markets. What Keynes develops in chapter 12 is a model where the heterogenous, subjective expectations of market participants lead to a financial market equilibrium in which prices are “subject to waves of optimistic and pessimistic sentiment, which are unreasoning and yet in a sense legitimate where no solid basis exists for a reasonable calculation” (p. 154). The implication is that prices can change “violently as the result of a sudden fluctuation of opinion due to factors which do not really make much difference to the prospective yield”(p. 154). Not only will prices be considerably more volatile than is justified by the long term expectation, prices will typically depend more on ‘what average opinion expects average opinion to be’ rather than on valuations which capture “the prospective yield of an investment over a long term of years” (p. 155). Prices are determined more by “speculation . . . the activity of forecasting the psychology of the market” than by “enterprise . . . the activity of forecasting the prospective yield of assets over their whole life” (p. 158). Though both Keynes and Knight have been duly recognized for examining the role of uncertainty on random economic outcomes, the predictions made about the impact of uncertainty on the evolution of financial markets are at odds. Knight argues that increasing the scale of activities and the liquidity of markets will permit firms to increasingly specialize and manage the risks, permitting a reduction in the scope of uncertainty. Keynes (1936, p. 158) has the opposite view: “As the organization of investment markets improves, the risk of the predominance of speculation does, however, increase”. For Knight, the impact of uncertainty is dissipating over time; for Keynes, it is increasing as equity security markets get more liquid. Even among those willing to recognize the significance of ‘true uncertainty’, agreement over the implications of uncertainty are difficult to obtain. Yet, the implications of uncertainty for ‘real-time’ equity security valuation remain. The key point to take away is that the handling of true uncertainty is an essential element in equity security analysis.

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Early in chapter 12 (p. 149), Keynes hints at a fundamental pricing model which can be used to value equity securities: “The outstanding fact is the extreme precariousness of the basis of knowledge on which our estimates of prospective yield have to be made. Our knowledge of factors which will govern the yield of an investment some years hence is usually very slight and often negligible . . . those who seriously attempt to make any such estimate are often so much in the minority that their behaviour does not govern the market”. In this context, the market is ‘the Stock Exchange’, which “revalues many investments every day” (p. 151). After observing that, due to the separation of ownership from management, the price of shares on the Stock Exchange will be determined by stock traders rather than by the ‘professional entrepreneur’ who has direct knowledge of the underlying business, Keynes asks a key question (p. 151): “How then are these highly significant daily, even hourly, revaluations of existing investments carried out in practice?” The answer provided to this question encompasses the philosophical foundations of the impact that uncertainty has on the human condition. McKenna and Zannoni (1993, pp. 400, 401) capture the basic issue where equity valuation decisions are concerned: “Situations may arise in which individuals may not have any knowledge at all concerning the probability distribution function of future outcomes”. Yet, decisions have to be made and “economic agents must create alternative mechanisms that enable decisions to be made in the face of uncertainty”. Confronted with uncertainty, the crux of the decision-making process relies on convention. In a remarkable precursor to the modern efficient markets hypothesis, Keynes observes that in the face of uncertainty the investor accepts the prevailing evaluation of market prices (p. 152): “. . . the existing market valuation, however arrived at is uniquely correct in relation to our existing knowledge of the facts which will influence the yield of the investment, and that it will change in proportion to changes in this knowledge”. In following this convention, “the only risk [an investor] runs is that of a genuine change in the news over the near future, as to the likelihood of which he can attempt to form his own judgment” (p. 153). 1.2.3

The Efficient Markets Hypothesis

Basic Insights As illustrated in Fig. 1.4, the degree of belief in the efficient markets hypothesis (EMH) is a philosophical position that divides the various possible

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Fig. 1.4 View of the world: No exploitable inefficiencies

Philosophy of investing Short run mis-pricing True value in the long run

Persistent deviation of prices from true value

Who They Are:

Modern Portfolio Theorists What They Do: Two Fund Separators mean variance optimizers

Fundamental

analysts

Value investors

Dow theorists

Market timers anomaly investors True believers

Technical

analysts

Rukeyser’s elves Partial Believers

herders Dis-believers

Strength of Belief in Efficient Markets

approaches to equity security valuation. Those who are the strongest believers in the EMH also adopt the ‘scientific’ approach to equity security valuation and argue strongly for optimal diversification strategies such as two-fund separation. Despite a number of apparent setbacks on the empirical front, strong proponents of the EMH continue to be unmoved. For example, after reviewing the accumulating evidence of regularities and anomalies in stock prices, Malkiel (2003, p. 60) still claims: “The evidence is overwhelming that whatever anomalous behavior of stock prices may exist, it does not create a portfolio trading opportunity that enables investors to earn extraordinary risk adjusted returns”. Equity markets are not perfect at determining prices but the mis-pricing does not provide systematically exploitable trading opportunities. In such a philosophical world, there is only value in the pursuit of optimal diversification; attempts at making gains through predicting individual security returns will ultimately be futile. The roots of the EMH are as murky as the hypothesis itself. There are hints of the EMH as far back as de la Vega with both J.M. Keynes (1936, ch. 12) and Irving Fisher (1930, ch. 13) having well-developed notions that could qualify as precursors of the EMH. The reference to ‘efficiency’ is misleading, as this term is also used to refer to a number of related concepts. For example, there is the ‘efficient frontier’ associated with the Markowitz optimization model and there is ‘Pareto efficiency’ associated with the properties of a perfectly competitive equilibrium in theoretical microeconomics.

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As presented by Fama (1970, 1976) and by numerous others, the efficient markets hypothesis is related to information processing. “An efficient capital market is a market that is efficient in processing information. The prices of securities observed at any time are based on the ‘correct’ evaluation of all information available at that time. In an efficient market, prices ‘fully reflect’ available information” (Fama 1976, p. 133, emphasis added). Perhaps the defining moment for the EMH came with Samuelson (1965). By proving that ‘properly anticipated prices fluctuate randomly’, Samuelson brought the theory of security pricing into congruence with a myriad of statistical results about security prices that had been developing since the early 1950s. An early example of this work, Kendall (1953) found that stock prices had no identifiable pattern. Prices evolve in a random fashion, with no predictable component. More precisely, successive changes in security prices were independent of each other. More recent research, e.g., Lo and MacKinlay (1988), has found some evidence of positive serial correlation in common stock returns over short intervals. In some cases, the evidence is only weak and does not extend much beyond weekly sampling intervals.20 However, using CRSP value weighted and equally weighted indexes, Campbell et al. (1997) provide somewhat stronger evidence of generally positive serial correlation for daily, weekly, and monthly stock returns (1962–1994). Lo and MacKinlay (1999) extend these results even further. This line of research on the randomness properties of stock prices speaks to one form of the EMH, whether current prices fully reflect the information in past prices. In this form, the EMH is often reformulated as the ‘random walk hypothesis’, e.g., Malkiel (1990). Different versions of the EMH are associated with different possible types of information sets, which are ‘fully reflected’ in security prices. Three versions are usually identified: weak form, where the information set is the past history of the security price (sometimes this form includes all market generated data such as up/down volume, number of 52 week highs and lows, etc.), the semi-strong form, where the information set is publicly available information, such as firm accounting data, newspaper articles, 20 There is disagreement about whether the Lo and Mackinlay (1988) results are evidence against the EMH. For example, Conrad and Kaul (1993) argue the results can be explained by other factors such as bid/ask spreads. The evidence about the random properties of successive price changes typically involves the use of closing prices. When intra-day transaction to transaction prices are used, there is stronger evidence in favor of short-term trending in prices.

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analysts recommendations, and so on, and; the strong form, where the information set is all publicly and privately available information, including insider information. If the EMH is correct, then it is not possible to achieve abnormal returns from trading on the available information set. When the weak form information set is defined to be a subset of the semi-strong form which is also a subset of the strong form, it follows that a strong form efficient market is also semi-strong form and weak form efficient. Similarly, it does not follow that a weak form efficient market will be semi-strong or strong form efficient. As will be discussed shortly, because the EMH is a joint hypothesis, rejection of any version of the EMH could be due to a rejection of the return generating model rather than the EMH. The focus on information processing provides a direct connection between security pricing and the evaluation of a conditional expectation. Specifying the security price, or some appropriate transformation of the security price, as the conditional expectation evaluated with respect to a particular conditioning information set makes a direct connection to the theory of stochastic processes, including results on martingale processes. Under the assumption of ergodicity, the connection to stochastic processes provides a structure for the statistical testing of hypotheses about security prices. The connection to martingale theory can be used to motivate the correspondence between trading of securities and gambling. More precisely, a martingale process can be identified with the fair game model that Feller (1957, p. 233–235) and many others use to motivate the law of large numbers. In turn, closer examination of the fair game model is useful in establishing a precise connection between gambling theory and the security pricing models used in Finance. Martingale theory has been something of a revolution in a number of areas of mathematics and mathematical statistics, including the solving of partial differential equations.21 The most basic definition of a martingale is (Karlin and Taylor 1975, p. 238): Definition: The Elementary Martingale Process A stochastic process {X(t) : t = 0, 1, 2, . . .} is a martingale if, for t = 1, 2, . . .: (i) E[|X(t)|] < ∞ (ii) E[X(t + 1)|X(0), X(1), X(2) · · · X(t)] = X(t) 21 The name ‘martingale’ is derived from a French acronym for a gambling strategy which involves doubling up bets until a win is achieved.

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Condition (i) is a restriction on the probability distribution from which the {X(t)} can be drawn, the unconditional expected value of X(t) has to be finite. This rules out processes with infinite mean values, such as the Cauchy process, but does admit processes with infinite variance, such as the stable processes with characteristic exponent between one and two. Condition (ii) is the martingale property which says that, given the information on the {X(t)} up to time t,the best prediction of the next (t + 1) observation is the current (t) observation. The conditioning information set can be expanded considerably to be, say, {Y (0), Y (1), Y (2), . . . , Y (t)} where {Y (t)} is some stochastic process or set of stochastic processes which could include {X(t)}. In this case (ii) can be expressed as E[X(t + 1)|Y (0), Y (1), Y (2) · · · Y (t)] = X(t), i.e., {X(t)} is a martingale with respect to conditioning information set {Y (t)}, where X(t) is a function of {Y (0), Y (1), Y (2) · · · Y (t)}.22 Within this framework, the strong, semi-strong and weak form versions of the efficient markets hypothesis can be represented by expanding the appropriate conditioning information set associated with the conditional expectation. For the weak form, the past history of prices is the conditioning information set; for the semi-strong form, the information set is potentially all publicly available information; and, for the strong form, the information set is all available information, public and private. However, while this interpretation of the EMH is appealing, a substantial amount of development is required. A useful starting point for this development is the fair game model. The connection of a martingale with a fair game arises when {X(n)} is the amount of money that a player has after n ε {1, 2, . . . , N } trials when playing a fair game. The game involved here is a repeated trial of some game of chance, e.g., throwing dice or flipping a coin. Following Feller, the fair game model requires two key assumptions: that the gambler has unlimited capital, i.e., no amount of loss can force termination of the game; and, that the total number of trials (N ) is fixed at the start of the game and independent of the way the game develops, i.e., the gambler cannot terminate the game at a favorable point. The first assumption prevents the game being reduced to the gambler’s ruin problem. The second assumption

22 In

more advanced mathematical treatments, the approach is to define {Y (t)} as a σfield of an appropriately defined probability space, e.g., Karlin and Taylor (1975, pp. 297– 325). Because the σ-field for a stochastic process increases as t increases, ergodicity conditions on the stochastic process can be satisfied. If, however, information is lost or is decreasing over time in some fashion, then ergodicity is problematic.

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prevents the game from being an optional sampling problem, where the gambler has the ability to terminate the game after a run of good luck. Given these two assumptions, the definition of a fair game follows by letting µ be the expected payoff from a winning gamble where µ = E[X(k)] < ∞. Letting γ = the cost (entrance fee, ante) required to undertake a single trial of the game, then it is often said that a ‘fair’ game occurs when γ = µ, though Feller wrangles at the use of this name because it is still possible for γ = µ and for the accumulated winnings to be positive or negative. For a game played to the fixed termination time, the expected winnings would be S(N ) = X(1) + X(2) + · · · + X(N ). Observing that the cost of achieving these winnings is N γ, then the net gain from playing the game would be S(N ) − N γ. Recognizing that the law of large numbers says S(N ) − N µ will become small as the number of trials gets large, it follows that when γ = µ the net gain or loss from playing the game will be small relative to N as N gets large. As Feller observes, it is possible for the net gain or loss of a fair game to be non-zero as long as the gain or loss is small when N gets large. To see the connection between the fair game model and a martingale, consider the expectation of S(n + 1) given the information on accumulated winnings up to time n: E[S(n + 1)|S(n), S(n − 1), . . . , S(0)] = E[S(n + 1)|X(n), X(n − 1), . . . , X(0)] = S(n) This result captures the essence of Feller’s (1966, p. 211, emphasis added) observation about the fair game model: “The idea of a fair game is that the knowledge of the past should not enable the gambler to improve on his fortunes. Intuitively, this means that an absolutely fair game should remain absolutely fair under any system of gambling, that is, under rules of skipping individual trials”. (For example, betting rules in a fair game such as ‘bet on tails after k heads in a row occur’ will not be successful.) The fair game model, the martingale process, and the expected value conditional on the past history of the random variable all come together to provide a foundation for the weak form of the efficient markets hypothesis. In the weak form version, the securities market is being modeled as a fair game. While it may be intuitively appealing to model the weak form of the EMH by taking the current price for a security to be a martingale with respect to the past history of security prices, the actual formulation of the hypothesis is more complicated. For example, consider the price of a nondividend paying stock where: P (t + 1) = (1 + R(t + 1))P (t). It follows that

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this price process will not follow a martingale unless expected returns are zero. More precisely, the price process will follow a submartingale: Definition: The Submartingale Process A stochastic process {X(t) : t = 0, 1, 2, . . .} is a submartingale with respect to {Y (t) : t = 0, 1, 2, . . .} if, for t = 1, 2, . . .: (i)

E[X(t)+ ] < ∞ where X(t)+ = max[0, X(t)]

(ii) E[X(t + 1)|Y (0), Y (1), Y (2), . . . , Y (t)] ≥ X(t) (iii) X(t) = f [Y (0), Y (1), . . . , Y (t)] Basically, a submartingale is a martingale with the ≥ replacing = that applies to the martingale definition, condition (ii). It follows that E[P (t+1)| Y (0), Y (1), . . . , Y (t)] ≥ P (t) whenever E[R(t+1)|Y (0), Y (1), . . . , Y (t)] ≥ 0, i.e., prices for non-dividend paying securities follow a submartingale. This result explains the reliance on returns, as opposed to prices, in testing asset pricing models. To see the statistical advantages of using returns instead of prices observe that if R(t + 1) = (P (t + 1) − P (t))/P (t) then, evaluating the expectation conditional on information available at t = 0, E[R(t + 1)] = (E[P (t+1)]−P (t))/P (t). Observing that R(t) = (P (t)−P (t−1))/P (t−1), then the requirement that security returns follow a martingale becomes E[R(t+1)] = (E[P (t+1)]−P (t))/P (t) = R(t) = (P (t)−P (t−1))/P (t−1). This reduces to the condition that E[P (t + 1)]/P (t) = P (t)/P (t − 1). (By taking logs, this condition can be formulated in terms of the log differences in prices.) It follows that, if the return generating process is ergodic, then it is returns, not prices, that follow a martingale. Various generalizations of this basic result have been explored. Recognizing that the return to holding a security is associated with compensation for invested capital, the relevance of using returns instead of prices may not extend to futures and forward contracts that, ignoring the opportunity cost of margin funds, do not require a cash outflow when created. Because of the key role that empirical testing plays in the methodology of modern Finance, it becomes imperative to identify a procedure or rationale for converting the stochastic price process to a martingale, if only because of the importance that martingale difference sequences can have in testing theory, e.g., Hendry (1995, pp. 733–738). The theory of classical hypothesis testing involves the laws of large numbers and the central limit theorem, results that rely on identically, independently distributed (i.i.d.) or, with appropriate adjustments, independent random variables.

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These results can be generalized using martingale limit theory that, in turn, depends on the properties of martingale difference sequences. These generalizations permit the assumption of independence to be relaxed to where the random variables are uncorrelated. Recognizing that sums of independent (and i.i.d.) random variables, expressed as deviations from the mean value, are martingales, it follows that the classical statistical results can also be formulated and derived using the properties of martingale difference sequences. A martingale difference sequence is constructed by differencing a martingale process. (In time series econometrics, martingale differences are referred to as ‘innovations’.) More precisely, if {X(t)} is a martingale with respect to {Y (t)}, then the martingale difference process {Z(t)} can be constructed by defining Z(t) = X(t) − X(t − 1). It follows that {Z(t)} has the property that E[Z(t + 1)|Y (0), Y (1), . . . , Y (t)] = 0. The analytical advantages of the using the martingale difference process is that standard results such as versions of Chebychev’s inequality and the laws of large numbers can be derived for {X(t)} with finite second moments, permitting asymptotic distributions to be derived for cases where the independence assumption is relaxed to require only uncorrelated random variables. The asymptotic distribution theory follows from the associated central limit theorem for the martingale difference sequence. (A fair game can be expressed as a martingale difference sequence where Z(t) = E[S(N + 1)|X(0).X(1) · · · X(N )] − S(N ).) 1.2.4

Testing the Efficient Markets Hypothesis

From a testing perspective, it is essential to recognize that the EMH necessarily involves a joint hypothesis. Any empirical test of the EMH, a hypothesis that is concerned with the efficient processing of information into market prices, is also a test of the model being used to generate returns (prices). Empirical rejection of the EMH could be due to a rejection of the model for the return generating process, to a rejection of the EMH, or both. To see this, observe that, if the EMH is true, then it is not possible to generate (positive) abnormal returns from trading on strategies exploiting the relevant information set. At any time t, this requires some hypothesis about the return generating process for E[R(t+1)|Y (0), Y (1), . . . , Y (t)] in order to determine when a return is abnormal, i.e., where the actual return minus the predicted return is positive, R(t + 1) − E[R(t + 1)|Y (0), Y (1), . . . , Y (t)] > 0. Where applicable, the trading strategy is associated with the model used to specify R(t + 1) while E[R(t + 1)|Y (0), Y (1), . . . , Y (t)] is the expected return that the return generating model indicates is appropriate.

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Following Fama (1976), the range of possible return generating models include: simple models, where the only restriction is that expected returns are positive; models of expected return resulting in the restriction that expected returns are constant over time, i.e., the conditional and unconditional means are equal; more sophisticated models that require expected returns to conform to the “market model” (see section 5.1.2); and, models that require expect returns to ‘conform to a risk return relationship’. In this classification, there is a progressive nesting of the model types. For example, the models that imply expected returns are constant over time also impose the restriction that expected returns are positive. Similarly, requiring expected returns to follow the market model is imposed when a time series of observations on {R(t+1)−E[R(t+1)|Y (0), Y (1), . . . , Y (t)]} is used to test market efficiency. Because expected returns are associated with the conditional distribution, the market model is used to update the conditional expectation to account for the market risk inherent in the strategy. Tests of market efficiency based on constancy of the expected return are typically based on an information set that only considers the history of past returns. While accurate processing of information is a noble goal for a security market, there are real difficulties in specifying tests of the EMH. Testing of efficiency also requires the ‘correct’ evaluation method to be specified. Hence, the EMH is inherently a joint hypothesis of efficiency and a return or profit generating model. To this end, Jensen (1978, p. 96) developed a more empirically testable definition of efficiency: “A market is efficient with respect to information set θt if it is impossible to make economic profits by trading on the basis of information set θt ”. Since economic profits are risk-adjusted returns after deducting transaction costs, Jensen’s definition allows market efficiency to be tested by considering the net profits and risk for trading strategies employing the information set θt . Jensen’s definition is further extended by Timmermann and Granger (2004, p. 25) where a more precise statement is given as to how the information variables in θt are used to generate forecasts: a market is efficient with respect to information set θt , a set of search technologies St and a set of forecasting models Mt if it is not possible to make economic profits by trading on the basis of signals produced from a forecasting model in Mt , defined over predictor variables in the information set θt and selected using a search technology in St . While definitions of EMH stress the relevance of trading rule performance, some empirical tests examine the time series of abnormal returns, other tests examine the properties of the sum of abnormal returns over some time period (cumulative abnormal returns). For example, consider empirical tests of the weak form EMH based on the significance of serial

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correlation coefficients of returns, e.g., Lo and Mackinlay (1988, 1999). If there are identifiable trends in returns, then time series models, such as the ARMA(p, d, q) models popularized by Box and Jenkins (1970), could be used to predict next period’s return from the history of current and past returns, including previous errors in forecasting past returns. The ARMA model would provide an atheoretical return generating model. However, if it was possible to use ARMA models to predict security returns, then under the EMH rational traders would seek out the profit opportunities by fitting the time series model and initiating a price adjustment process that would eliminate the predictable trends. If returns are not predictable using ARMA models, then returns are serially uncorrelated ‘white noise’. Hence, a test of weak form efficiency is that returns be serially uncorrelated. In general, the return generating model is used to determine if the return from the trading strategy is actually abnormal, e.g., accounts for systematic risk and provides an adequate return on invested capital. Given that the return generating model predicts that returns follow a martingale, empirical tests can be conducted by examining the statistical properties of R(t + 1) − E[R(t + 1)|Y (0), Y (1), . . . , Y (t)] = R(t + 1) − R(t) = Z(t + 1). Recognizing that the null hypothesis of no abnormal returns requires that E[Z(t)] = 0, the EMH can be tested by determining whether E[Z(t + 1)|Y (0), Y (1), . . . , Y (t)] = 0, i.e., the tests can be conducted on the martingale difference sequence {Z(t)}. Which specific version of the EMH is tested depends on the information set that is used in the return generating model to determine E[R(t+1)|Y (0), Y (1), . . . , Y (t)]. In practice, the econometric approach selected does not directly employ the martingale approach but, rather, will use an approach that possesses the martingale property in addition to imposing additional conditions. For example, tests of the weak form EMH can use a random walk model instead of a martingale. The random walk or ‘unit root’ process is a useful econometric model for testing the EMH, if only because of the substantial statistical theory that has been developed for this model. Different variations of the random walk are available. The basic random walk model is specified: X(t + 1) = µ + X(t) + u(t + 1), where µ is the constant ‘drift’ in the process and the u(t) is a random variable with a conditional mean of zero. Different versions of the random walk model can be formulated depending on the process being ‘driftless’ (µ = 0), whether {u(t)} is assumed to be i.i.d. (σu is constant over time) or independent (σu is not constant over time) or uncorrelated (requires only that E[u(t)u(t + 1)] = 0 and allows for higher moments of the distribution to be dependent). A specific distributional

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assumption such as normality may also be imposed on {u(t)} for testing purposes. Because of the failure to distinguish the specific form of the model being used, the random walk hypothesis has been the subject of considerable misinterpretation. Early tests of the statistical properties of security prices, such as the studies in Cootner (1965), often employed the random walk model. By taking an expectation conditional on the information available at t = 0 it possible to show that the driftless random walk obeys the martingale property, i.e., E[X(t + 1)|Y (0), Y (1), . . . , Y (t)] = X(t). But if returns are positive, modeling the statistical behavior of security prices with a driftless random walk is incorrect. If returns are assumed to be positive and constant than a random walk with drift is required. If returns are only constant then it is possible that the estimate of the drift may be biased because the return is time varying. In most cases, a more appropriate formulation is to specify the log of prices as following a driftless random walk: ln[P (t + 1)] = ln[P (t)] + u(t). Allowing u(t) to be only independent instead of i.i.d. allows for the time varying volatility that is a commonly observed characteristic of security returns. In general, there are a myriad of possible methods of testing the EMH. Because of the pervasive use of market efficiency in specifying asset pricing models, tests of such models are also indirectly tests of market efficiency. More immediate tests of the semi-strong form can be examined using event-study methodology, e.g., Campbell et al. (1997, ch. 4). Other tests use grouping methods and test for significant differences between groups using techniques such as regression analysis or variance ratio tests, e.g., comparing the returns from the month of January with other months or the returns from low capitalization firms with the returns from firms not in that group. It is even possible to use anecdotal studies, e.g., to examine the investment performance of successful individual investors such as Warren Buffett or Li Ka Shing or Ben Graham to identify heuristic characteristics not associated with lucky guessing or high initial wealth levels. Whatever the methodology selected, the acid test of market efficiency is the requirement that investors cannot make profits from exploiting the relevant information set after deducting all the costs of trading and making the appropriate adjustments for risk. This means that tests of market efficiency have to be, either directly or indirectly, related to trading rules. In most situations, it is possible to account for the risk in a trading rule by discounting the expected profit at an interest rate that is sufficient to account for the risk. The appropriately discounted expected

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profit can then be compared to the initial capital required to implement the strategy. Costs of trading are incorporated in the trading rule. There are various sources of trading costs such as commissions, bid/offer spreads, asynchronous prices and ‘shoe leather’. It is not enough to show that the relevant information is not fully incorporated in prices, e.g., by estimating a statistically significant serial correlation coefficient for returns. It is also necessary to demonstrate that it is possible to generate risk adjusted net profits from the market’s slow interpretation of the relevant information.23 Evidence of Anomalies For Elton and Gruber (1984, p. 379): ‘The efficient market hypothesis had a strange beginning’. This is because the initial development of the EMH did not follow the prescribed ‘scientific’ approach where a theory is initially suggested, followed by extensive empirical testing to see if the theory describes reality better than previously accepted theories. The EMH developed in the opposite way. Initially, extensive empirical tests were undertaken that demonstrated: ‘contrary to popular belief, certain types and ways of using information (usually past prices) did not lead to superior profits’. The EMH was developed to explain the empirical findings. This description captures many essential features of the process by which knowledge is ‘created’ in modern Finance. The epistemology that is prescribed in modern Finance requires that a theory or model is ‘suggested’ using logical deduction from stated assumptions. ‘Extensive tests’ of the model are then conducted to establish empirical validity. If the model is supported by the data it becomes part of received theory until a ‘better’, more empirically descriptive model is developed. If the model is rejected, the process of logical deduction is iterated until a model is identified that explains the ‘stylized facts’. In contrast to the prescribed epistemology, the EMH developed inductively. Initial results, such as those presented in Fama (1965) and Cootner (1965), provided ‘strong empirical evidence’ that changes in security prices, particularly common stock prices, were random or, at least, random enough. The empirical tests usually involved an examination of the 23 It

is well known that conventional statistical criteria, such as minimizing mean square error, may be inappropriate for identifying trading rules that are profitable. For example, the observation of statistically significant serial correlation in price changes or returns may still produce negative trading rule profits. Leitch and Tanner (1991) suggest the use of trading rule profitability as an alternative measure of parameter significance.

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serial correlation coefficients for the difference in the log of prices though, in some cases, the serial correlation for the difference in prices was examined. Recognizing that serial correlation tests can be affected by a small number of large observations (outliers), some studies also provided results for runs tests, e.g., Fama (1965). Though such tests typically have low power to reject the null hypothesis of random behavior, runs tests assess whether there are an inordinate number of positive or negative changes that occur in sequence. Results from the runs tests were much as with the serial correlation tests, daily time intervals indicated a slight positive relationship with longer intervals appearing random. Serial correlation and runs tests only examine statistical properties without making a direct connection to the evaluation of trading rules designed to exploit the potential profitability of non-random behavior. This issue was addressed in other early tests, such as those of Fama and Blume (1966), that compared the profitability of filter rules to buy-and-hold strategies. The filter trading rules examined in the early studies were relatively simple. For example, a k percent filter rule would be: if the price of a security rises k percent, buy the security and hold it until it drops k percent from a subsequent high. At that time the security is sold and a short position is established and held until the price rises k percent at which time the short is covered and a long position is again established. This process is continued until the end of the trading horizon is reached at which time the profits from the filter rule are compared with the return from buying the security at the beginning of the horizon and holding it until the end. Early tests of filter rules generally found that buy and hold was at least as profitable as pursuing a filter rule trading strategy. However, when k was small and the trading intervals were for daily or intra-daily moves then there was sometimes a small advantage in favor of the filter rule. Because small k% filter rules generate a large number of trades, these small profits would aggregate into sizable total profits. Fama (1976, p. 142) discusses this evidence: “When one takes account of even the minimum trading costs that would be generated by small filters . . . their advantage over a buyand-hold strategy disappears”. At the time, this was taken to be conclusive evidence against the profitability of technical analysis — the use of market generated data, such as prices and volume, to forecast future security price movements. Over time, the conclusion that technical analysis is a profitless exercise has become less certain to the point where Park and Irwin (2007, p. 804)) find: “the number of studies that identify positive technical trading profits is far greater than the number of studies that find negative profits”.

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The early evidence on the serial correlation of security returns (price changes), runs tests and filter rules facilitated an inductive process that led to the formulation of the hypothesis that the observed randomness is the outcome of efficient processing of information by the securities market. Though the use of induction in hypothesis development is an essential element of the scientific approach, the economic positivism expounded in modern Finance prescribed the initial development of a theory using logical processes, confronting the theory with empirical evidence and iterating as appropriate. Though this did not happen with the EMH, by the time of Fama (1976, p. 142) the inconsistency was largely ignored: “no null hypothesis, such as the hypothesis that the market is efficient, is a literally accurate view of the world. It is not meaningful to interpret the tests of each hypothesis on a strict true-false basis. Rather, one is concerned with testing whether the model at hand is a reasonable approximation to the world, which can be taken as true, at least until a better approximation comes along”. It seems that, through the empirical analysis of selected data, an agreeable method for determining when ‘a better approximation comes along’ is available. The possibility that ideas become entrenched and complicated issues cannot be resolved empirically is not part of the philosophy: “What is a reasonable approximation depends on the use to which the model is to be put”. Fama (1976, p. 142) uses the example that, since traders cannot use filters to beat buy and hold, it is reasonable for them to assume that traders would behave as if the market were efficient, at least for the purposes of trading on information in past prices. Yet, despite the ‘overwhelming’ academic evidence that stock markets are efficient with respect to the information available in past prices, technical analysts continue to flourish in the equity securities industry. Oddly enough, a detailed empirical study of the use of technical analysis by stock market participants is unavailable, there is only anecdotal evidence about the widespread use of technical analysis, e.g., Lo and Hasanhodzic (2009). There is considerably more evidence that the use of technical analysis is widespread in other areas of the financial markets. In the related commodity and foreign exchange markets, where the pool of traders is much smaller and easier to survey than the stock market, studies examining the use technical analysis stretch back to Smidt (1965). In foreign exchange markets, a number of surveys of find about 30%–40% of foreign exchange traders employ technical analysis to forecast exchange rates up to a 6-month horizon (e.g., Taylor and Allen 1992; Cheung and Chinn, 2001).

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Park and Irwin (2007) divide studies of technical analysis into ‘early studies’ and ‘modern studies’ with Lukac et al. (1988) being selected as the dividing line. This division seems to be roughly reflected in the variety of technical trading systems in use by practitioners. For example, Billingsley and Chance (1996) find about 60% of commodity trading advisors rely heavily or exclusively on computer-guided technical trading systems. The ability to use such systems increased significantly with the availability of desktop computing power. As reflected in Table 1.7, this enhanced computing power also facilitated a substantive increase in the statistical sophistication of both the technical trading rules being tested, such as neural network or nearest neighborhood regression from non-linear programming, and the procedures being used to evaluate the trading rules, such as the ‘reality check bootstrap’ (White 2000) or the genetic programming technique (Koza 1992) used to assess the degree of ‘data snooping’. As indicated in Table 1.8, there has also been a modern resurgence in studies of technical trading rule performance. Over time, an increasing number of empirical studies have presented various types of evidence in favor of rejecting the null hypothesis of the EMH. Traditionally, these results are classified according to whether it is the weak form or semi-strong form versions of EMH that has been rejected. Such rejections of the EMH are classified as ‘anomalies’ associated with the particular type of information considered. In contrast, rejections of the strong form version of EMH are not considered as anomalous where trading on insider information is the relevant information variable. As the weak form tests relate to ‘technical analysis’ and the semi-strong form tests relate to ‘fundamental analysis’, the empirical results for the two versions are typically considered separately, though there are good reasons to try to reconcile the results of the two versions. Rejections of the weak form include the January effect, as well as other calendar and seasonality effects such as the day-of-the-week effects, the weekend effect and the daylight-savings-time effect. Rejections of the semi-strong form include the small firm effect, the book-to-market effect, the neglected firm effect and the P/E ratio effect. By introducing a distinction between early and modern studies, Park and Irwin (2007) provide another approach to classifying empirical studies of EMH. Though only concerned with the profitability of technical analysis, a similar dichotomy could be developed for EMH studies of fundamental analysis. Park and Irwin identify a number of limitations in the early studies of technical analysis: a small number of trading systems were

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The Profitability of Technical Trading Rules in Modern Studies, 1988–2004.a 70

Number of studies Studies

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Profit range

Comments

A. Stock markets Standard Model-based bootstrap Reality check Genetic programming Non-linear Chart patterns Others Sub-total

2 7 0 2 3 4 8 26

2 4 1 1 2 1 1 12

2 3 1 3 0 1 0 10

4–17%b (1897–1998)

B. Foreign exchange markets Standard Model-based bootstrap Reality check Genetic programming Non-linear Chart patterns Others Sub-total

• For the DJIA, which is the most frequently tested series in the literature, results vary considerably depending on the testing procedure adopted. In general, technical trading strategies are profitable until the late 1990s but no longer profitable thereafter • Overall, variable moving average rules show the most reliable performance for the stock market over time • For several non-U.S. stock markets (e.g., Mexico, Taiwan, and Thailand), moving average rules generate substantial annual net profits of 10–30% until the mid-1990s

8 4 1 3 3 2 3 24

2 2 0 0 0 1 1 6

3 1 0 1 0 2 1 8

5–10%c (1976–1991)

• For major currencies, a wide variety of technical trading strategies, such as moving averages, channels, filters and genetically formulated trading rules, consistently generate economic profits until the early 1990s • Several recent studies confirm the result, but also report that technical trading profits have declined or disappeared since the early 1990s, except for the yen market

Source: Park and Irwin (2007) a Studies on equity (index) futures and options and foreign exchange futures are categorized into ‘stock markets’ and ‘foreign exchange markets’ studies, respectively. ‘Futures markets’ studies include studies on other individual futures markets or various groups of futures markets. b Through August 2004.

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Positive

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Table 1.8

Year 1960–1964 1965–1969 1970–1974 1975–1979 1980–1984 1985–1989 1990–1994 1995–1999 2000–2004b Total

71

Number of Technical Trading Studies, 1960–2004a .

Stock markets

Foreign exchange markets

Futures markets

Total

Relative frequency (%)

3 6 4 2 2 4 5 18 22 66

0 1 0 3 1 3 3 13 20 44

3 1 3 2 6 7 2 1 2 27

6 8 7 7 9 14 10 32 44 137

4.4 5.8 5.1 5.1 6.6 10.2 7.3 23.4 32.1 100.0

Source: Park and Irwin (2007). See Notes to Table 1.7.

usually considered, often only one or two trading rules; statistical significance tests were not conducted on technical trading returns24 ; the riskiness of technical trading rules was often ignored; the performance of trading rules was reported in terms of an ‘average’ across all trading rules, rather than best-performing rules for individual securities, e.g., Fama and Blume (1966); and, some of the substantial technical trading profits found in early studies are attributable to data snooping (selection) biases. A number of fascinating studies have appeared since Lukac et al. (1988) that address the limitations of the early studies (see Table 1.9). Summarizing the results of ‘modern studies’ of technical trading rules applied to stock markets, Park and Irwin (2007) find conflicting, sample dependent evidence. For U.S. stock markets, technical trading rules appear to be economically profitable through the late 1980s, but such rules fail to be profitable thereafter (Bessembinder and Chan 1998; Sullivan et al. 1999; Ready 2002). Similar results apply to stock markets in other developed countries. A number of studies find technical trading rules generated economic profits in emerging stock markets regardless of the sample periods 24 Park

and Irwin qualify this point by observing that, while there were some ‘early studies’ that measured statistical significance, this was done using tests that assumed trading rule returns were normally distributed. This is probably invalid since the distribution of these returns under the null hypothesis of an efficient market is not known. Furthermore, various studies report that technical trading returns are positively skewed and leptokurtic and, as a consequence, past applications of t-tests to technical trading returns may be biased.

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Categories for Modern Technical Analysis Studies, 1988–2004 Criteria

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Representative study Lukac et al. (1988)

Model-based bootstrap

21

Brock et al. (1992)

Reality check

3

Sullivan et al. (1999)

Genetic programing

11

Allen and Karjalainen (1999)

√

√

√

√

√

√

√

√

√

√

√

√

√

Conduct parameter optimization and out-of-sample tests Use model-based bootstrap methods for statistical tests. No parameter optimization or out-of-sample tests conducted Use White’s (2000) reality check bootstrap methodology for trading rule optimization and statistical tests Use genetic programing techniques to optimize trading rules (Continued)

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Distinctive features

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Data Transaction Risk Trading rule Out-of-sample Statistical snooping costs adjustment optimization tests tests addressed √ √ √ √ √

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Category

Number of studiesa

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Table 1.9

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Table 1.9

(Continued)

Category

Number of studies

Representative study

9

Gen¸ cay (1998a)

Chart patterns

11

Chang and Osler (1999)

Other

16

Neely (1997)

√

√

√

√

√

√

Distinctive features Use nearest neighbor and/or feed-forward network Use recognition algorithms for chart patterns Generally lack trading rule optimization and out-of-sample tests and do not address data-snooping problems

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Data Transaction Risk Trading rule Out-of-sample Statistical snooping costs adjustment optimization tests tests addressed √ √ √ √ √

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considered (Bessembinder and Chan 1995; Ito 1999; Ratner and Leal 1999). Considerable interest in technical trading rules was created by Brock et al. (1992) which Park and Irwin describe as “one of the most influential works on technical trading rules”. Brock et al. (1992) find strong and consistently positive results for the forecasting power of technical trading rules, using a 90-year sample for the DJIA. The model-based bootstrap method is used to evaluate trading rule performance. Because the EMH is a joint hypothesis, it follows that rejection of the EMH could be due to inadequate specification of the return generating process, rather than a violation of the accurate processing of information. An example of this is provided by the P/E ratio effect proposed by Basu (1977, 1983). The P/E ratio plays an important role in a number of the rules-ofthumb suggested by fundamental analysts, e.g., Graham (1949) suggests a criterion for buying a security is that the price does not exceed 20 times the average earnings over the previous six years (Oppenheimer 1981, p. 9). Using a sample of NYSE stocks, Basu presented empirical evidence that portfolios of low P/E stocks have higher average returns than portfolios of high P/E stocks, after appropriate adjustment is made for systematic risk of the portfolios using the capital asset pricing model (CAPM). Is this result due to a violation of EMH or to the inadequacy of the CAPM to adjust for risk or both? Perhaps the result could be proxying for some other type of anomaly such as the small firm effect? One characteristic of studies that reject EMH is the lack of persistence in such results. Of all the various effects, the January or turn-of-the-year effect — risk-adjusted returns are systematically higher in January than in other months — has had the strongest level of empirical support. As Haug and Hirschey (2006, p. 78) claim: “After a generation of intensive study, the January effect continues to present a serious challenge to the efficient markets hypothesis”. Heston and Sadka (2008) generalize the January effect to the ‘seasonality effect’ where returns for a given stock are higher in the same calendar month each year, again claiming strong explanatory power for this effect in the cross section of stock returns. In addition to firms with a January seasonal, this extends the result to firms that have a systematically higher return in a month other than January, expanding the universe of trading rules beyond the narrow possibility of exploiting the once a year January effect. Because it is a statistical result, there is no guarantee that the January effect will appear in any given year. In particular, Sullivan et al. (2003, 2001) is a ‘modern study’ of technical analysis that uses the bootstrap reality check methodology of White (2000) to examine the calendar frequency

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rules designed to exploit calendar effects: the Monday effect, the holiday effect and the January effect. Using a 1897–1998 sample for the DJIA, Sullivan et al. are able to identify a best trading rule with a bootstrap reality check p-value of zero, indicating the trading rule significantly outperforms a buy-and-hold strategy. However, when the sample is restricted to the most recent observations, 1987–1996, the best trading rule is changed and the return is statistically insignificant with a bootstrap reality check p-value of 0.98. Similar results are found for the S&P 500 futures data. Hence, Sullivan et al. (2003) find that it is premature to conclude that both technical trading rules and calendar rules outperform a buy-and-hold benchmark in the stock market. Dimson et al. (2001, p. 136) provide further confirmation: “For U.S. large-caps, there is no turn-of-the-year effect. Returns are not low in December, and January does not have the highest return, but ranks fifth.” Similar results are reported for the United Kingdom (if one ‘outlier’ is removed). Another example of an effect that appeared to be there but, in the end, appears not to be is the small firm effect — small firms have systematically higher risk-adjusted returns than large firms. This effect was initially proposed by Banz (1981) and Reinganum (1981). Despite considerable initial fanfare, Reinganum (1992) reexamines the empirical evidence and finds that small capitalization portfolios do outperform large capitalization portfolios, but this return behavior was volatile and reversible. Using a 1928–1988 sample, Bhardwaj and Brooks (1993) find contrary evidence: small firm stocks underperform large firm stocks. It is possible the small firm effect is compounded by the January effect. Dimson et al. (2002, p. 8) make the following observation about the size or small firm effect: “A frustrating feature of the size effect is that soon after its discovery the size premium went into reverse with smaller companies subsequently underperforming their larger counterparts. We show that this reversal was a worldwide phenomenon”. Where does all this to-and-fro on the EMH lead? The epistemology of modern Finance suggests that, if the evidence of anomalies is correct, new hypotheses will be formed that are ‘a better approximation’ to the world. However, such hypotheses would represent an assault on received knowledge. Academics who have invested large amounts of human capital in the ‘old theory’ would be faced with personal obsolescence and the battle lines would be drawn. Such is the case with the now emerging theory of behavioral finance. As a leader of the old guard, Fama (1998) is not persuaded either by the bulk of the evidence on market anomalies or by the evidence being provided by behavioral finance. Fama claims that behavioral finance does not impose an adequately defined alternative hypotheses to market

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efficiency. A similar comment is also advanced to explain much of the evidence on market efficiency anomalies: there is inadequate specification of alternative hypotheses.

1.3 1.3.1

Fact, Conjecture, and Rhetoric The Epistemology of Equity Valuation

Modern Finance academics face an enigma surrounding common stock valuation. Confronted with the practical difficulties of determining an ex ante value of a common stock, academics have found comfort in an analytical perspective based on investor rationality and market efficiency. Recognizing that market efficiency dictates against systematic abnormal gains to individual security selection, the upshot is an approach to equity security analysis which emphasizes an investment strategy based on optimal diversification and risk management. Analysis of the heterogeneous characteristics of individual stocks is avoided in favor of the search for sources of homogeneity (factors) across stocks. In Finance, various philosophical approaches compete to explain what constitutes knowledge and objective truth in valuing an equity security or determining an equity investment strategy.25 Finance is, at root, a human science, concerned with explaining and predicting that aspect of human behavior associated with financial activities. Much of interest has appeared in the epistemological debates about knowledge and objectivity in the human sciences since, say, Hayck’s The Counter-Revolution of Science (1955) or Gadamer’s Truth and Method (1960). Unlike the natural sciences, what is required in the human sciences is recognition that there are differing approaches to what constitutes knowledge when human behavior is involved. It is naive and intellectually chauvinistic to believe the route to knowledge and truth in, say, valuing equity securities is unproblematic, provided that one adheres to the analytical approach of modern Finance: it is inappropriate to conclude that deviations from the narrow parameters of

25 Much of modern Finance lies within the realm of positivism, also referred to as logical positivism or economic positivism, e.g., Friedman (1953), and Boland (1991) and Blaug (1992). Positivism strives to achieve a scientific approach, divorced from normative values, emphasizing quantification, measurement and empirical verification of hypotheses. Competing approaches include structural realism, critical realism, post-modernism and pragmatism, e.g., Lawson (1997).

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In a widely used and admired investments text, two of the leading figures in modern Finance Elton and Gruber (1995, p. 449) observe: The search for the “correct” way to value common stocks, or even one that works, has occupied a huge amount of effort over a long period of time. Attempts have ranged from simple mechanical techniques for picking winners to hypotheses about the broad influences affecting stock prices. At one extreme, the attempt to find a simple rule for selecting stocks that will have above-average performance can be likened to the search for a perpetual motion machine . . . At the other extreme the determinants of common stock prices are quite easy to specify in general terms. The price of common stock is a function of the level of a company’s earnings, dividends, risk, the cost of money and future growth rate. While it is easy to specify these broad influences, the implementation of a system that uses these concepts to successfully value or select common stocks is a difficult task.

the prevailing epistemology are ‘unscientific’ nonsense not worthy of academic consideration. Knowledge appears in various guises: empirical observations, logical deductions, and informed conjectures can all be part of the final picture. Making sense of the different facets requires that careful attention be given to the language being used. For example, a logical relationship derived from a theoretical model may have only limited empirical applicability. Yet, the logical relationship may be presented as though it has a strong ‘factual’ basis. This may confuse an uninitiated audience into concluding that the factual basis, which is logical, extends into the empirical realm. Academics in modern Finance are inherently attracted to logical facts, such as the capital asset pricing model or the Markowitz mean-variance portfolio optimization model. Whether logical facts have any ex ante empirical validity requires careful analysis that extends beyond the theoretical structure used to develop the model. Though this point may seem obvious, the resulting confusions are apparent even in introductory investments textbooks where logical relationships, such as the CAPM, are presented as though there were an empirical validity which corresponds to the logical validity. The term epistemology comes from the Greek word for knowledge. Simply put, epistemology is the philosophy of knowledge. The central question of epistemology is how individuals come to know or, in slightly different terms, how knowledge is created. Methodology is concerned with the methods that are used in creating knowledge and, as such, is more practical in nature. Positivism is a philosophical movement, concerned with

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epistemology, characterized by an emphasis upon science and scientific method as the only sources of knowledge. Though the roots of positivism can be traced back to Francis Bacon (1561–1626), the beginnings of the movement are usually credited to Auguste Comte (1798–1857). Over time, positivism evolved substantively to the point where, in the 1920s, a new version, known as logical positivism (also known as logical empiricism, logical neopositivism, neopositivism) emerged. Reflecting the German and Austrian roots of the so-called Vienna school, the leading founding figure is usually identified as Rudolf Carnap (1891–1970). However, the English philosopher A.J. Ayer (1910–1989) is usually credited with the most influential contribution Language, Truth and Logic (1936). The branch of positivism reflected in modern Finance can be traced to Friedman (1953). Comte argued the search for knowledge had gone through three historical phases: the theological, that was concerned with obtaining knowledge about God and spirituality; the metaphysical, where the search was for philosophical truths; and, the positive or scientific phase, that involved the search for objective facts or ‘positive truths’. It was this last phase that Comte associated with positivism. As initially conceived by Comte, the positivist approach to knowledge made a sharp distinction between the realms of fact and value. There was also a strong hostility toward religion and traditional philosophy, in general, and metaphysics, in particular. The positivist philosophy maintained that all sciences rely upon the same methodology for determining facts about the physical and material world. As such, there are no important differences between, say, biology, physics or economics. This was referred to as the so-called ‘unity of science project’. Facts are to be collected and summarized through a process of induction. Echoes of positivism constantly resonate through modern Finance. Elton and Gruber (1984, p. 273) provide an excellent example: “As the physicist builds models of the movement of matter in a frictionless environment, the economist builds models where there are no institutional frictions to the movement of stock prices” (emphasis added).26 The epistemology of modern Finance can be traced to Friedman 26 Other examples abound. Consider the following quote from John Cochrane, Myron S. Scholes Professor of Finance at the University of Chicago Booth School of Business, made in an early 2009 debate over the proposition, ‘This house believes that we are all Keynesians now’, sponsored by the Economist magazine (http://www.economist.com/ debate/days/view/283): “Of course we are not all Keynesians now. Economics is, or at least tries to be, a science, not a religion. Economic understanding does not lie in a return

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(1953) where the distinction between fact and value appears as a distinction between ‘positive economics’ and ‘normative economics’ (p. 4): Positive economics is in principle independent of any particular ethical position or normative judgments . . . it deals with ‘what is’ not with ‘what ought to be’. Its task is to provide a system of generalizations that can be used to make correct predictions about the consequences of any change in circumstances. Its performance is to be judged by the precision, scope, and conformity with experience of the predictions it yields. In short, positive economics is, or can be, an ‘objective’ science, in precisely the same sense as any of the physical sciences.

Much of Friedman (1953) is concerned with the issue whether a theory with unrealistic assumptions, even ‘wildly inaccurate descriptive representations of reality’, can be ‘important and significant’. For Friedman, the ultimate test of a theory was ‘whether it yields sufficiently accurate predictions’, not whether the assumptions are realistic. The concern of Friedman (1953) with the form of the theory being examined is consistent with the evolution of positivist epistemology. Initially, positivism placed heavy reliance on the inductive process of collecting facts. Spurred by the remarkable successes of the natural sciences during the late 19th and early 20th centuries, this view evolved into logical positivism, an epistemology that placed emphasis on theories and the logical deduction of hypotheses to test those theories as well as the collection of facts. The epistemology of logical positivism allows only two grounds for truth: there are deductive truths such as those in mathematics and formal logic, e.g., 12 − 3 = 9; and inductive statements that match reality precisely. As a consequence, truthful statements have to be verifiable to be meaningful. In logical positivism, statements have meaning relative to the conditions under which the statement can be verified. Friedman adapts this approach to where the test of verification for a hypothesis is the ability to predict. This is consistent with the tenet of logical positivism that a statement not describing an ‘experiential proposition’ carries no significance, i.e., it is not knowledge.

to eternal verities written down in long , convoluted old books, or in the wisdom of fondly remembered sages, whether Keynes, Friedman or even Smith himself. Economics is a live and active discipline, and it is no disrespect to Keynes to say that we have learned a lot in 70 years. Let us stop talking about labels and appealing to long dead authorities. Let us instead apply the best of modern economics to talk about what has a chance of working in the present situation and why”.

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Friedman (1953, p. 7) clearly reflects these tenets of logical positivism in what Boland (1991) has termed economic positivism: “theory has no substantive content; it is a set of tautologies . . . Factual evidence alone can show whether the categories of the ‘analytical filing system’ have a meaningful empirical counterpart, that is, whether they are useful in analyzing a particular class of concrete problems”. Statements that are verifiable provide a basis for building a science. Under positivism, science is the source of knowledge. As such, both positivism, in general, and economic positivism, in particular, share a fundamental commitment to empiricism, an epistemology where claims that have no empirical consequences are without meaning. Economic positivism extends empiricism by arguing that science can also seek to build theories to describe the regularities of cause and effect in order to explain the world. This requires theories to be expressed as a set of axioms or, less formally, basic assumptions. These theories have rules to systematically link the predictions with objective measurements of the real world. The connection to Friedman (1953), von Neumann and Morgenstern (1947) and innumerable other projects in positivist economics and modern Finance is apparent. At this point, the proponent of modern Finance is compelled to ask: so what is wrong with economic positivism? There are a number of answers to this question, some of which are given in the latter parts of this section. At this point, it is relevant to observe that positivism maintains that science is the only way to create knowledge, to allow individuals to understand the world well enough to predict and control outcomes. In the positivist framework, the objective world is viewed as deterministic, operated by laws of cause and effect that can be identified if the unique approach of the scientific method is correctly applied. Science is conceived as a mechanistic operation. It is possible to use deductive reasoning to postulate theories that can be empirically tested. Based on the results of these empirical tests, it is determined whether a theory ‘fits the facts’ or whether the theory needs to be revised in order to provide better predictions of reality. Ultimately, there is an objective reality that can be discovered if there is sufficient empirical information available to verify the ‘true’ deductive hypotheses. Criticisms of economic positivism are numerous. One type of criticism focuses on the misunderstanding of the process by which science is conducted. Is there really a unity of science? Are the procedures used in physics and chemistry directly applicable to economics or psychology? Do scientists really develop deductive hypotheses that are then ‘verified’

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on empirical data? Another related criticism observes that economic positivism says little or nothing about how axioms (or Friedman’s assumptions) are translated into possible testable hypotheses. In other words, positivism has no substantive insight into the process by which knowledge is created. Positivism is only interested in specifying the scientific process, without recommending criteria for selecting among permitted ideas. This leads to Friedman (1953) and the criteria of predictive ability. But, this leads to the problem of measuring predictive ability. The distinction between ex ante and ex post predictability is one key example of this type of problem in modern Finance. Positivism proposes that there is a unity of science. Certain developments in epistemology after positivism deny this proposition. As such, schools of thought have emerged that are concerned specifically with the epistemological problems arising in the human sciences. One such epistemology is critical realism, a school that observes all measurement is fallible is some way, e.g., Bhaskar (1978). For example, critical realists maintain that all observations are theory-laden and that individuals, in general, and scientists, in particular, are inherently biased by their cultural experiences, world views, and so on. Friedman (1953, p. 4–5) recognizes this issue but does not view it as a basis for ‘a fundamental distinction’ between economics and the natural sciences. For critical realists the challenge is how to move from a notion of objectivity that is inherently a social phenomenon to the identification of knowledge. If objectivity is not perfect, then how are these separate and imperfect individual interpretations of reality to be combined? Friedman (1953) provides a window to the 20th century development of the philosophy of the social sciences. In this development, words like ‘hermeneutics’ and ‘ontology’ are essential to the discussion, though references to notions such as “the questionableness of romantic hermeneutics” require knowledge of the philosophical developments to be correctly interpreted. Hermeneutics has a long history in philosophy, starting with problems of biblical exegesis. During the 18th and early 19th centuries, hermeneutics evolved into a more general theory of textual interpretation, aiming to provide a set of rules for accurate interpretive practice applying to a wide range of subject matter. Taking hermeneutics as the relevant method for the recovery of meaning, Wilhelm Dilthey (1833–1911) broadened hermeneutics to represent a methodology for the recovery of meaning that is central to understanding knowledge within the ‘human’ or ‘historical’ sciences.

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Strongly influenced by Martin Heidegger (1889–1976), Hans-Georg Gadamer (1900–2002) is ‘the decisive figure in the development of 20th century hermeneutics’ (Stanford Encyclopedia of Philosophy). Gadamer is part of a long line of thought that questions the ability to apply techniques of the natural sciences to the human sciences, e.g., Gadamer (1960, p. 6): “the real problem that the human sciences present to thought is that one has not properly grasped the nature of the human sciences if one measures them by the yardstick of an increasing knowledge of regularity. The experience of the socio-historical world cannot be raised to a science by inductive procedure of the natural sciences”. Though Gadamer’s notion of the human sciences may seem to have more applicability to, say, political science or sociology, it is difficult to evade the observation that the prices of securities are set in markets and are the outcome of a social interaction. Security analysis lies within the domain of the human sciences. Unlike the natural sciences, the human sciences have to allow for prejudice derived from authority. In contrast, methodologically disciplined use of reason cannot accept arguments based on authority for that involves not using one’s reason to reach conclusions. “If the prestige of authority takes the place of one’s own judgment, then authority is in fact a source of prejudices”. But the approach toward the human sciences proposed by Gadamer (1960, p. 249) does not view prejudice either negatively or positively. As such, authority as a positive prejudice provides a basis for knowledge: . . . the recognition of authority is always connected with the idea that what authority states is not irrational or arbitrary, but can be seen, in principle, to be true. This is the essence of the authority claimed by the teacher, the superior, the expert. The prejudices that they implant are legitimized by the person who presents them. But this makes them then, in a sense, objective prejudices, for they bring about the same bias in favor of something that can come about through other means. e.g., through solid ground offered by reason.

The process of interpretation and understanding is fundamental to the human sciences. While knowledge about an object in the natural sciences gets progressive deeper over time, the same is not true about the human sciences where great achievements of the past ‘hardly ever grow old’. For Gadamer, the interpreter is an essential component of knowledge in the human sciences: “the object appears truly significant only in the light of him who is able to describe it to us properly. Thus it is certainly the subject that we are interested in, but the subject acquires its life only from the light in which it is presented to us”. Subjects appear historically

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“under different aspects at different times or from a different standpoints” (p. 252). Insightful interpretations require the past to be echoed in the present. As such, the human sciences are involved not only in the accumulation of empirical results but in the transmission of an important source of authority: tradition. “That which has been sanctioned by tradition and custom has an authority that is nameless, and our finite historical being is marked by the fact that always the authority of what has been transmitted — and not only what is clearly grounded — has power over our attitudes and behavior” (p. 249). Gadamer sees an essential role for tradition in the human sciences (pp. 251, 252): “That there is an element of tradition active in the human sciences, despite the methodological nature of its procedures, an element that constitutes its real nature, and is its distinguishing mark, is immediately clear if we examine the history of research and note the difference between the human and natural sciences with regard to their history”. For Gadamer: “the natural scientist writes the history of his subject in terms of the present stage of knowledge. For him errors and wrong turnings are of historical interest only, because the progress of research is the self-evident criterion of his study. . . the human sciences cannot be described adequately in terms of this idea of research and progress”. Knowledge in the human sciences does not proceed by distancing and freeing ourselves from what has been transmitted through tradition. Rather, the problem is to find the relationship of the present with the traditions of the past. The positivist foundation of modern Finance depends on the premise that knowledge in the subject is obtained solely from the methodology of the natural sciences. Somehow, increasingly greater knowledge is obtainable about the natural phenomena of security markets, such as prices or returns, as increasingly larger amounts of data are examined or more precisely mathematical theories are derived. The historical evolution of markets is unimportant. The views of writers in the past, such as Graham and Dodd or J.M. Keynes or Irving Fisher, are only of historical interest, useful illustrations of how far knowledge has progressed since that time. Gadamer, and other philosophers of his ilk, would argue that this approach is predicated on the supposition that Finance is a natural science. However, the objects of interest in Finance are the result of human interactions and, as such, belong in the realm of the human sciences. If correct, knowledge of the subject could be substantively increased by proceeding beyond the scientific process to incorporate the notion of tradition and appreciate the contributions of authorities from the past.

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The Rhetoric of Finance

It is difficult to be an ardent practitioner of any branch of academic or vernacular Finance and not be at least slightly disturbed by the arguments put forth in McCloskey (1985, 1994), especially the frightening ‘American question’:27 If you’re so smart, why aren’t you rich? McCloskey observes: “The American question embarrasses anyone claiming profitable expertise who cannot show a profit”. Though McCloskey is concerned with reinterpretation of economic science as rhetoric, the arguments can be readily extended to Finance. In particular, economists have been quick to embrace modern Finance as part of their discipline under the guise of ‘financial economics’. Examples provided by McCloskey critiquing economic theory also extend readily to modern Finance. The American question is particularly biting for Finance academics who answer this question by claiming the search for abnormal returns is futile; those who have been successful have just been lucky, someone has to win the horse race.28 As evidenced in the awarding of the Nobel prize in economics to a number of important modern Finance researchers such as M. Scholes, R. Merton and H. Markowitz, there is considerable overlap between the subjects of Economics and Finance (Poitras and Jovanovic 2007). Many academic institutions feature the two subjects combined into a Department of Economics and Finance or some other such administrative configuration. There are also a number of journals with titles such as the Journal of Financial Economics or the International Review of Economics and Finance, reflecting the symbiosis of the two subjects. Despite the overlaps, there are distinct differences in the subjects. These differences extend beyond obvious observations such as economics is concerned with GNP, fiscal policy and trade theory while Finance is concerned with security returns, corporate capital structure 27 Other contributions to the rhetorical approach include Klamer et al. (1988) and Weintraub (1991). 28 Such bias is evident by examining the index for any of a number of textbooks used in introductory Investments courses, e.g., Bodie, Kane and Marcus (1999, 4th ed.; 2009, 8th ed.; 1989 1st ed.). The name index to the 2nd ed. has one listing each for Warren Buffett and Benjamin Graham – associated with two passing references made in the text. In contrast, Eugene Fama has twelve and Fischer Black has nine. Given Buffett’s reputation as ‘the world’s greatest investor’, such discrepancies are revealing of the type of bias found in academic treatments of equity valuation.

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and investment policy. This difference is reflected in a competing configuration for academic departments combining accounting and finance and in journal titles such as the Journal of Business Finance and Accounting or Accounting and Finance. McCloskey interprets economics as rhetoric — the art of persuasion. This approach to rhetoric follows Aristotle, as opposed to the Platonic interpretation that views rhetoric as flattery and cosmetics. Recognizing this distinction is fundamental to the points that McCloskey is making (1985, p. 40) as rhetoric has two definitions: one narrow and the other broad. The narrow definition originates with Plato and was made popular by the 19th century Romantics who elevated sincerity to the chief virtue. In the Platonic definition, rhetoric is cosmetic and superficial. An example of common usage is where the newspapers write: ‘Presidential Primary Campaign Mired in Rhetoric’ or in academic usage where rhetoric characterizes “the meretricious ornament obscuring the clear and distinct idea” (Ibid.). The Platonic notion of rhetoric is sharply different than the Aristotelan where rhetoric is ‘an ability to see the available means of persuasion’. This ability has considerable value and applications. Whereas Platonic rhetoric is without virtue, the classical Greeks saw persuasion (peitho) as a means to counter-act violence (bia): “All that moves without violence, then, is persuasion, peitho, the realm of rhetoric, unforced agreement, mutually advantageous intellectual exchange”. As such, rhetoric encompasses the use of logic and fact as well as metaphor and story. What is ‘logical’ is not without dispute. A ‘fact is a fact’ only relative to a conceptual scheme. As McCloskey points out, these points have been well known since Kant. Studies of science have shown repeatedly that facts are constructed by words. To summarize McCloskey’s point about the Aristotelan definition of rhetoric: “In this definition, a science as much as a literature has a ‘rhetoric’ ”. Whether the argument or discussion is made mathematically, verbally or metaphorically, the use of rhetoric is involved. With this definition of rhetoric in hand, McCloskey sets about to engage in a ‘conversation about conversation’. For McClosky, the ‘rhetorical approach’ is concerned with how academics and practitioners in a specific discipline persuade each other and the world. For academics, the conversations are found in journals, monographs and textbooks. For McClosky the conversations in journals raise ‘the puzzle of publication’. Speaking about economics, McCloskey (1985) describes the puzzle (pp. 31, 32): Even the most influential articles are puzzling. In Gary Becker’s article on “A Theory of the Allocation of Time” (1965), the Knowledge is

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presented in the rhetoric of the hypothetico-deductive model of science (“little systematic testing of the theory has been attempted . . . The theory has many interesting . . . implications about empirical phenomena”), but it looks more like a metaphor, an analogy between budgets of income and budgets of hours. In Robert Lucas’ article on “Some International Evidence of Output-Inflation tradeoffs” (1973), Knowledge is presented in the rhetoric of the Empirical Finding, but looks more like a reading of history, one of the many possible readings permitted by the data. One wonders whether economists could agree on what constituted the remarkableness of these remarks in the scientific conversation.

In considering the extensive journal debate over monetarism versus Keynesianism, McCloskey wonders: “What would be the point of publishing one’s prior convictions dressed up as ‘findings’ ?” Similar comments could readily be made about much of the journal literature in Finance. For example, consider the numerous articles on empirical tests of the CAPM that appeared during the 1970s, e.g., Fama and Macbeth (1973), and the studies on the cross section of expected stock returns during the 1990s, e.g., Fama and French (1992). Though dressed up in the rhetoric of the Empirical Finding, seeing the evidence from the the 1970s as one of the ‘many possible readings of the data’ is apparent in the articles from the 1990s. Throughout the conversations, it is apparent that the contributors have been strongly persuaded by the rhetoric of the hypothetico-deductive model of science that formulated and promoted the capital asset pricing model. The methods of persuasion involve the use of the metaphor of “the model ” and the active use of an authoritative style to suppress alternative stories. As with scientists and scholars in other disciplines, academics in Finance “use analogies, tell stories and adopt a persona” (p. 36). There is value in determining why some arguments work and others do not. Much like economists, academics in modern Finance are neurotic about ‘science’. “They think that knowing, really knowing, means following something called ‘scientific Method’. They think that if you don’t know it that way then you don’t know much” (p. 55). This is, more or less, the point being explored by Gadamer. McCloskey goes beyond the academic boundaries of Gadamer’s conversation to explore the pervasiveness of ‘Scientism’ in society. “Resistance to reason is dogma. It is unoriginal and uncontroversial to point out that Science is the modern dogma, and that after the sea of religious faith receded another religion flooded in: Scientism” (p. 64). The grip of Scientism “in the modern world is well illustrated in the service industries of Science, staffed by deans, journalists, publishers,

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foundation executives and grant administrators”. McCloskey observes: “In the dogma of Scientism, it is today’s credo, in substance or method or Nobel laureates, that is timelessly True. The service people protect the orthodoxy with a fierce devotion” (p. 68). Yet: “The service people of science forget that the only certitude is that yesterday’s timeless orthodoxy in science will become tomorrow’s laughingstock”. Being an economist, McCloskey is motivated by concerns in that discipline. His conversation often extends well beyond the limits of economics proper and issues that are essential in Finance do appear in flashes, comments made in the process of discussing some issue that is not quite so important in the context of economics. The problem of prediction is one such issue. Economists are concerned with prediction, in a way, but much of the core theory is developed using models without randomness. This tendency is evident in McCloskey’s (p. 72) description of the ‘American question’: The philosophical prestige of prediction probably arises from a still dominant but “discredited empiricist conception of science”. The economist’s response to the empiricist conception of science is the American question: if you’re so smart, oh predictor of human events, why ain’t you rich? The American question cuts deeper than most intellectuals and experts care to admit. The test of riches is perfectly fair if the expertise claims to deliver actual riches, in gold or glory.

Prediction is, or ought to be, the central concern of academic Finance. The core theory is concerned with decision making under uncertainty. Variables of interest, such as security prices and portfolios, are the outcome of social activity aimed at making profits or, more precisely, maximizing the expected utility of terminal wealth. To deal with the ‘American question’ Finance academics developed the EMH, a body of theory and empirical results designed to demonstrate ‘why we ain’t rich’. The core theory developed ‘rational, expected utility maximizing’ strategies for portfolio selection. The pervasive ex post empirical testing of these portfolio selection strategies again belies an avoidance of the American question. If the American question makes the economist uncomfortable, it makes Finance practitioners, i.e., those in the ‘vernacular’ Finance tradition, absolutely queasy. The level of concern between academic Finance, where the EMH provides some comfort, and vernacular Finance, where the appearance of superior performance is desired, has resulted in a divergence of both theory and practice. Whereas the academic Finance approach to equity valuation claims to be based on ‘rigorous mathematical theories and

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carefully documented empirical studies’, vernacular Finance has glorified inductive techniques that have achieved at least ex post success in predicting the future market prices of: individual stocks; or, specific stock indexes. As a consequence, vernacular Finance has adopted valuation techniques, such as technical analysis, that academic Finance adherents have claimed with some authority to have no validity. However, driven perhaps by the American question, academic Finance has slowly backed away from a strict EMH position. This queasiness about the American question within the academic Finance community is apparent in those proponents of anomalies in security prices, the students of behavioral finance. An anomaly in market prices is, by construction, an inefficiency, i.e., an opportunity to earn an abnormal return. Yet, in answer to the American question, proponents of behavioral finance are evasive (Shefrin 2000, p. 70): Knowing that prices are inefficient and exploiting that inefficiency are two different things. A lot of people seem to think that the message of behavioral finance is that beating the market is a no-brainer because errors cause mispricing. Well, it’s not easy money; just the opposite, in fact. One of the main messages of behavioral finance is that heuristicdriven bias and frame dependence get in the way. There was a lot of California gold waiting to be discovered in 1849, but how many prospectors actually got rich? Precious few.

Using the 1849 analogy, is not an anomaly evidence that gold had been discovered in a particular location? It seems that prospectors of behavioral finance have found the gold, in the form of anomalies, but are unable to convert it to riches because of ‘heuristic-driven bias and frame dependence’. The solution that McCloskey provides to the American question is comforting for economists: No one can be embarrassed by the American question who retains a proper modesty about what observation and recording and story-telling can do. We can observe the history of economics or the history of painting, and in retrospect tell a story about how security of commercial property or the analysis of vanishing points made for good things. An expert such as an economist is an expert on the past, and about the future that can be known without divine and profitable possession. Human scientists and critics of human arts, in other words, write history, not prophecy. Economics teaches this, the limit on social engineering. It teaches that we can be wise and good but not profitably foresighted in detail, even if we are economists.

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Unfortunately for those involved in Finance, especially the practitioners in the vernacular Finance community, the subject is directly concerned with social engineering, with out-performing through more accurate predicting. The limits on social engineering are real constraints, the grist for a range of conversations. This explains the fundamental need to deal with the problem of uncertainty. The ‘rational’ predictive part of human behavior is insufficient to provide explanations that can adequately address the American question. Much of the rhetoric in modern Finance reflects the comfort of the ‘wise and good’ academics with the rational explanations. However, having the deal with the American question on a daily basis, most Finance practitioners have to strive to answer the question by being, or at least appearing to be, rich. Recognizing that an adequate definition of ‘rich’ is needed, this book seeks to answer the American question by providing a detailed examination of the valuation techniques proposed by those who have been recognized for becoming ‘rich’ in terms of wealth accumulation through equity security valuation and selection.29 A colloquial statement of this method of answering the American question is: ‘identify those who are rich and see why they are so smart’. Included on the ‘smart’ list are predominately those from the vernacular Finance realm: Warren Buffett, Benjamin Graham, Alfred Cowles, Roger Babson, and, Philip Fisher. On the smart list from the academic realm are: J.M. Keynes, Irving Fisher, and, Frederick Macaulay. Though some of names included in this listing are well known, it is less well known that Keynes derived the bulk of his income from securities trading, e.g., Moggridge (1983, Table 1, p. 2). While Keynes was also involved in commodities speculation, it was in US equities trading where Keynes had the biggest financial success. Though Irving Fisher did have an abysmal record at predicting equity values, contributions to the creation

29 Another

potential answer is to claim, “I am rich, so listen to me”. This again illustrates why an adequate definition of rich is needed to avoid difficulties in determining which equity valuation techniques to emphasize. Individuals with relatively limited material wants and substantial labour income can achieve more than sufficient terminal portfolio values with equity valuation and selection methods that would be inconsistent with the objectives of a more hedonistic person. It is also important to avoid confusing riches obtained through the sale of equity valuation methods with those obtained through the application of such methods to security selection. For example, brokers at large investment banks generate sizeable bonus income associated with firm performance. In the near term, such bonuses are tied more to the ability to sell valuation techniques and associated information to clients rather than to the actual performance of the techniques.

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of the Cowles Commission and in developing a successful card indexing business warrant inclusion. All this supposes that rich means something like, ‘made lots of money’, which is not a particularly good yardstick. In particular, this ignores: the impact of initial and subsequent endowments; and, the inherent riskiness of the equity selection strategies employed. There are also those that, for whatever reason, developed equity valuation methods that have considerable predictive power without taking the next step to translating the model success into market profits.30 In effect, there is a speculative element in equity valuation that presents a real constraint for those with higher levels of loss aversion, such as those with limited endowments. In addition, success within the academic realm is predicated on different norms than the amount of money a valuation methodology has generated. As such, academic contributions can have insight into the equity valuation process without, somehow, being legitimized by producing ‘lots of money’. This leaves considerable scope for the inclusion of a range of interesting contributions on equity valuation by the likes of: David Durand, George Shackle, and, the modern Finance school. 1.3.3

Ergodicity and True Uncertainty

The use of ex post parameter estimates of means, variances and regression coefficients as proxies for ex ante parameters or variables such as expected returns, volatility and beta is a key feature in the practical implementation of economic theories, in general, and of modern Finance, in particular. A useful example is the use of the CAPM to estimate the expected return on a stock. Estimates of beta and the equity risk premium are obtained by taking as long a sample period as possible in order to obtain the highest degree of precision in the estimate. Some studies, e.g., Dimson et al. (2002) (101 Years of Global Investment Returns), use the length of the sample as evidence of importance of the results. In terms of estimating the mean for, say, the equity premium, the underlying logic is that the longer is the sample for the time average, the more accurate is the estimate for the future ensemble average of interest. A similar logic applies to increasing the 30 For example, the ex ante performance of an initially destitute person who is able to build a portfolio of, say, a half million dollars over a lifetime by successfully reinvesting meager savings from a minimum wage job could be compared favorably to the performance of Buffett who, by starting with much more, and being able to pursue strategies that were unavailable to the meager investor, was able to generate a much larger terminal portfolio value.

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number of firms used in a cross-section or increasing the sampling frequency in a time series. The validity of this rationale for using ex post estimates to proxy ex ante variables is embedded in the type of ergodicity assumption used to justify time reversible stationary distributions employed in arriving at the theoretical results. More precisely, if stationary distributions are time reversible: there is a homogeneity in the time paths such that it does not matter where in the time path an observation is located, it is only the distance between observations that matters. The possibility that there may be a heterogeneity of paths is also not permitted. For example, starting from S(0) if ex ante future paths that start by going up have a greater tendency to continue going up (success breeds success) and paths that start by going down have a greater tendency to continue going down (failure is contagious), the resulting ex ante ergodic distributions will be time irreversible, bimodal, and dependent on the selection of S(0). Do results such as the mean-square ergodic theorem apply to this relatively simple type of heterogeneous process? Empirical limitations of the time reversible ergodic framework are well known, e.g., Samuelson (1976). Without being subjected to a continuous series of shocks, the time paths for an ergodic process will ‘damp down’ over time, generating insufficient action to be consistent with observed time series for financial variables, in general, and equity security prices, in particular. Attempts to mitigate this damping behavior, such as imposing a GARCH variance process or adding a Poisson error process, are usually insufficient to generate the type and degree of observed volatility in equity prices. ‘Flexible’ estimation techniques, such as GMM, are employed to estimate model parameters because the underlying density functions are too complicated or ill-behaved to use maximum likelihood, the most powerful weapon in the statistical arsenal of time reversible ergodic process analysis. It is still not clear whether stock prices have unit roots or are fractionally integrated after suitable detrending, e.g., Gil-Alana (2006). The considerable efforts that have been expended on extending the ergodic model are still a work in progress. In response to the persistent inability to accurately model stock price processes, defenders of modern Finance observe that alternative hypotheses are insufficient and vague. For example, responding to accumulating evidence against the EMH, Fama (1998, p. 284) observes: A problem in developing an overall perspective on long-term return studies is that they rarely test a specific alternative to market efficiency.

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Instead, the alternative hypothesis is vague, market inefficiency. This is unacceptable. Like all models, market efficiency (the hypothesis that prices fully reflect available information) is a faulty description of price formation. Following the standard scientific rule, however, market efficiency can only be replaced by a better specific model of price formation, itself potentially rejectable by empirical tests.

The positivist epistemology requires that ‘the standard scientific rule’ produce a progression of knowledge to ‘a better specific model of price formation’. This presumes that human behavior can be modeled in a more precise and scientific manner, if only ‘better’ statistical techniques are applied to ‘the data’ or ‘better’ mathematical techniques are used to formulate ‘the model’. Perhaps a ‘vague’ alternative hypothesis is all that is possible. The calculations involved in determining the value of an equity security use future variables that are impacted by human behavior. Perhaps the complexity of these calculations defy a solution obtainable using time reversible ergodic processes? All this is not meant to imply that the subject of modern Finance has not made substantive contributions to understanding various aspects of equity security value; quite the contrary. Rather, the perspective and approach to what constitutes knowledge in modern Finance differs from those directly involved in the markets that determine prices for equity securities, such as security analysts and portfolio managers, and most of the investing public. Following Stickney (1997), academics involved in modern Finance focus on the average relationship between selected accounting information and stock prices across a large number of firms. The objective is to uncover commonality or factors of homogeneity across firms. Those directly involved in making transactions in equity markets, such as equity research analysts, examine accounting information and other data sources seeking individual firms that are incorrectly valued. It is the heterogeneity of firm characteristics that drives the analysis. As such, “inherent differences will always exist between research conducted across large sets of firms and that conducted on individual firms”. Accept the hypothesis that the valuation problem for equity securities involves analyzing sources of firm heterogeneity rather than finding sources of firm homogeneity. Confronted with the problem of determining in a particular ‘instance’ whether the ‘true value’ of the equity security differs from the market price, the words of Frank Knight (1921) ring clearly: “The essential and outstanding fact is that the ‘instance’ in question is so

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entirely unique that there are no others or not a sufficient number to make it possible to tabulate enough like it to form a basis for any inference of value about any real probability of the case we are interested in”. Applied to the problem at hand this implies: heterogeneity breeds true uncertainty. As evidenced in Kelsey and Quiggin (1992), considerable attention has been given extending the traditional theory of decision making under uncertainty to incorporate situations where probability distributions over future outcomes are not known. However, there is a considerable distance to travel before the additional complexity required, e.g., Quiggin (2007), translates into well defined decision rules applicable to practical situations of equity security valuation. While acknowledging practical limitations of key theories, advocates of modern Finance respond that alternative approaches are poorly specified and have more serious difficulties in both theoretical development and practical implementation. This position is only correct if the yardstick of positivism is used to measure performance. By design, the heterogeneous outcomes associated with the true uncertainty in equity security valuation defy techniques designed to identify elements of systematic homogeneity across securities. Keynes detailed how the use of ‘conventions’ to make decisions in the face of uncertainty can suddenly generate periods of excessive volatility in stock market prices when prevailing conventions are confounded by a change of circumstances, e.g., Poitras (2002a). Modern finance would use a Markov regime-switching stochastic process to model the resulting non-linearity. This would provide a potentially acceptable ex post method of finding a switch point and fitting the distribution of returns without providing much ex ante insight into when such a switch will occur, how large and how long the period of excess volatility will be and, most importantly, whether the direction of the move in prices will be up or down. Writing on the occasion of Franco Modigliani receiving the Nobel Memorial Prize in Economics, Merton (1987) observes (emphasis added): The Modigliani-Miller work stands as the watershed between ‘old finance’, an essentially loose connection of beliefs based on accounting practices, rules of thumb and anecdotes, and modern financial economics, with its rigorous mathematical theories and carefully documented empirical studies.

The possibility that ‘rules of thumb’ and ‘anecdotes’ may be the best method of dealing with the type of true uncertainty involved in arriving at a

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valuation for a specific equity security is not admitted. Such a possibility lies within the scope of rational intuitionism, a school of philosophy with roots in the work of Henry More (1614–1687), Samuel Clarke (1675–1729), and Richard Price (1723–1791). In the 20th century, intuitionism has impacted both moral philosophy and mathematics through the work of H.A. Prichard (1871–1947), G.E. Moore (1873–1958), and L.E.J. Brouwer (1881–1966). Intutitionism is an intellectual enigma. The basic notion is that intuition can be used to determine the truth of important propositions. How this is done, and why this is important, depends on the situation. In the 18th century, revelation of the ‘divine mind in the human mind’ supplied a solution not available to modern academics.31 In addition to the underlying vagueness inherent in intuitionism, the general belief that truth can be determined independently of logical and empirical inference is unacceptable to positivists. Despite this, intuitionism has produced some valuable insights. For example, in mathematics, Brouwer argued that the primary objects of mathematical discourse are mental constructions governed by self-evident laws. Mathematics is not concerned with developing from basic axioms the deep properties of existence but, rather, with the application of internally consistent methods to develop more complex mental constructs. It is well known that G.E. Moore was an important influence on Keynes and hints of rational intuitionism echo in The General Theory. The ‘years of high theory’ from 1926–1939 (Shackle 1967) produced a number of insightful approaches to resolving the difficult quandaries surrounding the distinction between risk and uncertainty identified by Knight (1921) and the use of subjective probability by Keynes (1921) to motivate the distinction. The impact of uncertainty and expectations play a fundamental theoretical role in tackling the profound macroeconomic problems of the Great Depression that eventually inspired the appearance of Keynes (1936). Though tremendous effort was given to working out the implications of uncertainty and expectation for macroeconomic problems, central issues such as the determination of liquidity preference or the marginal efficiency of investment have direct theoretical and practical connections to the equity valuation problem. Significantly, included in the contributions seeking to clarify and elucidate Keynes (1936) was Myrdal (1931, 1939) 31 For example, in moral philosophy, this permitted Richard Price to rely on the ‘moral certainty’ of Christian teaching as revealed in the Bible to argue against Hume’s attack on the truth of Christian miracles e.g., Poitras (2010).

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that clarified the economic significance of distinguishing between ex post and ex ante outcomes. It was George Shackle (1903–1992) that made the most substantive contributions to this line of inquiry in the era after WWII.32 There are a number of reasons why Shackle has been largely forgotten, outside of a small cadre of dedicated adherents. One reason is timing. The axiomatic approach to decision making under uncertainty introduced by von Neumann and Morgenstern (1947) was like an academic tidal wave that engulfed almost all competing approaches. “Shackle was the single critic of the probabilistic approach to decision making under uncertainty and of its crucial hypothesis of the additivity of probability distributions” (Meacci 2009, p. 226). Following Ford (1993, p. 697) “George Shackle believed passionately that economics was a subject whose substance had to be conveyed by language; the only flexible, versatile, means of expression”. Though sometimes sophisticated mathematics do appear in Shackle’s contributions, a convincing mathematical formalization was lacking. It was not until after his death that Gilboa and Schmeidler (1994) made substantive progress in formalizing non-additive probability. Earlier contributions to evidence theory going back to Shafer (1974) that deal explicitly with the element of ‘surprise’ in probability assessments have only recently been connected with Shackle. Shackle was an academic economist, with no ties to the world of ‘high finance’ or to a prestigious business school, concerned with issues such as the dynamic properties of an economic system. As such, it is understandable that modern Finance makes no reference to Shackle. Yet, there is so much of relevance in Shackle that can explain the ex post to ex ante gap that confounds the central models of modern Finance. Consider the following from Shackle (1958, p. 23): In the classical dynamics of the physicist time is merely and purely a mathematical variable. The essence of his scheme of thought is the fully abstract idea of function, the idea of some working model or coded procedure which, applied to any particular or specified value or set of values of one or more independent variables, generates a value of a dependent 32 Also important in developing alternative approaches to uncertainty is Nicholas Georgescu-Roegen (1906–1994). Similar to Shackle, expectations in the GeorgescuRoegen framework “cannot be reduced to any probabilistic decision-making model” (Fontini 2009, p. 324).

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variable. For the independent variable in a mental construction of this kind, time is a misnomer . . . The solution to the differential equation, if it can be found, is complete in an instantaneous and timeless sense.

As Harcourt (1981, p. 144) observes, in Shackle’s world “it is better to be vaguely right than precisely wrong!”

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CHAPTER 2

History of Equity Securities 2.1

2.2

2.3

Early History of Equity Security Markets 2.1.1 Origins of Joint Stock Companies . . . . . . . . . . 2.1.2 Early European Writers . . . . . . . . . . . . . . . 2.1.3 Manias, Manipulations, and Institutional Failure . Developments to Graham and Dodd (1934) 2.2.1 Reminiscences of the Stock Operators . . . . . . . 2.2.2 Origins of Equity Indexing . . . . . . . . . . . . . 2.2.3 Charles Dow and the Dow Indexes . . . . . . . . . 2.2.4 Irving Fisher, Stock Valuation, and the 1929 Crash Derivative Security Renaissance 2.3.1 Evolution of Stockjobbing . . . . . . . . . . . . . . 2.3.2 The History of Programmed Trading . . . . . . . . 2.3.3 Equity Fund Hodgepodge . . . . . . . . . . . . . .

. 98 . 119 . 127 . . . .

145 156 159 176

. 186 . 206 . 227

. . . the More Things Stay the Same “Directly and indirectly banks and big commercial houses were involved. In a crash, many of them would be ruined, and their bankruptcies would shatter the Paris money market and extend themselves as though by chain reaction to all the provincial centers, paralyzing business, and unleashing the social and political reactions. The minister Calonne, who directed royal finance during 1783–1787, understood the danger and feared it, not only for its political implications but also because any serious contraction of private capital would narrow the market for the annual loans on which his budgets depended. He therefore entered the market with treasury funds and tried to shore up prices by buying falling issues. At heavy cost, he liquidated private speculative contracts which, by their volume, threatened to bring on a general collapse. Scandals broke out. They were publicized. Nobles, clergymen, and even ministers figured in them. Rightly or wrongly the belief spread that the government was permitting irresponsible men to endanger the public prosperity, and the ill-fated ministerial interventions in the Bourse undermined confidence in the government, sapped its prestige, and, like the failures in finance and foreign policy, helped create a demand for a representative regime”. Taylor (1962, p. 951) describing activities on the Paris Bourse approaching the eve of the French Revolution. Substitution of New York for Paris and Paulson for Calonne makes for an eerie connection with the events of 2008–2009. 97

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Early History of Equity Security Markets Origins of Joint Stock Companies

Equity Shares in Antiquity The study of commercial life in antiquity is hampered by the limited and fragmented evidence available. Business activities during, say, the Middle Ages or following the introduction of the printing press in the 15th century, are captured in a substantial number of merchant archives, toll registers, company records, price courants, and the like that have survived. In contrast, information about Roman, Greek, Egyptian, Persian, Sumerian, and other ancient civilizations only survives in a relatively small number of sources. While archaeology has been able to fill in selected gaps, “the general inadequacies of the evidence accentuate the role of conceptualization in historical research” (Bang 2008, p. 3). The sources that are available deal with only a small slice of ancient history and cannot provide enough detail to construct an accurate historical record. Such sources typically deal only with a particular activity, e.g., classical literature or law, leaving no trace of many aspects of ancient life. Careful examination and scrutiny of available sources have to be supplemented by ‘artful’ interpretation. “Sources are . . . not self-explanatory. They must be interpreted to bring us to the ancient reality” (Ibid.). The problem of determining a value for equity claims in a business venture stretches back to the origins of capitalism in ancient societies. At least since Weber (1891), the peculiar characteristics of ancient capitalism have been recognized and explored. Due to the relative abundance of primary sources, the ‘political capitalism’ (Love 1991) of the Roman Empire has received the most attention, though the Greek city states appear to have had a more developed capitalist system than the Romans. Unfortunately, the records from Greek times often reflect the attitude of Aristotle (Politics, Book I, ch. 11, sec. 5) where discussing “the various forms of acquisition . . . minutely and in detail might be useful for practical purposes; but to dwell long upon them would be in poor taste”. Primary sources from even earlier times, such as the Sumerian cuneiform tablets and the Code of Hammurabi (circa 1780 BC), only provide hints about the contractual arrangements governing equity claims. However, the historical record is sufficient enough to indicate the relevance of such contractual relationships in those areas of ancient commerce where the pooling of capital resources was integral to the success of a business venture.

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Financing of commercial ventures in ancient markets often involved a bundled combination of equity and debt financing with allowance for insurance considerations. For example, the Code of Hammurabi states: “If a merchant lent money to a trader for benefit, and he saw a loss where he went, he shall pay back the principal of the money to the merchant. If, when he went on the road, an enemy made him give up what he was carrying, the trader shall so affirm by God and then shall go free” (Lewin 2003, p. 16). Such arrangements where wealthy individuals finance trading ventures also appear with the bottomry or sea loans of the ancient Greeks where some actual interest rate estimates are available. Circa 350 BC, Demosthenes gives accounts of a cargo of a thousand wine casks to be transported in a large oared vessel. When interest rates for regular loans were 12–18% without insurance, an interest rate of 22 1/2% was charged on the sealoan with provision for a further increase to 30% if the return voyage was delayed (Ibid.). In other cases, one partner would provide financing for the trading venture while the other partner would do the work, with a predetermined sharing of the profits of the venture upon completion. However, the personal liability of the lender would no longer be limited to the amount on loan. Various rudimentary forms of partnerships were the mainstay of commerce in antiquity. Such arrangements laid the foundation for the societas of the medieval Italian city states that evolved into more flexible partnership arrangements, especially the commenda and compagnie forms, e.g., Poitras (2000). In contrast to the flexible and impersonal modern corporation, kinship and close personal relations were often an essential component of business relationships in ancient times, if only because partners were severally liable for debts of a venture and personal bankruptcy attracted severe sanction. Long distance trade required a network of loyal factors in important entrepot centers. Because profits would typically be divided by the partners at the end of an individual venture according to the arrangements made when the venture was initiated, only when capital was allowed to continue in the business did the valuation of equity claims become relevant. Valuation of equity shares required for sale and transfer, such as might occur during probate, was complicated by the need to have partners with kinship or close personal relationships. As such, the need for accurate equity valuation methods was limited, if only because commercial equity was not sufficiently separated from the household balance sheet. Given this background, the need to pool capital in ancient societies led to the development of partnership arrangements that had legal

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status independent of the individual partners. This significantly increased the potential tradeability of partnership shares. Recognizing that similar arrangements likely appeared in earlier times, the Roman societaes publicanorum evolved a form of public trading in shares. While playing a fundamental role in tax farming, i.e., bidding on contracts for collection of taxes in specific parts of the Empire, the publicani were also involved in contracts for the construction and repair of major public works, billeting and supplying of the armies, and the transport of bulk cargoes within the Empire.1 Beyond this, there is far from complete agreement among historians. By some accounts, e.g., Rostovtzeff (1957), around the time of Cicero and Julius Caesar, public trading in such shares was conducted at the Forum, in Rome near the temple of Castor. In 59 BC, Cicero provides a description of the trading in such shares (Love 1991, p. 190). The societas office or individuals already owners of shares were sources for obtaining shares. It was common practice to trade ‘unregistered’ shares where purchasers did not become a socii; both Caesar and Cassius were reported to do so, presumably to evade the political fallout in the Senate associated with the perception of self-dealing. Though the roots of the publicani stretch to the beginnings of the Roman civilization, the influence of the societaes publicanorum was greatest during the middle and late stages of the Republic. Around 150 BC, the Greek historian Polybius recounted the following (Chancellor 1999, p. 5) in Rise of the Roman Empire: All over Italy an immense number of contracts, far too numerous to specify, are awarded by the censors for the construction and repair of public buildings, and besides for the collection of revenues from navigable rivers, harbours, gardens, mines, lands — in a word every transaction which comes under the control of the Roman government is farmed out to contractors. All these activities are carried on by the people, and 1 Because aggregate production was primarily agrarian, the bulk goods trade was important in ancient markets. While the movement of higher value goods by land was the basis of the caravan travel, waterborne transport was the mainstay for moving grain, pottery, wine, oil and other bulky commodities needed to sustain urban centers. Even as late as the Roman Empire, “the huge number of grain ships bringing supplies from Egypt and Africa to Rome have left hardly any trace in the archaeological record”. As such, the organization of this trade could have been closer to the bottomry loans common in seaborne trade of the Greeks. However, a surviving document from the second century AD, the Muziris Papyrus (Rathbone 2003), provides evidence of political capitalism dominating such trade. This interpretation is consistent with the need to have political influence to ease the burden of onerous customs duties and other charges that were common in the Roman Empire, especially after the collapse of the Republic.

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there is scarcely a soul, one might say, who does not have some interest in these contracts and the profits which are derived from them.

A Greek aristocrat held as hostage for 16 years in Rome, Polybius examined the growth of the Roman Empire with the aim of aiding Greeks to understand how Rome managed to rise to dominate the region. The subsequent growth in the Roman Empire led to evolution in the publicani. By the middle of the first century BC, immense tax farming opportunities were available at auction, primarily five year contracts for tax collection in Asia. Arguing for state support of the often abusive tax collection practices of the publicani Cicero observed: “financial confidence and the whole monetary system based on the forum here at Rome is bound up with and depends upon these Asian investments” (Love 1991, p. 188). In 61 BC, when the publicani significantly over bid for the Asian tax farming contract, Cicero argued successfully in the Senate for releasing the publicani from this contractual obligation (Fig. 2.1). While it is tempting to trace the origins of equity security trading to the societaes publicanorum, the historical record is insufficient to sustain such a claim. There is no specific evidence concerning either pricing or trading practices. It is known that the publicani had some elements of modern corporations, with ownership divided into shares (partes) with operational

Fig. 2.1

Marcus Tullius Cicero (106BC–43BC)

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control by magistri that constituted a board of directors headed by the manceps, e.g., Badian (1972). However, Roman law was focused on the individual and had difficulties recognizing rights and duties for associations of individuals. Following Gierke (1977, pp. 100, 101), the publicani were able to attain the appearance of continuous legal status that extended beyond the period for a particular contract because of the connection with Roman financial administration. In effect, the publicani “may be considered as vocational corporations but not as bodies derived from private law. Rather they appeared as political bodies that included social relationships of private law”. Legally, contracts were entered into with the manceps not with the societas. The specific listing of socii on contracts was only relevant to determining the collateral required to ensure fulfillment of the contract.2 2 Much more could be said about the extent of trading in publicani equity claims than is possible here. Further discussion requires considerably more background on the rigid, wealth determined Roman social structure. As Duncan-Jones (1982, p. 2) observes: “The Roman state was firmly oligarchic and timocratic. The ownership of wealth was the essential prerequisite for all the high statuses of public life . . . Entry to the Senate, the body of knights (equines), the judiciary, and the local town council was in each case controlled by a property qualification . . . The formal structure of civilian wealth qualifications represented ratios of 1:2:4:12 . . . the senator [must have] three times the wealth of the knight”. It was the equines that dominated the publicani. Recognizing that the equines roughly corresponded to the officer class, throughout Roman history building activity by the standing army during times of peace was commonplace. The publicani provided an expedient method of organizing such activities and compensating those involved. The organizational skills of past and present army officers was also well suited to the control and direction of large numbers of slaves involved in public works projects. Though much of the collection of tax farming revenues was done by local officials, the equines were well suited to managing any fallout from the often aggressive methods used by local tax collectors. If senators such as Caesar and Cassius traded unregistered shares this was likely done for political reasons and not for the possible income to be received. As such, the equity valuation involved is political and is not related to the modern equity valuation problem. Available evidence indicates that the wealth of senators was based on income from large landed agricultural estates with income from loans or ‘usury’ of not more than 5–10% (Duncan-Jones 1982, pp. 17–32). Recognizing the substantial difficulties with trading registered shares, it is likely that the Forum was used as a meeting place for those equines and possibly a senator or two seeking to trade unregistered shares. However, it is inaccurate to depict such trading as “an immense stock exchange where monetary speculation of every kind was going on” (Cunningham 1913, p. 164). It is even exaggeration to claim: “crowds of men bought and sold shares and bonds of tax-farming companies, various goods for cash and on credit, farms and estates in Italy and in the provinces, houses and shops in Rome and elsewhere, ships and storehouses, slaves and cattle” (Rostovtzeff 1957, p. 31). Following Chancellor (1999, p. 4), the Roman comic playright Plautus was probably more accurate in describing the Forum as a collection of “whores, shopkeepers, moneylenders, and wealthy men”. The observation by Polybius about the widespread use of publicani contracting in Roman society is only consistent

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Share Trading in 17th Century Amsterdam Though shares in joint stock companies are only precursors of modern common shares, the associated equity valuation problem has many similar features. The joint stock form of ownership evolved somewhat slowly from earlier forms of business organization. Most of the early joint stock companies retained some of the essential features of partnerships. Hecksher (1955, p. 392) makes an important distinction between partnerships and joint stock companies by referring to the latter as “capital associations of a corporative character”. As such, the early joint stock companies were an alternative form of business organization to the regulated companies which had a business structure evolved along the lines of the medieval guilds. The grant of monopoly for trade to a specific region required the corporative character of regulated companies. However, the capital was held by the individual member partners and not held jointly. While this worked effectively for trade that was relatively predictable, the hazards of long distance trade to areas little known eventually required the resources of capital associations to make sufficient investments in infrastructure. The regulated companies were associations of independent traders and merchants, each with their own independent capital, operating under a grant of monopoly in a specific type of trade. The Fellowship of Merchant Adventurers’ is an important example of a 16th century English regulated company with a loose monopoly over activities of English merchants trading on the Continent, e.g., de Roover (1949). In contrast, joint stock companies combined the capital contributions of shareholders. There was permanence in the stock capital independent of the individual shareholders. Equally as important, the joint stock company was subject to the control of a single management. Given this, a key legal difference between joint stock companies and modern publicly traded corporations involves limited liability, e.g., Shannon (1931), Bryer (1997), and Acheson and Turner (2008). It was not until the second half of the 19th century when legislative changes permitted limited liability to become commonplace in most countries. Prior to this time, limited liability required a special charter from the state. However, as Heckscher (1955, pp. 367, 368) observes: “From the economic standpoint, the chief interest of limited liability is ... whether it contributed to the idea of independent company capital”.

with an efficient oligarchic contracting method for determining compensation for the construction of public works and the collection of taxes.

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In addition to limited liability, joint stock companies had other differences from modern corporations. As late as the 18th century, transferability of joint stock shares was restricted in various ways. For example, there was a formal process requiring approval and registration of new shareholders in the record books of the company which required in-person attendance at the company transfer office. In addition, many of the earliest joint stock companies were involved in long-distance trade, with paid-in capital being dispersed together with any profits after the completion of a voyage. Sometime profits were distributed in the form of goods such as spice. Increases in capital were usually achieved by making calls on existing shareholders, rather than issuing new shares. It was during the 17th century that joint stock companies with modern features started to emerge (Davies 1952; Parker 1974; Carlos et al. 1998; Gelderblom and Jonker 2005). Starting with the creation of the Dutch East India Company (VOC) in 1602, significantly more modern joint stock companies emerged that included more readily transferred shares, a permanent capital stock, profits-only distributed as dividends and new equity capital requirements being raised by making additional issues of stock. Legal characteristics of the evolving joint stock companies gave impetus to the trading of equity securities on exchanges. Trading venues where a range of commodity and financial items are exchanged have a history stretching back to antiquity, as evidenced in the Forum trading in ancient Rome. From ancient times, such trading venues featured a considerable amount of foreign exchange trading. Recognizing the widespread use of variations on the bill of exchange, foreign exchange transactions were tied to the extension of trade credit. For both foreign and local merchants, such trading venues were ‘one-stop shops’ for financing and purchase of goods to be transported to a distant trading venue where the goods would be sold and the financing paid off. Prior to the evolution of exchanges dedicated exclusively to the trading of shares in the late 18th and early 19th centuries, shares in joint stock companies were traded along side other items. The collapse of Antwerp in 1585 destroyed the most important exchange of the 16th century. The resulting diaspora of important merchants contributed substantially to the rise of the important exchanges in Amsterdam and, to a lesser extent, in other centers such as London, where the Royal Exchange was established by Thomas Gresham in 1571 modeled after the Antwerp Exchange. Circa 1602, the Amsterdam Exchange was held in the open air on the New Bridge. It was not until 1613 that trading completely moved to the

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new building dedicated for the Amsterdam exchange. Trading in shares was only a small portion of the general activity on the Amsterdam Exchange, which was predominately in bills of exchange and commodities. By the beginning of the 17th century, it was apparent that trading in Amsterdam had become the successor to the Antwerp exchange that had fallen on hard times due to a combination of political, geographic and economic factors. In conjunction with the shift in trading activity, many of the traders also eventually relocated from Antwerp to Amsterdam and brought with them the forward contract and option contract trading techniques that had been successfully developed on the Antwerp exchange. Because these techniques facilitated speculative trading for future delivery, such derivative security trading was applied, almost immediately, to trading in Company shares. While Amsterdam had developed as an important commercial center prior to 1585 (van Dillen 1927; Gelderblom and Jonker 2005), the establishment of a permanent building for the Amsterdam exchange in 1611 marks a symbolic beginning of Dutch commercial supremacy. During the 17th and 18th centuries, trading of joint stock shares on the Amsterdam exchange exhibited many essential features of exchange trading in modern equity security markets. As early as the middle of the 17th century, trading on the Amsterdam exchange featured derivative securities for shares in the Dutch East Indies Company (VOC) and, to a lesser extent, the Dutch West Indies Company. This trade progressed to where contracts with regular expiration dates were traded and settled by payment of differences (Wilson 1941; Poitras 2009).3 By the beginning of the 18th century, the trade involved both Dutch joint stock shares and ‘British funds’. “With the appearance of marketable British securities, and the application to them of a speculative technique that was already well understood, the Amsterdam bourse became the scene of international finance at its most abstract and most exciting — gambling in foreign securities” (Wilson 1941, p. 79) (Fig. 2.2). Despite isolated instances of joint stock trading in other centres, the market for trade in VOC shares started in Amsterdam from the founding of the Company by the States General in 1602.4 Creation of the Company led to a call for initial subscriptions of capital. Prospects for the Company 3 The acronym VOC is a reference to the English to Dutch translation of the Dutch East India Company, as the Verenigde Oostindische Compagnie. 4 In addition to share trading in Amsterdam, van Dillen et al. (2006) makes reference to trading in shares also occurring in Hamburg, Frankfurt, Middleburg, Cologne, Rouen and in other locations. However, there is no evidence that this trade was anything other than small, occasional and generally unorganized (Barbour 1950, p. 76).

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Fig. 2.2

Amsterdam Exchange (1653) by Emanuel de Witte (1617–1692)

were generally perceived to be favorable among the moneyed individuals willing to invest in such a venture and the closing of the Dutch East India Company subscription lists found numerous individuals still desiring shares. These individuals turned to the Amsterdam exchange to purchase shares and, when this could not be done at par, a 14–16% premium emerged within a number of days (Ehrenberg 1928, p. 358).5 With such immediate returns, the potential for gain became apparent to exchange traders and the speculative trade in shares began in earnest with the selling of shares for deferred delivery not owned at the time of the sale. Given the difficulties associated with share transfer and a limited supply of shares available for trade, dealing for time instead of cash was fundamental to these early equity markets.

5 As shares were issued by specific chambers, trading was confined almost exclusively to those issued by the Amsterdam chamber. Even at later dates where trading in shares of other chambers emerged, shares of the Amsterdam chamber still demanded a substantial premium, for example, Barbour (1950, p. 77).

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Kellenbenz (1957, pp. 139–142) provides a useful summary the various types of transactions in the Amsterdam market during the second half of the 17th century:6 a. There were sales of real stock against immediate payment of cash. b. There were comparable sales where the money to cover payments was borrowed from individuals, up to four-fifths of its value. c. There were transactions in which future settlement dates were specified — that is, beyond the regular monthly settlement dates. These future contracts were seemingly used for both speculative and hedging purposes, both by speculators and by the lenders on securities. De la Vega implies that the latter parties always hedged by means of such contracts. Hypothecation, which was mentioned as early as 1610 (in the edict of that year), was permitted to the seller presumably during the period of the forward contract. Arrangements also were possible, and were fairly frequently resorted to whereby the date of the termination of a future contract could be postponed, apparently by mutual consent of the parties. This action was called ‘prolongation’. A large proportion of the foregoing future sales were really sales ‘in blanco’ — or short sales, as we would label them — even though such transactions were prohibited by laws of the state and of the city. d. There were options contracts. These were at least of the ‘call’ and ‘put’ varieties, which have persisted ever since . . . Option contracts were utilized sometimes for hedging purposes by bona fide investors, but more commonly for mere speculation . . . . Trading for future delivery was essential to the 17th century market for shares on the Amsterdam exchange (Barbour 1950).7 Such trading was 6 Kellenbenz also observes: “In addition there were purchases and sales of ‘ducaton’ shares. (Such transactions were of recent origin in 1688, and actually had been abandoned in the slump that had occurred . . . ) What this ‘ducaton’ trading amounted to is a bit uncertain . . . Scholars who have worked on this period assert that the ducaton shares were fictitious . . . ”. 7 The primary documentation associated with the Dutch Edict of 1610, which removed legal protection for ‘windhandel’ contracts, contains an important memoir, probably written by Isaac le Maire, which outlines arguments in favour of retaining short sales (van Dillen 1930; De Marchi and Harrison 1994). A number of arguments draw on the similarity of the trade in shares to the trade in goods: “the authors proceed from free trade in goods (perfectly conventional from a common weal point of view), move on to the freedom to make forward purchases of commodities (accepted practice for at least several decades), and end with the freedom to trade in shares. This bundling, as well as the progression itself, may have been intended to persuade the reader that (all) share

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necessary because the delivery and settlement process for traded shares was substantively different than the modern process. Though shares could be transferred, the process required the seller to be present at the Company offices for the transfer and to pay a transfer fee. The practice of same day settlement, delivery and transfer, as practiced in modern stock markets, was not usually possible. Origins of Stock Trading in London Chronological neatness suggests dating the commencement of stock trading in London with the ascendency of William III of Orange in 1688.8 This date is also intuitively appealing as William III was accompanied by an influx of Dutch persons and practices. However, prior to 1688 London was already trading government securities, including Exchequer bills and navy bills. In addition, there was some limited trading in the stock and debt of joint stock companies, in particular the East India Company, Royal African Company, and the Hudson’s Bay Company (Cope 1978, p. 2; Carlos et al. 1998; Michie 1999, ch. 1). Still, despite the development of highly sophisticated joint stock trading in Amsterdam by the mid-17th century, dealing in joint stocks and shares in London was ‘haphazard and unorganized’ before 1680, with a ‘highly developed market’, complete with trading in options and time bargains, only in evidence by the early to mid 1690s (Houghton 1694; Morgan and Thomas 1962, p. 21). A number of key factors contributed to the rapid development of English stock trading starting around 1690. One factor was the supply of joint stock issues. Just prior to this date a number of new joint stock companies had been created in areas such as fire insurance, paper making and street lighting. Combined with the established joint stock companies such as the East India Company and the Hudson’s Bay Company, circa 1688, there were about ‘15 joint stock companies . . . enjoying an active life’ (Morgan and Thomas 1962, p. 22). In addition, the political reforms associated with the Glorious Revolution permitted the commencement of the financial revolution in English government debt issues. Fueled by a ‘sudden surge’ in patenting (MacLeod 1986, p. 149), the period from 1688 to 1695 witnessed an explosion in new joint stock issues, in both shares and bonds, and in the trading practices should unquestionably be regarded as no different in principle from trade in goods” (De Marchi and Harrison 1994, p. 55). 8 For example, Dickson (1967) identifies the Revolution of 1688 as a defining event for London stock trading.

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supply of government debt. Included in these promotions was the particularly significant initial subscription for the Bank of England in 1694. Scott (1910) estimates by 1695 that there were no less than 140 joint stock companies. Clapham (1958) makes reference to “more than one hundred fifty companies, two-thirds English and one-third Scottish, [that] started lives most of which were brief and unfortunate” during the stock promoting boom of 1690–1695. Of all these issues, the Bank of England was the giant. The deal leading to the creation of the Bank had elements of the fantastic. The original plan has been attributed to the Scottish projector William Paterson, though “whether he was strictly the originator, or merely the mouthpiece of a City group, we cannot be quite sure”. In any event, the government was anxious to obtain large amounts of funds to sustain the 1690–1697 war of the Grand Alliance against France and, in exchange for £1.2 million, Parliament granted a charter to a joint stock bank with an effective monopoly on the note issue. The creation of some type of public bank in England by the end of the 17th century was expected. In the preceding century, various jurisdictions had evolved different forms of public banks. The Bank of Amsterdam, founded in 1609, played a key role in the settlement and transfer of funds. The Bank of Hamburg, an imitation of the Bank of Amsterdam, was founded in 1619 with the Bank of Sweden following in 1656. “On the coasts of the Mediterranean, the North Sea, the Baltic, English merchants of the seventeenth century came into touch with public banks: the influence of these merchants on government was on the increase and so were the public banks” (Clapham 1958, p. 3). Yet, the Bank of England was to be considerably more than a public bank of the 17th century. The Bank became the model ‘public bank’ of the 18th century. The Bank of England was novel in that it combined the notions of joint stock ownership and bank of issue. As the right to provide the circulating medium had historically been the preserve of the crown, it took a particular set of circumstances, combined with the loan of a considerable amount of cash to the government, to consummate the deal. Recognizing that payment by installment was common practice in the purchase of public offerings of both shares and government debt, the original Act of 1694 authorizing creation of the Bank provided for a maximum authorized borrowing of £1.5 million with payment of £1.2 million by January 1695.9 In order for 9 Shea (2007a) examines the pricing relationship between subscription shares and fully paid shares. Payment by installment was common practice, as was trading for future

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corporate privileges to be conferred, at least half of the subscription amount of £1.2 million had to be paid by the beginning of August 1694. This condition proved to be overly pessimistic. Within twelve days of the June 1694 subscription announcement date, the full amount had been subscribed (with 25% of the price paid up front). From the government’s perspective, the deal with the Bank of England involved a fully funded loan from the subscribers of the Bank. Derived from taxes on ship tonnage and duties on liquor the government undertook the obligation to pay 8% on the bulk of the £1.2 million. These regular debt payments contributed substantially to the success of the Bank subscriptions, compared to alternatives that were available in the security market (Clapham 1958, pp. 19–21): Water companies, most of them quite sound; treasure seeking companies, highly speculative; paper, linen, lead, copper, plate glass, bottle glass and mining companies; The Society for improving Native Manufacture so as to keep out the Wet, and the Company for the Sucking-Worm Engines of John Loftingh, merchant, at Bow Church Yard, Cheapside — a suckingworm engine was a fire hose — had all been projected and supported less or more. Among these, the Bank with its parliamentary backing, its high sounding name, and its guaranteed income from the taxes was a very attractive proposition.

However, though the potential stability of dividend payments on Bank of England stock was attractive to some investors, for the prime movers in the deal the main objective was the gains to be obtained from the banking business. Prior to 1696–1697, there were two venues for London stock trading, the Royal Exchange and Exchange Alley (Fig. 2.3). In the Royal Exchange dealers in stocks and shares “had a ‘walk’ near the centre of the building between the salters, the Italian merchants and the Canary merchants” (Morgan and Thomas 1962). However, due at least partly to abuses arising from the 1696 price collapse of various joint stock promotions, stock traders left the Royal Exchange, conducting business after that date in the environs of Exchange Alley. “There is a certain amount of mystery about [the stock dealers] withdrawal [from the Royal Exchange]. Scott refers to their being delivery. For example, a contract for the purchase of shares or government debt could be structured as a time bargain, with delivery in, say, a month and payment by installment from that date. Buyer and seller would then agree as to the appropriate deposit when the contract was created. The potential for speculative trading and stockjobbing is apparent.

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The Royal Exchange, London (1751) by Thomas Bowles (1712–1753).

turned out, whereas Duguid insists that they were so harassed by their fellow traders, and so short of space that they went voluntarily and in spite of the efforts of the City to prevent them” (Morgan and Thomas 1962, p. 27). Until 1773, when a group of brokers acquired a building in Threadneedle Street that was, for the first time, called the Stock Exchange, the history of London stock trading was intimately connected to Exchange Alley. Geographically, Exchange Alley is located across Cornhill Street from the Royal Exchange. Starting at Cornhill the Alley runs to Lombard Street (see Poitras 2000, Fig. 8.2 for a map). The Alley contained various coffeeshops that were the focus of stock trading. Circa 1696, the chief coffeehouses for stock trading were Jonathan’s and Garraway’s, though Sam’s Coffee House in the Alley and Powell’s and the Rainbow in Cornhill were also of some importance (Cope 1978): Jonathan’s was founded about 1680 by Jonathan Miles, and was from the start connected with financial business. The Garraways were a City family of the period, who were landlords of the Sun Fire Office in its early days. The coffee-house was started by Thomas Garraway in the early 1670s. The trend to financial specialization, using coffee-houses as a place of business, is typical of the period: other examples are Edward Lloyd’s Coffee House, a centre for marine insurance, and Tom’s and

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Causey’s Coffee House, used in their early days by the Hand in Hand Fire Office and the Sun Fire Office. Jonathan’s as a centre for dealers gradually superseded Garraway’s (which was concentrating on auction sales by the 1750s), and developed lineally into the Stock Exchange of 1772.

While there was apparently considerable, and almost certainly disreputable, ‘curb trading’ in Exchange Alley, various City orders, such as those of 1700 and 1703, were aimed at eliminating this type of trading. Following the Glorious Revolution of 1688, many of the speculative practices used in Amsterdam were adopted in England. However, if only for the large number of joint stocks on offer, this trade took a substantively different form than in Amsterdam. Despite the presence of initial trading at the Royal Exchange, the development of share trading was hampered in England by a combination of factors. Houghton’s 1694 contributions to his circular A Collection for the Improvement of Husbandry and Trade can be fairly recognized as containing possibly the first coherent and balanced description of early stock trading in London, e.g., Neal (1990, p. 17), though the description provided by Houghton is so brief that Cope (1978, p. 4) credits Mortimer (1761) with being the ‘first detailed description of the market’. In addition to providing a description of stock trading for ‘ready money’, the bulk of the contribution by Houghton is on the specific subject of options trading. For seven weeks in June and July 1694, Houghton dedicated the first page of his circular to discussing various aspects of stock trading. About 2 1/2 of the seven weeks are dedicated to trading in ‘puts and refusals’. On 22 June 1694, Houghton provides the following discussion of the process for cash trading of shares at that time: The manner of managing the Trade is this: The Monied Man goes among the Brokers, (which are chiefly upon the Exchange, and at Jonathan’s Coffee House, sometimes at Garaway’s and at some other Coffee Houses) and asks how Stocks go? And upon Information, bids the Broker buy or sell so many Shares of such and such Stocks if he can, at such and such Prizes. Then he tries what he can do among those that have stock, or power to sell them; and if he can, makes a Bargain.

From this brief description, it is apparent that the process of procuring and transferring shares could be complicated. Lags in the share trade and transfer process were associated with not finding sufficient shares available for sale or an absence of ‘monied men’ willing to purchase shares at a fair

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price. This led to the widespread use of derivative securities, both ‘time bargains’ and options, to provide sufficient liquidity to clear the market. Until well into the 18th century, London share trading was impacted significantly by Dutch investors and speculators conducting a considerable amount of their British securities trading outside the Amsterdam exchange at various locations in London. By construction, such trades took time to complete — if only for the time needed to draw bills of exchange between Amsterdam and London. Trading in both ‘time bargains’ and option contracts was widespread.10 These activities were the main components of the ‘stockjobbing’ associated with the trading of securities for future delivery. Following Mortimer (1761, p. 32):11 the mischief of it is, that under this sanction of selling and buying the funds for time for foreigners — Brokers and others, buy and sell for themselves, without having any interest in the funds they sell, or any cash to pay for what they buy, nay even without any design to transfer, or accept, the funds they sell or buy for time. The business thus transacted, has been declared illegal by several acts of parliament, and this is the principal branch of STOCK-JOBBING.

While the liquidity enhancing element of stockjobbing was a needed activity in the context of equity trading at that time, the ultimate result of such trading is reflected in the history of stockjobbing in England which was met with considerable and generally disapproving interest in Parliament and attracted the venomous attacks from numerous writers of the time, such as Daniel Defoe and Jonathan Swift.

10 There was variable use of the terms to describe derivative security contracts. ‘Time dealings’ was used to refer to both forward and option contracts. Though ‘time bargain’ was occasionally used to refer to all types of time dealings, de la Vega and others use ‘time bargain’ to refer only to forward contracts. In the terminology of the time, a time bargain was a usually a long dated, transferable to arrive contract that did not involve the expectation of delivery. 11 Mortimert makes no reference to the use of options in stockjobbing activities, giving some support to the position that Barnard’s Act of 1733 was effective in deterring this activity. In contrast to Mortimer, another early source — Defoe (1719) — makes no reference to forward trading, using examples which usually relate to cash transactions, for example, using false rumours to influence the stock price, the idea being to buy low on negative rumours and selling high on positive rumours (pp. 139, 140). However, it is not clear that Defoe had the best grasp of the financial transactions which were being done.

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Types of deals in Early English Stock Trading: A deal for ‘ready money’ or ‘money’: a transaction for immediate delivery, to be settled within no less than two days. Also called a deal for cash. A deal for ‘time’: a transaction for future settlement, effectively a forward contract in the security. Where a rescontre settlement system was in place, the transaction would typically have the next rescontre as the settlement date. When used generally, could also include reference to puts and refusals. Heavy horse and light horse: Subscriptions to government debt issues could be paid by instalment, with the first deposit generally being 15% (Mortimer 1761, p. 137), with further payments of 10% or 15% being required each month until the balance was paid. The full amount of the subscription could be paid in advance, with credit being given for the associated interest. During the period in which subscriptions were being paid, secondary market trading had to account for the unpaid balances on a specific security. Heavy horse referred to a security which was fully paid, while light horse had a balance remaining to be paid. Stockjobbers preferred to deal in the light horse, which required a smaller invested capital for the same notional principal, “they have an opportunity for sporting with, and gaining profit on, a nominal thousand, for the same money, that it would cost to buy a hundred, heavy” (Mortimer 1761, p. 138).

A number of attempts were made to regulate stockjobbing, starting in 1697 with an Act ‘To Restrain the number and ill Practice of Brokers and Stockjobbers’.12 In addition to restricting the number of practices of commodity brokers, this Act was designed to deal with three main difficulties associated with the trade in shares: unscrupulous promotion activities; manipulation of prices for shares; and, misuse of options. The pressures to further regulate stockjobbers intensified leading to the Bubble Act of 1720 and, following the South Sea Bubble, to the passage of ‘An Act to prevent the infamous Practice of Stock-jobbing’ in 1733, also known as Barnard’s Act. While this Act contained substantial penalties for speculative trading in options, the primary contractual vehicle for speculators, the Act was quite ineffective in eliminating this trade. However, Barnard’s Act was 12 A

broker in this period was an intermediary or mutual agent who served as a witness, for a commission, to contracts between two parties. In London, legal brokers had to be licensed and sworn. While much of the commodity and joint stock business was conducted through brokers, dealing was not confined to sworn brokers and, at various times, many unlicensed dealers operated in the market.

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successful in removing legal protection for these transactions, making the broker a principal in speculative transactions, responsible for completion of transaction in the event of default by a client. In turn, this led to the increased use of ‘dealing on margins’ as a method of speculation and the subsequent introduction of the London rescounters.13 The increased need for honesty and integrity in the settlement process was a significant factor leading a loose knit group of brokers to form the London Stock Exchange where access by the general public could be restricted. That speculating in shares using option contracts was present from the beginnings of London share trading in the 1690’s is evident from the discussion in Houghton (1694): Another time he asks what they will have for Refuse of so many Shares: That is, How many Guinea’s a Share he shall give for liberty to Accept or Refuse such Shares, at such a price, at any time within Six Months, or other time they shall agree for. For Instance; When India Shares are at Seventy Five, some will give Three Guinea’s a Share, Action, or Hundred Pound, down for Refuse at Seventy Five, any time within Three Months, by which means the Accepter of the Guinea’s, if they be not called for in that time, has his Share in his own Hand for his Security; and the Three Guinea’s, which is after the rate of Twelve Guinea’s profit in a year for Seventy Five Pound, which he could have sold at the Bargain making if he had pleased; and in consideration of this profit, he cannot without Hazard part with them the mean time, tho’ they shall fall lower, unless he will run the hazard of buying again at any rate if they should be demanded; by which many have been caught, and paid dear for, as you shall see afterwards: So that if Three months they stand at stay, he gets the Three Guinea’s, if they fall so much, he is as he was losing his Interest, and whatever they fall lower is loss to him. But if they happen to rise in that time Three Guinea’s, and the charge of Brokerage, Contract and Expence, then he that paid the Three Guinea’s demands the Share, pays the Seventy Five Pounds, and saves himself. If it rises but one or two Guinea’s, he secures so much, but whatever it rises to beyond what it cost him is Gain. So that in short, for a small hazard, he can have his chance for a very great Gain, and he will certainly know the utmost what his loss can be; and if by their rise he is encouraged to demand, he does not matter the farther advantage the Acceptor has, by having his Money sooner than Three Months to go to Market with again; so in plain English, one gives Three Guinea’s for

13 Rescounters

was the English terminology for the Dutch Rescontre.

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all the profits if they should rise, the other for Three Guinea’s runs the hazard of all the losses if they should fall.

This insightful description is quite remarkable in that Houghton was not an active participant in the market; Houghton was “not much concern’d in Stocks, and therefore (had) little occasion to Apologize for Trading therein”. As Houghton does not provide a discussion concerning speculation using ‘time bargains’, it is likely that many speculations were executed using option contracts. An important, but overlooked, feature of Houghton’s 1694 discussion appears in the contributions of June 29 and July 6 where samples of put and call option contracts are given in detail, e.g., Poitras (2000, pp. 350, 351). The use of standard contracts indicates that practices common in Amsterdam were adopted in London. As de la Vega observes for Amsterdam trade: For . . . time bargains the brokers use printed contract forms with the customary stipulations and conditions of the business. On these forms spaces are left only for names, dates, and prices . . . For the option business there exists another sort of contract form, from which it is evident when and where the premium was paid and of what kind are the signatories’ obligations.

With standardized forms and rescontre clearing, brokers were the vehicles for executing trades. As to the types of brokers, practices similar to those in Amsterdam appear to have been adopted in London. On practices in Amsterdam, de la Vega (p. 185) reports: There are two kinds of brokers. Some are appointed by the municipal authorities and are called “sworn” brokers, for they take an order to do business on their own account. Their number is limited, and it changes only in the case of death, or through special privilege, which is seldom conferred. The other class of brokers is called “free” brokers . . . clemency and indulgence toward these brokers prevail, instead of the sworn brokers attending actively to their own interest.

Unlike Amsterdam where free brokers “appear so faithful and concerned about their customers that they compensate by zeal what they lack in reputation”, the derivative security trading activities of free brokers operating in the London share market almost immediately involved some unscrupulous activities. During the emergence of trade in free standing option contracts, the conventional legal view in both Holland and England was that, while

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technically a gambling transaction, such contracts could be entered into by private parties willing to conduct such business without the guarantee that the courts could be used to enforce such contracts. However, in periods of speculative excess, the abuse of derivative security contracts, in general, and option contracts, in particular, produced a subsequent demand for further regulation. As Houghton reports, the organized options market that had emerged in London during the 1690’s was a venue for market manipulation:14 But the great Mystery of all is, That some Rich Men will join together, and give money for REFUSE, or by Friendship, or some other way, strive to secure all the Shares in a Stock, and also give Guinea’s for Refuse of as many Shares more as Folk will sell, that have no Stock: and a great many such they are, that believe the Stock will not rise so high as the then Price, and Guinea’s receiv’d or they shall buy before it does rise, which they are mistaken in; and then such takers of Guinea’s for Refuse as have no Stock, must buy of the other that have so many Shares as they have taken Guinea’s for the Refuse of, at such Rates as they or their Friends will sell for; tho’ Ten or Twenty times the former Price.

In modern parlance, this is a classic example of a short squeeze being executed against uncovered call option writers. The Act of 1697 limited some of the potential abuses that were perpetrated with options, but did not eliminate such trading. This left forward trading as the favored vehicle for manipulating security prices, an undesirable outcome of the “villanous” practice of stockjobbing.15

14 The early history of options trading in England can be found in Morgan and Thomas (1962). An early discussion can be found in Duguid (1901). Barnard’s Act was repealed in 1860. 15 The abuses associated with stockjobbing were due, at least partly, to the standard market practice of a significant settlement lag for purchases of joint stock. While there was a cash market conducted, often at or near the company transfer office, dealing for time had a legitimate basis in the practical difficulties associated with executing a stock transfer. This meant that when stock was sold for time, the short position had a considerable lead time to deliver the security. Trading involved establishing a price for future delivery of stock and paying a small deposit against the future delivery. In cases where the selling broker did have possession of the underlying stock when the transaction was initiated, there was little or no speculative element in the time bargain. However, this was not the case when the seller did not possess the stock. In addition, the purchaser for time did not usually have to take possession of the stock at delivery but, rather, could settle the difference between the agreed selling price and the stock price on the delivery date.

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There was considerable disagreement in the London broker community about whether options transactions were reputable. While potentially useful in some trading contexts, reputable brokers felt that options contributed to the speculative excesses common in early financial markets. While trading in options and time bargains did contribute to the most important English financial collapse of the 18th century, the South Sea Bubble of 1720, this event was due more to the cash market manipulations of ‘John Blunt and his friends’ (Morgan and Thomas, ch. 2). In any event, dealing in time bargains and, especially, options were singled out as practices that were central to ‘the infamous practice of stock-jobbing’. In 1721, legislation aimed at preventing stockjobbing passed the Commons but was not able to pass the Lords. It was not until 1733 that Sir John Barnard was able to successfully introduce a bill under the title: ‘An Act to prevent the infamous Practice of Stock-jobbing’. This Act is generally referred to as Barnard’s Act. Unlike the Dutch regulatory actions aimed at in blanco selling, the British approach was designed to regulate those features of stock dealings associated with excessive speculation, e.g., Morgan and Thomas (1962, p. 62). The main provision of Barnard’s Act (1733) states: All contracts or agreements whatsoever by or between any person or persons whatsoever, upon which any premium or consideration in the nature of a premium shall be given or paid for liberty to put upon or deliver, receive, accept or refuse any public or joint stock, or other public securities whatsoever, or any part, share or interest therein, and also all wagers and contracts in the nature of wagers, and all contracts in the nature of puts or refusals, relating to the then present or future price or value of any stock or securities, as aforesaid, shall be null and void.

A penalty of £500 was levied on any person, including brokers, who undertook any such bargain. All bargains were to be ‘specifically performed and executed’, stock being actually delivered and cash ‘actually and really given and paid’, and with a £100 penalty for anyone settling a contract by paying or receiving differences. Consistent with the 17th century Dutch restrictions on in blanco selling, it was further provided: “whereas it is a frequent and mischievous practice for persons to sell and dispose of stocks and securities of which they are not possessed”; anyone doing so would incur a penalty of £500. There is disagreement among modern writers, such as Cope (1978) and Dickson (1967), concerning the extent to which Barnard’s Act actually limited options trading. That it had some impact is evident. However, the extent of the impact is less clear.

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Despite Barnard’s Act making options trading illegal, options trading continued to the point where, in 1820, a controversy over the trading of stock options nearly precipitated a split in the London Stock Exchange.16 A few members of the Exchange circulated a petition discouraging options trading. The petition passed, and members formally agreed to discourage options trading. However, when an 1823 committee of the Exchange followed up on this with a proposal to implement a rule forbidding Exchange members from dealing in options (which was already illegal under Barnard’s Act), a substantial number of members voted against. A dissident group even began raising funds for a new Exchange building. In the end, the trading ban rule was rejected because options trading was a significant source of profits for numerous Exchange members who did not want to see that business lost to outsiders. The upshot is that, once the derivative securities contracts became exchange traded by traders already subject to the discipline of the fortnightly clearing process for shares, this was sufficient to prevent the significant speculative abuses that had plagued the previous OTC trading of option contracts and time bargains.

2.1.2

Early European Writers

Joseph de la Vega The emergence and growth of joint stock trading was accompanied by considerable public discussion and debate which is captured in the pamphlet literature and Parliamentary records of the time. However, unlike the pricing theories for fixed income securities that were relatively well developed by the end of the 17th century, e.g., Poitras (2000, ch. 6); Lewin (2003), much of the analysis of joint stock companies was concerned with describing manipulative trading practices by stockjobbers and proposing remedies for the ‘infamous practice’, rather than with developing methods of equity security valuation. For example, Di Marchi and Harrison (1994) describe the 17th century Dutch pamphlet literature which attacked the practice of short selling securities that were not owned by the individual making the short sale. Against the polemical backdrop of the pamphlet literature can be found a number interesting anomalies that stand out as early classics of security analysis: Joseph de la Vega’s Confusion de Confusiones (1688) and Thomas Mortimer’s Everyman his own Broker (1761).

16 Cope

(1978) takes a somewhat different view of these events.

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To say that Confusion de Confusiones is an isolated gem in the history of Finance is an understatement. The book itself is an oddity, initially written in Spanish, published in Amsterdam by a Jewish writer of Portuguese descent. Joseph de la Vega was the second son in a family of four sons and six daughters. His parents were Isaac Penso and Esther de la Vega. Though his formal name was Joseph Penso de la Vega Passarinho, according to custom he typically used the shortened name derived from his mother. Isaac Penso was born in Spain though the family’s ancestral roots appear to have been in Portugal. As was the case with many Jews in 17th century Spain, the Inquisition produced a forced emigration and his parents moved first to Antwerp, then Hamburg and finally Amsterdam. Joseph was likely born sometime around 1650, soon after the family had relocated to northern Europe (Kellenbenz 1957; Cardoso 2006). Isaac Penso achieved success as a banker in Amsterdam and became a prominent member of the local community. Though Jews in Amsterdam were relatively unrestricted in comparison to almost all other cities, there were still considerable barriers to Jewish participation in various trades. However, Jews were permitted to engage in activities such as wholesale trading in goods, shipping and banking functions such as money lending and money changing. Some Jews were also permitted to engage in brokering. Not surprisingly, Jews were central players in the business of trading stocks. Anecdotal evidence indicates that as much as 85% of Amsterdam stock trading circa 1700 was in the hands of Jews, many of which were of Iberian descent (Kellenbenz 1957, p. 128). Based on this, de la Vega was in an excellent situation to gather the type of information needed to write a detailed account of stock trading on the 17th century Amsterdam bourse. Confusion de Confusiones is written as four dialogues between a shareholder, a philosopher and a merchant. Each dialogue describes different features of the activities of the Amsterdam bourse in the later 17th century. In Confusion, de la Vega (1688, p. 156) demonstrates a modern understanding of the use of fundamental information to value stocks: The price of shares (in the Dutch East India Company) is now 580 . . . it seems to me that they will climb to a much higher price due to extensive cargoes that are expected from India, because of the good business of the Company, of the reputation of its goods, of the prospective dividends and of the peace in Europe.

Recognizing the uncertainties in seaborne trade and the difficulty in obtaining information about incoming cargoes, de la Vega goes on to describe how some traders could profitably trade on information about incoming

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cargoes from the East. He correctly recognizes that such information alone is insufficient but would depend also on European conditions and the safe arrival and unloading of cargo. Modern equity security valuation often involves determining the discounted value of expected future cash flows. This reliance of the valuation problem on expectations is explicitly recognized by de la Vega (1688, p. 165), who gives a ‘buy on the rumor, sell on the news’ twist to this story: The expectation of an event creates a much deeper impression upon the exchange than the event itself. When large dividends or rich imports are expected, shares will rise in price; but if the expectation becomes a reality, the shares often fall; for the joy over the favourable development and the jubilation over a lucky chance have abated in the meantime.

Recognizing that there are ‘natural reasons for this phenomenon’, de la Vega attributes this share pricing behavior to a struggle between bulls and bears over market sentiment: “the leaves tremble in the softest breeze, and the smallest shadow causes fear”.17 In the second dialogue, de la Vega (pp. 158, 159) provides four useful rules to guide investment activities in shares: The first principle: . . . Never give anyone the advise to buy or sell shares . . . The second principle: Take every gain without showing remorse about missed profits . . . The third principle: Profits on the exchange are the treasure of goblins . . . The fourth principle: Whoever wishes to win in this game must have patience and money.

Variations of the second and third of these principles could easily pass as commonsense advice given to modern security traders. The fourth principle is evidence that de la Vega, an astute 17th century observer of stock trading, was an adherent to ‘long-run investment strategies’. Combining this fourth principle with de la Vega’s recognition of the importance of fundamental information anticipates the approach to equity security valuation pioneered by Benjamin Graham more than 250 years later. Even though de la Vega identifies how the price of joint stocks can be determined by fundamental information, much of his dialogue is taken up 17 De Marchi and Harrison (1994, p. 62) appear to claim that de la Vega proposed a model where stock prices were a random process, quoting de la Vega as saying: “shares are enveloped in a veil of almost religious mystery such that the more one reasons the less one grasps, and the more cunning one tries to be the more mistakes one makes”. The solution, according to de la Vega, is to trade randomly. Is it possible to claim de la Vega was a precursor of the random walk model of stock prices?

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in a description of how prices will deviate from fundamental values based on the expectations of bulls and bears. In particular, the last of the four dialogues is concerned with detailing methods of market manipulation: “the acme of Exchange operations, the craftiest and most complicated machinations which exist in the maze of the Exchange and which require the greatest possible cunning” (Confusion, p. 191).18 The manipulation of securities markets in the 17th and 18th centuries was facilitated by the social practice of using securities for purposes of gambling. This practice was in keeping with the widespread public acceptance of gambling reflected, for example, in the use of lotteries to increase the attractiveness of government debt operations (Cohen 1953; Daston 1988). In addition to a detailed examination of the methods of market manipulation, de la Vega also makes a number of references to derivative security trading practices for joint stock shares on the Amsterdam exchange. For example, there is a general description (Fridson 1996, p. 155) of the potential gains to options trading: “Give ‘opsies’ or premiums, and there will be only limited risk to you, while the gain may surpass all your imaginings and hopes”. This statement is followed by a somewhat exaggerated claim about the potential gains: “Even if you do not gain through ‘opsies’ the first time . . . continue to give the premiums for a later date, and it will rarely happen that you lose all your money before a propitious incident occurs that maintains the price for several years”. Presumably, de la Vega has call options trading in mind, the possibility of trading put options appears later (p. 156). The reference to extending contracts is further elaborated in de la Vega’s discussion of the rescontre system (p. 181), a major technical innovation in clearing trades that emerged between 1650–1688, when the Dutch introduced quarterly settlements of forward and option contracts for share transactions on the Amsterdam exchange. Prior to this time settlement procedures had been less formal. Wilson (1941, p. 83) provides the following description of the settlement process (p. 181): The technique of speculation in the British Funds at Amsterdam . . . was a kind of gamble carried on every three months: no payments were made except on rescontre (settlement or carry-over), i.e., the period for 18 De

la Vega recognizes that the motives of gamblers and speculators were often somewhat nefarious, and that the presence of manipulation makes accurate pricing a difficult exercise: “shares are enveloped in a veil of almost religious mystery such that the more one reasons the less one grasps, and the more cunning one tries to be the more mistakes one makes”, e.g., de Marchi and Harrison (1994, p. 62).

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which funds were bought or sold and for which options were given or taken. Rescontredag (contango day) occurred four times a year, and on these occasions representatives of the speculators gathered round a table to regulate or liquidate their transactions, and to make reciprocal payments for fluctuations or surpluses. Normally these fluctuations were settled without the actual value of the funds in question being paid — only real investors paid cash for their purchases. Speculative buyers paid to sellers the percentage by which the funds had fallen since the last contango day, or alternatively received from them the percentage by which funds had risen in the same interval. After surpluses had been paid, new continuations were undertaken for the following settlement. In such a prolongatie (continuation) the buyer granted the seller a certain percentage (a contango rate) to prolong his purchase to the next rescontre: in this way he stood the chance of benefiting by a rise in quotations in the interval, without tying up his capital: he was only bound to pay any possible marginal fall.

A key feature of the rescontre was the concentration of liquidity that, for example, permitted prolongations to be done more readily (van Dillen 1927; Dickson 1967, p. 491). The term ‘rescontre’ was derived from the practice of Dutch merchants to “indicate that a bill had been paid by charging it to a current account — ‘solvit per rescontre’ as distinct from ‘per banco’, ‘per wissel’, and so on” (Dickson 1967, p. 491; Mortimer, Everyman, 5th ed., p. 28n). In addition to the references to extension of the option expiration dates, with regular marking-to-market, de la Vega takes up the uncertain legal interpretation of option contracts at a later point (p. 183) and explicitly recognizes that the Dutch restriction on short sales could impact put and call options differently: As to whether the regulation (banning short sales) is applicable to option contracts, the opinions of experts diverge widely. I have not found any decision that might serve as a precedent, though there are many cases at law from which one [should be able to] draw a correct picture. All legal experts hold that the regulation is applicable to both the seller and buyer [of the contract]. In practice, however, the judges have often decided differently, always freeing the buyer from the liability while holding the seller [to the contract] . . . If . . . the opinion is correct that it applies only to the seller, the regulation will be of no use to me [as a person wanting to seek shelter] when I receive call premiums, for in this case I am in fact a seller; but it will help me if I have received a put premium, as I am then the buyer of stocks. With regard to the put premium... law and legal opinion, the regulation and the reasons for the decisions are contradictory. The theory remains uncertain, and one cannot tell which way the adjudication tends.

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The bulk of option trading participants appear to have been speculators, attracted primarily by the urge to gamble, usually “men of moderate wealth indulging in a little speculation” (Wilson 1941, p. 105). In contrast, drawing from de Pinto (1771), Wilson (p. 84) observes that for trading conducted on the Amsterdam exchange during the 18th century: “Options were the province of the out-and-out gamblers”.19 Thomas Mortimer In contrast to the almost voluminous discussion of the nefarious practice of stockjobbing, 18th century English publications dealing with the use of security analysis to value joint stocks are relatively scarce. The success of Every Man His Own Broker by Thomas Mortimer speaks to the lack of such a guide prior to this time. Originally published in 1761 with a further fourteen editions to follow, the last being in 1807, the book was intended as a practical guide to investors seeking to make investment in the English security market without the aid of a broker. Cope (1978) describes Every Man his Own Broker as the first detailed account of the English stock market. Mortimer was compelled to write the book based on his experiences from dealing on his own at Jonathan’s without a broker in order to save the cost of brokerage. As a result of these activities, Mortimer managed to lose a ‘genteel fortune’ and, in the process, acquired a genuine hostility to stockjobbers and other such speculators. The book goes far beyond the basic objective of being a how-to-book for trading in the British funds to provide numerous insights on the workings of the English stock market (Fig. 2.4). A constant theme in Every Man is the need to be wary of “this medley of Barbers, Bakers, Butchers, Shoe-makers, Plasterers, and Taylors, whom the mammon of unrighteousness has transformed into Stock-Brokers” (p. xiii). This wariness is not to be restricted to tradesman turned stock brokers, for even stock brokers from the higher ranks of society can be corrupted as “both ancient and modern history, furnishes us with many remarkable 19 Wilson

(1941, pp. 84–5) describes the options trade: “A prime a ` d´ elivrer (a call) was the option which A gave to B, obliging him to deliver on the following rescontre certain English securities — say £1,000 East India shares — at an agreed price. If the speculation of the giver of the option was unsuccessful, he merely lost his option: if, on the other hand, the funds rose, he had the benefit of the rise. The prime a ` recevoir (a put) was the option given by A to B by which B was pledged to take from A on rescontre £1,000 East India shares, say, at an agreed price. B became, in fact, a kind of insurance for A, obliged to make good to him the margin by which the funds might diminish in the interval”.

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Fig. 2.4 Front piece for Everyman His Own Broker (1761) Thomas Mortimer (1730–1810).

instances of the basest actions being committed by men of high rank, and the most exalted stations in government, for smaller pecuniary advantages than those which might arise in cases here supposed” (p. 45). As for the types of advice to be suspected Mortimer observes: “Always suspect the man who wants to engage you to be continually changing the situation of your money, to be influenced by some private motive, unless you are a JOBBER yourself” (pp. 22, 23). Similarly, Mortimer also advises: “it is almost impossible for a broker, to give any gentleman, candid disinterested advice, when to buy into, or sell out of, the funds” (p. xvi). As for the specific topic of joint stock valuation, Mortimer (1761, p. 9) states: Every original share of a trading company’s STOCK must greatly increase in value, in proportion to the advantages arising from the commerce they are engaged in; and such is the nature of trade in general, that it either considerably increases, or falls into decline; and nothing can

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be a greater proof of a company’s trade being in a flourishing condition, than when their credit is remarkably good, and the original shares in their stock will sell at a considerable premium.

This reference to stock selling at a premium harkens back to a time when stock was issued with a par value. Writing at a time when accounting information for publicly traded securities was cursory, at best, Mortimer suggests that the ability of a firm to borrow was an important signal of fundamental value. In modern times, this could be translated into a statement about factors that would provide a basis for a firm to access credit markets such as the credit rating as well as the state of a firm’s balance sheet and debt service capacity. Mortimer also makes reference to the type of ‘advantages’ of the particular business of the firm. This hints at the sector specific approach to common stock investing which is pervasive in the modern securities industry. Mortimer proceeds to explain this general valuation approach using one of the important British public companies, the British East India Company, as an example: This, for instance, has always been, and still is the case of EAST INDIA STOCK in particular, not to instance any other. The present price of a share of £100 in the company’s stock is £134. The reason of this advance on what cost the original proprietor only £100 is, that the company, by the profits they have made in trade, are enabled to pay £6 per annum interest or dividend for £100 share. But then it is uncertain how long they may continue to make so large an annual dividend, especially in time of war; for several circumstances may occur (though it is not likely they should) that may molest their trade in their settlements, and diminish their profits. . .

It follows that Mortimer subscribed to the view that share price was driven by the sustainable level of dividend payout that, in turn, was affected by the various factors driving firm profitability. The dividend level is implicitly being compared to the prevailing level of interest rates. Dividends, firm profitability and interest rates drive stock valuation. This view is an early precursor of what, in modern times, is referred to as fundamental analysis.20 20 Modern

security analysis has a much more refined treatment of firm profitability, based on exploiting the much more elaborate accounting information now available. Graham and Dodd’s dictum that security analysis involves the use of financial statements would have been lost on Mortimer because, at his time, accounting information was quite rudimentary and was often proprietary.

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Perhaps the most interesting view presented in Every Man concerns Mortimer’s views on the superiority of fixed income investments over joint stocks. For example (pp. 20, 21): That shares in annuities, bought at a great discount, that is to say, greatly under par, are the cheapest and most advantageous to the purchaser; and considerably more profitable than any STOCKS bought at a high premium. Because the probability of the premium (given on any STOCK) totally subsiding in infinitely greater than that, the low price at present given for a 3 per cent Annuities should fall much lower; and there is a greater probability of their rising, and a greater likelyhood of its continuance, than there is, the premium now given on any STOCK should rise much higher, or continue so high as it is, for any number of years; therefore shares in STOCKS that bear a premium, are the dearest; and shares in funds or annuities under par, the cheapest to purchase.

Though difficult to translate into modern terms due to the differing characteristics of today’s security markets and those of 18th century England, Mortimer is arguing in favor of the superiority of fixed income investment over stocks when interest rates are high relative to the long term level of interest rates. This echoes the modern views of individuals in the trade such as Bill Gross of PIMCO Funds questioning the prevailing view that stock returns will outperform bond returns in the long run.

2.1.3

Manias, Manipulations, and Institutional Failure

Isaac le Maire and the First Market Manipulation in Joint Stocks Market manipulation, manias and institutional failure have been important features of stock trading since the earliest trades in joint stocks. General public sentiment about initial joint stock trading in Amsterdam was concerned with various schemes that were aimed at rigging the market. This concern generated much of the early analysis of joint stock trading, e.g., Gelderblom et al. (2009), van Dillen et al. (2006), De Marchi and Harrison (1994), and van Dillen (1930). Instead of developing analytical methods for determining the appropriate price of shares, much of the early discussion of joint stock trading centred on describing the negative features of the speculative trade that was taking place. Of course, attempts to manipulate markets did not originate with stock trading. For example, Aristotle in Politics refers to a Sicilian who cornered the cash market for iron by buying up all available supplies. Anecdotal evidence for even earlier examples of market manipulations can be identified. In any event, manipulations distort

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the price at which an equity security can be traded resulting in substantial divergence between intrinsic value and market price. The techniques of stock trading on the Amsterdam Exchange were inherited from those used to trade commodities on the Antwerp bourse (Gelderblom and Jonker 2005; Poitras 2009). Market manipulations were not uncommon in Antwerp. Perhaps the most infamous case happened in 1540 when Gaspare Ducci, “formed a ring which succeeded in creating panic on the Antwerp bourse and in cornering the factor of the King of Portugal. Ducci apparently had piled up a huge store of money by selling bills of exchange on his accomplices abroad” (de Roover 1949, pp. 159, 160). When the King of Portugal, through his factor, entered the market to pay off maturing debts, Ducci was the only lender with sufficient funds to lend. Such manipulations in the 16th and 17th century bill markets were reflected in the views of Sir Thomas Gresham, Gerard Malynes and others who were strong proponents of the view that a banker monopoly rigged the exchange market. Techniques required to corner or otherwise manipulate a security or commodity market were almost certainly common knowledge to the early stock traders in Amsterdam. Many traders had moved north from Antwerp following a sequence of events that undermined the political stability of Antwerp.21 One such trader was Isaac le Maire, who was able to obtain Fl.60,000 of Dutch East India shares in the initial subscription of 1602. Following the initial increase of 15%, the price of Dutch East India shares continued to appreciate steadily and, by 1607, had reached a high value of 300, triple the initial par subscription price of 100.22 By November 1608, the price had fallen to less than 140, and stayed in a range of 130– 180 for the next two years. The significant decrease in prices precipitated a notarial protest against the management of the company for improper use of shareholder capital. Around this point, le Maire joined together with eight others to form a private association to deal in East India Company shares “for their common profit” (van Dillen 1935, p. 25). The most noteworthy of the market manipulations engaged in by le Maire and associates constituted a ‘bear raid’ designed to depress the value 21 These events included the Dutch river blockade of 1572 and the siege of Antwerp by Spanish troops in 1585. 22 Barbour (1950) differs from De Marchi and Harrison (1994) in the description of the early price history of the VOC. The latter source has been taken as accurate in the following discussion. Following Barbour (1950), the impact of the bear ring on VOC prices was substantially greater.

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of Company shares. The group combined short sales for forward delivery, presumably settled using ‘differences’, with ‘cash’ sales of Company shares. Many of the actual cash sales of Company shares were long-dated, with delivery dates well beyond the conventional one-month-or-less delivery date. These activities were further supplemented by using their personal influence to spread unfavourable rumours about the Company’s prospects. As le Maire was at this time also engaged in attempts to found a rival French East India Company, these rumours had at least superficial validity. The profits on the transaction would be gained from forward short sales and, possibly, by less-than-a-month-to-delivery repurchases of the Company shares, made at lower prices than the initial sales. The trading activities of le Maire’s group were apparently successful in holding down the price of VOC shares. The potential impact of the bear ring on share prices attracted the attention of the Directors and other politically connected investors. The result was a period of political debate that included some of the first writings on stock market structure and performance. The debate ended in February 1610 with the passing of the first substantive legislation designed to limit stock market manipulation. Selling of shares in blanco, also known as the ‘windhandel’ or ‘wind trade’, was prohibited. More precisely, short selling of securities, defined to mean the sale of securities not owned by the seller, was banned. This ban covered both cash sales and forward sales. In addition, it was required that shares which were sold had to be transferred no later than one month after the transaction. Private sanctions included the expulsion of le Maire as a VOC shareholder. Unlike modern securities laws, many 17th and 18th century prohibitions imposed on security trading activities did not have criminal sanctions. Rather, edicts such as the 1610 prohibition on short selling removed the protection of the courts for the purpose of enforcing contracts. The inability of the edict to control the ‘wind trade’ speculation in shares was evident with the establishment of the Dutch West India Company in 1621, when shares were sold on a ‘when-issued’ basis, prior to the initial subscription. This prompted the issuance of another edict reinforcing the ban on selling shares not owned by the seller. Any trader seeking to repudiate a short sale could find refuge in the courts. Similar edicts in 1630 and 1636, during the time Frederick Henry held the office of Stadholder, led to the use of the term ‘appeal to Frederick’ to refer to a trader invoking the protection of the prohibition on short sales to avert payment on a losing position. In addition to the ban on in blanco trading, the various edicts required that

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share transfers be made within one month of the sale date. The ban on short sales was not permanent and the “occasion of renewal brought out anew sentiment for and against VOC” (p. 51). Despite opposition, the ban on ‘selling in the wind’, or windhandel trade, was repeated in 1624, 1630, 1636, and 1677. The connection between dealings for time and the potential for market manipulation and the early trade in VOC shares is recognized by Ehrenberg (1928, pp. 358, 359): From the beginning, the speculation in shares . . . as a means of gain depending on taking advantage of future price changes, made it appear extremely desirable to postpone the fulfilment of the bargains. In the case of bears, who had sold shares which they did not possess, this was an absolute necessity. Speculative future dealings made possible a twofold simplification of the technique of dealing. First, speculative dealings could be realized before the date of delivery. Secondly, settling days made it possible to use the same procedure that had done so much in the methods of payment, namely, set off. Both together resulted in an incalculable increase in turnover, since now only a little ready money and stock were required for very large dealings.

Significantly, “it was speculation [in forward and option contracts for VOC shares] which made the first modern stock exchange”. Speculators provided the liquidity essential for continuous trading and ‘accurate’ pricing. In turn, hedgers and traders seeking to acquire or dispose of stock positions provided the ‘honest’ liquidity needed to clear the market. De la Vega (p. 164) suggests that the relative composition of the speculative trading population changed over time, whereas “formerly twenty speculators ruled the exchange . . . Today there are as many speculators as merchants”. John Law and the Mississippi Scheme Almost from the beginning of trading in joint stocks, periods of seemingly irrational pricing have been observed. Providing theoretical explanations for such behaviour occupies a considerable amount of energy in modern financial economics. Yet, closer examination of specific historical events reveals an array of determining factors, with each event featuring its own particular profile. This observation is well illustrated in the two most significant episodes of seemingly irrational pricing in the 18th century: the Mississippi scheme in France and the related South Sea Bubble in England.

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Both these events came to a head in 1720, the collapse of the Mississippi scheme preceding that of the South Sea Bubble. Despite the proximity of these two events and similarities in certain details, the Mississippi scheme seems to have been the result of well-meaning but misguided policy while the South Sea Bubble had the distinct smell of fraud and manipulation. The Mississippi scheme was the brainchild of John Law (1671–1729), that colourful Scottish exile Schumpeter claims is ‘in the front rank of monetary theorists of all time’. The life and contributions of John Law have been examined in numerous sources, with Murphy (1997, 1991) being a particularly impressive account. The Mississippi scheme began in 1716 when Law was able to gain approval from the Duke of Orleans, the Regent of France, to establish the Banque Generale in Paris. Law’s bank was given authority to issue notes and to participate in the management of royal revenues. Initially, the note issue was restricted in size and, as a protection against debasement of the coinage, was made payable on demand in the coin in use at the time of issue. While France had some experience with paper currency, in the form of the billets d’etat issued by Louis XIV, this project was the first significant case in France of a private bank issuing paper currency. Somewhat to the surprise of the regent, Law’s bank met with resounding success and bank branches were soon established in other centres such as Lyons, Tours, Rochelle, and Orleans. There was also a noticeable positive impact on credit conditions and payment of state taxes. Around this time, the finances and general economy of France were in serious disorder, having suffered greatly from the excesses of the recently deceased Louis XIV. The regent seized on the opportunity and, in December 1718, Law’s bank was converted from a private to a public institution, the Banque Royale. This bank was conceived to be a note-issuing central bank, with provincial branches, to which was added a range of monopoly powers, over activities such as the sale of tobacco and the refining of gold and silver. One of the first acts of the Banque Royale was to print unbacked notes in the amount of one thousand million livres. This step was a harbinger of the financial mayhem that was to follow. Law’s private bank had been careful to restrict note issues to an amount that could be managed with the specie reserves that were within the control of his bank. Whether Law concurred with this unbacked note issue is not known, though his attentions were at least partly diverted by the granting in September 1717 of letters patent to a company with exclusive trading privileges on the western bank of the Mississippi River, in the area of the province of Louisiana. This company

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was formally known as the Compaigne d’Occident or, in slang, the Mississippi Company. The increasing value of the shares in this venture proved to be another success for Law, and in May 1719 the Mississippi Company was evolved into the Compaigne des Indes, which was granted further exclusive trading privileges in the East Indies, China and the South Seas. The creation of the new Compaigne des Indes was accompanied by an offering of fifty thousand new shares. Accounting for the method of payment, Law promised an annual dividend on the shares exceeding 100% that triggered an almost staggering interest in the new issue. What followed was a sequence of arrangements: first, to lease the bulk of the indirect taxes, the General Farms, in August 1719; and, starting in October 1719, to use the proceeds of further issues of Compaigne des Indes stock to pay off virtually all of the debt of the French government. Throughout this period there was frenzied, almost unbelievable, trading in shares of the company. Propelled by the unbacked note issues of the central bank, the scheme started to slowly unravel during 1720, collapsing completely during September. On 29 September 1720, the government announced Banque Royale notes would not be accepted for payments. In December, John Law fled to Brussels, fearing for his life. Prior to the financial collapse associated with the Mississippi scheme, Paris was on a path to be included with London and Amsterdam as a key European financial center. Despite the political and economic importance of France, various French characteristics retarded the development of financial markets during the 17th century. France tended to be a nation of small farmers; the explorers and traders that brought glory to her neighbors were relatively absent. It was the state that dominated economic development rather than the individual entrepreneurs that thrived in Holland and, after the Glorious Revolution, in England. Major state sponsored commercial ventures — such as Richelieu’s Company of One Hundred Associates (1627) and Colbert’s Company of the West Indies (1664) — were relatively unsuccessful compared to similar efforts by the Dutch and English. At the time of the Mississippi scheme, Paris lacked the central bourse that characterized trade in London and Amsterdam. Despite these drawbacks, the economic importance of France meant that Paris was an integral part of the international commercial network and that trading practices similar to those used in London and Amsterdam were the norm in financial markets, e.g., Neal and Quinn (2001). In the absence of a central bourse, stock trading and other financial activities such as trading bills of exchange took place at different locales

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Trading on the Rue Quincampoix during the Mississippi Scheme.

around Paris. At the time of the Mississippi scheme, between 1716 and 1720, stock trading was centered in the Rue Quincampoix (Fig. 2.5). It was here that John Law established the offices of the Compagnie des Indes (Mississippi Company) for the issue of shares in the company and, as a consequence, the legendary throngs gathered at the peak of share prices to purchase ‘les primes’, effectively at-the-money six-month warrants to purchase a share of company stock (Murphy 1997, pp. 213–217). It is one of the ironies of the Mississippi scheme that Law issued primes to undermine the stockjobbing by private traders — in this case trading of three to six month time bargains in company stock at prices (12,000–14,000 livres per share) considerably above the price (10,000 livres) that the stock had achieved at that point in the speculative bubble. Law reasoned that by issuing large amounts of primes with an exercise price of 10,000 livres, this trade would be ended. What Law did not anticipate was that the speculation had progressed to where shareholders would rush to sell a share at 10,000 to raise cash to purchase primes at a premium of 1,000 that granted the right to buy

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10 shares in the future at 10,000 each. The resulting downward pressure on cash share prices led, ultimately, to the collapse of the scheme. The South Sea Bubble Since the collapse of the bubble in 1720, the story of the South Sea Bubble has been told and retold, sometimes profoundly.23 The actual story begins with the first of the three great English joint stock companies, the Bank of England. This flotation was particularly successful, both as a business venture and, more importantly, for validating the effectiveness of using company charters as a vehicle for funding government debt. The basic scheme was quite ingenious: the government has the ability to grant monopoly privileges for certain activities, such as the right to conduct trade to a particular region or the right to issue the ‘coin of the realm’. The market can be used as a mechanism to capitalize the value of these rights that, in turn, can be sold in exchange for funding government debts, either new or outstanding as the case may be. The basic difficulty with this scheme is that the pool of such rights is small, with an even smaller number of truly valuable rights. The success generated by the Bank of England issue spurred calls for more such deals. However, the right to issue notes proved to be far and away the most lucrative monopoly that the British government could charter. The demand for new charters was such that (Morgan and Thomas 1962, p. 29): In 1698, the subscribers to a government loan were incorporated as, “The General Society entitled to the advantages given by an Act of Parliament for advancing a sum not exceeding two million for the service to the Crown of England”. The ‘advantages’ were that the subscribers were entitled to share in the trade to India, each in proportion to his subscription, and that such of them as chose might form a joint stock for carrying on their trade. 23 Dickson (1967, p. 90) references most of the sources available up to 1967. Neal (1990) includes some more recent references and Shea (2007) is a useful recent contribution. Dickson (1967, chs. 7, 8) is also an essential source for examining in detail the period of financial reform and reconstruction following the bubble. Of the available references on the bubble, Anderson (1764, 1787–1789) is seminal. As a clerk working for the South Sea Company during the bubble period, Anderson had first hand knowledge of events and practical details. Many of the insights found in later works can be traced to Anderson. Scott (1910–1912) has, perhaps, the most in-depth account though there are a number of points at which the discussion is incorrect.

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The right to trade with India was an important concession that had already been conveyed on the East India Company. Yet, the government had a limited number of viable concessions that could be exploited. The creation of the New East India Company came at the expense of the ‘old’ East India Company, creating an arrangement that was to prove unworkable. In 1702, the two East India companies were merged and once again Parliament made the traders pay for their privileges. The deal was for the company to assume the debt of the 1698 East India Company, £2 million at 8%, together with an additional £1.2 million, at no interest, English War Expenditure and Public Borrowing 1688–1763

Year

Total expenditure

Total income

Balance raised by loans

Col. (4) as % of (2)

1688–97 1702–13 1739–48 1756–63

£ 49,320,145 93,644,560 96,628,159 160,573,366

£ 32,766,754 64,239,477 65,903,964 100,555,123

£ 16,553,391 29,405,083 29,724,195 60,018,243

33.6 31.4 31.1 37.4

Source: Dickson (1967, p. 10).

English Government Long-Term Debts, at Michaelmas 1719 (Excluding Life Annuities) (1) Owed to companies (a) Bank of England (b) East India Company (c) South Sea Company (2) Redeemable Government Stock (3) Annuities for terms of years (a) Long annuities, £666,566 valued at 20 years’ purchase (b) Short annuities, £121,669 valued at 14 years’ purchase

£ 3,375,028 3,200,000 11,746,844

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Total

18,321,872 16,546,202

Total

15,034,688 49,902,762

13,331,322 1,703,366

Total long-term debts Source: Dickson (1967, p. 93)

£

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producing a total loan to the government of £3.2 million paying 5%. Such capitalized transactions were an immediate relief to a government spending, on average, 30% more than could be supported by revenue sources. By 1710, the pressures of financing a protracted war had become considerable. After tapping the two existing joint stock companies for additional funds, once again the government resorted to the granting of charters in exchange for paid-in share capital. The “Company of merchants of Great Britain, trading to the South Sea and other parts of America and for the Encouragement of the fishing”, better known as the South Sea Company, was given royal assent on 11 June 1711. During times of war, the government typically paid for the war effort using short-term debt such as Navy tallies and Army and Transport debentures. Circa 1711, the amount of this short-term unfunded debt was over £9 million. It was this debt that the South Sea Company agreed to assume. Compared to the operations associated with Bank and East India Companies, this deal was immense. For over two years, the South Sea Company was engaged in taking subscriptions, ultimately raising £9,177,968 for which the government was to pay annually £550,678 interest and £8,000 management fees. The early history of the South Sea Company was not good, due in part to funding the debt with tax sources that did not apply until 1715– 1716, interest to be paid on the debt from general revenue of the Treasurer of the Navy. During the almost predictable period of suspended interest payments, shareholders were obliged to accept bonds in lieu of interest, further increasing their stake in the Company. However, by 1717 the various encumbrances on South Sea stock had been eliminated, and Parliament further enhanced the attractiveness of South Sea stock by an enactment requiring that any deficiencies in interest payments from funded sources would be met with payments from the General sinking fund. By 1717, there was also renewed prospects for the most important segment of the monopoly business granted to the South Sea Company: trading with Spanish America. John Blunt is an oddity in the South Sea affair. He has, ultimately, been singled out as the kingpin of the manipulations that produced the South Sea Bubble, yet his initial involvement was by request of the Government. It was Robert Harley, then newly appointed Chancellor of the Exchequer, who, in August of 1710, sought out John Blunt, George Caswall, and Sir Ambrose Crowley for their advice on dealing with the pressures of government finance. That both Blunt and Caswall were affiliated with the Sword Blade Bank, the former as secretary and the latter as partner, was

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eventually to prove a fatal error. “Directors and officials of the Sword Blade held five seats on the Original Court of Directors of the South Sea Company and the provision of credit by the bank played an essential part in Blunt’s manipulations” (Morgan and Thomas 1962, p. 31). Another key element in the South Sea Bubble mix was the presence of a complicitous Minister, in this case John Aislabie, Chancellor of the Exchequer. Aislabie was a man of mixed character. As one of his contemporaries, Arthur Onslow, described him: “a man of good understanding . . . and very capable of business; but dark, and of a cunning that rendered him suspected and low in all men’s opinion . . . He was much set upon increasing his fortune and did that” (Dickson 1967, p. 95). In the summer and autumn of 1719, the apparent success of John Law’s scheme in France generated plans for similar ‘projects’ in Britain. One such project was proposed by John Blunt: to incorporate all of the National Debt, including that embodied into the Bank of England and the East India Company. The result would be a company very much like the company constructed by Law, with powers of note issue combined with profitable trading monopolies to support the interest income from government. Whatever John Blunt’s precise proposals were, the deal that was ultimately consummated left the two other joint stock companies in place, with the South Sea Company to undertake a conversion of the remainder of the relevant government debt, some £31 million. This was a considerable undertaking for a company whose primary earning asset was, itself, government debt. From this point, the essence of the scheme is captured by Cantillon (1755, p. 323): “a Bank with the complicity of a Minister is able to raise and support of the price of public stock and to lower the rate of interest in the State . . . and thus pay off the State debt. But these refinements which open the door to making large fortunes are rarely carried out for the sole advantage of the State, and those who take part in them are generally corrupted”. In the case of the South Sea Bubble, the Bank involved was the Sword Blade bank and the minister was John Aislabie. After a bidding process involving the Bank and the South Sea Company, the deal eventually reached was for the South Sea Company to be permitted to undertake the conversion of government debt into South Sea stock, with the South Sea Company agreeing to a reduction in the government debt payments to 4% in four years and an additional cash payment from the Company to the government that would range from £4 million to £7.5 million. For this deal to make financial sense, the company would have to convince current holders of the government debt to take less than equal

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par value in South Sea stock. If only the interest payments are compared, the promised income from South Sea stock would be considerably less than many debt holders were receiving. For the conversion process to be profitable, it was necessary to create the illusion that South Sea stock was more valuable than its potential earnings would justify. The resulting machinations of Blunt and his confederates is surpassed only by the magnitude of the collapse of the Mississippi scheme (Morgan and Thomas 1962, p. 32): Even before the bill became law, South Sea stock had risen above par, and Blunt and his friends now used every means in their power to enhance the rise. Their technique included carefully staged offers of stock for cash at a little above the current price; the use of this cash together with the Exchequer bills which the Company had undertaken to ‘circulate’ and its credit at the Sword Blade to support the market; the making of loans against the Company’s own stock, so enabling holders to buy still more; the promise of lavish dividends; securing the interest of prominent people by thinly veiled bribes; and extracting the utmost propaganda value out of current events from the peace negotiations with Spain to a carefully contrived reconciliation between the King and the Prince of Wales.

On 14 April 1720, one week after the passage of the Act, the company announced its first ‘money subscription’ at a price of £300 for £100 par value in South Seas stock. Debt holders were required to register for conversion by April 28, with terms of the conversion to be announced on May 19. To sustain the rate of conversion indicated by the first money subscription, the Company boosted the half-yearly dividend to 10%, where 3% was expected based on Company dividends prior to the conversion. Two additional, even fundamental, inducements were: the requirement of only a 20% (£60) downpayment on the subscription; and, in conjunction with the Sword Blade Bank, loans against stock. Following the debt-financed success of the first issue, the scheme proceeds with an additional £400 ‘money subscription’ at the end of April, with the King and the Prince of Wales being the first subscribers. And so it goes, on 19 May the conversion rate for government debt holders is announced as £800/£100, and this is followed by yet another money subscription, on 17 June, at £1,000. These prices were sustained by the announcement of a 30% dividend for the year and a guarantee of a 50% dividend for the following ten years. The most remarkable feature of the South Sea Bubble is the extent to which the fraud succeeded. In particular, the £1,000 money subscription was a triumphant success, with subscription lists including half

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of the House of Lords and more than half of the House of Commons. Even the sole voice of reason who spoke out against the initial South Sea scheme, Robert Walpole, was tempted into this scheme. Predictably, the scheme foundered. The Sword Blade Bank could not sustain the large loans that the South Sea Company was incurring to support the high price of the stock. In addition, the driving force behind the scheme was rising prices. In the early stages of the scheme, money could be borrowed for the initial subscription payment and the resulting subscription receipt sold ‘light horse’ in the market. In order to prevent an oversupply of subscription receipts, effectively in-the-money subscription warrants, the Company would enter the market and purchase both light and heavy horse securities, using credit extended by the Sword Blade Bank. In an upward rising market, the profit potential of this plan was immense. If the credit underlying prices collapses, prices peak and the ensuing price collapse is more intense than the rise. In the period between 8 September and the end of September 1720, South Sea stock fell from 670 to below 200. When the dust had settled, Aislabie and the directors of the Company had been required to forfeit a large part of their estates and arrangements had been made to do ‘rough justice’ to other participants (Morgan and Thomas 1962): The main points of the ultimate financial settlement were: The £7 million liability of the company to the state was cancelled. Borrowers against stock were to repay only 10% of their loan, but to have the stock which they had deposited against it cancelled. Outstanding calls on money subscriptions were cancelled and stock allotted to all subscribers on the basis of £100 stock for each £300 cash already paid. The parties to the August conversion received additional stock to bring their terms to the same as those of the May conversion. The remaining stock, after discharging all these obligations was divided proportionately among all holders, old and new . . . The net result was . . . to leave the cost of servicing the National Debt much as it would have been if the South Sea scheme had never been thought of.

Even though the scheme did not have a substantial fallout for the direct participants, there was one event produced by the South Sea Bubble that would have lasting consequences. The South Sea scheme involving the government debt conversion did not take place in a vacuum. The fantastic promotion of John Law was in the process of unwinding just as the South Sea scheme was beginning, though

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the full extent of the financial market collapse in France could only be guessed at the time. The markets in England and France were awash with speculative capital. In England, this produced a competing array of small joint stock promotions, involving companies either acting without a charter or using a charter that was not granted for the firm’s current activities. Scott identifies 120 such issues appearing between September 1719 and August 1720, with a potential market capitalization of £220 million. To stem the flow of speculative capital out of the market for South Sea shares, the South Sea Company was able to get the so-called ‘Bubble Act’ invoked. The Bubble Act was not a specific Act, per se. Rather, the Bubble Act was some clauses attached to a bill enabling the charter for two insurance companies, the Royal Exchange Assurance and London Assurance Companies; yet another instance of the government exchanging exclusive rights in exchange for the paid-in capital of the venture. These clauses prohibited promoters from “presuming to act as if they were corporate bodies and pretending to make their shares or stocks transferable or assignable without any legal authority”. The prohibition was extended to companies operating “under the authority of charters that were obsolete or had been given for some other purpose”. The effect of this Act was to severely restrict joint stock issues, leaving the two insurance companies, together with the Bank, the East India Company and what remained of the South Sea Company as the main components of the English stock market for the rest of the century. Little progress was made in joint stock company formation until the enabling of ‘letters patent’ in 1834 and passage of the Joint Stock Company Act (1844), e.g., Todd (1932) and Alborn (1998). The Paris Bourse on the Eve of the French Revolution The issuing of ‘les primes’ by the Compagnie des Indes at the height of the Mississippi scheme speculation is, perhaps, the most remarkable event in the history of equity security speculation. The extent of the Mississippi scheme went far beyond the considerable losses of investors. For two generations and longer, the French were wary of financial securities such as bank notes, letters of credit and company shares. There were government efforts to organize a formal stock market, with a 1724 order authorizing the creation of a stock exchange in Paris. Restrictions on the number of brokers (agents de change) implicitly encouraged the trading of securities in informal markets organized outside the exchange. Though scepticism of joint stock financing was widespread, this arrangement suited the French government which, from the collapse of the Mississippi scheme until the closing

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of the Paris bourse in 1793, managed to use the facilities of the Paris bourse to bring a considerable amount of debt to market (see Tables 2.4 and 2.6, Poitras 2000, pp. 70–72 for listing of issues by type and amount of funds raised). In particular, from 1777–1788 “Necker and his successors obtained more the 776 million livres in return for life annuities of 8–10 per cent constituted on from one to four ‘heads’ without regard to life expectancy” (Taylor 1962, p. 963) During the 18th century, French government loans were of two types: long term fixed rate annuities (rentes perpetuelles); and life annuities (rentes viageres). The life annuity issues that became an increasingly important element of French government finance as the 18th century progressed were the essential element in the emergence of exchange traded funds based on pools of such securities. Though life annuities could be traded, such trade was complicated by lack of market information about the life on which the annuity was written. Early attempts at creating a more tradeable security used the life of a well known individual, e.g., Louis XV or Frederick the Great (Taylor 1962, p. 962). The practice of issuing viageres without reference to age was not common prior to the dismissal of Turgot in 1776, while the ‘uniform rate’ for a life annuity after this time was “10 per cent on one ‘head’, 9 or 81/2 on two, 8 on three or four” (Taylor 1962, p. 961). Using actuarially sound pricing methods, the uniform rate prices for the single life annuity were fairly priced for an adult about age 50 (Velde and Weir 1992). For a number of reasons, interest rates on the life annuities, guaranteed by the monarchy, were high enough to be considered ‘scandalous’ (Taylor 1962, p. 965). This perceived mis-pricing led quite quickly to the creation of exchange traded funds based on pools of these annuities. Trading in these funds played a central role in the agioteur driven frenzies and manipulations that characterized the Paris bourse from the mid-1780s to the eve of the French Revolution. The investment scheme, colloquially referred to as ‘trente demoiselles de Geneve’ initially involved a number of Genevan banks creating ‘investment trusts’ or ‘syndicates’ that were formed by pooling life annuities issued by the French government. Even though there was an expected gain to purchasing life annuities written on young nominees, there was still the risk of unforeseen events. Extending Taylor (1962, pp. 992–996), Velde and Weir (1992) observe that the Genevan banks: developed lists of young girls from Genevan families to name as the contingent lives. The families were selected for their record of health and longevity. The girls were mostly between the ages of five and ten,

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and were selected only after surviving smallpox . . . The Genevan banks purchased large amounts on each life to reduce transactions costs, but pooled together annuities on enough different lives to reduce the risk. The most common number of lives in a pool was 30, hence the name of the scheme.

The banks then ‘resold small fractions of their pools of annuities to individual investors’. Sometimes the cash flows from the life annuities were passedthrough directly to investors, in other cases the cash flows were repackaged in other forms, such as tontines. Included among the investors were promi´ nent speculators, including the banker Etienne Clavi`ere (1735–1793), the most well known of all the French speculators operating at the eve of the Revolution (Fig. 2.6).24 As Clavi`ere observed in 1782, “The Genevans are

Fig. 2.6 24 Taylor

Etienne Claviere (1735–1793).

(1962) provides a detailed discussion on the activities of Clavi`ere and observes (p. 952): “We must remember that he was not the only speculator and in respect to the

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the first who have seen in the annuity loan a means of increase of fortune as advantageous to cultivate as most of the other objects of which industry is practiced”. All this reflects a relatively modern state of financial sophistication. In addition to capturing the gains from risk pooling, claims against the pools were “an easily negotiated asset . . . because the bank’s dispassionate selection of lives eliminated problems of asymmetric information and moral hazard” associated with life annuities written on single lives (Velde and Weir 1992). This process was facilitated by the substitution of “the paper of the investment trust for the paper of the annuities themselves”. In addition to capturing the French government’s perceived ‘scandalous’ mis-pricing of life annuities written on young, healthy lives, the pools were able to capture the risk premium available from portfolio diversification. The result was that the claims against the pools could be sold at yields well below those directly paid on individual life annuities issued by the French government. At what point the bankruptcy of the French monarchy could have been anticipated is difficult to determine. In any event, Taylor (1962, p. 964–966) provides an insightful examination of the ‘rationalization of the risks taken’ by the agioteurs as the bankruptcy approached. Over time, the investment technology developed by the Genevan banks spread to other countries, most notably the Dutch republic.25 The Dutch schemes, often organized by important brokers instead of banks, introduced an additional wrinkle. This involved using the surplus of interest received from the French government over interest paid to claim holders to buy back

volume of his affairs not even in the first rank”. Clavi`ere receives considerable modern interest because the quality of the primary sources — correspondence and accounts — associated with his activities. He also attracts modern interest due to his connection to Mirabeau. For a variety of reasons, not the least of which is an active desire to prevent public disclosure of trading activities, primary sources for the most important agioteurs or speculators have not survived. The most important secondary source on the correspondence of Claviere with other speculators is still Bouchary (1938). 25 Precisely when schemes to capture the benefits of diversification appeared is unclear. Such schemes likely appeared gradually as the supply of different types of securities became widely available for trade. For example, Goetzmann et al. (2005, p. 2) report on a 1774 scheme (Negotiatie onder de Zinspreuk Eendragt Maakt Magt) where the manager of the fund was directed to hold, as closely as possible, “an equal-weight portfolio of bonds from the Bank of Vienna, Russian government bonds, government loans from Mecklenburg and Saxony, Spanish canal loans, English colonial securities, South American plantation loans and securities from various Danish American ventures, all of which were traded in the Amsterdam market at the time”.

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shares in the pool. In some cases, the allocation of surplus was not complete, with the residual cash flow going to the brokers who originated the scheme (Alter and Riley 1986, p. 28). In any event, the ‘share buyback’ feature would act to reduce the number of claims on the fund, thereby increasing potential future returns of pool claimholders. In summary, the pooling scheme involved many modern notions including: the gains to diversification; investment trust/mutual fund origination; security pass-through; and share buybacks. This combination of features provides strong support for the selection of the ‘trente demoiselles de Geneve’ as an appropriate historical starting point for the theory of portfolio diversification. The creation of tradeable equity claims against a pool of securities reflects the remarkable level of sophistication that financial markets at that time had achieved about the notions that Markowitz and others were to explore almost two centuries later under the guise of ‘modern portfolio theory’. In particular, the investment scheme that first appeared in 1771 reflected intimate understanding of the gains accruing to portfolio diversification (Taylor 1962; Alter and Riley 1986; Velde and Weir 1992). However, by the 1785 peak of an agioteur driven speculative frenzy on the Paris bourse (Taylor 1962, pp. 965, 966), the bankruptcy of the state was all too apparent; the suspension of payments in 1788 and 1789 was a case of ‘not if but when’. Oddly enough, it was agioteurs that were willing to engage in large operations supporting the French government annuity loans as the end neared. For the agioteurs, ‘political action was an important technique of speculative success’ and the use of ‘intrigue, propaganda and manipulation’ had proved sufficient in the past. As Claviere observed in 1786: “My fortune, it must be said, is bound to that of the Kingdom. I cannot conceive of the risk of bankruptcy in a country so favored by nature”. ´ In the history of equity security markets, Etienne Clavi`ere is remembered as the bear speculator able to commission the great French revolutionary, orator and politician M. le comte de Mirabeau (1749–1791) to distribute anti-agiotage polemics and tracts designed to support an uncovered bear squeeze of longs with forward contracts (vente ` a terme) in a number of joint stock companies starting around 1785.26 A number of such operations 26 Etienne ´

Clavi` ere (1735–1793) was another of the remarkable figures that populated 18th century equity security markets. Originally from Geneva, Claviere was involved with the democratic leaders of the Geneva Republic and, as a result of the collapse of the popular revolution, was forced to take refuge in Britain in 1782 together with other Swiss expatriates. Many of these expatriates later moved to Paris, where some were engaged in ‘banking’ before the revolution. Claviere, in particular, became acquainted

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were launched against the Paris Water Company. This trade was sustained by the reappearance of joint stock share issues starting around 1777 with the Paris Water Company and in 1778 with the Discount Bank. The bear squeeze involved spreading negative sentiment, depressing the cash price in order to permit the bear syndicate to purchase shares for values well below the delivery price on the short vente ` a terme position. The closing of the Paris Bourse and the abolition of French joint stock companies were two consequences of the turmoil of 1793. These events mark a symbolic end to the rudimentary financial transactions of the 18th century, just as the official recognition of the new-style Paris Bourse in 1801 marks the beginning of more sophisticated and accepted equity security trading practices.

2.2 2.2.1

Developments to Graham and Dodd (1934) Reminiscences of the Stock Operators

Early Stock Exchanges The valuation of equity securities is intimately connected to the methods employed to trade such claims. In turn, increases in the aggregate supply of equity securities over time has produced changes in trading mechanisms. The emergence of exchanges specializing in the trading of equity securities was a long process, starting in the early 17th century and continuing until the 20th century. For much of this time, stock exchanges were more important as venues for trading government debt securities — debt securities were commonly referred to as ‘stocks’, e.g., ‘debenture stock’, whereas ‘shares’ was the terminology commonly used to denote equity claims in joint stock companies. In 1840, for example, of the £1.3 billion in securities available for trading on the largest securities exchange in the world — the London stock exchange — only 11% had not been issued by governments, with much of the remaining percentage attributable to the government linked Bank of England, East India Company and South Sea Company stock. Though joint with Mirabeau, Brissot, and other popular leaders. Mirabeau, who had a high opinion of Claviere’s talents, used his assistance in composing speeches and essays on financial matters. Another important expatriate Swiss, Etienne Dumont, claimed the Swiss banker was the author of almost all of Mirabeau’s works on finance. Claviere was chosen deputy to the National assembly in 1791, and was Girondist minister of finance from March till June, 1792. He was arrested with other influential Girondists in June, 1793, on account of Girondist opposition to the extreme measures of Robespierre and other revolutionary leaders. In December 1793, Claviere committed suicide to escape the guillotine. His wife poisoned herself two days afterward.

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stock shares from a variety of geographical locales were traded in London, it was common for ventures to be floated on the local stock exchange. The earliest exchanges lacked formal organization, even where trade was conducted in a centralized location. In the 17th century, trade in VOC shares on the Amsterdam exchange was conducted in a fashion similar to commodities. Access to the exchange was open to the public with brokers and those seeking to trade shares gathering around one of the 46 pillars in the exchange building to conduct business (see Fig. 2.2). It was not until 1787 that brokers in Amsterdam established an organization aimed at controlling default risk by restricting access to trading. Following Michie (1999, p. 3), a stock exchange can be defined as: “A market where specialized intermediaries buy and sell securities under a common set of rules and regulations through a closed system dedicated to that purpose”. Under this definition, the first stock exchange was established by government decree in Paris in 1724. However, because entry was restricted to the 60 agents de change, much of the trade was conducted outside the stock exchange building at other venues around Paris. Hence, even though there was a formal stock exchange, it was not the primary venue for trading stocks. In addition, it was not until the 1780s that the French recovered from the distrust of joint stock shares created by the Mississippi, substantially restricting the overall trade in shares. By the middle of the 18th century, the more substantial securities brokers in London “were looking for ways of conducting their business in greater comfort and away from the disreputable hangers-on of the market” (Morgan and Thomas 1962, p. 68). An attempt in 1762 by a club of 150 brokers to obtain exclusive rent of Jonathan’s failed when the courts upheld the rights of access by those being denied access. Subsequently, in 1773 a group of brokers acquired a building in Sweetings Alley off Threadneedle St. that was called the ‘Stock Exchange’. However, while some trade did gravitate to the new venue, there were no formal rules regarding membership, trading and the like. Access was open to the public on payment of a daily admission fee. In addition, trading continued to take place at various locales around London, especially in the Rotunda of the Bank of England building that had opened in 1765. In addition to free admission, the Rotunda building was where transfers for Bank of England stock and, more importantly, government debt issues were executed. Though the volume of trade was much greater than in Paris, this London stock exchange was ‘neither exclusive or dominant’ in the London securities market (Michie 1999, p. 32).

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The evolution of the London stock exchange took a dramatic turn starting with the French Revolution in 1789 and the closure of the Paris bourse in 1793. The subsequent occupation of Amsterdam by French troops in 1795 meant that two of the most important financial centers in Europe — Paris and Amsterdam — were disrupted. These events triggered an exodus of important bankers, brokers and other merchants to London, providing further impetus to the emergence of London as the dominant financial center for trading stocks and shares in the period from the early 19th century until WWI. Against this late 18th century backdrop, the British government greatly expanded the stock of national debt to fund military expenditures.27 The eventual result was that “on 3 March 1801 a London Stock Exchange formally came into existence that not only provided a market for securities but also incorporated regulations on how business was to be conducted”. With this move, the exchange moved from an open to a closed market designed to ensure “that all those who participated both obeyed the rules and paid for the necessary administration” (Michie 1999, p. 35, 36). In effect, the first modern stock exchange was born. From this beginning, there developed during the 19th century an international network of stock exchanges with London being the dominant exchange for international issues of stocks and shares with Paris having a greater role for Europe and the Mediterranean. This growth was facilitated by the sometimes massive increases in government debt and corporate share issues due to events such as the Napoleonic wars, the railway construction boom through much of the 19th century, the U.S. Civil War, and the transition of businesses to publicly traded joint stock companies. Changes in communication technology, such as the telegraph and the telephone, contributed to the evolution of the local and regional exchanges from being sources of capital for smaller, locally located enterprises toward specialization in specific securities, e.g., South African exchanges for gold stocks; New York for American securities. The exchanges located in national financial centers increasingly “provided the most liquid market in which money could be readily employed or securities quickly sold” and so attracted business from throughout the country (Michie 1999, p. 6).

27 Michie (1999, p. 34) reports that the English national debt increased by about £500 million to £744.9 million between 1790 and 1815. Following Kaplan (2006) and Ferguson (1998), the substantial increase in the supply of debt available for issue and trade precipitated the creation of banking dynasties, most notably the House of Rothschild.

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Accompanying the development of stock exchanges was a gradual transition in the sophistication of the investing public and the businesses seeking to attract capital. Shares in joint stock companies came increasingly to be perceived as ‘investments’ instead of ‘gambling’ vehicles. The increasing liquidity of stock markets substantially reduced the difficulty of purchase and sale, further encouraging trade. While these social transitions took place somewhat more quickly in Paris and London, by the beginning of the 20th century New York was on a comparable footing. This somewhat later social development is consistent with the ‘dramatic expansion’ that took place in U.S. stock markets from the mid-1880s to the late 1920s (O’Sullivan 2007). Yet, these comparable historical developments mask fundamental differences in the workings of the financial markets in Europe and America. As it turns out, these differences — arising from ‘trading for account’ versus ‘daily cash settlement’ — had a significant impact on the development of securities markets over the next century. U.S. Stock Operators Almost from the beginning of equity securities trading in the United States, it is evident from some articles in the financial press that the practice of equity security valuation was more than rudimentary. This is not that surprising when it is recognized that valuation practices in the United States were transplanted from European centers, such as London, Paris, and Amsterdam, where there was more than a century of prior development in equity securities trading. With this in mind, it is not easy to pick a starting point for a discussion of relevant U.S. contributions from those in the trade and financial press. In general, the published contributions chronologically increase in depth and understanding of equity security valuation issues. This development is roughly consistent with the growth of New York as the world’s financial capital. As late as the 1820s, Philadelphia had as strong a claim as New York to be the nation’s financial capital. In the period before the Civil War, London was still, by far, the world’s dominant securities market. Even with the sizable influx of funding issues associated with the Civil War, around 1866 London still had a market cap of around $10 billion compared to $3 billion for New York (Gordon 1999, p. 123). Despite the availability of expertise in the industry, before Graham and Dodd (1934) there was no U.S. source which systematically developed the techniques of the fundamental approach to equity security valuation. Armstrong (1848) is strongly in the genre that stocks are gambling transactions conducted in a trading environment characterized by corners,

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bubbles and ‘fancy stock manoeuvres’. Biographical and autobiographical accounts of those involved in the industry, such as Henry Clews Fifty Years on Wall Street (1908) or Edwin Lef`evre Reminiscences of a Stock Operator (1923) present a similar picture. This does not mean that the methods of equity security analysis being used at the time were inadequate compared with those used today. Rather, the available studies were strongly influenced by the institutional and cultural milieu of the times. Insightful accounts of more modern equity valuation methods, such as Hartley Withers Stocks and Shares (1910), required a cultural maturation that permitted security investments to be seen as a socially acceptable means of financial improvement. From the beginning of trading in joint stocks, a range of trade publications covering a number of different facets of the securities industry, in general, and equity security analysis, in particular, have appeared. In the United States, the Commercial and Financial Chronicle was a key source until it was superceded by the Wall Street Journal (first published in 1884).28 The business section of the major newspapers, such as the New York Times in the United States and the London Times in England, also were important sources. As daily or weekly publications, these sources did not usually proceed much beyond a focus on current events until the turn of the century. By the 1920s, it was common for the financial press reporting on equity securities to feature a number of indexes, volume statistics and the like. Though the discussion in articles appearing in the financial press often involved valuation aspects of specific stock issues, there was no scope to present a reasoned development for the methods of security valuation. Much like a business reporter today, the financial reporter would gather information from those involved in the trade knowledgeable about security analysis as it pertained to the topic of the interest. In examining the various stories and accounts of the activities of market participants, it is possible to go back as far as, say, 1792 when the twentyone individual brokers and three firms signed the Buttonwood Agreement “not to buy or sell from this day for any person whatsoever any kind of Public Stock, at a rate less than one quarter per cent Commission on the specie value, and that we will give preference to each other in our negotiations” (Eames 1894, p. 14). This arrangement was eventually to evolve into the New York Stock Exchange (NYSE), a name that was introduced in 1863 as a name change for the Regular Board of the New York Stock and 28 Wendt

(1982) discusses the history of the Wall Street Journal.

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Exchange Board. The NYSE emerged as the dominant exchange for trading stocks in New York with its merger with the Open Board of Brokers in 1869 (Gordon 1999, pp. 95, 124, 125). The New York Stock and Exchange Board, formed in 1817 (Eames 1894, p. 18), could trace its pedigree to the Buttonwood Agreement. The Open Board was a relative newcomer that flourished in the face of the flood of issues arising from the Civil War. Until the emergence of a dominant exchange, stock trading in New York was scattered across a range of venues. For example, in 1856 Gordon (1999, p. 87) reports there were 360 railroad stocks, 985 bank stocks, 75 insurance stocks, in addition to hundreds of corporate, municipal, state and federal bonds and other types of stocks being traded in New York. Of these most were not traded on the New York Stock and Exchange Board, the lineal precursor of the NYSE, as the Board did not trade new and untested issues. These issues were curb traded. The primary venue for curb trading was various lamp posts in the Wall Street area where brokers who were not Board members, as well as some Board members, would meet to trade securities. Though the volume of curb trading was usually higher than trading on the Board, the market cap of curb issues was lower. In contrast to curb trading, activities of the Board were conducted at daily auctions which were held in fixed quarters. The tales of American stock operators predate the Buttonwood Agreement. Notoriety was, and still is, the result of doing something on a grand scale, often in conjunction with a massive bull market speculation, or the creation of a colossal conglomerate or the execution of an immense market manipulation. An early example is William Duer who was at the center of a 1791–1792 speculative scheme to inflate the value of bank stocks, particularly the Bank of New York (Gordon 1999, p. 40–45). The scheme was based on leveraged speculation and trading on insider information. At the height of the speculative frenzy, a number of banks were incorporated that, ultimately, did not open. As such, these stocks represent an early U.S. instance of bull market ‘paper hanging’. The collapse of the scheme resulted in bankruptcy for many of the players, including Duer. The scheme prompted Alexander Hamilton to write: “Tis time there should be a line of separation between honest Men and knaves, between respectable Stockholders and dealers in the funds, and mere unprincipled Gamblers”. This seeking of the line of separation is a task that has occupied regulators up to the present day. The formation of the New York Stock and Exchange Board in 1817 also marks the beginning of the Wall Street career Jacob Little, the first of a long

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line of big-time Wall Street speculative operators (Gordon 1999, pp. 59–62, 89–90). Unlike Duer who only used Wall Street as a trading venue, Little made a career on Wall Street. Though Little was also a broker, gaining membership to the Board in 1825, it is his activities as a speculator that made his reputation. Little’s trading strategies were typically short-term, aimed at anticipating market movements. During his career, Little made and lost four fortunes in speculative trading activities. In the end, he was unable to recover from his last insolvency brought on by the market panic of 1857. From that time, until his death a few years later, Little ended his Wall Street career as a trader of penny stocks and odd lots. Though Little was primarily a short seller, he made his first fortune in a 1834 short squeeze involving the Morris Canal and Banking Company. The objective of a short squeeze in a stock issue is to gain control of the quantity of that stock available for trading (the ‘float’ or ‘floating supply’) at a time when a sizable amount of stock has been sold short by traders who do not have a sufficient amount of stock to deliver. As was the case in the squeeze on Morris Canal and Banking, the capital requirements for gaining control of the stock for delivery usually involves a group or pool of speculators operating in concert. When the time comes for the short to make delivery of the stock, the short has to enter the market to buy — but there is no supply available because the short squeezers have already gained control. The result is a rapid rise in stock prices as short sellers bid up prices to tempt new supply onto the market (either from accounts of long-term investors or from the short squeezers). At Little’s time, most short sellers were brokers that had sold stock they did not own to investors, speculators or other brokers. The short position was sometimes the outcome of longer settlement periods than in modern times. In other cases, the objective of both parties was to engage in speculative forward trading, resulting in delivery dates on the short that could be many months in the future. Prior to the wide reaching regulatory reforms of 1933–1934, stock market self-regulation was an important theme of government policy toward the securities market. Yet, self-regulation suffered from the conflicting interests of the legitimate brokers, who recognized the negative impact associated with widespread unscrupulous trading activities, and the big-time speculators, who saw the market as a conduit for achieving big profits from a range of trading schemes. Many practices that are illegal in modern markets were considered fair game, such as trading on insider information or the formation of pools to engage in trading activities aimed at creating price movements favorable to speculation on stock price changes. The process

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of reform using self-regulation was slow and problematic. It was not until November 1868, just prior to the merger of Open Board and the New York Stock and Exchange Board, that registration of securities and 30 days notice of new issues was required of companies listed on the two Boards. Imposition of the listing requirements had an immediate impact on the activities of the big-time speculators, Daniel Drew, Jay Gould, and James Fisk, involving the Erie Railway. The 1864–1869 manipulations associated with the securities of the Erie are almost epic, reflecting the state of securities markets of that time. On one side of the struggle was ‘Commodore’ Cornelius Vanderbilt, a giant in the transportation industry, who wanted to control the Erie in order to be able to control the pricing of railway freight rates into and out of New York City. On the other side was a group including Drew, Gould, Fisk, and other big-time speculators who were seeking to control the Erie as a vehicle for making speculative gains through manipulation of the company’s security issues. The machinations of the two camps has been captured in some of the early classics of business finance, e.g., Adams and Adams, Chapters of Erie (1871) and Henry Clews, Fifty Years on Wall Street (1908). The struggle between these two groups is the epitome of the problems that prevailed in securities markets of that time, e.g., Medbury (1870, ch. 9), Gordon (1999, ch. 6) (Fig 2.7).

Fig. 2.7 Bulls and Bears on Wall Street (1879); by William Polbrook Beard (1825–1900)

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Vanderbilt was concerned with securities markets only as a vehicle for creating and managing a business empire, primarily involving railways. As part of the ongoing process of expanding this empire, Vanderbilt moved to acquire a controlling position on the Erie board of directors during the late summer and early fall of 1867. Vanderbilt had been involved with the Erie as recently as 1865, when he resigned from the board over concerns about the evident manipulations in the stock that took place during 1864– 1865. A major player in these manipulations was Daniel Drew, also a board member who, conveniently, served as treasurer. In his position as treasurer, Drew was able to issue securities, and in 1866 had done so by loaning the company $3.5 million in exchange for 28,000 unissued shares and $3 million in convertible bonds that had the provision that the 30,000 shares obtained from conversion could be reconverted back into convertible bonds. This provided Drew with the ability to expand and then contract about 10% of the outstanding stock — providing effective control of the floating supply. When Vanderbilt was unsuccessful in using his influence to control the Erie board of directors, starting in January 1868 he moved to gain control of the company by making purchases of as much of the outstanding stock as could be obtained. The speculators saw this as an opportunity to issue more convertible bonds that became a conduit to print stock certificates that were then sold to Vanderbilt. From late February to mid-March, Drew and his group were able to sell 100,000 newly issued shares. The absence of registration and listing requirements prevented the New York Stock and Exchange Board from knowing what was happening. All this was set against a backdrop of corrupt judges issuing injunctions and arrest warrants and legislators being bribed to pass laws favorable to one or the other of these groups. On 19 April Vanderbilt was able to strike a deal with Drew, Gould and Fisk and recoup his potential losses from his stock dealing. Following this, Gould and Fisk continued to manipulate Erie stock issues, until listing and registration requirements were introduced by the two Boards. Gould attempted to resist the requirements, even trying to establish a new exchange for the purposes of trading Erie stock. In September 1869, Gould capitulated and agreed to the new regulations. At that time, it was revealed that the number of Erie shares outstanding was around 700,000, about double the 351,000 shares outstanding at the time of the Vanderbilt agreement of April 1868. To modern observers, events surrounding the Erie have the appearance of a classical farce. A business titan attempting to rest control of a railway company in order to implement a pricing cartel enters battle with a group

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of big time speculators seeking to use the company as a vehicle for generating profits from stock price manipulation. Drew, Gould and Fisk are usually lumped in with Andrew Carnegie, J.D. Rockefeller and Commodore Vanderbilt and recognized as the ‘Robber Barons’ who dominated American industry through their financial dealings in the 1870–1890 period, e.g., Geisst (1997, ch. 3). The activities of the robber barons took place against a backdrop of increasing concentration of economic power in the hands of the trusts such as American Telephone and Telegraph, General Electric, Standard Oil and the American Tobacco Company. The trusts were formed largely as a way of dealing with the legal restriction that corporations had up to around 1900 that prevented the holding of stock of other corporations. During the 1890s there were about fifty trusts operating throughout the United States, involving most of the major industries. This number includes some agricultural trusts that were concentrated primarily in the South. Trusts were formed as a legal device largely to circumvent state corporation laws that restricted the ability of a corporation to expand using mergers and takeovers. Prior to the changes in state corporation law that started with New Jersey during the 1890s, the ability of a corporation to act as a holding company was quite limited. Trusts provided a legal avenue around these restrictions. In a trust, the companies being merged or taken over would exchange the common shares in the original corporations for trust certificates that possessed a claim to earnings of the trust as well as voting rights to elect the trustees that ran the trust. Standard Oil, for example, had nine trustees. Trust certificates traded like common stocks on the stock exchanges. The trust was a useful legal mechanism for the takeover ambitions of the emerging industrialists. Instead of having to issue new shares to raise new capital for a takeover, trusts could pay for the takeover using trust certificates or internal sources of funds. Due to changes in various state corporation laws, the trusts had a relatively short life span. The legal status of trusts did not prevent various states from initiating legal actions under other grounds, such as the common law restrictions on monopoly, aimed at preventing the increasing monopolization of specific industries. In addition, the public perception of economic and social problems posed by the trusts were addressed in 1890 with the passage of the Sherman Anti-Trust Act. Though this Act did not result in many successful prosecutions, it did provide a federal definition and jurisdiction for what constituted a monopoly. The trusts gradually reorganized as holding companies and trust certificates were replaced by common

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shares. Standard Oil, for example, completed the shift in 1899. Whether it was trading in trust certificates or the common shares, the changes in American industrial structure were good for Wall Street. The importance of trading in shares of these industrial companies gradually came to surpass the railroads. The volume and value of trade on the NYSE doubled between 1875 and 1885 with more growth on the horizon. Yet, despite the growth, the securities markets of that era justly deserved the public perception as a speculator’s haven. Clews (1908, p. 19), a veteran broker and investment advisor with fifty years experience on Wall Street from 1857–1907, provides an informed view of ‘How to Make Money on Wall Street’: To the question often put, especially by men outside of Wall Street, “How can I make money in Wall Street?” there is probably no better answer than the one given by old Meyer Rothschild to a person who asked him a similar question. He said, “I buys ‘sheep’ and sells ‘dear”’. Those who follow this method always succeed. There has hardly been a year within my recollection, going back nearly thirty years, when there has not been two or three squalls in “the Street”, during the year, when it was possible to purchase stocks below their intrinsic value. The squall usually passes over in a few days, and then the lucky buyers of stocks at panic prices come in for their profits ranging from five to ten per cent on the entire venture. The question of making money, then becomes a mere matter of calculation, depending on the number of squalls that may occur during any particular year. If the venture is made at the right time — at the lucky moment so to speak — and each successive venture is fortunate, as happens often to those who use their judgment in the best way, it is possible to realize a net gain of fifty per cent. per annum on the aggregate of the year’s investments.

Coming from an individual so intimately connected to the dealings of ‘the Street’, it is difficult to deny the essential role played by speculation in U.S. securities markets of the time. Given the numerous abuses associated with common stocks, the disposition of the small investor to favor bonds over stocks during this period is understandable. Many of the systemic problems raised by the predominance of speculators in securities markets persisted until the regulatory reforms following the Great Depression. The introduction of legislation such as the Securities Act (1933) involved a radical realignment of the federal government’s role in securities markets. The collapse of securities markets from late 1929 to early 1933 was sufficient to end the period of self-regulation that had

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largely governed securities trading up to that time. Yet, the period of selfregulation was not without contributions. Many of the tools needed to lay the foundation that Graham and Dodd used to launch modern security analysis had evolved without government intervention. The growth of securities markets witnessed the emergence of professionals who made their living in the market and had a vested interest in making sure the game was played, if not always fairly, at least according to accepted rules. For example, the listing and registration requirements imposed by the newly formed NYSE were a direct assault on Jay Gould’s manipulations of Erie Railroad Company securities. 2.2.2

Origins of Equity Indexing

The ‘Vernacular’ versus the ‘Academic’ The distinction between ‘vernacular’ and ‘academic’ analysis has been introduced by intellectual historians and sociologists of science studying the popularization of investments in stocks and shares during the 19th century, e.g., Preda (2006, p. 150).29 Vernacular analysis is aimed at ‘real time’ financial decision making and is typically anecdotal, imprecise and uses language that is intellectually accessible by the broad population. It is “a heterogenous set of practices, know-how techniques and rationalization procedures”. In contrast, academic analysis is “a body of homogenous, abstract, formalized explanations” aimed at the community of academics staking claim to the subject area. It is theoretical, precise and involves language that is intellectually accessible mainly by academics involved in that community. Such a distinction continues to the present with modern Finance being the dominant school of academic analysis while trade publications, market commentary, newsletters and the like associated with ‘the Wall Street approach’ dominate the vernacular. Dating from the last quarter of the 19th century, the origin and development of equity indexing lie at the intersection of the academic and vernacular approaches. While advice manuals and financial periodicals have a much longer history, the dramatic expansion of joint stock issue supply in the first half of 29 In examining opinion on futures market speculation during the late 19th and early 20th centuries, Jacks (2007) refers to ‘populists’ versus ‘theorists’ which also corresponds to a distinction between the vernacular and academic views. Jacks connects ‘theorists’ with ‘professionals’, which is consistent with the absence of a sizable community of ‘academic’ theorists. The vernacular ‘populists’ were typically anti-speculation and the ‘professional’ theorists were usually involved in the trade and opposed to government intervention.

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the 19th century initiated a demand for information about equity securities from the general public. Especially after 1840, this expansion was associated with railway companies that often required substantially more capital than could be financed locally. This coincided with an increasing international integration of European and American markets for stocks and shares that took place in the second half of the 19th century, development that continued until the beginning of WWI. This transformation resulted in widespread use of internationally diversified portfolios, particularly in the United Kingdom (Rutterford 2006).30 In order to attract the middle class investor, the social and moral perception of security investments had to be transformed from one of ‘evil gambling’ to ‘social good’ based on rational and scientific principles. The result was the emergence of a vernacular ‘science of financial investments’ that has, from emergence to the present, had a complicated relationship with the development of the academic ‘science of financial investments’, e.g., Jovanovic (2006). Considerable confusion has been created over time by a failure to identify the connection between vernacular and academic approaches to the equity valuation aspect of the science of financial investment. Similar confusions can found in almost all areas where scientific ideas are needed, e.g., medical research, nuclear energy and global warming. A range of questions can be identified. Are vernacular and academic approaches basically the same, differing mainly by the level of rigor? Or, are vernacular and academic approaches ‘incommensurable’ (Preda 2006, pp. 150, 151) with aims and principles that are only marginally similar? Do vernacular approaches produce rationalizations for financial investment decisions that influence academic theories? To what extent do vernacular theories set the framework with which the general public interprets the results of academic contributions? In the context of equity security valuation, in general, and the use of equity indexes, in particular, answering such questions is made more difficult by the mixing of actors from the vernacular and academic realms.

30 For example, Hautcoeur (1997) identifies 238 financial periodicals published in Paris during 1881. A somewhat similar list could be assembled for London, with some important sources being: Chadwick’s Investment Circular; Beeton’s Guide; and the Investor’s Monthly Manual. Following Ott (2008), O’Sullivan (2007) and Michie (1986) the retail investor in the United States emerged somewhat later than in Europe, with 1885–1890 being identified with “the origins of conservative belief in the ability of laissez-faire financial markets to provide economic security and justice for all’ (Ott 2008, p. 619). Means (1930) is an early study documenting these changes.

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In some ways, it is not surprising that equity indexes first appeared in the vernacular realm even though the introduction and subsequent use of indexes does represent a major advance in the sophistication of market participants. The almost simultaneous appearance of such indexes in 1884 by Banker’s Magazine in the United Kingdom and the Dow Jones and Co. Customer’s Afternoon Letter is the first known appearance in trade publications (Hautcoeur and Petit-Konczyk 2006). Instead of using the stock index to determine the direction of the stock market, academics at the time were more concerned with the stock index as a predictor of business conditions, e.g., Mitchell (1910, 1916); Copeland (1915). The need for reasonable sample sizes, appropriate estimators and careful empirical analysis prevented an earlier examination of the subject. The divergence in usage is reflected in the following academic criticism of the Dow Jones Industrial index by Copeland (1915, pp. 532, 533): The stock market index of the Wall Street Journal has been more commonly used for showing movements of security prices; but amongst the twelve industrials which it formerly included there was one quotation for United States Steel preferred, one for United States Steel common, one for United States Rubber preferred, and one for United States Rubber common. The weight thus given to steel and especially to rubber seems to have been unwarranted.

The computational problems of generating an average value for 24,000 price quotations covering 40 NYSE stocks over a 26-year period was ‘bewildering’ (Mitchell 1916, p. 655) for academics but posed little difficulty for the less precise Dow Jones index generated by the vernacular approach. For various reasons, the literature on equity security analysis prior to WWI is populated primarily by contributions from the vernacular approach. Contributions from those in the trade and the financial press, such as Clews (1908), Alexander Noyes (Klein 2001), Edwin Lef`evre (1923) and Hartley Withers (1911), were typical; though contributions with a more academic flavor were beginning to appear, e.g., Lowenfeld (1909); Babson (1910, 1911). Works written by academics, designed primarily to appeal to other academics, appear in strength following WWI. Included in this grouping are contributions by Irving Fisher, Edgar Smith, John Maynard Keynes and John Burr Williams.31 Even though some members of the academic grouping, such as Irving Fisher and J.M. Keynes, did make some 31 Though Edgar Smith was also a financial analyst and investment manager during the 1920s, he is included in the academic group as many of his contributions were targeted

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contributions that could easily be included in the second grouping, there is generally a different flavor to the contributions of the two groupings. This dichotomy between academic and trade publications serves to reinforce the importance and relevance of Graham and Dodd (1934): a book written by individuals with academic standing that is fundamentally concerned with the types of problems that are at the core of what practitioners do. Graham and Dodd (1934) redefined the role of academics in relation to the practice of security analysis. Benjamin Graham (1894–1976), the senior author of the book, was well suited to this task. Born in London, England in 1894 as Benjamin Grossbaum, he immigrated to the United States in 1895. Following an undergraduate education at Columbia University, Graham graduated in 1914 and went to work at the Wall Street firm of Newburger, Henderson, and Loeb, performing mostly lower level tasks. By 1920, Graham had worked his way up to partner. During the 1920s, Graham went on to form a number of investment firms in which he was a principal. It was a keen mind and a wealth of market experience that Graham brought to his classes at Columbia University where, starting in 1928, Graham was a part-time instructor of investment classes. It was in one of these classes that David Dodd was a student.

2.2.3

Charles Dow and the Dow Indexes

A key historical initiative in the popular science of financial investments involved increasing the availability of accurate information to the individual investor. Similar to the telecommunications and computer driven technological revolution that has transformed modern securities markets, the 19th century witnessed: the development of telegraph lines in the 1840s; the introduction of the ticker tape in 1867; the availability of the local telephone line in the late 1870s, direct phone links via cables around 1890 and the use of congestion reducing private phone lines around 1900. The securities industry was at the forefront in implementing these new technologies. It was during the 1890s that the NYSE required listed companies to produce annual reports. Though, even with this change, many of the annual reports that were produced did not have much substance by modern standards, the rise of the professional investment advisor necessitated that some useful information be made available. Though much of the trade literature of at the academic audience, e.g., Smith (1927, 1931). In McCloskey’s terminology, Smith was actively involved in conversations with academics.

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Fig. 2.8

Charles Dow (1851–1902)

the time is largely concerned with pontificating on the good or evil of speculation, or glorifying the deeds of the big-time speculators or documenting use of the securities market to propel the rise of a business titan, the ‘green shoots’ of an emerging ‘science of financial investments’ is apparent by the turn of the century. The financial press spearheaded a number of important innovations. Of particular importance is the introduction of price indexes to measure the performance of the aggregate stock market: it is Charles Dow (1851–1902) who is often credited with being the father of the modern stock market index (Fig. 2.8). Dow is also important in having, together with Edward Jones and Charles Bergstresser, founded Dow Jones & Co., the company that created the Wall Street Journal. Charles Dow is a caricature of the changes that were taking place in the United States securities markets in 1879. Dow was a life long newspaper journalist who converted to covering financial news after covering a mining story for the Providence Journal in 1879. That Dow was able to achieve success in financial reporting by feeding the growing need for information to do security analysis. In 1880, Dow moved to New York where he started with a stint reporting on mining stocks. In 1882, he joined together with Edward Jones, a fellow reporter from his days in Providence who also had relocated to New York, to form Dow Jones & Company. With offices behind a soda shop located next door to the entrance of the NYSE, the main activity of the company was to collect and distribute ‘flimsies’ or ‘slips’ containing market news of the day. It was in this ‘Customers Afternoon Newsletter’ that on 3 July 1884 the first

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version of the index appeared. The price-weighted average was calculated by summing the prices of the stocks in the index and dividing by the number of stocks. According to Siegel (1998, p. 55), Dow began publishing a daily index of actively traded, high capitalization stock started in February of 1885. The original index contained 10 railways and 2 industrials. This collection was roughly consistent with the importance that railway stocks had in the stock market of that era. Dow expanded the index four years later to cover 18 railways and 2 industrials. The same year (1889), Dow Jones & Co. started the Wall Street Journal. At this time the Commercial and Financial Chronicle was the most important financial newspaper. (Judging from accounts of Richard Wychoff (1930, p. 44), the Chronicle continued to be the leading source of financial news until after Dow’s death.) Recognizing the importance of the emerging industrial sector, in May 1896 Dow changed the index to a 12-stock index of industrial stocks. The first version Dow Jones Industrial Average appeared in the Wall Street Journal in October 1896. The index of 20 railway stocks, the precursor of the modern Dow Jones Transportation Index, was renamed the Rail Average (Tables 2.1 and 2.2). The original 12 stocks of the Dow Jones Industrial Average (DJIA) reflect the nature of the stock market at that time. The stocks were: American Cotton Oil, American Sugar, American Tobacco, Chicago Gas, Distilling and Cattle Feeding, General Electric, Laclede Gas, National Lead, North American, Tennessee Coal and Iron, U.S. Leather and U.S. Rubber. All but U.S. Leather survives today in some form, though only General Electric remains in the DJIA. In 1916, the DJIA was expanded to 20 stocks and to 30 stocks in 1928. The use of 30 stocks has continued up to the present day. Only three stocks (American Sugar, General Electric and U.S. Rubber) of the original twelve appear in 1916, with 7 of the 20 from 1916 appearing in 1928. Oddly enough, American Tobacco and North American reappear in 1928 after being left off the 1916 list. This reflects the ongoing practice, still used today, to update the average to reflect the changing composition of trading, market capitalization and industrial composition of the leading common stocks32 . The Science of Equity Valuation Following Jovanoic and LeGall (2000, 2001) and Jovanovic (2006) notions central to modern Finance — such as the random walk hypothesis and the 32 The complete history of changes in the Dow Jones Averages can be downloaded from the Dow Jones website: www.dowjones.com.

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Components of the Dow Jones Industrial Average July 17, 2009.

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ICB subsector

Weight PCT

USD close

MMM AA AXP T BAC BA CAT CVX CSCO KO DD XOM GE HPQ HD INTC IBM JNJ JPM KFT MCD MRK MSFT PFE PG TRV UTX VZ WMT DIS

Diversified Industrials Aluminum Consumer Finance Fixed Line Telecommunications Banks Aerospace Commercial Vehicles & Trucks Integrated Oil & Gas Telecommunications Equipment Soft Drinks Commodity Chemicals Integrated Oil & Gas Broad Diversified Industrials Computer Hardware Home Improvement Retailers Semiconductors Computer Services Pharmaceuticals Banks Food Products Restaurants & Bars Pharmaceuticals Software Pharmaceuticals Nondurable Household Products Property & Casualty Insurance Aerospace Fixed Line Telecommunications Broadline Retailers Broadcasting & Entertainment

5.438202247 0.883318928 2.422644771 2.072601556 1.114088159 3.574762316 2.937770095 5.628349179 1.772687986 4.349178911 2.382886776 5.922212619 1.006914434 3.455488332 2.132238548 1.624027658 9.975799481 5.119273984 3.188418323 2.370786517 4.999135696 2.392394123 2.099394987 1.292999136 4.833189283 3.493517718 4.649956785 2.557476232 4.191011236 2.11840968

62.92 10.22 28.03 23.98 12.89 41.36 33.99 65.12 20.51 50.32 27.57 68.52 11.65 39.98 24.67 18.79 115.42 59.23 36.89 27.43 57.84 27.68 24.29 14.96 55.92 40.42 53.8 29.59 48.49 24.51

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New York SE New York SE New York SE New York SE New York SE New York SE New York SE New York SE NASDAQ NMS New York SE New York SE New York SE New York SE New York SE New York SE NASDAQ NMS New York SE New York SE New York SE New York SE New York SE New York SE NASDAQ NMS New York SE New York SE New York SE New York SE New York SE New York SE New York SE

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3M Co. Alcoa Inc. American Express Co. AT&T Inc. Bank of America Corp. Boeing Co. Caterpillar Inc. Chevron Corp. Cisco Systems Inc. Coca-Cola Co. E.I. DuPont & Co. Exxon Mobil Corp. General Electric Co. Hewlett-Packard Co. Home Depot Inc. Intel Corp. Interntl. Bus. Machines Johnson & Johnson JPMorgan Chase & Co. Kraft Foods Inc. Cl A McDonald’s Corp. Merck & Co. Inc. Microsoft Corp. Pfizer Inc. Procter & Gamble Co. Travelers Cos. Inc. United Technologies Co. Verizon Comm. Inc. Wal-Mart Stores Inc. Walt Disney Co.

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Table 2.1

1896

Components of the Dow Jones Industrial Average: 1896, 1916, 1928, 1997, 2003. 2003

American Beet Sugar American Can American Car & Foundry American Locomotive American Smelting American Sugar American Tel & Tel Anaconda Copper Baldwin Locomotive Central Leather General Electric Goodrich Republic Iron & Steel Studebaker Texas Co. U.S. Rubber U.S. Steel Utah Copper Westinghouse

Allied Chemical American Can American Smelting American Sugar American Tobacco Atlantic Refining Bethlehem Steel Chrysler General Electric General Motors General Railway Sig. Goodrich International Harvester International Nickel Mack Trucks Nash Motors North American Paramount Publix Postum, lnc. Radio Corp. Sears Roebuck Standard Oil (N.J.) Texas Corp. Texas Gulf Sulphur Union Carbide U.S. Steel Victor Talking Machine Westinghouse Electric Woolworth

Allied-Signal Alcoa American Express American Tel & Tel Boeing Caterpillar Chevron Coca-Cola Du Pont Eastman Kodak Exxon General Electric General Motors Goodyear Hewlett-Packard IBM International Paper J.P. Morgan Johnson & Johnson McDonald’s Merck Minn. Mining Philip Morris Procter & Gamble Sears Roebuck Travelers Group Union Carbide United Technologies WalMart

Alcoa Altria (Philip Morris) American Express American Tel & Tel Boeing Caterpillar Citigroup Coca-Cola Du Pont Eastman Kodak Exxon General Electric General Motors 3M Co. Hewlett-Packard Home Depot Honeywell IBM Intel International Paper Johnson & Johnson J.P. Morgan Chase McDonald’s Merck Microsoft Proctor & Gamble SBC Communications United Technologies WalMart

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163

1916

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American Cotton Oil American Sugar American Tobacco Chicago Gas Distilling & Cattle Feeding General Electric Laclede Gas National Lead North American Tennessee Coal and Iron U.S. Leather pfd.

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associated ‘science of the stock market’ — can be traced to the latter half of the 19th century when French writers such as Jules Regnault (1834– 1894) and Henri Lef`evre (1827–1885) extended the positivist program of Auguste Comte (1798–1857) to financial markets. Alex Preda (2005, 2006) details the social and economic developments that laid the foundation for this early progress towards the modern theory of efficient markets. The needed cognitive and cultural background required transforming financial investing into a science, altering public perception to see financial securities as investments rather than gambling. Consistent with the central role of London in the global securities market, similar developments to those in France were emerging in the United Kingdom where the founding of the Foreign and Colonial Government Trust in 1868 “was the first British investment trust, designed to provide investors with the opportunity . . . to allow ordinary investors to earn the higher yields that were available on overseas government bonds, compared with domestic Consols . . . to reduce the risk of possible loss through default on coupon or final payment by investing in a range of different securities” (Rutterford 2009). While French contributions to the science of the stock market included a number with an academic bent, U.K. contributions were decidedly in the vernacular realm.33 By the beginning of the 20th century, the vernacular contributions had progressed to where Lowenfeld (1909, esp. p. 25) was able to use analysis of price charts for representative debt issues, preferred shares and ordinary shares in eight different countries to conclude the following ‘law’ for ‘the foundation of profitable investment’: The realizable values of all securities controlled by the Stock Exchanges of any one country are entirely under the influence of the general state of trade of that country.

This law led to the lesson (p. 26): 33 This is not to say that there were no academic contributions. Giffen (1877), for example, considers the causes of fluctuations in the prices of stock exchange securities. After considering the relationship between prices and the quantity of money, Giffen examines the impact of changes in money supply on ‘the state of credit’ and the associated impact on the price of securities. Market manipulations, security price cycles and the sources of panic on the stock exchange are all considered. In chapter IX, Giffen gives direct consideration of the valuation of securities. Equity securities are considered as part of a continuum of income producing investments: “After the best securities [of first-rate states such as France, England, Germany and the United States] come the obligations of all but the first-rate governments; the shares, whether preference or ordinary, in railways, gas-companies, banks, ships, and other undertakings, the variety being endless and the estimation most various” (pp. 87, 88).

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Every investor who places his money exclusively in the investments of any one country is simply speculating on the future trade prosperity of that country.

Recognizing that the “trade prosperity of each country differs from that of all other countries, so the price movement of stocks in each country differ from those of all other countries” (p. 40), Lowenfeld proposes the following international diversification rule: If an investor divides his capital equally among a number of stocks, every one of which is under a different trade influence, then each of these divisions of his capital will constitute a distinct investment risk, and a true system of arranging investment risks is thereby established.

This ‘top-down’ equally weighted by country approach to diversification differed from the more ‘bottom up’ conventional approach of selecting securities on the basis of a portfolio yield target and the associated quality of the securities being purchased. The title of Lowenfeld (1909), Investment: An Exact Science reflected the remarkable transformation in public attitudes regarding stocks and shares that had taken place in the United Kingdom from around 1870 until WWI. Lowenfeld (1909) was one of a number of textbooks that extended contributions appearing in the Financial Review of Reviews, first published in 1905, and associated with the Investment Registry, founded in 1881. The Investment Registry was one of a number of managed funds that used the portfolio management methods of ‘average investment trusts’ (Scratchley 1875; Hutson 2005). Based on the initial success of the Foreign and Colonial Trust, the key insights behind the average investment trust are outlined in the ‘Publisher’s Note’ to Lowenfeld (1909): The key to investment success lies in a true system of averages with the view to the depreciation in one portion of the securities held being counterbalanced by a simultaneous rise in another portion of them. The proper and systematic selection of stocks is the whole secret of Capital Stability, and in Capital Stability lies the whole science of successful investing.

From the perspective of the history of equity securities, it is the traded claims against the different managed funds that is significant. Starting with the Foreign and Colonial, the ‘stocks’ held by the funds were, initially, all bonds. This is consistent with the typical British investor of that period: “Many belonged to the upper and upper-middle classes . . . who lived on the income from their invested capital. Security of

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capital and regular interest payments were therefore vital” (Hutson 2005, p. 441). For example, Rutterford (2009) lists the eighteen debt securities of the 1868 Foreign and Colonial trust totaling about £1 million initial market value, spread over 14 countries, with the smallest market value being a £15,000 New South Wales 5% coupon and seven country positions being about £100,000: Spanish 3%; Italian 5%; Turkish 5% and 6%; Austrian 6% and 5%; Chilian 6% and 7%; Egyptian 7% and 7% Railway Loan; and, Peruvian 5%. The combined market value of the United States (10/40), Nova Scotia 6% and Brazilian 5% positions was about another £100,000 with the remainder being made up of Russian Anglo Dutch company bonds (£80,000), Danubian (£60,000) and Portugese (£50,000). A number of the securities, such as the Spanish, Portugese, Italian, and Turkish bonds, were selling well below par value, indicating the likelihood of default on coupon payments. The ‘exact science of investments’ made a number of substantive contributions to equity valuation. Prior to this, ordinary shares were assessed for valuation on much the same principles as debt securities. Safety of capital and income received were the two chief characteristics. The initial average investment trusts aimed to employ equally weighted, geographically diversified portfolios to improve the safety of capital. As Lowenfeld (1909, p. 10) observed: “The safety of Capital is obtained by its even division over a number of sound stocks of identical width of fluctuation, and every stock held must also be subject to an entirely different market influence”. Due to the declining coupon rates on British government and corporate bonds between 1870–1900, this approach to diversification also coincided with a potential increase in income received due to the higher, sometimes much higher, yields on foreign bonds. For example, the weighted average yield on the Foreign and Colonial Trust of 1868 was just over 8% at a time when British government bonds were yielding around 3.5%. An essential insight from the science of investments for equity valuation is that value is conceived in a portfolio context. In addition, there is explicit recognition that the values of stocks within a given country are, more or less, all subject to ‘the influence of the general state of trade of that country’. In the context of modern Finance, this would correspond to the one factor model where expected returns on individual stocks depend on a combination of the riskless rate of interest and the expected return on the market. However, unlike modern Finance theories of equity value, the problem of identifying an appropriate market index is avoided by exploiting the low correlations between ‘stock’ markets in different geographical locations

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that applied at that time. The equity value of a geographically diversified portfolio was distinguished from the value of a domestically diversified portfolio involving “a mixed assortment of British stocks . . . That any counterpoise of this sort is ever to be derived from an all-British Investment List is an absolutely vain hope” (Lowenfeld 1909, p. 23). British Equity Valuation on the Eve of WWI The 1890’s is a potential reference date for exploring the origins of the ‘value investing’ approach to equity valuation, e.g., Graham and Dodd (1934, p. 14) make specific reference to ‘the last three decades’ of security analysis. This suggests the first decade of the 20th century as a possible starting point for examining early contributions to the value investing approach. Though written by a financial journalist from ‘the City’ in London, Hartley Withers (1867–1950) was not without ‘scientific’ stature in the vernacular world of pre-WWI British security markets, e.g., Withers (1908). As such, Withers (1910) provides an helpful benchmark for examining the techniques of equity security analysis that predate Graham and Dodd. Though written by a journalist, Withers’ objective was ‘to glean among the best brains of the world of finance’ and ‘to pass on the gleanings to readers’. There is ample attention given to both English and U.S. securities markets. Withers (1910) contains twelve chapters. After an initial chapter on the historical evolution of securities, starting from the 16th century, Withers proceeds with a chapter on the form of securities, dealing with the topics such as the definitions of stocks, shares and bonds and the difference between registered and bearer securities. While this material is somewhat pedestrian, the next four chapters are recognizable precursors of Graham and Dodd (1934). The first of the four chapters details how the capital structure of companies relate to the various classes of securities. In this chapter there are the expected topics such as the role of the shareholders in choosing the board of directors, the difference between preferred and ordinary shares and stock splits. The presentation is structured around the fictionalized creation of the ‘Hygienic Tooth-powder Company’ by ‘Mr. Cleanbite’ who lives in Brixton and has a small dental practice in Finsbury Circus. The dentist has developed an effective toothpowder but does not have the capital for making it on a large scale. As chance would have it, one of his business neighbors in Finsbury Circus, “a certain Mr. Mortimer . . . who carries on the mysterious profession of company promoter, underwriter, financier, and organizer of syndicates” happens to visit Cleanbites dental office for treatment of a painful molar. The machinations and complications of the ensuing

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formation of a public company, complete with issuing of stock, selection of the board of directors, watering of stock and so on reflects a solid understanding of the initial public offering. Having laid this foundation, Withers proceeds to a chapter with detailed examination of prospectuses. Chapters five and six can fairly be considered as early gems of equity security analysis, in the sense of the Graham and Dodd mantra: “All security analysis involves the use of financial statements”. Chapter five is a detailed dissection of the balance sheet and income statement of Babcock and Wilcox Ltd., a well-known engineering firm at that time. After going over items on the liabilities side of the balance sheet, Withers (p. 127) observes: It is when we come to the assets side of the balance-sheet that its difficulty really begins. On the liabilities side we have been faced with sums about which there is no doubt. Every penny that the company has to account for to its shareholders or pay to its creditors is a definite penny, no more and no less. But when we look into the assets that it holds against these liabilities there is room for infinite variety in the meaning of the figures attached to them.

Withers goes on to demonstrate that the simple process of accounting for asset values according to the values paid for purchase is ‘quite useless as a guide to its actual position at the moment’. This lays the basis for chapter six which is concerned with the notions of depreciation and profitability. The connection of these concerns with Graham and Dodd (1934) are apparent where Part VI is composed of four chapters concerned with the implications of asset values for balance sheet analysis. In addition, Part V is concerned with analysis of the income account and has a chapter on ‘the relation of depreciation and similar charges to earnings power’. Accounting standards were considerably less well defined at the time Withers was writing. Rules and practices that are taken for granted today were either non-existent or subject to dispute. Legal decisions associated with bankruptcies, securities frauds and the like often acted as a barrier to implementing sound accounting practices. This leads Withers (p. 151) to make the following statement about the position of the auditor: The position of an auditor of a joint stock company is doubly difficult, from the indefinite and hazy nature of his duties, and from his relation to the shareholders and the Board. As we have seen, his duties are reduced by legal pronouncements to those of a checking-clerk, and the fees that he receives are very inadequate to the real importance of his task; while in practice, if a company gets into difficulties, the auditors

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are always likely to be blamed for not having pointed out that the published figures, though correct, were not veracious. Though originally, as a rule, appointed to be watch-dogs in the interests of the shareholders, to see that the Board and the officials are publishing true and correct statements. Their duty is to the shareholders, but their direct relations are with the Board and officials. When they take a high view of their duties, and call attention in their reports to matters which ought to be amended, it sometimes happens that their action is very foolishly resented by the shareholders, whose best interests they are trying to serve, and they sometimes get removed from office for having done their duty well.

In light of the recent historical events surrounding the Enron bankruptcy and the collapse of one of the big five accounting firms, Arthur Anderson, this statement seems almost prophetic. After three chapters, one on government and municipal securities, one on the stock exchange, and one on stock exchange transactions, Withers concludes with three remarkable chapters that explicitly deal with the implications of the distinction between speculation and investment, a distinction that also plays a key role in Graham and Dodd. Yet, Withers in these chapters goes beyond Graham and Dodd in some ways. The last three chapters of Withers have many elements that later appear in J.M. Keynes (1936, ch. 12). It is difficult to do justice in a short discussion. Chapter 10 is concerned with the price movements of securities. In this chapter, Withers starts by recognizing the role of psychological factors in determining stock prices, “price movements are chiefly a psychological question” (p. 283). After an insightful observation about the impact of dealers on pricing (“it often happens that an unexpectedly favourable traffic return or dividend announcement makes the dealers in a market raise the price of stock because they infer a quick rush of buying that will follow it”), Withers recognizes that share pricing ultimately has to be supported ‘by the action of the public’. Withers follows this introduction with a discussion that is clearly reminiscent of Keynes: One curious result of this dependence of securities on public opinion in the matter of their price movements, is that it is often dangerous to be too clever and far-seeing concerning the influences that may be expected to improve or depress prices. It has happened before now that long-sighted operators have foreseen trade developments or other happenings that could not fail ultimately to have an important effect on prices, have backed their opinion by buying the securities likely to be

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affected, and have lost money by being too keen of vision. All that they foresaw may have happened, but if its effects did not dawn on the intelligence of a large enough number of buyers, the stocks that ought to be affected would not move . . . It is not enough for a stock to be worth buying. It must be recognized to be worth buying by the multitude before it will go up in price. Further, the fact that a stock may be absurdly over-valued will not for a moment prevent its rising still further if there are folk enough who believe that it is still cheap and are prepared to back their opinions by buying it.

This is not the only connection to Keynes (1936, ch. 12). After examining the bull and bear operations of speculators, Withers observes that the impact of such operations on security prices are “more or less temporary” and “what finally determines the price of a security is what the real investor thinks about it. Bulls and bears produce the waves on the surface, real buying and selling are the flow and ebb of the tide which determine the depth of the water” (pp. 293, 294). This followed by the remarkable statement: “The real investor . . . is likely to be guided by convention”. Though the connection to the elaborate process of decision making under ‘true uncertainty’ is unrecognized, Withers does dedicate substantial discussion to the social status of the real investor, “in most cases a member of the upper or middle classes of society” and the various social and psychological factors that would influence the conventions that guide their investment decisions, e.g., “old-time convention had been very much in favour of investments at home”. It is difficult to tell whether Keynes was aware of Withers (1910) as Keynes did little referencing of the ideas gleaned from others and no reference is given to Withers in Keynes (1936). The last two chapters of Withers (1910) are devoted to detailed examination of ‘the real investor’ and ‘the speculative investor’. After recognizing that making such a distinction is artificial because “every investor is a speculator, and the difference between the two classes is finally, like most other differences, one of degree”, Withers observes that real investors “look most of all to security of income and least to the hope of capital appreciation, while the pure speculator sets no store by income, and looks entirely to the chance of being able to make a big profit by a resale” (p. 317). Between these polar extremes are a range of speculative investors and investing speculators. The motivations of these speculative investors and investing speculators are of interest. In particular, much like the ‘value investor’ of modern times, the investing speculator can follow the course “of buying good securities which the investing public is at present neglecting, knowing that some day or other it will come back to them, and in the meantime

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earning a good round yield on his money by buying stocks which are discredited”. A final point of interest in Withers (1910) are two “well known saws on the subject of investment” that are explored: ‘the higher the yield, the lower the security’ and ‘never put all your eggs in one basket’. On the latter saw Withers makes the remarkable (why?) statement: “expert advisers of the public are fertile in schemes for scientific distribution of risks by climate, or by geography, or by industries, etc”. Withers finds that neither of the old saws is “quite sound”. The text ends with an exhortation (pp. 344, 345): “ . . . the preceding pages have been written in vain if they have not shown that stocks and shares and market movements are a weltering chaos of uncertainty and haphazard guesswork, based on figures that often mean nothing — or worse than nothing, because they seem to mean so much — and on gusts of opinion blown hither and thither by causes which have no logical connections with the merits of the stocks affected. Whosoever is wise will ponder these things and try to be a real investor, exposing himself as little as possible to speculative anxieties and pitfalls”. Roger Babson and the Barometric Indices It is a quandary that Roger Ward Babson (1875–1967) is remembered today primarily for founding Babson College in Wellesley, Massachusetts instead of other important contributions that transformed equity security markets. In particular, together with his wife Grace, Babson founded Babson’s Statistical Organization, the first U.S. investment advisory company aimed at providing advice to individual as well as institutional investors.34 The founding of the Babson Institute (later Babson College) was part of the pioneering effort that revolutionized the U.S. financial services industry, making Babson a considerable fortune in the process. A graduate of MIT in 1898, Babson acquired a considerable academic reputation over his career. Initial contributions included a number of influential papers in the Annals of the American Academy of Political and Social Sciences (Babson 1910, 34 The

original company was founded in 1904 as Babson’s Statistical Organization (BSO). The company was later called Business Statistics Organization and then Babson’s Reports. Combined with some forecasts made prior to 1904, the continuous forecasts for BSO and later named versions is consistent with the same used for the unnamed ‘best forecaster’ in Cowles (1944). In 1986, Babson’s Reports was sold to United Business Service Company which became Babson-United Investment Advisors, Inc. and the weekly newsletter became United & Babson Investment Report. In 2001, this Report ceased publication. Further information can be obtained at www.babson.com.

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1911) and a paper Babson presented at the 1911 meetings of the American Statistical Association (1912). Babson (1910a) is a useful survey of financial information sources available at the time. From that point, Babson went on to publish over 40 books, including Business Barometers, which reached eight editions, to be followed by Business Barometers for Profits, Security, Income, which had ten editions. He was a Fellow of the Royal Statistical Society of London. In the academic realm, Babson was part of the pre-history of the institutional school of economists that commences with the manifesto of institutional economics — Walton H. Hamilton (1919) — and the establishment of the National Bureau of Economic Research (NBER) in 1920 (see Sec. 3.1). Proposing a ‘modern’ and ‘scientific’ empirical approach analogous to that used in the natural sciences, institutionalism aimed to replace the theoretically driven neoclassical approach to economics that dominated economics prior to WWI, e.g., Yonay (1994). By the time that institutionalists were in vogue, Babson was firmly ensconced in the vernacular realm. In addition to a newspaper column, which commanded 16 million readers, he also wrote hundreds of magazine and newspaper articles. The intellectual influence of Babson within the vernacular community is evident from W. P. Hamilton (1922), The Stock Market Barometer, which is the defining work of the classical Dow Theory. In the United States, Babson pioneered the use of ‘barometers’ to guide a market timing strategy of equity selection (see Fig. 2.9). Being a Dow theorist, Hamilton based his barometer on the behavior of market generated data, especially the Dow indexes. The Babson barometer was based on ‘12 headings’ covering ‘25 subjects’. The headings are: building and real estate; bank clearings; business failures; labor conditions; money conditions; foreign trade; gold movements; commodity prices; investment market; condition of crops; railroad earnings; and, social conditions. Each of these “twelve main subjects have by custom come to be known among merchants as the twelve barometric indices of the condition of trade” (Babson 1910, p. 114). The ‘scientific’ approach to equity valuation of the American Babson stands in stark contrast to the ‘scientific’ approach of the British Lowenfeld (1909) and the ‘average investment trusts’. Instead of diversifying geographically to maintain stability of capital and a specified level of regular income, Babson proposes a market timing strategy based on the leading indicator properties of the barometer: The safest and most successful method of investing is to watch the barometer figures on the twenty-five subjects . . . and then to buy and

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Fig. 2.9 Composite plot of the actual barometer figures for surface conditions (Bason 1910, p. 122)

Note: If action and reaction are equal, an area at D equivalent approximately to the areas A, B or C must be consumed before another depression. In other words, if the plot of the new Summary Barometer Figures rapidly works upwards, prosperous conditions will last only a year or two: but if the figures remain constant, thus giving a horizontal line, prosperous conditions may last several years. Also, it should be remembered that, although manufacturers and merchants can count on good business during the entire area, yet the stock market usually turns before one-half of the area is consumed and the bond market when about one-fifth or one quarter is consumed. to sell only when these subjects plainly show which to do, confining all purchases to the very highest grade securities. By such a method purchases are made only at the end of a long period of declining prices, after which securities are held from two to four years until the figures on these twenty-five subjects show that prices have about reached the top. Then they are sold, the proceeds reinvested in short-term municipal notes and high-grade bonds maturing in from one to three years, or else deposited in banks. During these years a panic invariably comes when this money will again purchase, at from 20 to 50 per cent less price, the same high-grade securities that were sold a few years previous. (Babson 1910, p. 132)

Babson further observes: “By this process an investor averages an annual income of about 8 per cent. from money invested in the highest grade bonds,

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and about 16 per cent. from money invested in the highest grade stocks”. While the numbers depend on the specific sample that Babson used for calculation, the basic point is clear: accurate market timing is the safest course to higher returns. In a dinner organized by the American Statistical Association (ASA) on 17 April 1925 about forecasting security prices, Frederick Macaulay was asked to provide a critical review of the use of the barometer chart presented by Roger Babson. “He raised the question, in regard to Mr. Babson’s chart, as to whether it was not just as difficult to predict areas above and below trend, as to forecast the course of the stock market” (ASA 1925, p. 249). The point illustrates the growing divide between the vernacular and academic approaches to Finance that were emerging in the U.S. during the 1920s. For Macaulay and other institutional economists of the era, the stock market was one of a number of exogenous variables that could be used to predict the general direction of the economy. It was difficult to predict the economy, let alone the direction of the stock market. For Babson, the objective was to provide a method for combining available data relevant for predicting the direction of the stock market in order to implement a market timing strategy. This requires an infrequently occurring, discrete random variable to be predicted. Hence, Macaulay and Babson may have been talking at cross purposes. Throughout the 1920s a variety of ‘barometer’ measures were developed. For example, consider the 17 April 1925 ASA dinner again. In addition to Babson, William Peter Hamilton (The Stock Market Barometer 1922) also presented at the dinner; as did Paul Clay of Moody’s Investors’ Services who also engaged in forecasting ‘the course of the stock market’ using, first and foremost, “our trade barometer, which is a weighted average of the barometrical trade returns. Trade conditions are bullish or bearish in accordance with the movement of this trade barometer, except that an excessive rise far above normal is bearish, while an excessive decline far below normal is bullish”. That Hamilton and Babson were familiar provides an interesting connection between two of the most remarkable equity security market predictions. On 5th September 1929, Babson gave a speech saying “Sooner or later a crash is coming, and it may be terrific”. Later that day the stock market declined by about 3%. This became known as the ‘Babson Break’. Hamilton wrote his last editorial as editor of the Wall Street Journal on 25 October 1929 titled: ‘The Turn of the Tide’.

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The Founding of Babson College (from www.babson.edu) Beginning in 1908, Roger Babson offered through Babson’s Statistical Organization a correspondence course on how to sell bonds. This endeavor was an instant success and courses in economics, finance, and distribution soon followed. He then saw the need for a private college that specialized in business education. In June 1919, in a special letter to clients of the B.S.O., Roger Babson announced the establishment of a school of business administration to provide not only practical but also ethical training for young men wishing to become business executives. On 3 September 1919, with an enrollment of 27 students, the Babson Institute (renamed Babson College in 1969) held its first classes in the former home of Roger and Grace Babson on Abbott Road in Wellesley Hills. From the very beginning, Roger Babson set out to distinguish the Babson Institute from other colleges offering instruction in business. The Institute provided intensive training in the fundamentals of production, finance, and distribution in just one academic year, rather than the standard four. The curriculum was divided into four subject areas: practical economics, financial management, business psychology, and personal efficiency, which covered topics such as ethics, personal hygiene, and interpersonal relationships. The program’s pace did not allow time for liberal arts courses and it was assumed that students would learn these subjects elsewhere. Believing experience to be the best teacher, Roger Babson favored a curriculum that was a combination of both class work and actual business training. Seasoned businessmen instead of career academicians made up the majority of the faculty. To better prepare students for the realities of the business world, the Institute’s curriculum focused more on practical experience and less on lectures. Students worked on group projects and class presentations, observed manufacturing processes during field trips to area factories and businesses, met with managers and executives, and viewed industrial films on Saturday mornings. The Institute also maintained a simulated business environment as part of the students’ everyday life. The students, required to wear professional attire, kept regular business hours (8:30 a.m. to 5:00 p.m., Monday through Friday, and 8:30 a.m. to noon on Saturday) and were monitored by punching in and out on a time clock. They were also assigned an office desk equipped with a telephone, typewriter, adding machine, and Dictaphone. Personal secretaries typed the students’ assignments and correspondence in an effort to accurately reflect the business world. Roger Babson prepared his students to enter their chosen careers as executives, not anonymous members of the work force.

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Irving Fisher, Stock Valuation, and the 1929 Crash

Fisher’s Prediction The roots of modern Finance can be traced, without much difficulty, back to Irving Fisher. As time has advanced, a tendency has emerged to start the chronology of modern Finance with Markowitz., e.g., Markowitz (1999) and Rubinstein (2002). Given the substantive institutional changes in securities markets that have taken place since WWII, this tendency is understandable. However, Fisher’s seminal contributions spanned so many related areas, from index numbers to the theory of interest to the use of mathematical analysis in valuation problems, that Fisher can reasonably be identified as having laid the foundations for the theoretical superstructure that dominates the landscape of academic Finance. Siegel (1998, p. 44), for example, refers to Fisher as ‘the founder of modern capital theory’. Yet, Fisher’s importance to security analysis extends beyond his academic contributions. Fisher harks back to an era when leading academics, such as J.M. Keynes, also played important roles outside the academic realm. In addition to writing investment newsletters and giving speeches to business leaders on financial topics, Fisher also started a profitable card indexing firm based on an invention that he had patented. Prior to the stock market collapse of 1929, his personal net worth was around $10 million.35 Based on this background, it is somewhat unfortunate that, in the annals of securities analysis, Fisher is most remembered for comments and prognostications made just prior to the stock market collapse of 1929 and in

35 The life of Irving Fisher extended well beyond the world of academics, e.g., Klein (2001, p. 86–88). Born in 1867, the son of a Congregationalist minister, Fisher studied mathematics and political economy at Yale University. The claim that Fisher was a self-made business success has to be tempered by the fact that in 1893 Fisher married Margaret Hazard, daughter of Rowland Hazard, a wealthy woolen manufacturer. As a wedding gift, the happy couple was presented with a palatial abode in New Haven. It was not until 1912 that Fisher developed his card index system that he marketed through his Index Visible Company. In 1926, this company was merged with its major competitor to form what was eventually to become the Remington Rand Company. During the 1920s he was able to turn part of the house into a home for his Index Number Institute, staffed by more than a dozen people. The Institute prepared a weekly newsletter that was distributed to various newspapers around the world. Having suffered and survived tuberculosis in 1898, Fisher was for the rest of his life devoted to pursuing and promoting clean living. This part of his life found him to be a confirmed prohibitionist and one of the founders and organizers of the American Eugenics Society. This Society was an active promoter of the cause of ‘race betterment’.

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the following year, e.g., Fisher (1930). Siegel (1998, pp. 43, 44) provides a lively description of a most telling incident: It was a seasonably cool Monday evening on October 14, 1929 when Irving Fisher arrived at the Builders’ Exchange Club at 2 Park Avenue in New York City. Fisher, a professor of economics at Yale University and the most renowned economist of his time, was scheduled to address the monthly meeting of the Purchasing Agents Association . . . Members of the association and the press crowded into the meeting room. Fisher’s speech was mainly designed to defend investment trusts, the forerunner of today’s mutual funds. But the audience was most eager to hear his views on the stock market. Investors had been nervous since early September when Roger Babson, businessman and market seer, predicted a “terrific” crash in stock prices. Fisher had dismissed this pessimism, noting that Babson had been bearish for some time. But the public sought to be reassured by the great man who had championed stocks for so long. The audience was not disappointed. After a few introductory remarks, Fisher uttered a sentence that, much to his regret, became one of the most quoted phrases in stock market history: “Stock prices have reached what looks like a permanently high plateau”. On October 29, two weeks to the day after Fisher’s speech, stocks crashed. Fisher’s “high plateau” transformed into a bottomless abyss.

Keen to promote the notion of ‘Stocks for the Long Run’, Siegel is something of an apologist for Fisher. The depth of Fisher’s misconceptions are not adequately explored or recognized. For example, the actual quote by Fisher could be more accurately given as: “Stocks have reached what looks like a permanently high plateau . . . I expect to see the stock market a good deal higher than it is today within a few months” (Klein 2001, p. 201). Fisher was not the only prominent academic bulling the stock market. For example, just prior to the crash, Charles Amos Dice, a professor at Ohio State, published New Levels for the Stock Market (1929) which provided a range of arguments as to why stock prices had to continue climbing. Irving Fisher and Equity Valuation Though Fisher was only a leading voice in a chorus of academics cheering the virtues of stock investment, it is disturbing to see the soundness of his arguments being undercut by the brutal reality of the collapse in stock prices. Fisher’s outstanding academic and public reputation was justly deserved. He was a careful and methodical researcher employing valuation models that are similar to those employed today. For example, Fisher (1930,

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p. xxii) explicitly uses discounted cash flow valuation to arrive at estimates for common stock prices: Since every stock price represents a discounted value of the future dividends and earnings of that stock, there are four reasons that may justify a rise in the price level of stocks: (1) Because the earnings are continually plowed back into the business instead of being declared in dividends, this plowing-back resulting in an accumulation at compound interest, so to speak; (2) Because the expected earnings will increase on account of technical progress within the industry; (3) Because less risk is believed to attach to those earnings than formerly; (4) Because the “basis” by which the discounting is made has been lowered.

Writing at the end of 1929, following the 40+% decline in stock prices of September to mid-November, Fisher (1930) explores all of these four points in detail and concludes (p. 267–269): “the general plateau of the stock market is still the plateau of 1926–1929, still 55% higher than it was in 1926, and still higher than any previous plateau . . . For the immediate future, at least, the outlook is bright”. Fisher went far beyond a simple recognition that earnings were the key factor driving stock prices (p. 67): “The percentage increase in prices of stocks should be equal to the percentage increase in earnings per share if the ratio of price to earnings were to remain constant”. Yet, the available data indicated that from 1922–1927 industrial stock prices increased at 14.1% per year while ‘total profits’ (earnings?) increased only 9%. This difference Fisher attributed to the gains to common stock from the low ‘rate of return on preferred stock’ that permitted a greater share of the earnings growth to be captured by the common stock. In addition, the plowing-back of earnings permitted industrial corporations to purchase new plant and equipment that enhanced earnings capacity. Fisher recognized that the plow-back rate for industrial corporations had increased since 1927 and viewed this as a reinforcing force (p. 80): “During the long bull market there was the record of increased real income, while plowed-back earnings gave promise of future values resident in the productive and consuming plant of the nation that were properly reflected in a heightened level of stock prices”. Fisher (1930, p. 67) credits E. L. Smith with the argument that the plowing-back of earnings was the main factor driving the increase in common stock prices. Fisher (p. 66) puts the argument this way: The increase both in dividend payments and in plowed-back earnings during 1929 over 1928, was not only a primal cause of the new plateau of stock prices, but gave promise of continuing prosperity to business for

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1930. This increase should minimize the effects of the panic, which was largely restricted to the stock market. When earnings are turned back into a business it is in order to increase the rate of profits according to the same method by which interest is compounded on savings. There has always been a plowing-back of earnings, but it has been especially done in the last few years.

Having proposed the importance of plowing-back of earnings, Fisher (p. 81) asks the question: “Are the conclusions . . . with respect to the increased rate of plowed-back earnings, stated with too great optimism?” Fisher addresses this question with a reasoned analysis of the behavior of the aggregate priceearnings (P/E) ratio. Modern security analysts are well versed in the difficulties of interpreting P/E ratios. Earnings can be an elusive number that, to be adequately interpreted, requires careful inspection of additional information from the financial statements and other sources. Unlike modern stock market prognosticators, Fisher was hampered by lack of data on earnings and many other variables that are considered essential today for doing security analysis. For example, data on both a price index of industrial stocks and the associated earnings of those companies, calculated by the Standard Statistics Company (later to merge with the publisher of Poor’s Manual to form Standard and Poor’s), are only available from May 1927. Fisher was able to obtain his estimate of the increase in earnings of industrial companies over 1922–1927 of 9% from a government report (Committee of Recent Economic Changes). From the bulletin of the National City Bank of New York he was able to obtain evidence that the increase in earnings from 3Q 1928 to 3Q 1929 was 14%. Excluding railways and utilities, the remaining manufacturing and trading companies had a gain of 15%. Given the state of financial reporting requirements prior to the Securities Act (1933), the crude earnings numbers that Fisher had to work with are somewhat suspect. Fisher (1930, p. 88) observes: “There are also difficulties to be faced in the choice of stocks that publish annual earnings figures, and in those stocks where there is concealment of earnings for tax evasion purposes”. Fisher is also somewhat unclear about what P/E multiple to apply to individual stocks: The price-earnings ratios of the old-fashioned type should be perhaps ten times annual earnings, which is the traditional ratio for a fair selling price for stocks during the period prior to 1922. But for the new type of rapidly expanding corporation the price-earnings ratio might be 100 to 1, or even literally to infinity in the initial stages of investment when earnings are not being realized.

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With this background, Fisher proceeds to examine the aggregate stock price index and earnings data from the Standard Statistics Company. Examining the aggregate data (industrials including railways) Fisher concludes that the 9.8 P/E for November 1925 was justified. It was 40% below the peak of 16.2 in January 1929 and lower than the previous low of 11.2 for May 1927 “the earliest month for which such statistics are available”. In addition to examining the aggregate P/E data, Fisher made a number of astute observations about the behavior of aggregate and individual stock prices in the months surrounding the crash. In particular, Fisher observes that the run-up in prices was selective (p. 93): “As the market marched to its peak about half of the groups listed [on the NYSE] receded in price, while half went up”. It was the high flyers that came crashing down. Using his own index for aggregate stock prices that took in all NYSE groups, Fisher estimates that stocks fell 38% overall during the crash, with railways down only 28%, the most speculative stocks fell over 50% (Fig. 2.10). He attributes the downturn in ‘the best stocks’ to the impact of ‘overextension of loans’ to buy stocks. After reviewing the data surrounding the crash, Fisher remained a bull (p. 98): “ . . . the precipitous fall in the market went too far, in the light of sound reasons justifying the long bull market, namely, Fig. 2.10

∗

Price-earnings ratio, 1928–1929∗

For all Industrial common shares earnings increased far more rapidly than the increase of stock prices during 1929. But this group is open to the objection that it is a variable group of stocks from Fisher (1930, chart 10).

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justifiable expectation of great and increasing earnings, the fact they were so generously plowed-back, the warranted expectation of safety through diversification of investments and, finally, a consequent lowered basis of discounting the future as apparently reflected in price earnings ratios”. The Common Stock Theory As were many others at the time, Fisher was deeply impressed with the work of Edgar L. Smith on the long run performance of common stocks versus bonds. Prior to the appearance of Smith’s Common Stocks as LongTerm Investments (1924), Fisher (1912) held to the prevailing view that stocks would outperform bonds in periods of rising prices, while bonds would outperform stocks during periods of falling prices. Smith carefully demonstrated that this view was mistaken. Harold (1934, p. 46) summarizes what subsequently came to be known as the common stock theory: Proponents of the theory do not claim that a given stock is a better investment than a given bond nor that any group of stocks are better than any group of bonds. The theory, as expounded by Smith and van Strum, is that over long periods diversified portfolios of common stocks in leading corporations yield the investor more income, more safety, more market value per portfolio, and also that such commonstock investments, as a group, keep better pace with the cost of living than do bonds as a group.

Smith took care in recognizing that the stock holdings had to be welldiversified across companies that represented the major industries. In addition, stocks had to be held a sufficient period to permit liquidation at favorable prices. Smith recognized that the length of the holding period to liquidation could be as long as six years — extending to 15 years in extreme cases. Fisher (1930, pp. 198–200) explicitly recognized the contribution of Smith (1924) to “a material change during [1923–1930] in the estimate of the public as to the risk of investing in common stocks”. Fisher (1930) is well off the mark in terms of predicting future stock price movements. Yet, Fisher (1930, ch. 13) is an excellent illustration of why Fisher can be considered as laying the methodological foundation for modern Finance. The chapter is concerned with “Flight from Bonds to Stocks” — developing a theoretical basis for the rationale of why stocks are a superior long run investment than bonds. Fisher first explores the notion that bonds are ‘far safer’ than stocks. Working with Smith’s data, Fisher adjusts for the impact of price level changes and estimates the yield on a bond investment for 1866–1885, a period of falling prices, as 11.7% in real

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terms (6.8% nominal), the same calculation for 1901–1922 was 1.1% real (4% nominal). “This analysis indicates clearly enough that during periods of marked fluctuations in the general price level, bonds have a speculative character . . . bonds are not, as compared with a well-selected and diversified portfolios of stocks, what they have been cracked up to be . . . even when prices are falling they are not usually superior to stocks” (p. 202). In a precursor of modern portfolio theory, Fisher (p. 203) identifies “five reasons for the now proved fact that stocks are a better investment than bonds”: first, because the stockholder stands to win as well as to lose; second, because modern dividend policy is toward steadiness; third, because a portion of stockholders’ earnings is reinvested for him and ultimately yields further dividends; fourth, because the unstable dollar tricks the bondholder, but any effect on the shareholder is largely neutralized; and fifth, because diversification can correct the irregularities of the stockholder’s income but not that of the bondholder.

Fisher recognizes that Smith, K. van Strum and other writers emphasize the importance of diversification — he does not claim originality on this point. Yet, Fisher was a vocal and active proponent of ‘investment trusts’ run by ‘expert counsel’ — precursors of modern closed end funds and mutual funds. For Fisher, diversification had to have another element added: “It is the principle of constant inspection or check-up as to the status of companies issuing stocks, and constant turnover accordingly . . . For the sound investor in common stocks must turn them over constantly, selling those that are losing in value and investing in those that are gaining” (p. 207). The skilled investment counsel situated in investment trusts were an essential element to achieving the gains associated with diversification that allowed stocks to be a superior investment than bonds. Based on the limited data available, Fisher was able to observe the phenomenon, common to periods of intense speculation in stocks, of substantially increased equity issues at the end of the 1920s. A comparison is made between corporate financing during the first eight months of 1925 ($2.353 billion in long and short term corporate bonds with $804 million in stock issues) with the first eight months of 1929 ($2.360 billion in long and short corporate bonds with $4.794 billion in stock issues). Fisher also observes that the bond issues in 1929 had relatively more equity related provisions such as conversion features. Oddly enough, Fisher interpreted this data as a positive development for stock valuation. Fisher failed to foresee

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the precipitous fall in stock prices in the two plus years from 1930–1932. More importantly from the standpoints of individual investors at that time, he also failed to foresee that the general level of U.S. stock prices would not recover to 1929 levels until after WWII.36 As late as Fisher (1939), when the extent of the stock market collapse was all too evident, Fisher still argued: “there is considerable evidence to support the conclusion that stocks in general sold at about three-quarters of their true value as measured by the return to the investor”. In continuing to support ‘the common-stock theory’ in the aftermath of the collapse of equity values associated with the Great Depression, Fisher is not alone. Bierman (1991, 1998) continues a tradition stretching back to Eiteman and Smith (1953) and Harold (1934, p. 59) where, at the depths of the equity security market downturn, it was concluded: “the common-stock theory stands upon a firm base, shaken by the developments of 1932, but not destroyed”. Similar empirical results were presented in Bosland (1937) for the 1890s to the early 1930s. However, Bosland (1937, p. 73) reflected an increasing wariness of the common stock theory by U.S. observers: “no criticism of the common stock theory of investment is so impressive as the one which warns that the findings of the past may be of little value for the future. Specifically, the question is whether the factors favorable to increased common-stock earnings in the earlier period are likewise favorable for the period we have now entered, or, if not, whether new factors affecting common stocks have entered the picture”. Fisher never wavered in support of common stock theory, despite considerable empirical evidence suggesting otherwise. It is convenient to look back on what Fisher said and conclude that he was just another prognosticator that got it wrong. Yet, Fisher was so much more than another prognosticator. With all the skills and information at his disposal, Fisher fails to provide an able answer to problems confronting vernacular Finance, such as the American question. Based on as careful an implementation of the scientific approach as he could muster, Fisher was a strong proponent of stocks for the long run — a view that, in his time, proved to be profoundly incorrect. Perhaps more personally disturbing to Fisher was that his long time academic rival, J.M. Keynes, was so much closer to the mark both academically and in the world of vernacular Finance. 36 This was not the case in the United Kingdom where aggregate stock price levels had recovered to 1929 levels by 1936.

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Investment Activities of J.M. Keynes Among inter-war economists with high academic standing, it is often claimed that J.M. Keynes stands out when vernacular measures of valuation performance are used. In other words, it is claimed that Keynes was an ‘exceptionally gifted’ investor. Though there is some truth in this, the record is far from transparent. The overall record is a mixed bag of successes and failures. Included in the failures is a 1919 partnership with O.T. Falk that invested mostly in foreign exchange. Beginning with an initial capital of £30,000 raised from personal savings and those of family and friends, Keynes was decimated on a bullish dollar play that found the partnership being would up in April 1920 with a £22,275 loss, almost all of the initial capital. Almost bankrupt, Keynes was able to call on Sir Ernest Cassel from his network of influential friends to provide an emergency loan of £5,000. That Keynes eventually managed to leave an estate of about £450,000 (including valuables such as pictures and rare books) at a time when his annual income from academic sources seldom exceeded £3,000 indicates some vernacular success. However, the bulk of this amount came at the end of his life, during the years of WWII, where his financial assets increased from £188,353 in 1940 to £436,000 in 1945. The considerable amount of detail that has been accumulated on the activities of Keynes the fund manager, speculator and investor is primarily because of the academic importance that Keynes achieved. This is not to say that Keynes was unrecognized in the world of vernacular Finance. For example, Keynes did have some impact changing the security selection and portfolio management policies of certain types of investment funds. These relationships started in November 1919 when Keynes commenced a relationship managing funds for King’s College, Cambridge; intially as second bursar, becoming first bursar in 1924. Keynes was a director of a number of investment trusts — the A.D. Investment Trust (1921– 1927), the Independent Investment Company (1923–1946), and the P.R. Finance Company (1924–1936) — in addition to important duties with two insurance companies. The most noteworthy of these duties involved creation of a separate fund, the Chest Fund, that engaged in active management of ordinary shares, currency and commodity futures. Information on the security market activities of J.M. Keynes can be found in a number of biographies, e.g., Skidelsky (1983) and Muni (1994). There are also secondary sources such as Muni (1995, 1996), that examine the overall investment record in order to dispose of the “myth about Keynes

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that he was exceptionally gifted as an investor”. In contrast, Chua and Woodward (1983, p. 232) explicitly examine only the performance of the Chest Fund and conclude: “Keynes was an outstanding portfolio manager”. The definitive source on the basics of “Keynes as an Investor”, the Collected Writings of John Maynard Keynes, vol. XII, ch. 1 (Moggridge 1983), makes considerable use of the Keynes papers in the King’s College Archives, Cambridge and numerous other primary sources, such as the records of the investment funds Keynes was involved in managing.37 Using tax information, Keynes’ income is broken down by years into academic (including royalties for books) and other (mostly investment and trading income) annually from 1908–1946 (Table 1, p. 2). This source indicates that by 1914– 1915, Keynes was generating almost 30% of his income through investment activities: “operating on his own account on a modest scale and providing investment advice for friends” (Moggridge 1983, p. 1). While interesting, the income figures associated with taxation become less interesting as Keynes investment activities took on scale following 1919. Additional information on the sources of Keynes’ investment income by source (Table 4, p. 12) indicates that Keynes investment and trading income was considerably under reported due to dividend income from U.S. sources being excluded. The intricate details of Keynes trading activities appear in Tables 3–6 of Moggridge (1983, p. 11–14). Recognizing that Keynes also engaged in futures speculation that would not appear on a report of assets, Keynes was heavily invested in ordinary shares throughout the entire period. Over the quarter century from 1920–1945, holdings of common stocks ranged from a high of 98.1% of the market value of securities held in 1930 (!), to a low of 43.1% in 1932 when 55% of the assets were bonds — the only year over the period when bond holdings exceeded 25%. In turn, from 1927–1939 the portfolio leverage ratio of loans for purchasing securities over net asset value of securities held was often over 1 and always well above 1/2. In 1930, the leverage ratio was almost five times. Starting from a negative net asset 37 Mini (1995, p. 50) provides a detailed breakdown of the performance of the P.R. Finance Company, founded in 1923. The fund is of particular interest because prominent members of the Bloomsbury group were substantial shareholders. It is likely that Keynes took a particular interest in the management of this fund. It is unfortunate that the fund was wound up in 1935, just prior to Keynes achieving his most remarkable personal investment performance. Given this, £1 invested in the fund in 1923 would have returned £1 7s. 7.68d in 1935. The loss of over £98,000 on fund capital of £115,000 during the 1929-1931 period also cannot be ignored. On balance, the return received does not represents the quality investment performance that would receive special merit in vernacular Finance.

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position of −£1,837 on 20 August 1919, Keynes is able to rebuild a modest capital of £40,000 by 1926. It is at this point that Keynes embarked on a program of leveraging. Following a considerable reduction in outstanding loans from £65,000 in 1930 to £11,965 in 1931, Keynes embarked on a massive increase in leveraging that took the loan position to almost £300,000 in 1936 with net assets growing from £12,525 to over £500,000. Following immense losses in 1937, when the net value of security assets fell from £506,522 to £214,244, Keynes began to gradually unwind overall position leverage. When the dust settled the gains that remained originated largely on trading U.S. equity securities that began in 1932 with an initial 10% of the security portfolio market value being invested exclusively in U.S. common stocks. By 1937, U.S. equity investment has grown to 43% of market value with 26.6% in common stocks and 16.4% in U.S. preferred shares. The dollar value of gains on U.S. equities goes from $15,900 in 1932 to $212,500 in 1934, $526,800 in 1935 to $585,200 in 1936. This increase in value was fueled by an increase in leveraged purchases that resulted in an increasingly larger number of shares that generated further capital gains, that increased the collateral permitting further borrowing until a massive (−$733,000) loss appears in 1937. Over a lifetime, gains from currency speculation and commodity futures speculation were modest compared to the considerable gains achieved mostly by leveraged purchasing of U.K. and U.S. common stocks. 2.3 2.3.1

Derivative Security Renaissance Evolution of Stockjobbing

To the uninitiated, much confusion is created by applying modern security market norms to historical events. As a consequence, valuable historical lessons can be misinterpreted, to the detriment of those seeking insights such as investors attempting to value equity securities or regulators seeking to maintain a level playing field for efficient equity security trading. The use of derivative security contracts in the trading of equity securities is a case in point. Poitras (2002) refers to a “derivative security renaissance” that characterized the last quarter of the 20th century. In combination with a revolution in computing and communications technology, the removal of a plethora of restrictions on derivative security trading and related ‘stockjobbing’ types of transactions has transformed trading practices in modern equity security markets. Innovations such as ‘credit default swaps’ and ‘double short exposure’ exchange traded funds on equity indexes

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and commodities raise important questions concerning ‘unnatural’ (Armstrong 1848) fluctuations in market prices associated with the availability of such securities. Centuries of history detailing the abuse of derivative security contracts has been ignored in favour of a ‘brave new world’ vision for innovative financial security trading. With this in mind, consider a theme that appears repeatedly in stock market history since the late 17th century: the nefarious practice of ‘stockjobbing’. Following Attard (2000, p. 7), “the term ‘stockjobber’ has been used pejoratively since the seventeenth century to describe any person who dealt fraudulently, speculated, or simply traded on his own account”. The considerable contemporary discussion and analysis of early English stockjobbing activities was particularly venomous. Consider, for example, the full title of a Daniel Defoe work on the subject: The Anatomy of Exchange Alley or, A System of Stock-Jobbing: Proving that Scandalous Trade, as it is now carried on, to be Knavish in its private practice, and Treason in its Public (1719). Stockjobbing, it seems, was much more than simple dealing in shares and government funds. Defoe’s views on stockjobbers is quite clear: if you talk to them of their occupation, there is not a man will own it is a complete system of knavery; that it is a trade founded in fraud, born of deceit, and nourished by trick, cheat, wheedle, forgeries, falsehoods, and all sorts of delusions; coining false news, this way good, this way bad; whispering imaginary terrors, frights, hopes, expectations, and then preying upon the weakness of those whose imaginations they have wrought upon, whom they have either elevated or depressed.

Though Defoe is among the best at thrashing the stockjobber, Thomas Mortimer provides a much more insightful description of stockjobbing activities that is consistent with the modern colloquial interpretation of stockjobbers as cheats and fraudsters. Defoe’s interpretation of stockjobbing fails to identify key features of this activity with particular relevance for modern equity security markets. Remembering that ‘stock’ often referred to government debt issues as well as ‘shares’ in joint stock companies, consider Adam Smith’s (1763, p. 251) description of stockjobbing in the Lectures: The practice of stock-jobbing, or the buying of stocks by time has, too, on all occasions, a very considerable influence on the rise and fall of stocks. The method in which this practice is carried on is as follows. A man who has not perhaps £1000 in the world, subscribes for £100,000, which is to be delivered at several fixed times, and in certain portions. He therefore

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hopes to get these several portions sold out to great advantage by the rising of the stocks before they fall due, but as anything he is worth would go if the stocks should fall, he uses all means to make them rise, he spreads reports at Change Alley that victories are gained, that peace is to be concluded, &c. On the other hand, they who want to purchase a stock, and want that it should fall, propagate such reports as will sink the stocks as low as possible, such as that war will continue, that new subscriptions are thought on, &c. It is owing to this that, in time of war, our newspapers are so filled with invasions and schemes that never were thought of.

The stockjobber is being depicted as a gambler using the leverage obtained through time contracts, manipulating the market with rumours aimed at facilitating a quick profit. In contrast, Mortimer (1761, pp. 33, 34) gives a precise description of the ‘sorts’ of individuals involved in stockjobbing: STOCK-JOBBERS may be divided into three different sorts. The first are foreigners, who have property in our funds, with which they are continually JOBBING. The second are our own gentry, merchants, and tradesmen, who likewise have property in the funds, with which they job, or, in other words, are continually changing the situation of their property, according to the periodical variations of the funds, as produced by the divers incidents that are supposed either to lessen, or increase the value of these funds, and occasion rises or falls of the current price of them. The third and by far the greatest number, are STOCK-BROKERS, with very little, and often no property at all in the funds, who job in them on credit, and transact more business in the several government securities in one hour, without having a shilling of property in any one of them, than the real proprietors of thousands transact in several years.

Mortimer explicitly identifies the blurring of the dealer and broker functions. This is reflected in the common language of the time that “used broker and jobber as interchangeable terms” (Dickson 1967, p. 494).38 However, Mortimer is quite clear that stockjobbers also include others than just brokers. What was stockjobbing? Mortimer (1761, p. 27) has a useful description: Now, the Dutch and other foreigners have so large an interest in our public funds, has given rise to the buying and selling of them for time, by which is to be understood, the making of contracts for buying and 38 Dickson (1967, pp. 493–497) has a detailed analysis of the available evidence on dealer activities as reflected in the transfer records.

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selling against any certain period of time; so that the transfer at the public offices is not made at the time of making the contract; but at the time stipulated in the contract for transferring it; and this has produced modern STOCK-JOBBING, as I shall presently shew. Nothing could be more just or equitable than the original design of these contracts, nor nothing more infamous than the abuse that has, and still is made of it.

In keeping with the modern day renaissance of derivative securities, stockjobbing in the 18th century was also associated with forward trading of securities. According to Mortimer (p. 32):39 the mischief of it is, that under this sanction of selling and buying the funds for time for foreigners — Brokers and others, buy and sell for themselves, without having any interest in the funds they sell, or any cash to pay for what they buy, nay even without any design to transfer, or accept, the funds they sell or buy for time. The business thus transacted, has been declared illegal by several acts of parliament, and this is the principal branch of STOCK-JOBBING.

Mortimer makes no reference to the use of options in stockjobbing activities, giving some support to the position that Barnard’s Act of 1734 was effective in deterring this activity. Almost from the beginning of English stock trading, attempts were made to severely restrict stockjobbing. The first important piece of legislation was the 1697 Act ‘To Restrain the number and ill Practice of Brokers and Stockjobbers’. This Act did not actually have much application to stockjobbing, as conceived by Mortimer. Rather, stockjobbing was conceived as ‘pretended’ brokerage. From the preamble to the Act (Morgan and Thomas 1962, p. 23): whereas divers Brokers and Stock-Jobbers, or pretended Brokers, have lately set up and on most unjust Practices and Designs, in Selling and Discounting of Talleys, Bank Stock, Bank Bills, Shares and Interests in Joint Stocks, and other Matters and Things, and have, and do, unlawfully Combined and Confederated themselves together, to Raise or fall from time to time the Value of such Talleys, Bank Stock, and Bank Bills, 39 In

contrast, Defoe (1719) makes no reference to forward trading, using examples which usually relate to cash transactions, for example, using false rumours to influence the stock price, the idea being to buy low on negative rumours and selling high on positive rumours (pp. 139–140). However, it is not clear that Defoe had the best grasp of the financial transactions which were being done. One quote of interest is “the bear-skin men must commute, and pay differences money” (p. 148), indicating that forward trading mechanisms similar to those used in Amsterdam were in place in London, circa 1719.

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as may be most Convenient for their own private Interest and Advantage: which is a very great abuse of the said Ancient Trade and Imployment, and is extremely prejudicial to the Public Credit of this Kingdom and to the Trade and Commerce thereof, and if not timely prevented, may Ruin the Credit of the Nation, and enndanger the Government itself.

Stockjobbers were seen as interlopers in the legitimate trade of brokerage. As a consequence, the Act specifically restricted the trade of brokerage to those brokers licensed by the City of London. The Act then limits the number of licensed brokers to one hundred. Though it had some impact, the Act of 1697 was insufficient to stem the stockjobbing abuses, as reflected in the need for subsequent English legislation. Unlicensed brokers continued to operate throughout the 18th century and licensed brokers were often involved in dealing activities, e.g., Dickson (1967, pp. 493–497). Trading practices in both Amsterdam and Paris also involved licensed and unlicensed brokers. Though there were definitely political considerations in its passage, the English Bubble Act of 1720 was designed to eliminate the rampant ‘stockjobbing’ in the initial public offerings of the numerous bubble promotions (Harris 1994). That options still played a significant role in stockjobbing activities, both during and after the South Sea Bubble, is reflected in the specific inclusion of restrictions on options trading in Barnard’s Act of 1733, which also attempted to restrict speculative time bargains. Various other unsuccessful attempts to get antispeculation and anti-stockjobbing bills passed were launched. Some general themes of modern interest emerge from a closer inspection of the activities involved in the nefarious practice of stockjobbing. The negative outcomes that were identified arose from a combination of factors, including: the lack of separation between brokerage and dealing functions; the abuse of time contracts and privileges; and, the inability to regulate access to market trading by fraudsters and manipulators. Each of these factors continues to plague modern equity security markets, despite ongoing efforts by government regulators and self regulatory organizations to mitigate undesirable outcomes. It was around the last quarter of the 18th century that the functions of jobbing and dealing began to converge. Regulations on the London Stock Exchange aimed at preventing conflict of interest between jobber and brokerage activities by prohibiting member firms from engaging in both capacities date from 1847. Following a restatement of the ban in 1878, the Exchange entrenched this separation of brokerage and jobbing functions in regulations of 1908 and 1912. Following

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Attard (2000), this separation of function was only removed in the Big Bang financial reforms of 1986. Brokers have been an essential feature of markets since ancient times. Brokers were used to do business in a wide range of commodities, from cloth and wool to copper and saltpetre.40 Various jurisdictions imposed laws governing the ability of individuals to engage in brokerage and when brokers were required in a business transaction. For example, a 1697 English law restricted to 100 the number of brokers permitted to transact business in joint stocks. Similar restrictions were imposed by the French government in setting up the Paris bourse following the collapse of the Mississippi scheme, though trading by unlicensed brokers on the Coulisse in the 19th century did play a fundamental role in bourse development (Walker 2001). Another example is from medieval Bruges, where alien merchants were required to use local brokers even where a broker was not necessary.41 Heuristically, brokers do business by connecting buyers and sellers, charging a commission for this service. A broker does not take a position in the security being traded. In contrast, dealers buy and sell for their own account. Dealer activity can take various forms, some of which can create conflicts of interest with the brokerage function. Modern equity markets have blurred the distinction between brokers and dealers. Even the United Kingdom abolished the long established distinction in the Big Bang financial reforms of 1986 . This has led to a variety of difficulties. In particular, during the lead up to the collapse of the technology stock bubble in 2000 inaccurate brokerage house recommendations touted IPO’s that the investment banking arm of a number of broker-dealers

40 In the Advertisements section of A Collection for the Improvement... Houghton would provide various lists, such as those for Counsellors and Attorneys on 20 July 1694. In a 6 July 1694 listing which also included Coaches and Carriers, Houghton provided a list of Brokers, in this case for Corn (2), Dyers Wares (3), Exchange (6), Grocery (7), Hemp (1), and Silk (10), with the number in brackets representing the number of names listed as brokers. 41 Buckley (1924, p. 590) makes the following observation about the treatment of the English merchants of the Staple in Bruges: “It was, apparently, an important concession which the city Bruges made to the English merchants of the Staple in 1559, when it was agreed that the latter should be free of brokers when buying. It was asserted in 1562 that in most foreign countries no ‘stranger’ bought or sold except through a sworn broker, and the English Statute Book contains a number of regulations of similar import. Such arrangements were general, being due to the universal prejudice against foreigners”. Buckley (p. 591) also makes another observation which is indicative of the pervasiveness of brokers at Gresham’s time: “Dealings in Bills of exchange without the intervention of a broker were exceptional”.

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were bringing to market. In the most high profile case, the subsequent prosecution of Frank Quattrone, former star investment banker with Credit Suisse First Boston, illustrates the difficulties in penalizing such manipulations.42 That Quattrone was able to obtain hundreds of millions in ‘overdue’ compensation payments after his 2004 conviction was overturned on appeal reflects the modern difficulties of preventing firms from exploiting the advantages of combining the investor information aspect of full service brokerage with the dealing function associated with equity IPO distributions. In the U.S. broker-dealers are subject to oversight by the SEC and by the self-regulatory functions of exchanges. The SEC reacted to this particular round of difficulties associated with lack of sufficient broker-dealer separation by introducing Reg. AC in April 2003. What is a Derivative Security? The negative feature of stockjobbing most often identified by informed observers at the time was the abuse of time contracts and privileges. Such contracts appear as derivative securities contracts in modern markets. This has a number of implications for equity security valuation. In an insightful early examination of security markets, Sir Robert Giffen (1877, p. 85–93) identifies four general causes for differences in security prices: “the security and safety of the income yielded by the investment,” “the difference of marketability”, “the effect of extrinsic regulations, such as those of the law courts, which direct the investment and re-investment of funds,” and “the estimation of the public . . . in favouring some securities more than others by qualities unconnected with the solidity of income or mere marketability”. The advantages of derivative security trading relate to the first two causes and the disadvantages with the last. Disentangling these elements has created problems from the first trades in equity securities. Yet, while severe bans and restrictions on various aspects of derivative 42 This

is not to say that CSFB and Quattrone were the central players in the misuse of analysts ratings to tout questionable stocks. Rather, the 28 April 2003 press release by the SEC, NASD, NYSE and New York state attorney general Eliot Spitzer names 10 Wall Street firms in the landmark $1.4 billion settlement for conflicts of interest with Salomon Smith Barney getting the highest penalty at $400 million and CSFB and Merrill Lynch at $200 million. Morgan Stanley and Goldman Sachs also had fines greater than $100 million. It was the investigation by Eliot Spitzer that commenced in 2001 of the internet research analysts at Merrill Lynch, led by Henry Blodget, that eventually led to the settlement with a much larger number of firms that were found to be engaging in predatory activities.

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security trading that were imposed prior to the current renaissance period were reasonably successful in curbing speculative abuses, the bans and restrictions also resulted in losses associated with reduced market liquidity and increased price volatility. Despite being a widely used term, it is difficult to precisely define a ‘derivative security contract’. In particular, all derivative securities involve a traded contingent claim, where some essential feature, typically the price, is derived from some future event. This event is often, though not always, associated with a security or commodity delivery to take place at a future date. However, defining derivative securities as tradeable contingent claims is not precise enough because financial markets are riddled with contingent claims, not just those associated with derivative security contracts. In addition, contingent claims may be combined with other security features or traded in isolation. In some cases where the contingent claim involves an equity security transaction to take place at a later date, such as with a convertible bond or convertible preferred share, the traded value of the contingent claim and the underlying security is combined. Recognizing that such bundled securities could also be defined as derivative securities, the definition is usually restricted to only include cases where the contingent claim contract is unbundled or ‘free standing’ (FASB 2000).43 This includes the following types of contracts: forwards and futures; options, rights and warrants.44 43 The modern renaissance in derivative security trading has posed considerable problems for the accounting profession. In order to address the accounting problems raised by the use of derivative securities in firm risk management and for other purposes, the notion of ‘free standing derivatives’ was introduced. This reference to free standing derivatives is precise accounting terminology borrowed from the financial accounting standard FAS 133. Being ‘free standing’, derivative securities pose fundamental problems for conventional methods of preparing accounts. This point has not been lost on the accounting profession which has been engaged in ongoing attempts to produce a set of standards that permit an accurate financial presentation of the accounts of the firm, which do not permit substantial discretionary variation in the accounts. In a perfect world, two otherwise identical firms, both involved with using derivative securities, would not be able to present accounts which were substantively different, based on discretionary accounting choices, such as the method used to recognize gains or losses on the offsetting spot position. 44 Of these contracts, rights and warrants are not examined. Though commonly used, there are difficulties with this definition. For example, combinations of bundled contingent claims can produce payoffs that are approximately identical to the payoffs for combinations of derivative securities, e.g., simultaneous buying and selling of equal cash value in bills of exchange with different maturity dates produces a payoff that is equal to a calendar spread using currency forward contracts.

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Significantly, the historical use of derivative securities in equity security trading developed differently in the United States from Europe due to differing cash market settlement practices. More or less from the beginning of security trading in the U.S, “each day is a settling day and a clearing day for transactions of the day before . . . This is a marked difference from European practice” where “trading for the account” involves monthly or fortnightly settlement periods with allowance for continuation of the position until the next settlement date (Emery 1896, p. 82). In effect, the U.K. and continental stock exchanges used settlement methods that directly involved the use of extendible, short dated time contracts. On settlement day, there was a continuation process for a buyer seeking to delay delivery that involved the immediate sale of the stock being delivered and the simultaneous repurchase for the next settlement date. As this transaction would involve the lending of money, an additional ‘contango’ payment would typically be required. Daily or short dated settlement had dramatic implications for derivative security trading in the U.S. stock market. Instead of trading for time with regularly scheduled settlement dates and allowance for continuation as in Europe, it was often more expedient to speculate by selling (shorting) stocks and buying stocks on margin. Armstrong (1848, p. 10) makes a telling observation: “When such a time operation as is desired cannot be conveniently obtained, it is customary to buy the stock for cash, and then borrow as much money upon it as possible, and deposite the certificate of Stock with the lender as security for repayment of the amount borrowed. The market value less five or ten per cent can almost always be obtained”. As Poitras (2002, p. 6) observes, derivative securities are difficult to define because similar payouts can often be obtained by combinations of other securities. For example, a long position in a time contract for purchase of stock with delivery in 30 days and a margin deposit of 5% has similar cash flows to a purchase of stock using a 30-day loan for 95% of the purchase price. Use of day-to-day ‘hypothecation’ to finance inventories instead of ‘trading for the account’, at times, has had severe implications for liquidity in the U.S. short-term credit markets, especially following the Great Depression and, more generally, during the gold standard period. In addition to the important contributions on this issue by Keynes, other economists of the time were also concerned with this issue, e.g., Machlup (1940). As a consequence of a largely cash market for equity securities, the venue for evolution of derivative security trading in the United States was in the bulk commodity markets where, during the 19th century, exchange trading of derivative securities experienced a revolution that can be attributed to

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the subtle impact American culture had on specific business practices. Writing in 1896, Emery (1896, p. 7) captures the main theme: “The American people are regarded by foreigners as the greatest of all speculators”. This drive to speculate facilitated American innovations in derivative securities. “It was not until the (19th) century . . . that the system [of dealings for time] became widely developed and not until the great expansion of foreign trade in the last fifty years that it became of great importance”. The start of the modern renaissance in equity derivative security trading can be identified with the commencement of trading on the Chicago Board Options Exchange in 1973. Though equity option trading in the United States began as early as 1790 and time bargains even earlier, both played a significant role at one time or other in various market manipulations. As early as the 1890s, option pools were in operation. Two general types of pools were present in the 1920s: trading pools and option pools, with the latter being the most common. While trading pools acquired stock on the open market, option pools would acquire all or most of its securities by obtaining call option contracts to purchase stock at favorable prices. These options were acquired OTC from various sources, such as the corporation, where the options took the form of warrants, as well as large stockholders, directors, officers, large speculators and banks. While there was considerable diversity in the maturity of the options granted and the types of schemes involved, the primary objective of the option pool was to benefit through manipulation of the common stock price. The option pools were symptomatic of the types of abuses that contributed to the 1929 stock market collapse. The regulatory response implemented in the 1930s, culminating in the Securities Act (1934), was to prohibit all activities aimed at manipulating market prices and trading on insider information. Franklin and Colberg (1958, pp. 29, 30) illustrate the importance of options trading in the 1929 market collapse: Testimony before the Senate Committee on Banking and Currency in 1932 and 1933 disclosed that many of the financial abuses of the 1920s were related to the use of options. A favorite device of large stockholders was to grant options without cost to a pool which would then attempt to make these profitable by “churning” activities designed to bring the general public in as buyers of the stock. In addition, long-term and even unlimited-period option warrants were issued frequently in connection with new stock issues.

During the wave of securities market reform following the financial market collapse of 1929–1933, considerable attention was given to terminating

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option trading all together. One of the most profitable pools was the Sinclair Consolidated Oil option pool of 1929. While Sinclair stock was selling in the $28 to $32 range, a contract was obtained from Sinclair granting the pool an option to buy 1,130,000 shares at $30 per share. The pool then purchased 634,000 shares in the open market to bid up prices. The pool exercised its option, then liquidated all its holdings while the stock was selling in the $40 range. The pool also sold 200,000 shares short as the price fell. The pool’s total profit was approximately $12.5 million from the following sources: $10 million profit from optioned shares purchased at $30 per share, $500,000 profit from shares purchased in the market, and $2 million profit from the short sales. In the process of developing a regulatory response to the market abuses which contributed to the financial market turbulence of 1929–1933, it was accepted that the abuses associated with option pools would become illegal. However, in addition to the use of options in pool operations, there were other, more legitimate reasons for stock option trading. In the end, the brokerage industry was able to avoid the outright ban associated with commodity options. The initial legislation aimed at regulating the securities markets, the Fletcher–Rayburn bill (1934), called for a total ban on stock options. The brokerage industry was able to prevent this result. Instead, the Securities Act (1934) empowered the newly created Securities and Exchange Commission (SEC) to regulate the market and introduced the Put and Call Brokers and Dealers Association (PCBDA) (1934) which was designed to act as a self-policing agency, working closely with the SEC and other agencies to avoid further direct government regulation. It was member firms of the PCBDA which formed the basis for the OTC market trading of options which took place in the period leading up to the creation of the Chicago Board Options Exchange (CBOE) in 1972–1973. To appreciate the major advance that the CBOE represented, consider the state of equity option trading prior to the CBOE. Franklin and Colberg (1958, p. 22) describe the general state of equity option trading at the end of the 1950s: Practically all of the Put and Call business in the US is handled by about twenty-five option brokers and dealers in New York City. The brokers operate through [the PCBDA]. All the contracts in which they deal are guaranteed or indorsed by member firms of the New York Stock Exchange . . . The Put and Call business is largely self-regulated, but a great deal of the aura of secrecy which surrounds this activity seems to stem from the early 1930s when the threat of strict regulation or even legislative extermination haunted the entire options trade.

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At this time, the options market was relatively small. Self-regulation, both by the exchanges and by the PCBDA, coupled with the ability of the SEC to require reporting of options trading, were sufficient to prevent the abuses of previous years. However, the markets were relatively illiquid and it was difficult to resell positions. Upon closer inspection, though the options being traded through the PCBDA were transferable and, in a sense, protected by a clearing mechanism, some common drawbacks of OTC trading of derivative securities were present. In addition to illiquidity, trading in the market primarily involved large institutional investors writing overpriced options to small investors seeking to gamble in stocks with limited capital. In effect, OTC trading was aimed at capturing rents from control of the information and transactions technology of options trading. Among other significant regulatory changes introduced by the Securities Act was the requirement that all option sellers post margins. Unscrupulous activities such as granting brokers options for touting a stock were banned together with the use of options to trade on inside information. In addition to the increased government regulation, self-regulation by the PCBDA also played on important role. Despite the success in reducing market abuses, the options traded in the OTC market were often illiquid, making it difficult to resell or transfer a given options contract to another party. In 1972, this started to change with the creation of the Options Clearing Corporation, as a subsidiary of the CBOE. In following years, the American, Philadelphia, Pacific and Midwest stock exchanges also introduced options trading. Trading on the CBOE commenced in April 1973 with 16 stock options. While initial interest in options trading was limited, by 1977 volume had increased substantially to the point where put options were introduced. The ensuing implications of inter-exchange competition undermining the self-regulatory function of exchanges, a phenomenon which has overtaken derivative markets in recent years, was not adequately appreciated at the time. The advantages associated with combining options with cash trading, a tradition on European exchanges stretching back to early 19th century France (Viaene 2006), are unrecognized. The common use of option contracts to trade equity securities can be traced to the 17th century. Such contracts made sense in the equity markets of the time, due to the difficulties of locating shares for sale. For a time contract, a deposit would be paid — typically similar in size to the premium on an option contract — and a price established for future delivery. The buyer’s right to refuse delivery would produce a higher settlement price than for a time contract. The abuse of time contracts, in general, and option contracts, in particular, led to various regulations restricting usage. While important

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merchant manuals of the 18th century, such as Jacques Savary, Dictionnaire Universel de Commerce (1730) and Malachy Postlethwayt The Universal Dictionary of Trade and Commerce (1751), have detailed discussion of the trade in actions, there are no entries for privileges, prime a ` d´elivrer or prime a recevoir; premiums; jeu d’actions; or puts and refusals. With the exception ` of Houghton (1694), the important sources on the 17th and 18th century stock options trade are either sufficiently obscure or were part of the numerous legislative attempts to regulation or abolish the trade. It is not until the 19th century that knowledge and understanding of equity options trading moved outside the narrow confines of a small group of specialized traders and gradually acquired increased reputation in Europe (Poitras 2009). The German option contract (pr¨ amiengesch¨ afte) that concerned Bronzin early in the 20th century (Hafner and Zimmermann 2009) differs from the options traded in modern markets which have inherited characteristics associated with historical features of U.S. options trading. Following Emery (1896, p. 53), the pr¨ amiengesch¨ afte “may be considered as an ordinary contract for future delivery with a special stipulation that, in consideration of a cash payment, one of the parties has the right to withdraw from the contract within a specified time”. As such, this option is a feature of a forward contract with a fee to be paid at delivery if the option is exercised. Circa 1908 on the Paris and Berlin bourses, the premium payment at maturity was fixed by convention and the ‘price’ would be determined by the setting the exercise price relative to the initial stock or commodity price. In Castelli (1877, p. 7), the premium to be paid at maturity “fluctuates according to the variations of the Stock to be contracted”. In contrast, the modern call option is a tradeable ‘privilege’ of ‘refusal’ with fixed terms where an agreed upon fee would be paid in advance. In the modern approach, both puts and refusals are buyer’s options. The seller writes the options. If the option is a feature of a forward contract, a call option arises because the buyer for future delivery can refuse to take delivery, a put option arises because a seller for future delivery can withdraw.

A Modern View Like so many other innovations in equity markets, both practical and theoretical use of derivative securities alters the equity valuation problem. Following Giffen (1871), precisely how the valuation problem is impacted depends on the ability of ‘extrinsic regulations’ to adapt to the changes. History suggests a predictably ad hoc reaction of government regulators

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to challenges posed by the derivative security renaissance and the related technological revolution in equity trading. In the present circumstance, important self-regulatory functions performed by stock exchanges have been undermined by the emergence of competing ETN’s, pay for order flow practices and ‘dark pools’ for off-exchange securities trading that dramatically increase the potential for ‘stockjobbing’ behavior. Despite the possibility of severe market disruption indicated by a sequence of accumulating events stretching back at least to the crash of 1987, it was not until the ‘unnatural’ collapse of various key financial institutions in late 2008 that government regulators began the move to reverse the direction of change in the regulatory environment. The deficient regulation of the stockjobbing activities of hedge funds, private equity and venture capital funds is another example of the general incoherence in the modern regulatory environment. Little seems to have changed since Abken (1994, p. 19) summarized the regulatory status quo on OTC contracting which, ultimately, was the trading venue responsible for distributing the bulk of the ‘toxic assets’ that created the financial crisis of 2008: The central policy issue in derivatives regulation is whether further federal regulation is appropriate or whether the existing structure can oversee these markets. The six federal banking and securities regulators believe that the current regulatory structure is capable of supervising the OTC derivatives markets. Policy makers need to be cautious about changing regulatory structures because such alterations often bring unintended and unforeseen consequences.

As Poitras (2002) observes: “regulatory denial conveniently sustains a status quo solution”. The Securities Act (1933, as amended 2008) makes specific reference to both options and futures contracts written on securities. Extending the scope of the Securities Act to include derivative securities captured the growth and importance of these contracts. Yet, the resulting jurisdictional conflict between the SEC, CFTC and other governmental entities has inhibited the integration of cash and derivative securities markets, creating an ideal environment for stockjobbing across regulatory environments. Poitras (2002, 2009) dates the modern renaissance in derivative securities from the creation of the Chicago Board Options Exchange in 1973 and the introduction of a range of exchange and OTC traded derivative securities over the following decades. Historically, derivative securities trading, especially options trading, has been the subject of considerable criticism

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and legislative sanction due to the potential for speculative abuses. The last quarter of the 20th century and the beginning of the 21st century is remarkable in the breadth and depth of derivative securities trading. Securities markets both in the US and globally have embraced these new products. The financial engineering industry has become an important profit center for many of the largest firms in the securities industry. Within academic Finance, the virtues of derivative securities are expounded in introductory investment texts and advanced courses. The importance of financial engineering has permitted a proliferation of advanced graduate programs with titles such as Masters in Financial Engineering. Yet, the renaissance in derivative securities has had its blemishes. Due to a significant number of high profile and expensive losses, trading of derivative securities attracted considerable attention by the 1990s (e.g., Poitras 2002, ch.1). The list of companies involved is striking, as is the size of the losses. From Barings Bank to Sumitomo Corporation to China Aviation Oil, from Long Term Capital Management to Proctor and Gamble to Amaranth Advisors LLP, losses ranging from hundreds of millions to billions of dollars have been reported. Such events induce a state of uneasiness among policy makers, corporate managers, investment professionals, even academics. While it is tempting to draw glib generalizations about the apparent misunderstanding of risk management practices, closer inspection reveals a decidedly more complicated situation. In some cases, the relevant lessons that could be learned cannot be convincingly determined, due to the veil of corporate secrecy surrounding specific events. In cases where the activities and motivations of the participants can be precisely determined, it seems that different debacles raise different types of quandaries. Upon closer inspection, it seems that some so-called debacles were not debacles at all. Large losses associated with derivative security trading are not unique to recent times. Even though the largest losses in absolute terms have happened more recently, this is consistent with the increasing use, availability and complexity of derivative products. This has produced an evolution in the types of problems which are arising. Since the dawn of the renaissance in the early 1970s, there has been a progressive relaxation in the United States of a range of restrictions on derivative security trading, many of which had originated in the anti-speculation atmosphere of the post-Depression era. In conjunction with this relaxation, there has been an almost bewildering expansion in the variety of derivative securities being traded, both on the OTC markets and on the futures and options exchanges. From financial

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commodities to energy to equities to currencies, it is difficult to keep track of the rapid progress which has been and is being made in the development and application of derivative securities.

Short View of Short Selling Following Poitras (2002), the renaissance in derivative securities has created an incoherent regulatory environment due to conflict among: regulators competing for jurisdiction; and, different political jurisdictions competing for trading order flow. At the heart of the conflict is the regulation of short selling. By design, derivative security contracts provide the ability to replicate a given cash flow with different combinations of securities. Hence, ignoring transactions costs and other sources of equity market pricing friction, the presence of a functioning options market readily permits the creation of short positions. This poses a problem where there are restrictions on short selling the same equity security in the cash market. As illustrated by Bris et al. (2007, Table 1, pp. 1037–1040), restrictions on cash market short selling vary widely across jurisdictions. Most emerging markets do not permit any short selling or lending of securities. Even in developed markets where some form of short selling is usually permitted, a range of regulations restricting cash market short selling are in place. Perhaps more importantly, these regulations have been evolving in the direction of removing restrictions on short sales. Replication of cash flows is an essential characteristic of derivative security trading. In a perfect market, combining a written call position with a purchased put at the same exercise price and time to expiration will produce the payoff on a short forward position if the net premium is ignored. In contrast, a short sale position in the cash market typically originates with, say, the stock purchased on margin at a broker–dealer. Such stock is eligible for the securities lending needed to legally execute the short sale. Other sources of stock for short sales are: broker–dealer inventory; stock available for lending from other broker–dealers; specialized firms that locate stock for a fee; and, off-shore entities. The short sale involves the broker–dealer lending this stock to a short seller that has a margin account with the firm. The stock is then sold in the market and the funds deposited in the short sellers account. The account is then subjected to margin requirements on the value of the stock sold short that depend on a variety of factors such as: the exchange the stock is traded on; and, the particular broker-dealer involved in the short sale.

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The following margin requirements for short sales were obtained from a popular U.S. discount brokerage firm:

Short sales stock value $5 & over + Option eligible $3 & over Between $1.50 and $2.99 Between 25c/ and $1.493 Under 25c/

Minimum margin required (as % of the market value) 130% 150% $3 per share 200% 100% + 25c/ per share

Precisely how it is determined which non-cash assets are eligible for satisfaction of margin requirements will depend on the particular broker–dealer involved in arranging the short sale. Given this, it is apparent the cash market has rules in place to prevent excessive speculative leveraging using short sales of stocks to generate funds for alternative uses. In order to prevent a replicating strategy using written calls, purchased puts and borrowed money to counteract the cash market restrictions, it is necessary to impose sufficient margin requirements on written option positions. Incoherence emerges when jurisdictions compete and rules needed to deter speculative excesses are relaxed or eliminated as being ‘no longer necessary to maintain market volatility’ or ‘contrary to the goal of achieving the lowest possible execution price’. A Letter from Jim Cramer The presence of derivative securities, combined with rapid market information transmission and inexpensive trade execution, opens a range of replication trades to hedge traders and other risk arbitragers. As is turns out, profitable trades often appear involving portfolios with a short stock position. To satisfy the almost insatiable demand from hedge funds and others seeking speculative profit from trades involving a short stock position, a number of specialist firms have emerged that locate stock available for short sale. Dealers and other trading firms participate in the creation of ‘naked’ short positions. The regulatory response of 2009 was to seek amendment to Rule 201, Regulation SHO, introduced in 2007, that replaced Rule 10a-1

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that permitted short sales only on an uptick. Rule 10a-1 was in place since 1938 and the political role of large investment banks and hedge funds seeking to eliminate this rule for stockjobbing purposes is a history yet to be written. The erratic and volatile market behavior of equity prices since Regulation SHO was introduced produced a regulatory response to amend Reg SHO by reintroducing a modified form of uptick rule. The public comment period in 2009 included the following submission from Jim ‘Booyah’ Cramer and friends that succinctly summarizes many of the important issues at hand. To: SEC Chairman, Mary Schapiro From: Jim Cramer, William Furber, Eric Oberg, Scott Rothbort Re: Reinstatement of the Uptick Rule We the undersigned believe in not just free markets, but fair markets. While the practice of short selling equities can contribute to the market in terms of liquidity and price discovery, if left unchecked the practice can impede capital formation. We believe that a relatively simple check that was in place for nearly seventy years, the “Uptick Rule”, helped serve the markets well in balancing various participants’ interests. We therefore urge the SEC to reinstate such a price test rule, and specifically would urge a plus tick rule over other alternatives such as a ‘best bid’ or ‘circuit breaker’ test. When the Uptick Rule was initially implemented in the late 1930s, there was an implicit acknowledgment that companies were not commodities. There was recognition that the capital markets served the broader purpose of capital formation; that companies create products, provide services, employ citizens and pay taxes and thus there was an interest to promote market integrity and protect interstate commerce. In 1963, the SEC’s Special Study reiterated the Uptick Rule as being a simple, but effective, mechanism for balancing the various competing interests: allowing for relatively unrestricted short sales in advancing markets, eliminating short selling as a tool for driving the market down by preventing short sales at successively lower prices, and preventing short sellers from accelerating a declining market by exhausting all available liquidity thus leaving long sellers to sell at successively lower prices. Indeed in 2007, with their report on the Regulation SHO Pilot Study, the SEC’s Office of Economic Analysis made the express point that in the context of a “Tick Test”, short sellers were liquidity providers, but without such a price test they could readily become liquidity takers. An Uptick Rule validates short sellers as liquidity providers, thus should help remove stigma with the practice. When considering the objectives of protecting investors and capital formation, it seems that the Tick Test seems to balance the interest of both the short seller and market integrity, and therefore ought to be

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reinstated. Furthermore, the undersigned not only support the letter of the rule, but also the spirit and intent of the rule. A rule with myriad exemptions and carve-outs will not fulfill its purpose. Therefore, we urge the SEC to enforce not just the letter of the law, but also be mindful of the principle of the rule. There has been considerable attention around the topic of the Uptick Rule because of a confluence of issues that, while independent, are interrelated around the practice of short selling. One of the most obvious related areas of unease is the practice of naked short selling. This is a fraudulent practice that appears to have been laxly enforced in the past. Naked short selling is essentially the creation of shares out of ‘wholecloth’, shares that never had to undergo SEC review, diluting the rights of existing shareholders, placing a price control on a stock and thereby inhibiting capital formation. No doubt, there is genuine concern from all market participants to put an end to this egregious practice; this is not an issue of ‘balancing interests’, but instead an issue of enforcement, and we urge the SEC to continue to step up their efforts in this regard. Naked short selling simply cannot be tolerated. Another question that has arisen is the proliferation of levered ‘shortside’ sector based ETFs. These funds have mushroomed with the elimination of price tests, and have raised innumerable issues in the markets. These ETFs were somehow approved by the Commission, despite seemingly obviating the margin rules set forth by the Federal Reserve. There is an entire body of evidence that shows a relaxation in margin constraints brings more noise to a market by drawing in uninformed traders. These funds have exacerbated volatility and created significant selling pressure during the downturn. The great irony is that these products, due to their construct, do not even work for longer term holders, so in reality these are speculative instruments meant for intraday trades, not for hedging or for investment. As intra-day speculative short selling vehicles unchecked by a plus tick test, they are sopping up available liquidity, rather than providing liquidity. In the past there was a ‘diversification exemption’ for Rule 10a-1. While such an exemption may be understandable for a broad based ETF, it does not seem to make much sense with regards to these ‘shortside’ ETFs. If such an exemption was applied here with regards to the underlying hedging activity, then people would simply use these funds as a dodge for the Uptick Rule much as they are used as a dodge for the margin rules. The proliferation of complex, algorithmic trading has also contributed to rapid-fire, unchecked short selling. There have been many comments about how embedded the code is in these program trades that would be impossible to reverse. This is a very specious argument. If the programmers can create code to trade thousands of stocks a second, they can surely accommodate a plus tick test.

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To be appropriately comprehensive, the Commission will need to address these concerns, as well as many others including married put abuse and ‘dark pool’ trading, in order to level the playing field for all participants. It is when too many exceptions are created, or rules are not enforced, that integrity and confidence suffer. In conclusion, we the undersigned urge the Commission to promote market integrity and capital formation, and to help uphold free and fair markets. We support the re-implementation of the Uptick Rule in not only form, but in substance, as it best balances the interests of all market participants. Thank you for your consideration, [signed] Jim Cramer, William Furber, Eric Oberg, Scott Rothbort.

From this, there is at least one conclusion to draw regarding the impact of ‘extrinsic regulation’ on equity valuation: do not assume that government will be effective in eliminating stockjobbing practices that distort market pricing. For that matter, it is even possible that regulators will unwittingly change the rules to favor those engaged in ‘nefarious’ practices that produce ‘unnatural’ equity market outcomes. Equity markets have always attracted participants that seek to gain unfair advantages from weakness in the rules. At times, the volatility and mis-pricing created by the activities of such participants is sufficiently widespread that profitable equity security trading opportunities can arise. While reasonably successful at eventually identifying problems, legislators and governments typically react in an ad hoc fashion, and only act forcefully in response to market failures. Neither is forward looking; not seeking to adapt in advance to changes, even though sound analysis to guide such adaptation is available. For example, Langevoort (1985) details many issues that eventually emerged in the 1990s and Stout (1988) questions the dedication to pricing efficiency that now threatens the traditional system of self-regulation with government oversight, e.g., Markham and Harty (2008). The mechanisms of self-regulation are blunt and often take some time to establish. The financial market milieu within which self-regulation takes place also tends to: favour the status quo; prevent competitive pressures; and, resist technological improvements. In particular, the self-regulatory function of exchanges has been under attack in the face of substantial changes in transactions technology. The traditional mutual, non-profit form of national or regional exchange ownership has been replaced by international exchange networks that are publicly traded entities. One of the challenges confronting modern equity valuation is to make sense of the implications of such factors, especially the revolution in market trading and

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communications technology. The available universe of equity securities has been increased dramatically, both domestically and internationally. Gradual deregulation of traditional brokerage fees that began in the 1970s has significantly reduced the cost of trading equity securities. However, regulatory changes accompanying these developments have substantively increased the systemic uncertainty associated with equity trading. 2.3.2

The History of Programmed Trading

What is Programmed Trading? In a sense, programmed trading could be traced back to the introduction of the telegraph, the ticker tape and the telephone in the 19th century. These technological advances permitted profitable trading opportunities from inter-exchange arbitrage and increased brokerage and related market making opportunities due to enhanced market liquidity. For example, a ‘programmed’ inter-exchange arbitrage would be manually executed by clerks paid to monitor the system used to track the prices. When the differential of the same securities in two markets reached a certain point, a trade would be attempted to sell in the expensive market the same security simultaneously purchased in the cheaper market. More than a few firms were engaged in this type of activity, so considerable effort was dedicated to having the most efficient price gathering network. At various times, exchanges have imposed specific rules to regulate the process. Large firms with a brokerage or dealing business that also made it profitable to maintain a trading unit had a particular advantage in this business. While interesting, such historical examples only serve to highlight the importance of technological change for the equity trading process. For purposes of practical equity valuation, the trading process determines the market value of the equity claim relative to the unit of account. Whatever the theoretical intrinsic value, it is the market value at which the equity security will be traded that is ultimately of interest. It follows that an assessment of the changes in telecommunications and computing technology that have altered the modern equity trading process is required. The transformation has been nothing short of astounding. In a relatively short period of time, information and execution costs for virtually all market participants have fallen dramatically. Information flow about market prices and ability to execute trades is almost instantaneous. A range of ‘new’ and ‘innovative’ derivative securities were introduced, especially on the lightly regulated OTC markets. All this opened a range of both speculative and market

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making trading strategies that were previously unavailable. Regulators have reacted to these changes with relative indifference, if not encouragement. The nomenclature associated with the study of programmed trading is unsettled. As defined here, the class of ‘programmed trades’ includes: the ‘program trades’ associated with portfolio insurance strategies; equity index arbitrage and other cash and carry arbitrage trades connecting derivative markets and cash markets; and, execution related cash and derivative security trades such as inter-exchange arbitrage and ‘flash trades’. The basic element is that the trade can be executed computer to computer, without the need for human intervention. Modern programmed trading can be traced to the introduction by the NYSE of an automated order execution system — the Designated Order Turnaround (DOT) system — in 1976 that was upgraded in 1984 to the include the Super-DOT system for limit orders. Initially intended to automate small orders, the system also was useful to those placing large dollar value orders divided into smaller components, as with index arbitrage and many program trades. The DOT system had the desirable execution feature that market orders were executed by the specialists within three minutes. Initially set at lower share quantity levels, by the time of the 1987 crash orders up to 2,100 shares were eligible for DOT execution. Larger orders were eligible for trade at the opening and, more significantly for program traders, on limit orders. When orders for a large number of stocks are combined, as in the case of index arbitrage or program trading, the order size can be considerably larger than intended for a system designed to execute small orders. Prior to the crash of October 1987, combining the maximum number of shares permitted under DOT for each company in the S&P 500, for example, added up to approximately $40 million (Wigmore 1998, p. 40). At the time of the crash, the number of such trades submitted for DOT execution was so substantial that the execution system could not handle the order flow. It is ironic that the lack of trading system computing power played such a role at the end of the 1980s whereas the next two decades have been characterized by the opposite: the rise in competition among various trading platforms due, in part, to an increasing abundance of computing power. As detailed by Markham and Harty (2008), “the ECN’s arrived in force in financial markets beginning in the early 1990s in the form of automated trading systems for institutional traders in the third market”. The electronic communications network (ECN) and related automated trading system (ATS) has grown from this beginning to engulf the traditional trading practices of equity security markets.

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Stock exchanges, in some form, have always been a fundamental component of equity trading. To function effectively, exchanges and those participating in the exchange process, such as exchange members and market makers, have to be at least modestly profitable. ECN’s and related systems have revolutionized the ways that profits can be earned from the exchange process. Broadly defined, ECN’s encompass a variety of computer-based systems for trading. This includes electronic order routing systems, associated with processes involved in routing a customer’s order to a particular trading platform. The legitimate market making firm associated with the infamous Bernard Madoff recently pioneered the introduction of a pay-for-order-flow market making model where large broker–dealers and other institutions would be provided free execution in exchange for the right to capture order flow. Historically, order routing has been a source of both broker–dealer and exchange member profits. In order to access the trading process, the customer would be assessed a brokerage charge, with negotiated portions paid to the broker-dealer and the exchange. Due to the relentless progress of technology, this model has broken down. The fatal blow to the traditional brokerage fee model of profit generation at the NYSE was the removal of Rule 390, approved by the SEC in 2000. Similar to Rule 5 on the AMEX, Rule 390 was an NYSE rule associated with the self-regulatory function of exchanges. The rule prohibited off-exchange trading also referred to as ‘off-board trading’ of listed stocks. At least since the introduction of SEC Rule 19c-3 in 1980 permitting such off-exchange trading, the stock exchanges have resisted the introduction of this rule. The position of the SEC is reflected in the lengthy discussion of justifications for rescinding the rule detailed in Release No. 34-42758: Off-board trading restrictions such as Rule 390 have long been questioned as attempts by exchanges with dominant market shares to prohibit competition from other market centers. On their face, such restrictions run contrary to the Exchange Act’s objectives to assure fair competition among market centers and to eliminate unnecessary burdens on competition. The NYSE has defended Rule 390 on the basis that it was intended to address market fragmentation by promoting interaction of investor orders without the participation of a dealer, which also is a principal objective of the Exchange Act. Even granting the importance of this objective, however, Rule 390 is overbroad as a tool to address market fragmentation — it applies in many situations that do nothing to promote investor order interaction. In the after-hours context, for example, it creates an artificial incentive for trades to be routed to foreign markets. Rule 390 also effectively restricts the competitive opportunities of electronic communications networks (‘ECNs’), which use innovative

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technology to operate agency markets that offer investors a high degree of order interaction. To avoid the anticompetitive effect of the Rule, some ECNs even have indicated that they would accept the very substantial regulatory responsibilities associated with registering as a national securities exchange, thereby foregoing the streamlined requirements available under Regulation ATS. Rescission of Rule 390 will eliminate these distortions of competition. The Commission will address legitimate concerns about assuring an opportunity for interaction of investor orders in the context of its ongoing review of fragmentation issues.

The drive to achieve an ‘anticompetitive’ solution to equity security trading that produces the cheapest possible price for a particular type of trade fails to recognize the threat to the self-regulatory structure that has historically been responsible for restraining many ‘stockjobbing’ practices. Reducing these threats to the status of an ‘ongoing review of fragmentation issues’ is inviting yet another regulatory failure. The decimation of traditional brokerage fees that accompanied the rise of computerized trade execution has produced a number of other initiatives to offset losses of traditional sources of profitability. In particular, given the relatively low cost now associated with individual trade execution, exchanges and exchange members are driven to seek higher order volume in order to produce revenue offsets. This change has affected all financial markets, including the derivative exchanges. As Markham and Harty (2008, p. 939) observe, the drive to higher volume trading has produced systemic changes in the marketplace: The exchanges’ focus on electronic trading highlights the change in their best customers; from smaller volume commercial hedgers and locals, to large volume special investment vehicles. This change ushered in a growing demand for greater electronic access to the marketplace, and trade matching algorithms that are efficient, volume-centered, preserve anonymity, and promote a marketplace where market news is decentralized.

In the equities markets, ‘special investment vehicles’ include high frequency traders, often operating as hedge funds. As in the derivative security markets, the global challenge of increasing volume and inter-exchange competition has been met with an ongoing consolidation of exchanges in the equity markets. Following a conversion of stock exchanges to publicly traded equity securities during the 1990s and later — the NYSE demutualized and become publicly traded only in 2005 — this has generated the creation of global exchange networks such as NYSE Euronext which absorbed the AMEX in 2008.

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Maintenance of the self-regulatory function of exchanges becomes complicated when exchanges are globalized and have publicly traded equity. Because each of the component exchanges is responsible to a national regulatory body, there has been a drive to achieve harmonization of regulations across exchanges. In 2004, the NYSE component of NYSE Euronext created NYSE Regulation, Inc., a not-for-profit corporation with responsibilities to enforce marketplace rules and federal securities laws. NYSE Regulation also oversees NYSE Arca Regulation and NYSE Amex Regulation through regulatory services agreements undertaken when the NYSE merged with Archipelago in March 2006 and with the AMEX in October 2008. In 2007, NASD Regulation merged with NYSE Regulation to form the Financial Industry Regulatory Authority (FINRA). Harmonization of rules in Europe have reached the point where there is single rulebook governing trading on Euronext’s equity security and derivatives markets associated with passage of the Markets in Financial Instruments Directive (MiFID) in November 2007. In addition to placing more emphasis on home state supervision, the MiFIF abolished of the ‘concentration rule’ that, similar to NYSE Rule 390, permitted member states to require broker-dealers to route client orders through specific regulated markets. Even with increased volumes, ECN’s still reduce per trade exchange profits from brokerage, a traditional source of exchange revenue. However, it is the automated trade execution feature inherent in ECN trading that poses a greater threat to the life blood of exchange floor execution. Specialist trading systems, such as that on the NYSE, or pit trading, as on the Chicago derivative exchanges, are antiquated compared to the anonymous trade matching algorithms of an ECN. As a consequence, the NYSEEuronext merger “was followed by a dismantling of a considerable portion of the NYSE floor, and resulted in the layoffs of hundreds of NYSE employees. The number of people employed by specialists on the NYSE floor was cut in half and the number of specialist firms was reduced to seven, down from 40 in the 1990s” (Markham and Harty 2008, p. 910). In this process, the cost of trading equity securities has declined dramatically. Offsetting the associated gains for equity valuation is the increased uncertainty associated with the exchange process arising from systemic changes in the marketplace for equity securities. Path Independent Portfolio Insurance By fragmenting trading activity and providing a plethora of platforms for regulatory arbitrage, programmed trading related to the exchange process

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threatens the centerpiece of the national self-regulatory process: the securities exchanges. In contrast, programmed trading related to ‘program trading’ involves the implementation of risk management strategies that fall under the general title of portfolio insurance.45 Whatever the source, it is likely that significant reductions in execution costs and data transmission times will amplify the equity market pricing implications of program trading. This follows because the associated market destabilizing trading strategies will be available to a greater group of players. Since the implementation of curbs on program trading following the market crash of October 1987, regulators have slowly moved to ease the ability to execute program trades to the point where, on 7 November 2007, the NYSE abandoned curbs on program trading citing ineffectiveness in curbing market volatility as the reason.46 A more likely reason was the drive to increase exchange volume, as program traders and index arbitragers can account for as much as 50% of exchange volume on some trading days. The loss of this business to competing exchanges, ECN’s and off-shore trading platforms was a substantial threat to the publicly traded NYSE Euronext. In the context of equity valuation, the elimination of regulatory restraints on program trading supports the expanded use portfolio insurance schemes based on dynamic trading strategies. This creates a quandary. On the one hand, for the individual investor the presence of inexpensive portfolio insurance based on dynamic trading expands the payout universe associated with equity securities. Hopefully, this increases the intrinsic and, eventually, the market value of equity securities. On the other hand, such dynamic trading strategies also create systemic uncertainty by increasing the potential for destabilizing or ‘unnatural’ price volatility that other types of portfolio insurance do not. This follows because dynamic portfolio insurance trading strategies require the sale (purchase) of equity securities as 45 Prior to the elimination of curbs on program trading, the NYSE defined a ‘program trade’ as the execution of trades involving a basket of at least 15 stocks from the S&P 500 or where the value of the basket is at least $1 million. 46 While program trading curbs were ended, market circuit breakers were not. Each quarter the NYSE sets circuit breaker levels at 10%, 20%, and 30% of the average closing price of the DJIA for the month preceding the start of the quarter. First quarter 2009 levels are 850 points, 1,700 points, and 2,600 points respectively. Depending on the point drop that happens and the time of day when it happens, different actions occur automatically: Prior to the program trading rules being removed, the NYSE curb on program trading was imposed for moves in the NYSE Composite Index of greater than 190 points from the previous close. Curbs remained in place for the rest of the trading day or until the gain or loss had decreased to 90 or fewer points. When ‘curbs were in’, program sales (buys) were only permitted only on upticks (downticks).

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the market is falling (rising). As such, dynamic trading has different cash market implications than other forms of portfolio insurance arising from the replication properties of derivative securities. In turn, concepts from financial engineering can be used to illustrate the different security allocations in portfolios associated with different insurance schemes. The basic mechanics of ‘path independent’ portfolio insurance can be isolated from the put-call parity arbitrage condition for a non-dividend ∗ paying stock: S +P = C +Xe−rt . Where the concern is portfolio insurance, S refers to the price of a portfolio of stocks (instead of an individual stock), X is the exercise price (strike price), t∗ is the time to expiration measured as the fraction of a year remaining to expiration, P is the price of a put written on the portfolio with exercise price X and time to expiration t∗ , C is the call price written on the portfolio with the same X and t∗ as the put, and r is the riskless interest rate. Dividends have been ignored for simplicity of exposition. As stated, put–call parity provides two path independent insurance strategies. One strategy is S + P , buy puts against the portfolio. If S is an index portfolio, relevant exchange traded puts may ∗ be available. Another strategy is C + Xe−rt , buy calls and invest the remainder in appropriately dated bonds. Again, if the portfolio is an index portfolio, exchange traded calls may be available. One important advantage of this strategy is that transaction costs in bond markets are typically lower than transactions costs for stocks and the bond portfolio can be actively managed, e.g., by riding the yield curve, to earn potentially higher returns than the S + P approach. While the path independent strategies have some desirable features, there are some drawbacks. One disadvantage is the inability to accurately replicate insurance for portfolios that do not track an index for which there are traded options, i.e., the relevant portfolio options are not available. Constructing a portfolio of options using options on the individual stocks will be more expensive and there is the possibility that not all stocks will have traded options. Using index options as surrogates for the portfolio options eliminates the potential for gains from individual security selection. Combining index options with options on individual stocks raises the problem of finding the appropriate combination of these options to replicate the payout on the desired portfolio. Another disadvantage is that the maturity dates for options may not be long enough to match the portfolio’s investment horizon, i.e., there is insufficient ‘time invariance’. This requires options positions to be rolled forward which is more expensive and has pricing risk.

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Dynamic Trading Strategies To handle these types of problems, dynamic trading strategies have been developed that involve actively trading portfolios composed of stocks and bonds in order to replicate the payoff on an insured stock portfolio. Such strategies are intuitively appealing to large institutional investors such as pension funds and insurance companies that already hold stock/bond portfolios that are actively managed. These strategies can be illustrated by substituting the Black-Scholes formula into the put-call parity condition: ∗

∗

S + P = SN [d1 ] − Xe−rt N [d2 ] + Xe−rt ∗

= SN [d1 ] + Xe−rt (1 − N [d2 ]) ∗

= w1 S + w2 Xe−rt , where N [d] is the cumulative normal distribution evaluated at d with d1 and d2 as specified in the Black-Scholes formula, e.g., Poitras (2002, p. 441). The weights w1 and w2 indicate the proportions of the portfolio held in stock and bonds in order to achieve insurance with an exercise price of X and time to maturity of t∗ . Unlike the portfolio optimization models, the weights here will not sum to one, as the relationship is derived to equate values on the rhs and lhs. The sum of the weights will be close to one but not equal to one unless the put value is zero. From a practical perspective, it is important for the potential portfolio insurer to identify why dynamic replication strategies, i.e., strategies dynamically replicating a call option payoff using stock/bond positions, should be used. Related to this are subsidiary issues concerning how to replicate and when to replicate. In this vein, large fund managers would consider the liquidity needed to establish large enough positions using derivatives and whether there are suitable X and expiration dates available. For example, while a well-diversified fund (e.g., an index fund) could make use of options or futures written on the appropriate index, funds targeted at non-systematic risk are more likely to be obligated to use dynamic replication strategies. However, even a well-diversified fund may find that available expiration dates on traded derivatives are not long enough, i.e., sufficient ‘time convexity’ cannot be achieved. Because the dynamic replication strategies can be designed to theoretically achieve almost any desired expiration date and exercise price, this provides another reason for the use of these strategies. To illustrate the use of dynamic replication where dividends are paid on the portfolio, consider the creation of a synthetic put option for an index

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portfolio. Given that the dividend yield on the index is q, Hull (1989, p. 204) shows that the delta of a European put on the index is ∆P = exp{−qt∗ }[N [d1 ] − 1] = exp{−qt∗ }(∆c − 1) where d1 =

ln


S X

 + r−q+ √∗ σ t

σ2 2



t∗

Assuming that S = 300, X = 290, r = 0.09, q = 0.03, σ = 0.25 and t∗ = 0.5, evaluation of the delta of the put gives ∆ = −0.322. It follows that if dynamic replication of a put is being used that 32.2% of the index fund should be sold and invested in (riskfree) fixed income securities. From the properties of the put delta (Poitras 2002, p. 486), as the value of the index fund drops, the delta of the put will become more negative, indicating that a larger proportion of the index fund has to be sold, i.e., a larger fraction of the portfolio will be invested in fixed income securities. A similar result would hold where the value of the index was increasing. In this case the delta of the put would be less negative, indicating that fixed income securities should be sold to purchase more units of the index fund. In this case, the proportion of the portfolio invested in the index fund would increase. In practice, dynamic trading strategies have to deal with the realities of discrete trading. Rules have to be determined about how large a movement in S is required before the rebalancing decision is executed. There are a number of possible methods of specifying a rebalancing trigger value. A common approach, e.g., Rubinstein (1985), is to assume that the trigger value is 5%. From this point, upside movements of S will produce increasing weights for S which lag the continuously rebalanced weights, resulting in a slight reduction in portfolio value. A similar result happens for downside movements of S where the reduction in S weights lag the continuously rebalanced weights, again resulting in a slight reduction in portfolio value. Hence, the simple introduction of discrete rebalancing results in a deterioration of the performance of the dynamic replication strategy. Being path dependent, the terminal portfolio value can take a range of values, depending on the particular time path realized by S. For the path independent case where S is insured by buying P , the distribution of portfolio value can be determined precisely because the terminal portfolio value does not depend on the particular time path realized by S. This does not happen with discrete rebalancing.

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As discussed in Poitras (2002, pp. 523, 524), there is nothing unique about a portfolio of domestic stocks. The notions of portfolio insurance can be applied to any commodity. One useful extension involves insuring the domestic currency value of a foreign stock position. Much as with dynamic portfolio insurance for domestic stocks, dynamic portfolio insurance for a portfolio of foreign stocks can be derived by combining put–call parity for domestic stocks with put–call parity for currency options. The objective is to dynamically trade a portfolio composed of domestic bonds, foreign bonds and foreign stocks in order to achieve the same payout as a path independent portfolio composed of a foreign stock plus a foreign put option for the foreign stock portfolio and a currency put option. To protect the foreign currency value of the foreign stock, the trading between the foreign stock and bond positions proceeds much as in the domestic case. To achieve currency protection, if the exchange rate increases, the value of the domestic currency rises relative to foreign currency, then the dynamic strategy involves selling foreign bonds and buying domestic bonds. If the exchange rate deteriorates, the domestic bond is sold in favor of buying the foreign bond. With some manipulation, the Black-Scholes formula for a call can again be substituted into the put-call parity condition to derive the appropriate portfolio weights.

Alternative Paths to Portfolio Insurance Though portfolio insurance techniques were popularized during the 1980s, heuristic forms of portfolio insurance have been used for decades. For example, a form of portfolio insurance can be achieved with the systematic use of order placement strategies, such as stop-loss and limit orders which have been acceptable market practice at least since the 19th century. These types of trading dependent strategies suffer from the defect of being ‘path dependent’, an undesirable property for insurance schemes. In addition to trading related techniques, option replication strategies using stock/bond combinations were also likely in use, though in the realm of proprietary management practices. These techniques also suffer from the defect of path dependence and, in the absence of ‘Greek’ information, would probably have been imprecise (Poitras 2002, ch. 9). The application of option replication to specifying dynamically traded stock/bond portfolios was not of academic interest until much later, after the development of the Black–Scholes formula. As for the history of insurance related financial products, some of the insurance schemes of the late 17th and 18th centuries did offer payouts

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based on specific outcomes associated with joint stock performance. Being introduced prior to the development of actuarial science, these insurance schemes were more like gambling than insurance. In more recent history, Benninga and Blume (1985) report the selling of insurance against investment losses in the United Kingdom as early as 1956. In the United States, Gatto et al. (1980) report on portfolio insurance plans offered to individuals by both the Harleysville Mutual Insurance Company and Prudential Insurance Company of America. Brennan and Schwartz (1987) observe that the Harleysville plan was the first without any element of mortality insurance. Academically, Brennan and Schwartz (1976) were the first to make the connection between the potential for integrating insurance and equity returns. Leland, O’Brien, Rubinstein and Associates were important proponents in the marketing of dynamically traded option replication strategies to institutional clients. The explosion in the use of the various types of portfolio insurance techniques can be traced to the introduction of exchange trading in options. Liquid options markets made possible the implementation of numerous portfolio insurance strategies. Even more strategies were permitted with the development of futures and options markets for stock indices. Analytical contributions based on Black–Scholes resulted in further portfolio insurance strategies being introduced. Many ‘alternative paths to portfolio insurance’ (Rubinstein 1985) were proposed and implemented. The widespread use of dynamically traded portfolio insurance techniques has been identified as an important contributing factor in the October 1987 stock market ‘crash’, e.g., Tosini (1988). Academic understanding of notions associated with portfolio insurance have expanded considerably since the early work by Leland (1980) and Rubinstein and Leland (1981). The 1987 ‘crash’ provided a textbook illustration of the inadequacies of the academically inspired option replication strategies; sizable unexpected losses were experienced by investors holding what were expected to be ‘insured’ portfolios. One of the fundamentals driving institutions to use dynamic trading strategies was the absence of risk management products with maturities and other characteristics that captured the time profile of their particular risk exposures. Since the crash of 1987, an array of OTC and exchange traded risk management products have been introduced which greatly enhance the ability to implement path independent strategies. Included in the list of such new products would be: long dated exchange traded option products, such as LEAPS for individual stocks and longer dated index options and equity swaps. Despite these improvements, the bulk of contract liquidity on

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both the exchanges and OTC is still concentrated in short dated contracts (see Table 2.4). The relative absence of strict mark-to-market rules in OTC contracts provides a strong incentive to use short dated contracts.

An excerpt from the testimony given by George Soros to the U.S. House Committee on Banking, Finance and Urban Affairs, 13 April 1994. I must state at the outset that I am in fundamental disagreement with the prevailing wisdom. The generally accepted theory is that financial markets tend toward equilibrium and, on the whole, discount the future correctly. I operate using a different theory, according to which financial markets cannot possibly discount the future correctly because they do not merely discount the future; they help to shape it. In certain circumstances, financial markets can affect the so-called fundamentals which they are supposed to reflect. When that happens, markets enter into a state of dynamic disequilibrium and behave quite differently from what would be considered normal by the theory of efficient markets. Such boom/bust sequences do not arise very often, but when they do they can be very disruptive, exactly because they affect the fundamentals of the economy . . . Generally, hedge funds do not act as issuers or writers of derivative instruments. They are most likely to be customers. Therefore, they constitute less of a risk to the system than the dynamic hedgers at the derivatives desks of financial intermediaries. Please do not confuse dynamic hedging with hedge funds. They have nothing in common except the word ‘hedge’.

An important element in the modern renaissance in derivative securities was the emergence of trading in stock index futures. Sufficient liquidity in these futures contracts has facilitated the trading of futures options on these indexes. The first stock index futures contract, based on the Value Line Index, was introduced in February 1982 on the KCBT. The most important stock index futures contract, the S&P 500 traded on the CME/IMM, was introduced shortly thereafter in April 1982. A raft of stock index futures contracts has appeared since that time, starting with the introduction of the NYSE Composite on the NYFE in May 1982 and the Major Market Index on the CBT in 1984. More recently, there has been the introduction of foreign indexes traded on US exchanges, such as the Nikkei 225 on the CME. This has been accompanied by the trading of domestic equity indexes on futures markets around the world, including markets in Japan, Hong Kong, Holland, Australia, England, France, Germany, Switzerland, and Canada. Another recent development has been the start of trading in the DJIA index futures in October 1997. The slow pace associated with the introduction

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of the DJIA contract was not due to a lack of interest in such a contract. On the contrary, perceiving considerable demand, the CBT had attempted to introduce a DJIA contract as early as July 1984. However, these plans were thwarted by Dow Jones and Company which initiated legal action to prevent trading of the contract. What ensued was a process lasting over a dozen years, ending with the CBT eventually introducing DJIA futures and options contracts.

The Crash of October 1987 The beginning of the modern renaissance in derivatives trading starts with the launch of the CBOE and the subsequent beginning of trade in selected financial derivatives, both on the exchanges and OTC. As equity markets adopted derivative securities, techniques of financial engineering progressively were adopted to assist in the risk management activities of institutional investors. Adoption of techniques progressed to the point where delta hedging and portfolio insurance played a central role in the stock market crash of October 1987. Unlike like previous market manipulations involving derivative securities, this event was not generated by the desire for unwarranted gains but, rather, as fallout from the desire to innovate, to apply the techniques of financial engineering in pursuit of enhanced portfolio management outcomes. Ex post, the equity price volatility related to this event created undervaluations sufficient to provide remarkable trading opportunities. The recent ex post re-emergence of these techniques in the slow market crash of 2008–2009 argues for a close inspection of events surrounding the crash of 1987. The causes of the stock market crash of 19–20 October 1987 have been debated ad nauseum. The analysis includes: reports by the exchanges, e.g., the CME and the NYSE; the regulators, e.g., reports by the SEC, the GAO, the CFTC and the Brady Commission; and academic studies, e.g., Edwards (1988) and Tosini (1988). For sheer attention and regulatory impact, the crash of 1987 could be the disaster of disasters. Incremental reforms were made to market practices, ranging from the introduction of trading circuit breakers triggered by large market moves to rules impacting the capitalization of specialists on the NYSE trading floor. Physical hardware changes were also made to the execution system for processing orders on the NYSE. As reflected in the comments of George Soros, another fallout from the crash was the drastically reduced use of stock markets for dynamic trading strategies designed to achieve replication of an untraded option payoff. Such

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schemes had been actively promoted to institutional investors by a number of the leading finance academics, including Fischer Black and Mark Rubinstein.47 In retrospect, the crash of 1987 still has many lessons for the present, if only these lessons could be adequately understood. Too often, it seems, analysis of the crash has the flavor of an apology for the current method of oversight. Tosini (1988, p. 35), a director at the CFTC at the time of the crash, is an excellent example: “there are many profound, complex and farreaching issues before the CFTC, as well as other federal agencies and the Congress, concerning stock market and derivative market activities and performance during October . . . the call for ‘further research’ has hardly ever been more timely”. The various reports made some key observations, e.g., the Brady Report (1988) (U.S. Department of Treasury 1988) recognized that the markets for stocks, stock options and stock index futures were actually one integrated market “linked by financial instruments, trading strategies, market participants and clearing and credit mechanisms”. Despite this integration, the regulatory and institutional structure which was designed for separate markets was unable to deal with ‘inter-market’ pressures. The Brady Commission recommended a number of reforms designed to provide for a more integrated approach to market oversight. The crash of 1987 speaks directly to the problems raised by the systemic change in financial markets brought on by the modern renaissance in derivative securities trading. Various events were replayed in the 1990s because some lessons were not fully understood. This happened because the analysis of the event, on the whole, focussed on the specific events and did not adequately account for the singularity of the event. Katzenbach (1987) details the chain of events. As measured by the Dow Jones Industrial Average (DJIA), the U.S. equity market had achieved a peak of 2,722 in August of 1987. P/E ratios for the S&P 500 were averaging 23, relatively high considering the potential for negative market sentiment. In modern parlance, the equity market was due for a correction. On Wednesday 15 October 1987 there was a news release reporting an unexpectedly large U.S. trade deficit, 47 Katzenbach

(1987) gives a partial listing of key players implementing portfolio insurance strategies for large institutional investors as: Leland O’Brien Rubinstein Associates, Aetna Life and Casualty, Putnam Adversary Co., Chase Investors Mgmt., JP Morgan Investment Mgmt., Wells Fargo Investment Advisors; and, Bankers Trust Co. This list does not include the wannabes at Goldman Sachs, Salomon Bros., Nomura and other firms seeking to gain status in this area. Goldman Sachs was the firm which employed Fischer Black at this time.

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banks raised prime rates and there was considerable downward pressure on equity prices. The S&P 500 fell from over 314 to below 306. Despite a calming statement by Treasury Secretary Baker on the Thursday, the S&P 500 fell again to 298. When some negative PPI and industrial production numbers hit the market at the open on Friday, the stage was set. Significantly, even though things were gloomy, none of this was a shadow of events about to unfold. This leads to a key observation about the crash: it was a severe pricing event which was not associated with a correspondingly severe negative information inflow to the market. The crash actually started on Friday 17 October 1987. In the face of the somewhat negative sentiment, the DJIA fell a record 108 points. The S&P 500 started the day at 298 and fell to around 282. These were significant market moves that, all things considered, may have presented some buying opportunities. Over the weekend, there was some chatter about a dispute between the United States and Germany over interest rates, leading to speculation that the United States might let the dollar fall, an event which would be negative for U.S. equities. There was the usual carry over on foreign markets, such as Tokyo and Australia, though the wave of intense selling had not yet hit international markets. The New York market opening was confronted with news that the United States had attacked Iranian oil platforms in the Persian gulf, which almost surely added to the rush of sell orders. At the open the DJIA was down 67 points. The S&P 500 futures contract on the CME fell 18 points at the open. At a time when daily 100 million share volumes were uncommon events, the NYSE processed 50 million shares in the first half hour. Despite the market turbulence, a 10 a.m. meeting of NYSE officials and major brokerage houses did not feel a trading halt was needed. The sequence of events which was to follow was structured around two institutional procedures. The first concerns the method of executing stocks on the NYSE. Historically, stocks trades on the NYSE involved a floor broker for a member firm walking the order to the NYSE trading post for that stock and executing the trade directly with the specialist or with another broker using open outcry. At the time of the 1987 crash, this was still the case for block trades involving 10,000 or more shares. This manual method of trading was inefficient and costly for trades involving large bundles of stocks which have to be sold at once. Such trades were not only being done by index arbitragers, but also by a wide range of market participants. To improve market performance for these traders, the NYSE introduced the Designated Order Turnaround (DOT) in 1976. This system permitted

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the computerized execution of small trades. Effectively, brokers with member firms could enter trades into a computerized order system, permitting trades to be entered in brokers’ offices. Upon receiving the order, the DOT system would automatically route the trade to the appropriate NYSE specialist, where it would be executed. The whole process takes a matter of minutes. The success of the DOT system led to a new and improved version, the Super-Dot, being implemented in 1984. This new system enhanced execution times and access. This remarkable progress in information technology created its own demand from a growing legion of program traders. This category includes a range of trading strategies, including portfolio insurance and index arbitrage. Program traders could enter the exact weights for a portfolio of stocks which could be executed simultaneously by computer entry. Prior to DOT and Super-Dot, execution risk in such strategies was an important deterrent. Yet, the interaction between the progress in information technology and the ability to introduce new financial engineering products was not well understood at the time. Hints of the crash of October 1987 were observed on 11–12 September 1986 and on 23 January 1987 when ‘excessive’ stock market volatility was observed. These preliminary tremors attracted some attention, and efforts were made to track the activities of program traders through the DOT system. A poll by NYSE of specialists and floor traders found that, almost without exception, program trading was done through the DOT. On average, in the year leading up to the crash, DOT orders from program traders were found to average around 18% of all DOT trades with over 28% of all orders on 19 October 1987 being due to program traders. In addition to the DOT, the other essential institutional feature to consider in evaluating the crash of 1987 was the short sale rule. More precisely, the SEC Act prohibited short selling of securities, except when the short sale either: takes place below the last sale price of that security; or, at the last price, if that price is above the preceding price. Like the SEC Act, this rule had origins in the anti-speculator atmosphere of the post-Depression era. The idea is that the rule prevents excessive and accelerating downward pressure on prices during a market downturn. However, there is no such rule on futures markets. As such, dynamic portfolio insurance strategies could be implemented by shorting stock index futures, instead of attempting to short the underlying stocks. In addition, the single digit percentage margins on futures contracts were only a small fraction of the 50% margins on stocks. These substantive differences across markets can be attributed

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to the regulatory competition between the CFTC, which regulates futures markets, and the SEC, which regulates securities markets. portfolio insurance is a category which includes a range of trading strategies. One important strategy involves dynamically trading stock index futures in order to replicate the payoff on a portfolio composed of the underlying index and a put option. The reason that dynamic trading was used is associated with the relatively limited array of path independent option products available. Exchange traded option maturities were a maximum nine months, not all stocks had traded options, index options were relatively illiquid and the OTC market lacked sufficient liquidity to provide options with the exercise price variation and longer term maturity dates that many institutional investors desired. Even though absence of arbitrage requires that cash-and-carry arbitrage conditions apply to the spot and futures markets, the sheer volume of trading on October 19 meant that a wide price spread between the underlying stock index futures and the stock index was seemingly inevitable. What emerged was much worse: an information technology breakdown. The rush of sell orders effectively crashed the DOT system. At 11:45 a.m. the ticker was approximately 1h behind and a number of stocks had yet to open because of the lack of an orderly market. By 2 p.m. volume had reached 400 million. The final numbers for October 19 were 603 million shares traded, with a drop of 508 points (23%) on the Dow and 80.75 points on the S&P 500, a loss of nearly 30%. At the bell the ticker was approximately 130 minutes behind. This slaughter on the stock exchanges led to a flurry of overnight activities. As the U.S. market collapse spread overseas, there was complete or almost complete trading halts on Tokyo and Hong Kong. There was an unprecedented drop on the London FT Index. The opening of the New York market was preceded by reassuring statements and actions from the FRB, major banks were lowering prime rates and the NYSE shut down the DOT system to prevent the execution of program trades. A temporary and partial trading halt was imposed just after 11 a.m. as the market approached 180 on the S&P futures, while the cash market was trading just below 220. This seemed to spell the end of the crash. Prices recovered and by 2 p.m. the spread between cash and futures narrowed close to normal levels, though the spread did widen as the close approached. At the end of the day, the DJIA was up 102 points on volume of 608 million shares. Due to actions taken to combat the crash, there was strong recovery of the dollar and a decline in interest rates. The low prices combined with the sudden brightening of the economic picture led to a buying spree, both

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in the United States and offshore. By the close Thursday 20 October, the market had recovered about half of what was lost on Monday. The crash of 1987 was, at the time, considered to be an unprecedented security market event. It exposed serious weaknesses in a regulatory system that was designed to fight the battles arising from old technology. The problems originated from an inability to assess and structure the rapid changes in equity and derivative securities markets. The crash was a debacle that was created by a well intentioned need to innovate, to improve portfolio management of large financial institutions. As it turns out, the portfolio insurance programs based on dynamic trading were generally unable to deliver the protection ex post which was claimed ex ante. The situation for which the insurance was most important, the protection of losses in the event of a market collapse, led to preconditions which prevented the outcome from being achieved. The dynamic trading programs could only get so big and it was not possible for more than a small fraction of market participants to successfully pursue such strategies. In addition, there are numerous untold stories of other strategies, such as delta hedging by option traders, which also contributed to the crash. Undoubtedly, such traders also contributed to the selling via both the DOT and floor trading which only added to the downward pressure on prices.

The Slow Motion Crash of 2008–2009 The crash of 1987 is a fitting backdrop for the equity market valuation event that began in September 2008 and terminated in March 2009. The Dow Jones Industrial Average fell 22.6 per cent on 19 October 1987, its steepest one-day decline ever, according to the Stock Trader’s Almanac. During the final half-hour of trading, the Brady Commission reports that program trading represented about 12.2 per cent of total trades. The slow motion market crash actually began two decades later in October 2007 with the S&P 500 approaching 1,600. Perhaps it was a coincidence that the NYSE dropped curbs on program trading in November 2007. The precipitous market drop represented by the price of the S&P 500 ETF (SPY) starts from that point until the end in March 2009 (see Fig. 2.11). The bulk of the drop happened from September to November 2008 where the price of SPY appears discontinuous in the scale used in Fig. 2.11. It is difficult to shake the suspicion that the wholesale removal of impediments to short selling and enhancement of market technology to facilitate program trading strategies over a relatively short calendar time period did play a central role in the

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10 year price history of SPY (08/99-08/09).

unprecedented slow motion crash of 2008–2009. The dramatic spikes in SPY trading during the slow crash only serve to reinforce suspicions. In the context of equity security valuation, this raises a number of questions and issues. In a world where the direction of change is left unchecked or allowed to continue, it is difficult to avoid pessimism. Equity security markets have historically imposed a layering of rules that aimed at smoothing downside moves in the equity market. Consider the traditional uptick rule for short sales. This rule aims to reduce the volatility of upside moves fueled through margin buying by increasing the supply of stock available for short sales during such events. Similarly, short sellers are prevented from adding to a general ‘rush to the exits’ by long-only investors. In addition, it is possible that short sale positions may be liquidated as the supply of stock available for short sale is reduced by margin calls and sales associated with stock purchased on margin. From a vernacular Finance perspective, the removal of such rules imply greater market volatility and, over time, a ceteris parabus reduction in the value of equity securities due to the removal of the implied real insurance premium provided by the short sales restrictions. Available statistical evidence indicates that “in markets where short selling is either prohibited or not practiced, market returns display a significantly less negative skewness” (Bris et al. 2007, p. 1029). The practical implication of such results is ‘not that extreme returns become more frequent’, rather that without short sales restriction extreme returns ‘become

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more negative’ (Ibid, p. 1032). Not surprisingly, academic reaction to empirical evidence that short sales restrictions ‘hinder price discovery’ is to focus attention on the theoretical connection with market efficiency. An influential early contribution, Diamond and Verrecchia (1987), establishes a connection between short sales constraints and the speed of adjustment to changes in market information. More precisely, short sales constraints create an asymmetric impact for negative and positive information events. The significantly less negative skewness reported by Bris et al. (2007) is consistent with this theoretical result. More recent theoretical studies along these lines, e.g., Abreu and Brunnermeier (2002, 2003); Hong and Stein (2003), even claim that short sales constraints can produce bubbles and generate excessive volatility. Academics are generally pleased with results such as Danielsen and Sorescu (2001) that find the reduction of short sales constraints results in statistically negative future returns, in this particular study due to increased short sales using options. “This suggests that negative information is incorporated into price slowly when short selling is constrained . . . Not only do short sales constraints reduce overall price efficiency, but also such an effect is stronger when there is negative information” (Bris et al. 2007, p. 1035). Being an “impediment to price discovery”, numerous academic studies provide considerable backing for regulators seeking to reduce short sales constraints. However, from an equity security valuation perspective, it is as if J.M. Keynes never wrote anything about the negative impact that the casino element in stock market pricing has on aggregate economic activity. Given revolutionary advances in computer and communications technology, the need for an orderly equity market withdrawal in the face of severe headwinds has been increased, not decreased, as academic studies and the regulatory trend would suggest. Restrictions on cash market short selling are more, not less, necessary. A useful ‘rule of thumb’ from vernacular Finance regarding the value investing approach to equity valuation is: ‘Follow the money’. Businesses are not necessarily run for the shareholders. For example, the car companies, professional sports teams and ‘rust belt’ industries have found out that present and contingent future employee compensation can exhaust shareholder claims against cash flow, even though the business may outwardly appear viable. In this vein, who benefits from easing of the rules on short selling? At the top of the list is a narrow constituency of hedge funds and related speculative vehicles and speculators that employ trading strategies depending on short sale positions, e.g., Bekaert and Harvey (2000). For

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example, derivative markets are replete with instances of ‘short-the-cash’ and carry arbitrage opportunities, e.g., Poitras (2002, esp. ch. 4). Another beneficiary is the program traders that are able to use cash market short sales as an alternative route to portfolio insurance, whatever the implications for the aggregate value of equity securities. Finally, the exchanges or ECN’s that are able to capture the considerable trading associated with such activities will also benefit.48 Figure 2.11 illustrates the implications for those unable to follow the money. 2.3.3

Equity Fund Hodgepodge

What are Managed Funds? The management of funds has a history that dates back to antiquity. Political, religious and clan organizations have, at various times, been responsible for the management of social resources to provide for the destitute, sick and elderly or to meet the needs of government. For example, the publicani of the Roman empire were involved in the collection of taxes within the territories of the empire. This required management of funds that accumulated as taxes were paid and involved arrangements made for disbursement of these funds to the government in Rome. In contrast, the history of managed funds is much shorter. In the context of equity security valuation, a managed fund requires at least two basic characteristics: there needs to be a fund manager; and, more importantly, there needs to be a tradeable equity claim associated with the fund. In a sense, the early royally chartered English joint stock companies such as the Bank of England and the East India Company were managed funds. This follows because the equity capital raised from the joint stock issue was exchanged for government debt resulting in a balance sheet that had a sizeable portion of government loan stock on the assets side of the balance sheet. Due to the legitimate business component of the early English joint stock companies associated with the grant of monopoly in the royal charter, the managed fund component of the equity security price was not traded in isolation. Such a broad definition of managed funds supports the view that 48 Using a new SEC database started in 2005, Diether et al. (2009) report that short sales represent 24% of NYSE and 31% of Nasdaq share volume with most short selling being done by institutions as opposed to individuals. Cohen et al.(2007) discusses the costs of cash short selling while Diether et al. (2009) overview possible short selling trading strategies. Dechow et al. (2001) examine the implications of short selling for fundamental analysis.

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managed funds have been part of equity security markets from the beginning of trade in VOC shares. Joint stock companies evolved out of partnerships where the need to pool capital to fund ventures was required. The VOC in particular was formed by combining the equity of smaller Dutch trading companies. In effect, joint stock shares are a claim against a closed end fund of equity capital used to create and perpetuate a business venture. The managers of the fund are those in charge of running the company. While this stretches the definition of ‘fund’ considerably, the basic principle is clear: a tradeable share in a managed fund has similar characteristics to other types of tradeable equity securities. As evidenced in the Mississippi scheme and the South Sea bubble, in many situations it was not the government debt component of the asset value that drove market pricing of the equity security. A similar comment applies to the actuarially sound life insurance companies that commenced operation during the last half of the 18th century, e.g., Lewin (2003), even earlier if companies selling other types of insurance such as the London Assurance and Royal Exchange Assurance chartered in 1720 are recognized. Such companies managed a fund of financial assets and had a traded equity security. However, again there is a mix of a legitimate business component and the managed fund element. All this leads to an additional restriction: the assets held by the managed fund must be tradeable securities. In effect, a managed fund is a tradeable equity security that holds other tradeable securities. In this amended definition, tradeable is broadly defined to include, say, no load mutual funds. In this case, the broker–dealer sponsoring the fund makes a market by being willing to buy or sell at net asset value. Recognizing that managed funds involve the creation of tradeable securities, it follows that such funds can capture payoff characteristics not achievable with, say, individual common stocks. The practical realization of this result during the 18th century marks a feasible beginning to what has evolved into the modern managed funds industry. One of the insights of modern Finance is that the expected return on a capital asset depends only on the risk of that asset within an efficiently diversified portfolio, after adjustment for the level of the risk free return. In other words, it is only the undiversifiable or systematic part of risk that matters for determining the expected return, “and this can be defined only in the context of an investment portfolio” (Levi and Sercu 1991, p. 26). By reducing transactions costs and the like, intermediaries can benefit investors by creating tradeable funds composed of individual security combinations. The precise method or ‘style’

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used to create a particular fund differs considerably over time, depending in part on the types of securities available. The decidedly uneven evolution of this industry reflects the relative sophistication achieved by national and global securities markets at a given point in historical time.

Structure of Early Managed Funds The earliest managed funds were closed end funds, traded on the Paris bourse and other venues starting in the 1760s, invested in debt securities of the French government. The managers were, initially, Genevan bankers though the investment schemes were soon adopted in other centers, such as Amsterdam, and applied to other securities, such as the debt of different sovereign governments (Taylor 1962). The use of debt issues was a least partly due to the relative lack of joint stocks available, though gross mispricing by the French government of the life annuities being purchased by the earliest funds also was an important initial impetus. Restrictions various European countries adopted following the bubbles of 1719–1720 hampered the ability to issue joint stock, reducing the available supply of such equity securities for inclusion in managed funds. Not until the 20th century do funds composed exclusively of ‘ordinary shares’ or common stocks become popular. Funds that purchased common stocks for earnings compounding and capital gains purposes instead of the higher dividend yield on common shares than preferred or debenture stock do not appear until the 1920s. A confusing semantic feature appearing in primary sources for pre-20th century equity markets is the use of ‘stock’ for debt issues and ‘shares’ for common stock. These definitions were conventional in 18th and 19th century British security markets at a time when dividend yield comparison was a common method of equity valuation. Following Armstrong (1848, pp. 5, 6), ‘stock’ was standard American usage for both ‘shares of stock’, i.e., common stock, and “government and state stocks . . . upon which a certain rate of interest is allowed”. However, when common stock valuations were being specifically discussed, reference is made to ‘par value of the shares of this Company’. By the time Lowenfeld (1909) refers to ‘the selection of stock for investment’, ‘stock’ was defined loosely to include a range of debt, preferred shares and ordinary shares. While modern ‘stock’ markets are primarily secondary markets that trade common stock, it was not until the latter part of the 19th century that ‘ordinary shares’ attracted much attention on the ‘stock exchanges’ where trading of debt securities was, by far, the most important. At this time, valuation of ordinary shares was

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driven by factors that were characteristic of debt security selection: safety of capital and stability of income. During the 1868–1914 period when ‘average investment trusts’ were popular, ordinary shares were only gradually assuming importance in the United Kingdom. From a legal perspective, this is understandable as it was not until the Companies Acts of 1856 and 1862 that limited liability and readily available company registration encouraged funding using ordinary shares. In any event, other sources of financing were available for companies and, in addition, there was a plentiful supply of foreign sovereign debt issues to attract the U.K. investor seeking to make up for the progressively falling British government bond yield during this period. For example, the yield on British consols fell from about 3.5% in the early 1860s to below 2.5% around 1900 (Hutson 2005, p. 445). In contrast, with consol yields around 3.25%, the Foreign and Colonial Government Trust was able to obtain attractive yields between 5% and 6% on the highest quality (New South Wales, Nova Scotia) British colony bonds and yields as high 15.5% on the least attractive Turkish bonds. Though coupons may be suspended from time to time on low quality sovereign credits, the full force of the British government could be used to ensure at least some return of principal on such sovereign issues. The evolution of managed funds proceeded considerably during this period (Burton and Corner 1968; Rutterford 2009). Though a number of building societies, mutual savings associations and friendly societies organized previously had features of managed funds, the Foreign and Colonial Trust was different enough to be considered the first of the British investment trusts. The trust was chaired by Lord Westbury, the AttorneyGeneral that had championed the Fraudulent Trustee Bill (1857) and the Bankruptcy and Insolvency Bill (1861). The legal structure of a trust was preferred to that of a limited liability company due to the unsavory reputation that companies had attained following the panic of 1866 that was fueled by the registration of less than credible limited liability companies following passage of the Companies Act. This panic was another instance of speculative excess that had characterized the first half of the 18th century including: the foreign government bond craze of the 1820s and 1830s; and, the railway bubble and bust of 1845–1847. The Foreign and Colonial was established primarily with the aim of providing investors of lesser means, that depended on receiving a steady investment income, with a ‘safe’ diversified investment vehicle capable of achieving returns above those being offered on British government securities.

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The success of the Foreign and Colonial led to five subsequent issues by 1872 and the creation of eight other investment trusts by 1874 (Burton and Corner 1968, p. 17). Circa 1875, the London Stock Exchange listed 18 trusts growing to 70 listed trusts by the end of the decade, numbers that included different issues by the same investment trust (Rutterford 2009). Some of these early trusts were not well designed and there were abuses, such as the over-judicious use of founder shares. A legal challenge in 1879 led to virtually all trusts converting to limited liability companies, e.g., the Foreign and Colonial converted from trust to investment company status in 1879. This marks the historical beginning of another semantic confusion between the ‘investment trust’ — which is legally organized as a trust with trustees and contractual similarities to a bond indenture — and the ‘investment trust company’ or investment company — which is a limited liability company. Among other implications, conversion to company status permitted managed funds: to issue different classes of debt, preferred shares and ordinary shares; and, to depart from the fixed investment list and, to some extent, actively trade securities. The relevance of the legal distinction between trusts and companies continues to modern times with the ‘Halloween 2006 massacre’ of the corporate tax exemption for the unit trust structure by the Government of Canada that decimated retirement savings of small investors. The early investment trusts charged a small front-load fee and annual management fee to pay for fund expenses, not unlike modern managed funds. There was also considerable variation in the investment style of the early trusts. For example, whereas the Foreign and Colonial selected government bonds outside the United Kingdom, the Scottish American Investment Trust selected only U.S. railway bonds. Investment trust features prior to the conversion to company status were dramatically different from modern managed funds (Hutson 2005, pp. 448–450). In particular, the funds were fixed. A trust was created by issuing shares or participation certificates and the funds raised used to buy specific amounts from a predetermined list of securities. Once selected, the portfolio could not be changed except in narrowly defined circumstances. The trust had a fixed life — 24 years for the Foreign and Colonial — and promised to pay a fixed dividend. To allow for the creation of a reserve against unforeseen events that could impact future dividend payments and to make allowance for future capital to redeem shares, an actuary was employed to determine the correct initial difference between the underlying portfolio yield and the fixed fund dividend payment

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so that ‘in all probability’ all certificates could be redeemed within 24 years with a capital surplus still remaining (Rutterford 2009). The theoretical sophistication of the early investment trusts reflects a careful attention to actuarial detail. These ‘average investment trusts’ were built on: “The principle of distribution of risk by embodying in a Trust a number of undertakings” (Share Investment Trust prospectus, 1872). Unfortunately, the subsequent history of investment trusts and investment trust companies did not fulfill the early promise. Even before the conversion to corporate status, problems were emerging in the governance structure and with the use of leverage. Unlike modern mutual funds that are restricted in the use of leverage, there was a number of reasons for early managed funds to use leverage. For example, it was common for initial subscriptions to be partly paid, with the balance to be carried by the company using loans that would be paid down as subscriptions became fully paid. It was a small step to where the fund would be constructed using borrowed money to purchase additional securities that would result in a higher residual payment to founder shares. The abuse of leveraging became particularly acute as the conversion to corporate status permitted funds greater discretion to actively manage the security portfolio and to adjust the composition of equity securities issued by the fund between ordinary, founder and preferred shares.

From Investment Trusts to Mutual Funds The contributions of Henry Lowenfeld, Sir John Fowke Rolleston and others associated with the Investment Registry that supported the Financial Review of Reviews were inspired by the various failings that emerged in U.K. investment trust companies during the last two decades of the 19th century. Whereas the prudent use of reserve funds had protected the early investment trusts from the bond defaults arising during the 1874–1876 economic downturn, this was not the case for the 55 investment trust companies — up to 100 if hybrids investing in other than tradeable securities are counted — that had been listed on the London stock exchange by 1890. The spread of the Barings crisis that began in 1890 saw dividends being suspended, many trusts folded and merged, and trust share values collapsed. By the end of the recession of 1893, only seven trusts had market value greater than issue price (Hutson 2005, p. 448). In this process, a number of poorly managed trusts with self-serving management practices were exposed. In the aftermath of this debacle, Lowenfeld and others sought to restore the actuarial foundations that the original investment trusts had established.

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Despite the efforts of Lowenfeld and others, investment trusts in the United Kingdom did not regain the luster of the late 1880s until the boom years of 1924–1929. By this time, the United States had been propelled by World War I into a position of economic importance that was reflected in the size and development of equity security markets. “By mid-1928, the U.S. investment trust sector had overtaken that of the United Kingdom, with an aggregate capital of $1.2 billion compared with an equivalent $1 billion in capital for British investment trusts” (Rutterford 2009). It was during the 1920s that managed funds, traded primarily in the US equity markets, emerged with investment styles and characteristics closer to actively managed funds traded in modern equity markets. In particular, from the classical closed-end, fixed investment trust model inherited from the United Kingdom, the American equity security markets of the late 1920’s developed the closed end fund, active investment management company model. This allowed for actively managed funds that invested exclusively in common stocks: emphasizing capital gains to obtain the compounding power of reinvested earnings; and, hopefully, to make speculative gains from a combination of leveraging and experienced management producing sound stock selection and market timing decisions. Such trusts also attracted interest from U.K. investors during the 1924–1929 period. Though examples of investment trusts in America go back to the 19th century, the few U.S. trusts that appeared prior to 1924 followed the U.K. closed end, fixed trust model with the exception that common stocks of U.S. companies were the primary assets of the trusts. By 1924, only 18 investment trusts had been formed in the United States (Chamberlain and Hay 1931, p. 104). Following Rutterford (2009), an important factor in the investment trust boom that developed in the period from 1924–1929 was: “the support given to investment trusts [by] a number of influential authors, most notably Edgar Laurence Smith, Leland Robinson, P.W. Garrett, Irving Fisher and Marshall Williams”. The leading figure in the common-stock theory, E.L. Smith, was president of The Investment Managers’ Company and had a direct business interest in establishing legitimacy for the practices of the ‘new style’ investment management companies. In addition to touting stocks for the long run, Smith (1924) also recommended the use of professional investment managers able to periodically alter the composition of the fund portfolio. In addition to being a strong proponent of the ‘common stock theory’ advanced by Smith, Irving Fisher was also a strong proponent of actively managed funds run by investment professionals. ‘Incessantly

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vigilant management’ was needed to see that ‘blue chips did not turn pink’ (Rutterford 2009). This recommendation was based on a seemingly obvious point that inflexibility in the holdings of a fixed trust reduced overall returns as poorly performing securities could not be replaced. This point would have little relevance for the type of U.K. fixed trust that the Foreign and Colonial had become since 1905. The conversion to corporate status in 1879 resulted in the five individual trusts, each with less than 20 securities, being combined into a single fund holding 90 securities. By 1905, there were 280 securities held by the fund almost exclusively selected for purposes of geographical diversification, stability of income and safety of principal (Rutterford 2009). Unlike the classical fixed investment trust, the averaging inherent in a particular investment list was not predetermined and some variation in the portfolio, and the capital structure of the fund, was permitted because the number of securities held was large. Not unlike the earlier excesses of the U.K. investment trust companies in the decade prior to the Barings crisis, tragic excesses appeared in the flexible U.S. investment trusts and investment management companies of the late 1920s. In the explosion of new issues that saw a more than doubling of managed fund assets from 1928–1929, the lack of available common stock for purchase saw trusts and investment companies purchasing the equity securities of other trusts and investment companies. In contrast to the classical fixed U.K. investment trust that invested in a published list of globally diversified portfolio of “Class I” fixed income securities — sovereign and high quality corporate bonds and preferred stock — US investment company managers concentrated on the common stock of a small number of large domestic corporations. The flexible fund feature and corporate structure permitted investment managers to avoid the publication of the specific securities held in the managed fund at any time. Another aggravating factor in the excesses was the use of fixed income securities — primarily associated with preferred shares, though some companies also issued debt — to finance fund capital while fund assets were almost exclusively in common stock. The failure of the U.S. investment management companies of the late 1920s marks a key event in the history of equity security analysis. More precisely, it was the speculative investing practices of the actively managed U.S. investment trusts that inspired Graham and Dodd (1934, p. 52) to identify the ‘new era’ theory of investing: Certainly, through many years prior to 1928, the typical investor had been interested above all in safety of principal and continuance of an

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adequate income. However, the doctrine that common stocks were the best long-term investments resulted in a transfer of emphasis from current income to future income and hence inevitably to future enhancement of principal value. In its complete subordination of the income element to the desire for profit, and also in the prime reliance it placed upon favorable developments expected in the future, the new-era style of investment — as exemplified in the general policy of the investment trusts — was practically indistinguishable from speculation. In fact this so-called investment could be accurately defined as speculation in the common stocks of strongly situated companies. [emphasis added]

Though Irving Fisher, one of the leading figures in the pre-WW II history of academic Finance, is considered infamous in vernacular Finance for the brutal call on the stock market in 1929, in the history of equity securities it was touting of the shares in US investment management companies that was arguably more tragic. Oddly enough, J.B. Williams “followed Irving Fisher in valuing stock as the present discounted value of the expected stream of income from owning it, so that the value of a stock would be the discounted present value of the expected stream of dividends, reduced by some factor to compensate for uncertainty” (Dimand 2009, p. 91). It was this discounted cash flow model that Graham, Dodd and Cottle (1962) later recommended for estimating intrinsic value. Following Rutterford (2009), at the peak of the market in 1929 there was some 675 investment companies in the United States and United Kingdom holding over $7 billion in assets. This included 193 investment ‘management’ companies with $2.7 billion in assets, with both U.S. and U.K. investors participating in these actively managed funds. The benefits of the conservative U.K. fund structure is evident in the managed fund performance during the market downturn that started in October 1929. From a peak in 1929 to June 1931, the Standard Statistics common stock index of 30 U.S. investment trusts had fallen more than 75% while the Institute of Actuaries common stock index for15 U.K. investment trusts fell just 17% from the March 1928 peak to March 1931 low (Economist, 30 June 1931). Allen (1938, p. 237) presents somewhat different numbers with the same general dimensions. Describing the U.S. investment fund industry (Allen 1938, p. 233) observes: “From 1930 to 1934, nearly 200 of the 540 managementcompany units of all types in existence at the end of 1929 had disappeared through merger, voluntary dissolution, or failure”. Where some 200 U.S. investment trusts disappeared, there were no similar impacts on U.K. trusts. At the worst, a number of U.K. trusts had to pass dividends. The inevitable outcome was a dramatic change in U.S. managed funds during the 1930s.

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Investment Company Act (1940) Together with the Investment Advisors Act (1940) (IAA), the Investment Company Act (1940) (ICA) was the last of a number of pieces of major legislation that reformed U.S. securities markets following the collapse of equity security prices from 1929 to 1933. The initial piece of legislation, the Securities Act of 1933, was concerned with the issuing of new securities. The Securities Exchange Act of 1934 deals with regulations for the trade in securities after issuance. It is this Act that governs: the registration of exchanges; the registration of securities listed for trade on the exchanges; and, sets rules for fair conduct. The Securities and Exchange Commission was created by this Act to oversee these activities. While these two Acts covered much of the ground needed to establish a firm legal foundation for U.S. securities trading, there were still some more focused issues that needed to be legally clarified. These issues were sorted out by passage of the Trust Indenture Act (1939), that dealt with bond issues and, finally, to deal with the excesses of the U.S. investment companies, the IAA and ICA. This historic transition roughly marks the beginning of the modern mutual fund industry. Initially, the U.S. managed fund industry responded to the collapse of the flexible, actively managed closed end investment company model with a fixed, open end unit trust model. About 150 such U.S. trusts with capital of $400 million were issued in 1929–1931 (Rutterford 2009). These funds had some similarities to classical U.K. investment trusts such as: no use of loans to buy securities; a fixed and published investment list; and, passive security selection strategy. While this explicitly prohibited active management, the open-ended feature made some trading necessary. Over time, this created difficulties as the list of available securities was limited. This was made even more difficult by the preference for common stocks of large U.S. companies and rules requiring the sale of shares if the dividend was passed. Not only did rules regarding passed dividends further restrict the initial list, it also exacerbated a bear market in shares of these favored companies brought on by a negative dividend event, as these unit trusts acted in concert with forced sales of shares. Allen (1938) provides helpful background on the state of the U.S. investment management industry in the period leading up to the passage of the ICA. In particular, there was the relatively poor performance of investment company common stocks: “Over the entire period 1930–1936, their composite record did not quite equal that of the stock average and was decidedly inferior to that of bonds or of a bond-stock composite. Their

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record, moreover, was inferior to that of the older British companies over the same period” (pp. 236–237). Recognizing that none of the so-called investment trusts were legally trusts, Allen (p. 251) divides the common stock of investment companies into ‘leveraged’ and ‘nonleveraged’. Having identified the poor performance of leveraged investment company stocks since 1929 and characterizing the shares in such investment companies “among the most speculative stocks in the market”, the unleveraged investment company stocks are divided into: mutual; and, nonmutual. Of these, the rapid development of mutual companies since 1929, where “the shareholder is able to resell his holdings at any time at (approximately) liquidating value”, was identified as ‘highly desirable’ (p. 253). As early as 1936, the federal government was providing Revenue Act incentives for management companies to convert to the ‘good’ form of mutual fund organization — incentives that eventually evolved into the ICA model of non-leveraged, managed and diversified, open ended mutual funds that still dominate the modern managed funds industry. In contrast to the income driven, geographically diversified U.K. investment trust that invested primarily in fixed income securities and high quality, dividend paying common stocks, the early American investment company was concerned with ‘managed diversification in common stocks’ which requires that “the long-run record of investment companies in this country will rest in large part on the validity of the common-stock theory of investment”(Allen 1938, p. 234, 248). Similar to Cowles (1944), Allen explores the strategies used by a cohort of the most successful investment companies: “This group included such wellknown companies as State Street Investment Corporation, Lehman Corporation, General American Investors, National Bond and Share, Fourth National Investors, U.S. and Foreign Securities, and Tri-Continental Corporation” (p. 239). In addition to a group of investment companies with successful security selection strategies involving both debt and equity, “a number of these investment companies built their portfolios around a flexible common-stock policy, involving a sharp shift into (primarily) cash and United States government securities in 1930–1932 and back into common stocks just preceding or at the beginning of recovery” (p. 247). A World of Exchange Traded Funds The ICA imposed a range of restrictions on the activities and capital structure of U.S. investment companies. Tight control was placed on the use

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of debt which is prohibited for open end funds, including mutual funds. Closed end funds are permitted to have one issue of preferred and one class of debt, covered by at least 200% and 300% with assets at market value. In addition, the ICA also facilitated the development of the open ended fund that had become popular in the 1930s. From passage of the ICA in 1940 until the present, open ended mutual funds with managed diversified portfolios have proved to be an overwhelming success compared to all other types of managed funds. The Investment Company Institute (www.ici.org) provides a variety of statistics on investment funds. Virtually all of the data provided is for the US only, such as the assets of money market funds, though information on global mutual fund assets is also reported. At the end of July 2008, the following asset values were reported.

Global Mutual Funds U.S. Mutual Funds U.S. Money Market Funds U.S. Exchange-traded funds (ETFs) U.S. Closed End Funds U.S. Unit Investment Trust deposits

$18.15 trillion $10.431 trillion $3.579 trillion $639.93 billion $201.15 billion $2.08 billion

Though mutual funds still dominate the managed fund landscape, Table 2.5 illustrates the dramatic recent collapse in asset values for mutual funds, in general, and equity security mutual funds, in particular. From a peak in 2007 at over $12 trillion, equity mutual funds are now at one half that value and could soon be surpassed in size by money market mutual funds. Though calls for the demise of the managed diversified mutual fund may be premature, there are a number of factors other than the global decline in the equity markets to account for the dramatic drop in assets under management at mutual funds. One factor, the impact of higher fees on fund performance, has been recognized at least since Allen (1938, p. 242) observed: “that expense-tax ratios have been excessively high for investment companies as a group is indicated by the inferior record which these companies have made over the period”. At a time when most managed funds were closed end, Allen also observed that the ‘closed end fund discount’ can be explained by poor performance relative to fees charged: “investment company shares continue to sell on the market at prices below liquidating values,

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Table 2.5 Total Net Mutual Fund Assets, 2004–2009:Q1 (Billions of U.S. dollars, end of period). 2004

2005

2006

2007

2008 Q1

Q2

Q3

2009 Q4

Q1

All Reporting 16,165 17,771 21,823 26,151 24,807 24,649 21,645 18,917 18,152 Countries1 Equity 7,219 8,333 10,508 12,446 10,605 10,437 8,618 6,497 5,912 Bond 3,313 3,450 3,871 4,277 4,221 4,184 3,793 3,388 3,381 Money market 3,323 3,364 3,864 4,961 5,615 5,591 5,424 5,786 5,799 Balanced/mixed 1,445 1,566 2,049 2,632 2,495 2,476 2,159 1,773 1,668 Other 398 512 676 884 885 975 823 676 641 Source: Investment Company Institute (www.ici.org) with data obtained from National mutual fund associations; European Fund and Asset Management Association provides data for all European countries except Russia. 1 Components may not sum to total because of rounding or unclassified funds.

evidence that investors feel that operating results after expenses have not been as satisfactory as returns from direct investment in common stocks”. Faced with a decline in assets under management during the bear market of 2000–2003, the GAO estimates that the largest mutual fund managers in the United States raised their fees by an average of 11% from 1999–2001. As illustrated in Table 2.5, the equity security component of the U.S. mutual fund industry faces systemic problems associated with the poor performance of equities over the past decade. It is difficult to achieve sufficient upside performance to justify management fees when the overall market is down. In addition to the systemic problem of attracting and retaining funds when returns are poor to negative, mutual funds sustained a serious image hit in 2003 as a result of illegal late trading and market timing practices by certain hedge fund and mutual fund companies. Coming shortly after the $1.4 billion settlement reached with the SEC surrounding the fraudulent touting of investment banking clients by the research department of the brokerage division, the mutual fund scandal was more technical in character and conducted on a much smaller scale. However, the perception of wrong doing was widespread and well published due to the prosecution of the case by the same white collar crime buster responsible for initiating the stock touting investigation: New York State Attorney General Eliot Spitzer. The initial case uncovered by Spitzer, acting on a phone tip, involved a New Jersey hedge fund, Canary Capital Partners LLC, conducting ‘late trades’ with a Bank of America run mutual fund. Soon joined by the SEC,

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the investigation grew to include ‘market timing’ violations by some major mutual funds, including: Janus; Bank One (One Group); and, Strong Capital. As with the initial Canary Capital Partners case, hedge funds were often involved as counter parties. In some instances, a financial intermediary affiliated with the mutual fund would lend the hedge funds the money being used to purchase the fund shares. For late trades, the fund permits trading in fund shares after 4:00 p.m. at the closing price for trades done prior to 4 p.m. As Spitzer observed in the initial indictment, this is “like allowing betting on a horse race after the horses have crossed the finish line”. Less insidious is market timing, where the fund permits certain individual traders to do more trading than permitted by the fund prospectus. Fees and expenses for mutual funds are based on an estimate of how often the shares will be exchanged. Permitting certain traders to engage in additional trading, especially where the trading strategies involve switching between the funds and cash, imposes unwarranted costs on the other fund investors. The travails of the managed, diversified mutual fund model has led to a market demand for other types of managed funds. This has led to the development of a new type of managed fund: the unleveraged, fixed, open ended exchange traded fund. Though relatively low transaction fee index funds were made available through a few mutual fund companies previously, the first attempt at a launch of an ETF was the Index Participation Shares, an S&P 500 proxy, traded briefly on the AMEX and the PHLX. A lawsuit by the CME which traded a similar futures index was successful in getting a trading halt. This makes the Toronto Index Participation Shares (TIPS) that commenced trade on the Toronto Stock Exchange in 1990 as the first continuously traded ETF. In January 1993 the AMEX launched SPDR, known colloquially as ‘Spiders’, now trading as SPY. This particular ETF soon achieved the largest asset value of any ETF. From these early beginnings in index funds, the number and size of ETF’s has grown dramatically, to include securities and commodities across geographical boundaries. Table 2.6 illustrates the recent development of exchange traded funds. One advantage of the fixed fund model is lower management fees. As such, the incentives for ETF trading originating in Canada were the highest. Based on a 20-country study by Khorana et al. (2009) and a U.S./Canada study by Ruckman (2003), Canadian investors were saddled with the highest equity security mutual fund fees of any country. Such fees can be broken into: fees paid directly for fund manager services (MGT); total expenses, which when divided by the market value of funds under management gives

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Total Investment Company Assets (Millions of dollars, end of period).

Broad-based equity Date

Sector

Total Total Broad Natural Real All funds market Large cap Mid cap Small cap Based-Other Commoditiesa Consumer Financial Health resources estateb Technology 183,544 162,651 177,328 176,378 175,651 167,339 171,730 179,560 187,303 163,634 161,208 184,774 164,640 135,247 137,230 144,178 149,707 151,939 164,274

30,686 29,977 29,511 32,169 33,902 32,876 31,172 32,913 30,111 24,167 22,976 25,064 22,832 20,008 21,386 25,818 25,781 25,987 29,049

28,124 26,526 28,256 28,058 31,156 26,156 30,597 32,680 37,119 26,619 24,489 27,577 23,959 20,482 21,817 25,353 27,068 27,380 31,263

10,683 10,115 10,149 10,413 10,444 9,015 9,105 9,416 8,986 8,463 8,307 9,118 8,464 6,977 7,711 8,767 9,553 9,812 11,107

32,827 36,337 36,019 33,518 36,514 40,775 38,096 34,035 37,561 29,177 31,813 35,728 40,787 47,548 51,252 50,310 58,219 58,460 58,333

4,754 4,793 5,088 5,024 4,914 4,839 5,273 5,405 6,344 5,121 5,237 4,676 4,242 3,948 4,025 4,426 4,563 5,562 5,557

11,306 11,036 13,674 15,217 13,341 15,043 17,269 19,181 20,965 17,259 15,751 15,640 11,370 9,164 12,612 15,151 16,733 17,091 17,055

7,031 6,916 6,324 6,530 6,683 6,130 7,496 8,217 7,737 6,952 6,475 6,544 6,349 5,570 6,150 5,808 6,135 5,830 6,490

15,821 17,467 16,367 18,680 20,177 21,209 19,313 17,223 16,757 13,189 12,994 12,037 11,168 10,517 11,370 12,846 14,653 14,137 15,399

8,029 8,022 8,637 9,981 8,763 8,909 9,218 10,020 10,562 7,065 6,994 7,456 6,744 5,425 5,546 7,277 7,376 7,440 8,244

6,908 6,428 6,796 7,438 8,132 7,316 7,382 7,581 6,176 5,191 4,817 4,542 4,194 4,140 5,038 6,180 6,576 6,886 8,489

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21,152 20,769 20,812 22,177 22,951 21,529 21,553 22,436 20,357 18,213 18,000 19,628 17,801 15,815 17,183 19,158 20,465 20,891 22,762

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568,725 559,311 571,109 595,955 610,311 578,065 582,786 585,974 579,510 482,318 478,045 531,287 495,382 449,669 482,018 529,661 581,927 590,335 639,928

History of Equity Securities

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1/31/2008 2/29/2008 3/31/2008 4/30/2008 5/31/2008 6/30/2008 7/31/2008 8/31/2008 9/30/2008 10/31/2008 11/30/2008 12/31/2008 1/31/2009 2/28/2009 3/31/2009 4/30/2009 5/31/2009 6/30/2009 7/31/2009

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Table 2.6

(Continued)

241

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Bond

Other Single Emerging Government Municipal Corporate International Utilities sectors Global International Regional country Hybrid markets bond bond bond bond 9,464 10,413 10,150 10,865 11,981 12,076 11,311 10,972 9,248 7,141 7,966 9,090 8,770 8,838 10,122 10,006 12,601 12,744 13,529

56,930 56,711 55,440 58,407 59,252 54,549 52,213 50,152 43,236 34,857 36,456 42,951 37,122 32,067 33,501 38,136 42,913 41,944 46,212

10,397 10,510 9,891 10,998 10,703 8,893 8,630 7,999 6,771 5,431 5,399 5,822 5,149 4,357 4,783 5,430 6,161 6,507 7,262

23,084 23,453 21,844 23,670 23,903 21,811 20,744 18,679 16,421 12,832 12,280 11,941 10,935 9,456 9,872 11,348 14,241 14,563 16,641

119 138 146 170 170 176 175 175 158 135 132 132 125 118 126 139 146 150 158

60,988 67,904 64,021 72,829 77,132 64,488 64,107 59,182 52,745 40,863 37,936 43,879 41,737 39,965 46,826 57,920 73,131 73,297 83,013

21,934 22,932 22,299 22,761 22,763 23,365 24,908 25,819 27,012 25,181 26,511 27,768 29,735 30,569 32,925 34,429 35,620 36,903 37,370

Source: Investment Company Institute Exchange Traded Fund Supplemental Report. Note: Components may not sum to total because of rounding. a The funds in this category are not registered under the Investment Company Act of 1940. b This category includes funds both registered and not registered under the Investment Company Act of 1940.

690 764 1,062 1,275 1,398 1,497 1,539 1,682 1,672 1,732 1,911 2,183 2,533 2,820 3,060 3,378 3,704 3,971 4,444

14,767 15,565 16,159 17,117 18,031 18,679 19,033 20,113 20,202 19,812 21,503 25,740 28,356 29,514 31,500 34,620 37,171 39,142 42,377

352 618 871 1,018 1,253 1,547 1,825 1,846 1,748 1,450 1,349 1,518 1,564 1,502 1,566 1,704 2,017 2,309 2,651

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3,638 4,191 4,517 5,363 4,911 4,125 4,280 4,765 5,019 3,677 3,318 3,193 2,778 2,244 2,458 3,342 3,294 3,230 3,787

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5,499 5,077 5,747 5,899 6,185 5,724 5,817 5,924 5,299 4,157 4,224 4,285 4,030 3,378 3,960 3,940 4,098 4,163 4,463

Valuation of Equity Securities

1/31/2008 2/29/2008 3/31/2008 4/30/2008 5/31/2008 6/30/2008 7/31/2008 8/31/2008 9/30/2008 10/31/2008 11/30/2008 12/31/2008 1/31/2009 2/28/2009 3/31/2009 4/30/2009 5/31/2009 6/30/2009 7/31/2009

Hybrid

November 3, 2010 10:47

(Continued).

Global/International Date

242

Table 2.6

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Table 2.7

243

Equity Security Mutual Fund Fees, 2002 (in %)

Country Australia Canada France Germany Switzerland United Kingdom United States 20 Country mean

MGT

MER

AMER

1.09 1.96 1.04 1.05 1.47 1.07 0.62 0.90

1.17 2.56 1.22 1.17 1.47 1.18 1.11 1.29

1.41 3.00 1.88 1.97 2.03 2.28 1.53 1.80

Note: MOT = managers services; MER = management expense ratio; AMER = adjusted MER to account for further load fee

the management expense ratio (MER); and, a load fee adjusted MER (AMER) that adjusts for differences in load fees across funds not included in the MER. Total expenses includes management services, administration, servicing the account, transfer agent fees, audit and legal, and so on. Kohrana et al. (2009, pp. 1287, 1288) provide the following comparison of equity security mutual fund fees (in percent) in Table 2.7: The incentive to innovative based on shortcomings in the managed, diversified, unleveraged mutual fund has not been limited to ETF’s. As Edwards (1999, p. 191), observes: “hedge funds are to a large extent the creation of the legal restrictions imposed on mutual funds and other institutional fund managers”. What is a Hedge Fund?49 Hedge funds are a fitting metaphor for the uncertain state of equity markets early in the 21th century. It was a network of feeder hedge funds that Bernard Madoff used to pull off the largest Ponzi scheme in history, lasting from the early 1990s until the collapse in late 2008. It was hedge funds run 49 Estimates

for the size of hedge funds vary, if only because it is difficult to track entities that are not registered. In 2007, Price Waterhouse Cooper estimated $2.17 trillion in assets under management compared to over $24 trillion for mutual funds (Cumming and Johan 2008, n.1). Given the substantial leverage used by many hedge funds, the actual capital invested would be much less. Poitras (2005, p. 566–568) examines the history of hedge funds, starting with Alfred Jones (1901–1989) research for a Fortune article in March 1949 that led to creation of the first limited partnership hedge fund in 1952. Evans (1965) is an early contribution to the history and development of certain hedge fund strategies.

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by Bear Stearns that were implicated in the distribution of the toxic mortgage assets that led to the financial market meltdown of late 2008. Another hedge fund, Amaranth Advisors LLC, lost $6 billion trying to manipulate the natural gas market in February and April 2006, the bankrupt firm eventually being required to pay a $7 million fine to the CFTC for market manipulation. The first hedge fund distributed to Canadian retail investors in 2004 — Portus Alternative Asset Management — was soon discovered to be an intricately designed legal structure aimed at providing the fund manager with unlimited discretion to move capital offshore into a network of offshore hedge funds. The collapse of the fraud in February 2005 resulted in hundreds of millions in losses to investors, some of which was ultimately covered by the investment management companies that directed clients to these products. At least since the collapse of LTCM, similar red flags to those appearing in the Madoff, Bear Stearns, Amaranth and Portus cases have been apparent in hedge fund activities. The term ‘hedge fund’ is generic, being used to describe a variety of different fund strategies that loosely share some similar characteristics. In the aftermath of the LTCM debacle (Dunbar 2000), the President’s Working Group on Financial Markets (PWGFM) (1999, p. 40) defined the term “to refer to a variety of pooled investment vehicles that are not registered under the federal securities laws as investment companies, broker–dealers, or public corporations”. A similar definition appears in an SEC staff report on hedge funds appearing in 2003 (SEC 2003), with the clarification that a hedge fund “is not registered as an investment company under the Investment Company Act”. This recognizes ongoing efforts by the SEC to regulate hedge funds under the Investment Advisors Act (1940), e.g., Pekarek (2007). The continuing lack of regulatory oversight is not due to vigilance by US regulators. Despite repeated recommendations and attempts to regulate hedge funds dating to the 1960s, the defining characteristic of hedge funds is still: “pooled investment vehicles that are not registered under federal securities laws”. To achieve this, hedge funds are organized as limited partnerships or, in some jurisdictions, limit liability companies with shares that are not publicly traded (van Berkel 2008). While this seemingly disqualifies a hedge fund from consideration as a tradeable equity security, hedge funds are designed to avoid the restrictions imposed on tradeable securities, without losing certain essential characteristics that would otherwise require such consideration. Much is made by modern Finance academics of the different hedge fund categories and that “hedge fund investment strategies provide greater

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diversification opportunities and may result in higher risk-adjusted returns for investors” (Edwards 2006, p. 46). Some even claim: “the hedge fund industry may have played more of a role in creating liquidity and making markets efficient than the mutual fund industry” (Stulz 2007, p. 193). On balance, Stulz (2007) captures the ‘bullish’ stance of modern Finance academics on hedge funds: “regulation should leave alone financial innovators who dream of new strategies and find savvy well-funded investors to bet on them”. Prior to the market downturn of 2008–2009, there was even considerable progress toward retailization of ‘alternative asset classes’ such as hedge funds and private equity funds because such funds “can pursue investment and speculative strategies that are not open to other institutional fund managers, . . . avoid the costs associated with regulatory oversight, and . . . use whatever fee structure they believe to be optimal” (Edwards 1999, p. 191). Viewed as a type of managed fund, the characteristics of classical hedge funds are: actively managed; leveraged; regulatory free rider; and, de facto investment companies disguised as limited partnerships. Though a hedge fund does not directly issue securities, because fund size changes with redemptions and additional investments, hedge funds can also be classified as open ended funds with restrictions on redemptions. In any case, hedge funds possess essential characteristics of the types of managed funds that the ICA and IAA were designed to stamp out. There are sound historically based rationales for restricting highly leveraged speculative trading activities by unregulated entities. The costs associated with regulatory oversight are important to maintaining the stability and integrity of financial markets. Free rider funds that are able to avoid such regulatory costs are at an advantage to funds that do pay such costs. From an historical perspective, permitting unregulated financial entities that operate in securities markets with the primary objective of making speculative profits is ill conceived and reckless and results in increased potential for severe market disruption.

Regulation of Hedge Funds In order to avoid the registration requirements specified under U.S. federal securities laws for securities companies, hedge funds have to satisfy a number of specific conditions. Exemption from the Securities Act (1933) is achieved by having no public offering. This is an issue with using the ‘funds of hedge funds’ approach as a strategy to retailize hedge fund investing. Whether it is possible to issue a tradeable equity security holding assets

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that would not otherwise be considered be tradeable depends on the jurisdiction. Similar regulatory quandaries arise with the exemption from the ICA achieved by being a ‘private investment company’. Hedge funds have two possible avenues to qualify as private investment companies, either the ‘100-person exemption’ (sec. 3(c)(1)), or the ‘qualified purchaser exemption’ (sec.3(c)(7)) that permits up to 500 qualified investors. While there is often the perception that hedge funds are privately structured and closely held entities qualifying because the primary investors are high net worth individuals, in practice the 100-person exemption is not used because the institutional investors in hedge funds satisfy the test for ‘qualified purchaser’. Each institution, such as a pension fund or investment bank, is counted as a separate investor. Because such institutions could contain investments from thousands of investors, the actual ‘size’ of the hedge fund would be much larger than the small number of institutions investing in the fund. Hedge funds have been an ongoing headache for regulators. Since the collapse of LTCM, there has been a parade of hedge fund related problems. Still, a formal legal definition of a hedge fund is lacking: “The term ‘hedge fund’ is not defined or used in the federal securities laws” (PWGFM, p. 40). One of the attractive features of hedge funds is the avoidance of certain legalities associated with registration, information filing, taxes and so on; though some U.S. hedge funds do register under the IAA. To achieve the exemption from federal securities regulations, a hedge fund is typically structured as a pooled investment vehicle, that is privately organized, closely held among a small number of partners and run by professional investment managers, typically on an incentive fee basis. The master-feeder organizational structure of such funds often involves a corporation domiciled outside the United States in tax havens such as the British Virgin Islands or Bermuda, e.g., Greene et al. (2007). The various characteristics of a hedge fund all interact to create a type of managed fund that falls through many of the cracks in the securities laws of the US and other countries. One avenue for dealing with hedge funds is enhanced regulation to bring such funds within the scope of regulatory oversight. To date, such legislation is still not forthcoming though the determination to act is apparent. Even though hedge funds do not fall within the scope of the SEC Act or the ICA, regulators still have made ongoing efforts to subject hedge funds to a number of other U.S. statutes, especially the IAA. To date these efforts have been thwarted in federal court proceedings, especially the Bulldog Investors

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case upholding the exemption of hedge fund advisors from the IAA, e.g., Pearson and Pearson (2007), Pekarek (2007, 2007a) and Mann (2008). Barring direct regulation, indirect regulation of hedge funds occurs through the array of financial institutions which hedge funds need to conduct business. For example, the SEC imposes capital, margin and reporting requirements on broker–dealers, which are essential counter-parties or clearing members for hedge funds. Included among these requirements are risk assessment rules specified in the SEC Act to “establish record keeping and reporting requirements for subject broker–dealers and their affiliates whose business activities are reasonably likely to have a material impact on the financial and operational conditions of the broker–dealer” (PWGFM, p. 42).

Hedge Fund Strategies The situation surrounding regulation of hedge funds is complicated because hedge funds are not the only managed funds which seek such specific exemptions from U.S. securities laws. For example, venture capital pools, private equity funds, venture capital funds, asset securitization vehicles, family estate planning vehicles and investment clubs can receive such treatment. As a consequence, another defining feature of hedge funds is the types of strategies which the funds pursue. Given the restricted scope of other types of funds seeking exemptions, hedge funds can exhibit considerable variation in strategies. “There is no single market strategy or approach pursued by hedge funds as a group. Rather, hedge funds exhibit a wide variety of investment types, some of which use highly quantitative techniques while others employ more subjective factors” (PWGFM 1999). The diversity of hedge fund strategies extends to the types of securities traded (PWGFM, p. 9): Many hedge funds trade equity or fixed income securities, taking either long or short positions, or sometimes both simultaneously. A large number of funds also use exchange-traded futures contracts or over-thecounter derivatives, to hedge their portfolios, to exploit market inefficiencies, or to take outright positions. Still others are active participants in foreign exchange markets. In general, hedge funds are more active users of derivatives and of short positions than are mutual funds and many other classes of asset managers.

However, behind all the confusion about hedge fund typology, the basic intuition is relatively clear: hedge funds combine long positions in certain

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The MARhedge Hedge Fund Categories MARhedge is an important source of information and news about the hedge fund industry. Data available through MARhedge has been thoroughly examined in Ackermann et al. (1999). In order to provide some degree of organization to this mismash of hedge fund strategies, MARhedge (www. MARhedge.com), classifies hedge funds into eight broad categories: Global Macro funds: take positions on changes in global economic conditions in equity, FX and debt markets. Use derivatives, including index derivatives, and leverage. Global funds: similar to macro funds but targetted at specific regions, often involving stock picking. Long-only (US Opportunistic) funds: are like traditional equity funds but with the hedge fund characteristics of leveraging and incentive fees for managers. Strategies for these funds include Value, Growth and Short-term trading. Market-neutral funds: the basic objective of these funds is to be long in one group of securities and short in another group, such that market risk is controlled or neutralized. This can be done in a number of ways: by going long one group of stocks and short another group, seeking to benefit from superior stock picking skills; conversion arbitrages, which are long in underpriced convertibles and short in the underlying stocks; stock index arbitrages; and, fixed income arbitrages, which are long, say, off-the-run Treasuries, and short on-the-run Treasuries. Sectoral hedge funds: have an industry focus; short-sale funds, which short sale over-valued securities, investing the balance in indexes or fixed income securities Event-driven funds: target special situations, specifically distressed securities of firms in reorganization or bankruptcy as well risk trading in takeovers, e.g., buying the target and selling the acquirer. Short Sales funds: the fund is positioned to benefit from market declines. These funds can be index driven or can be based on stock picking. Funds of hedge funds: funds of hedge funds, sometimes leveraged. Within each of these general groups, a variety of different strategies could be pursued. Similarly, some funds may be involved in activities covering more than one fund category.

securities with short positions in other securities. Such ‘hedging’ strategies can be relatively low risk where the securities being traded are highly correlated., e.g., the ‘on-the-run’ versus ‘off-the-run’ Treasury security arbitrage run by John Merriweather, first at Salomon Brothers and subsequently at LTCM. Because the price differences involved in achieving a profit are small, substantial leverage is required and warranted. Such hedge fund strategies

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will, directly or indirectly, involve leveraging. However, many other hedge fund strategies do not have sufficient correspondence between the short and long positions to warrant the degree of leverage that is being partially hidden from public view by these managed funds operating under exemptions from securities laws designed to deter such excessive leveraging. Hedge funds are not conventional investment vehicles. Investor liquidity is often compromised with “lock-up periods of one year for initial investors and subsequent restrictions on withdrawals to quarterly intervals” (Ackermann 1999, p. 834). The regulatory exemptions that hedge funds work under severely restricts the ability of hedge funds to advertise to attract capital. Another untypical feature of hedge funds concerns the management (Ackermann 1999): Hedge funds are . . . characterized by strong performance incentives. On average, hedge fund managers receive a 1 percent annual management fee and 14 percent of the annual profits. For most funds this bonus incentive fee is paid only if the returns surpass some hurdle rate or “high-water mark” — meaning there is no incentive fee until the fund has recovered from past losses. Although incentive fees and high-water marks could lead to excess risk taking under some conditions, there are countervailing forces that my dampen risk. Hedge fund managers often invest a substantial amount of their own money in the fund. Furthermore, the managers of US hedge funds are general partners, so they may incur substantial liability if the fund goes bankrupt.

In contrast to mutual funds which have a much longer history that has been intensively studied, hedge funds only started to receive academic attention in the mid 1990s, though work on managed futures funds and commodity pools, which started somewhat earlier, is also applicable, e.g., Irwin and Brorsen (1985), Elton, Gruber and Rentzler (1987), Edwards and Ma (1988), Cornew (1988), Irwin et al. (1993), Edwards and Park (1996). As data has accumulated on hedge fund activities, a voluminous number of studies has appeared on various aspects of hedge funds. Among the useful studies directly on hedge funds are Klein and Lederman (1995), Fung and Hseih (2000, 2002), Brown et al. (1999, 2001), Schneweiss and Spurgin (1998), Ackermann et al. (1999), Liang (2000), Gregoriou (2002), Goetzmann et al. (2003), Patton (2009), and Griffen and Xu (2009).

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CHAPTER 3

Modern Equity Security Valuation

3.1

3.2

3.3

Foundations of Old Finance 3.1.1 Graham and Dodd, Security Analysis (1934) . . . 3.1.2 Mitchell, Macaulay and the Institutionalists . . . . 3.1.3 Lasting Insights: Graham, Dodd and Cottle (1962) Value Stocks and Growth Stocks 3.2.1 Value Stocks Versus Growth Stocks . . . . . . . . 3.2.2 The Growth Stock Philosophy . . . . . . . . . . . 3.2.3 The Warren Buffett Synthesis . . . . . . . . . . . . Modern Finance and New Finance 3.3.1 Conquering the Old Finance . . . . . . . . . . . . 3.3.2 Two Fund Separation and Exchange Traded Funds 3.3.3 From Modern Finance to New Finance . . . . . . .

. 252 . 258 . 270 . 278 . 281 . 289 . 301 . 309 . 321

What Is Knowledge? Knowledge can be transmitted in a variety of forms. For example, following the tenets of economic positivism, knowledge is obtained by providing the logical development of a desired proposition, starting from initial assumptions and proceeding deductively until the proposition is established. When possible and appropriate, the validity of the proposition is then subjected to empirical verification. This method of obtaining knowledge can be contrasted with, say, the Socratic approach that develops notions using an interrogatory interplay. Various other methods that have been used to transmit knowledge include: the parables of the New Testament; the sayings of Confucius or Sun Tzu; and the fables of Aesop. Even Grimm’s fairy tales or Mother Goose nursery rhymes convey knowledge in a fashion that is different than the ‘scientific’ approach. Yet, it is difficult to claim that knowledge provided by these different sources does not have value relative to knowledge obtained using the ‘scientific’ method. Following Warren Buffett (Cunningham 2002, p. 82), it is even possible to go in the other direction and claim that, in the valuation of equity securities, false-scientific precision can shed more heat than light on matters of relevance. 251

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Foundations of Old Finance Graham and Dodd, Security Analysis (1934)

Graham and Dodd (1934) is a product of the severe collapse in the corporate securities markets that started in October 1929 and continued until February 1933. This is evident from page one: “Any present examination into financial principles or methods must start with recognition of the distinctive character of our recent experiences, and it must face and answer the numerous questions which these experiences inspire”. For Graham and Dodd, ‘recent experiences’ stretch back to 1927, where the advance to the October 1929 peak is identified as beginning. Words like ‘unprecedented’, ‘tidal wave’, ‘special causes’, and ‘unparalleled effects’ are used to describe this period relative to the usual ‘repetition of business and stock market cycles’ that typically characterize stock market price behavior. In contrast, a number of recent studies, e.g., Santoni (1987), Bierman (1991, 1998), have concluded that “overall [the] stock market was not obviously excessively high in September 1929 and the business outlook was favorable. Thus the October crash did not occur because the market was too high” (Bierman 1998, p. 17). Such views lend support for the position that Irving Fisher held regarding equity valuations during the crash period. Were Graham and Dodd incorrect in their observations about security markets events that were, perhaps, too close to be judged accurately? This seems unlikely. If Graham and Dodd were correct, then Bierman and the other observers have misinterpreted the significance of ‘the crash of 1929’ by focusing on the mechanics of common stock valuations surrounding the crash instead of dealing with the role of the crash in contributing to the ongoing collapse of stock market values that continued until February 1933. Based on analyses starting from Fisher (1930) and continuing to the present, it is evident that theoretically sound rationales for the level that stock prices attained in 1929 can be provided. Yet, consistent with the argument of J.M. Keynes in The General Theory, e.g., Chap. 11, the crash acted by changing investor perceptions; it was the severity of the negative shock to the perception of the prospective return to investments that was the key driving factor behind the aggregate economic problems that plagued the industrial world in the 1930s. Security valuation requires more than a mechanical application of predefined rules. The uncertainty inherent in common stock returns can be resolved in different ways, depending on the impact of the historical context

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on investor psychology. Graham and Dodd (1934, p. 6) clearly recognized this point: we do not accept the premise that the 1927–1933 experience affords a proper norm by which to judge the future of investment. The swing of the speculative pendulum during this period was of such unprecedented amplitude as to warrant the belief that it will not recur in similar intensity for a long time to come. In other words, we should regard it more as an economic phenomenon akin to the South Sea Bubble and other isolated instances of abnormal gambling frenzy than as an indication of what the typical speculative cycle will be. As a speculative experience, the recent cycle differed from previous ones in kind rather than degree; but in its effects upon the investment fabric it had unique characteristics, seemingly of a nonrecurrent type.

This is by no means an isolated quote, e.g., “One of the striking features of the past five years has been the domination of the financial scene by purely psychological elements” (p. 11). The impact of the historically abnormal previous five years of common stock pricing on the analysis and principles advanced by Graham and Dodd (1934) is systemic, it affects the whole text. Graham and Dodd were concerned about the inadequacies of an approach to equity security analysis that appeared in the latter part of the 1920s. Graham and Dodd (1934, p. 307) referred to this approach as ‘The New Era Theory’: During the postwar period, and particularly during the latter stage of the bull market culminating in 1929, the public acquired a completely different attitude toward the investment merits of common stocks . . . The new theory or principle may be summed up in the sentence: “The value of a common stock depends entirely upon what it will earn in the future”. From this dictum the following corollaries are drawn: 1. That the dividend rate should have slight bearing upon the value. 2. That since no relationship apparently existed between assets and earning power, the asset value was entirely devoid of importance. 3. The past earnings were significant only to the extent that they indicated what changes in earnings were likely to take place in the future. This complete revolution in the philosophy of common stock investment took place virtually without realization by the stock buying public and with only the most superficial recognition by financial observers.

Graham and Dodd (1934, p. 52) were clear that “the new-era style of investment — as exemplified in the general policy of the investment

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trusts — was practically indistinguishable from speculation”. For those with the valuations of the NASDAQ-5000 tech stock bubble still fresh in historical memory, these statements by Graham and Dodd (1934) have a timeless quality. By referring to “a completely different attitude toward the investment merits of common stocks”, Graham and Dodd’s observations about the New Era Theory implicitly make reference to previous approaches to equity security valuation that, presumably, took a more informed view of “investment merits”. As such, Graham and Dodd (1934) represents a revival of the “advance of security analysis [that] proceeded uninterruptedly until about 1927, covering a long period in which increasing attention was paid on all sides to financial reports and statistical data”. The ‘new era’ was a diversion where facts and figures were “manipulated by a sort of pseudo-analysis to support the delusions of the period” (p. 14). The reliance on the analysis of financial reports permits a rough correspondence between the development of equity security analysis and the emergence of the professional accountants required to prepare the corporate accounts. “The importance and prestige of security analysis has tended to increase over the years, paralleling roughly the steady improvement in corporation reports and other statistical data which supply its raw material” (GDC 1962, p. 24). In the pre-1933 world of security market self-regulation, a professional self regulating accounting profession was needed to ensure that financial reports issued by companies would be a reliable source of information. Compared to the British security markets, professional accounting was relatively slow to develop in the United States. A useful reference date is 1882 when the Institute of Accountants and Bookkeepers was formed in New York state. The Institute issued certificates upon successful completion of a comprehensive examination. This development was significant because it reflected the growing need for independent accountants to prepare and audit accounts. While, in 1884, there were only 81 independent accountants “listed in the city directories of New York, Chicago and Philadelphia. Just five years later there were 322” (Gordon 1999, p. 173). In 1887 the precursor of the modern day American Institute of Certified Public Accountants was established as the American Association of Public Accountants. Recognizing the important role of states in regulating the accounting profession, in 1896 New York state established the legislation that designated criteria for individuals to be qualified to prepare and audit company accounts. This New York legislation, which was soon adopted by other states, is responsible for introducing the term certified public accountant.

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Defining Security Analysis In contrast to Withers (1910), Graham and Dodd (1934) is a significant advancement in terms of depth and breadth of analysis. Seeing that Withers was a financial journalist recounting ideas that he had gleaned from discussions with market practitioners, this is not surprising. By 1934, Graham was a market practitioner, par excellence, with a wealth of personal experience about the practice of security analysis to draw on. In addition, in the quarter of a century separating these two texts there was also a substantive increase in the breadth and depth of available accounting and other statistical information that is an essential ingredient in security analysis. The two texts were also separated by a major security market event, the collapse of security markets from 1929–1933. Yet there are enough significant similarities that Graham and Dodd (1934) can be seen to be part of a progression of ideas about security analysis. The seminal status often attributed to Graham and Dodd (1934) is due more to the impact and influence that the text had, rather than to the seminal nature of the ideas being presented. Graham and Dodd (1934) possesses constant themes that can be found in previous contributions to equity security analysis, such as Withers (1910). These themes include the relevance of the distinction between investment and speculation, the emphasis on the use of financial statements to form opinions, and the problems raised by the vagaries of market pricing. For example, chapter 4 of Graham and Dodd (1934) is dedicated to ‘distinctions between investment and speculation’. On the vagaries of market pricing, Graham and Dodd (p. 23) explicitly recognize that the ‘intrinsic value’ of a security may well differ from the market price: . . . the influence of what we call analytical factors over the market price is both partial and indirect — partial because it frequently competes with purely speculative factors which influence the price in the opposite direction; and indirect, because it acts through the intermediary of people’s sentiments and decisions. In other words, the market is not a weighing machine, on which the value of each issue is recorded by an exact and impersonal mechanism, in accordance with its specific qualities. Rather we should say that the market is a voting machine, whereon countless individuals register choices which are the product of and partly of emotion.

Together with ‘inadequate or incorrect data’ and ‘uncertainties of the future’, the ‘irrational behavior of the market’ is a principal obstacle to the success of the security analyst.

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In a way, Graham and Dodd deal with the philosophical implications of the process of generating knowledge in the field of security analysis. Knowledge in the human sciences does not progress in the same linear fashion as in the natural sciences where more theoretical and empirical information is obtained about a given phenomenon. In the human sciences authoritative contributions can be timeless. Graham and Dodd (1934) is an excellent example of this point. To be sure, the historical context has changed since the text was written, but many of the insights still retain contemporary value. Consider the following comment about the objectives of security analysis (p. 14): Analysis connotes the careful study of available facts with the attempt to draw conclusions therefrom based on established principles and sound logic. It is part of the scientific method. But in applying analysis to the field of securities we encounter the serious obstacle that investment is by nature not an exact science. The same is true, however, of law and medicine, here also both individual skill (art) and chance are important factors in determining success or failure. Nevertheless, in these professions analysis is not only useful but indispensable, so that the same should probably be true in the field of investment and possibly in that of speculation.

It seems that in seeking a definition for security analysis, Graham and Dodd were grappling with many of the epistemological issues raised by Gadamer (1960) and others. In surveying the scope of security analysis, three functions are identified by Graham and Dodd (1934): descriptive; selective; and, critical. Of these, it is the selective function that deals with “whether a given issue should be bought, sold, retained, or exchanged for some other” — the other two functions deal with the preparing of company reports or evaluating the terms and conditions of a particular security issue. For purposes of equity valuation, it is the selective function that is of greatest interest, while the descriptive and critical functions are needed in the process of determining an estimated value, that can be above or below the observed market price. Equity security selection is based on heuristic rules regarding the difference between the estimated value and the market price. This is consistent with equity security valuation and selection methods going back to the earliest trade in joint stocks. Also following a long tradition, Graham and Dodd refer to this estimated value as the ‘intrinsic value’ of the security. What is “Intrinsic Value”? In Graham and Dodd (1934) and all later editions, the key element in the selective function is the ‘intrinsic value’ of the security. Significantly, the

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precise definition of intrinsic value evolved through the various editions. Initially, the concept is proposed in a rather vague fashion: “the intrinsic value is an elusive concept. In general terms, it is understood to be that value which is justified by the facts, e.g., the assets, earnings, dividends, definite prospects, as distinct, let us say, from market quotations established by artificial manipulation or distorted by psychological excesses” (Graham and Dodd 1934, p. 17). This is remarkably similar to the notion of ‘intrinsic value’ proposed in Armstrong (1848, pp. 6, 7): The market price of Securities is principally determined by their intrinsic value, that is, the state of affairs of the Company which the Stocks represent, the amount of dividend which they pay, the state of interest, &c. We say principally, but not entirely. The prices of all Securities for the investment of Capital, the value and returns being unaltered, are affected more or less by the general condition of the country, as it may be influenced by foreign and domestic affairs, and especially by the state of the money market . . . we can draw a distinction between then natural elevations and depressions [of market prices] which are inevitable, and those unnatural ones which are the effect of design.

As much of Graham and Dodd (1934) is concerned with appropriate methods for determining the intrinsic value of a security, it may seem odd that only a vague definition is proposed. Yet, in adopting a relatively vague definition of intrinsic value, Graham and Dodd (1934) was following a long established line of inquiry. The origins of ‘intrinsic value’ determination are not clear. Cantillon used the term in the Essai sur la nature du commerce en g´en´eral which was written in French around 1730 and published posthumously in English in 1755 (Murphy 1986). Though Cantillon uses the term in relation to determining a par value between land and labour, the analysis is explicitly concerned with the difference between intrinsic value and market price. The connection between the ‘intrinsic value’ proposed by Cantillon and the modern notion of ‘opportunity cost’ identified by Thornton (2007) is intriguing. As a prominent financier during the Mississippi scheme and South Sea bubbles, Cantillon was deeply influenced by the workings of the securities market. As in other aspects of the Essai (Poitras 2000, pp. 401, 402), it is possible that concepts gleaned from his activities as a financier were an inspiration for his contributions to political economy. Graham and Dodd (1934) is often credited for defining security analysis to mean “the use of fundamental analysis to value securities issued by publicly traded corporations”. This has led to the mantra: “All security analysis involves the use of financial statements” (e.g., GDC 1962, p. 105).

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As such, security analysis is intimately connected to accounting practices. Yet, this interpretation of Graham and Dodd is too narrow. Determination of the intrinsic value requires analysis of both quantitative and qualitative factors. Quantitative factors are associated with statistical information from the income statement, balance sheet and additional data on factors such as capacity utilization, unit prices, costs and the like. Qualitative factors include: the nature of the business; the relative position of the company in the industry; physical, geographical and operating characteristics; the character of management; the longer term outlook for the unit, industry and business in general. Precisely how all these elements fit together to form an assessment of intrinsic value is the essence of equity security valuation. With the appearance of Graham, Dodd, and Cottle (1962), intrinsic value is identified with discounted cash flow valuation of equity securities. 3.1.2

Mitchell, Macaulay and the Institutionalists

Founding of the NBER Close on the heels of the manifesto of institutional economics — W. P. Hamilton (1919) — the establishment of the National Bureau of Economic Research (NBER) in 1920 was an important milestone in the emergence of institutionalism as, arguably, the dominant school in American economics in the inter-war period. While institutionalism as an intellectual force was not able to recover from the post-WW II ‘measurement without theory’ criticism leveled by Koopmans (1947) and others, this school of economic thought made contributions to the conduct of economic policy and government practice that survive to present. Following Rutherford (2001), the institutionalist agenda emerged in the immediate aftermath of WWI and was propelled by a desire to support an enhanced role for government in the economy to achieve much needed social and economic reform. This created a demand for improved economic data and policy analysis that were the touchstones of institutionalism. Proposing a ‘modern’ and ‘scientific’ empirical approach analogous to that used in the natural sciences, institutionalism aimed to replace the theoretically driven neoclassical approach to economics that dominated economics prior to World War I (WWI), e.g., Yonay (1994). While Thorstein Veblen (1857–1929) is often recognized as the “intellectual inspiration for institutionalism” (Rutherford 2001, p. 174) and John R. Commons (1862–1945) is credited with playing a key role after 1924, it is Wesley Clair Mitchell that served as a founding father of the movement,

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as a guiding light during its development and as the originator of the most significant intellectual contribution of the movement, the empirical measurement of business cycles, e.g., Klein (1983). Mitchell received his college education and, in 1899, a doctorate from the University of Chicago. During this time he studied with and was deeply influenced by Veblen, J. Laurence Laughlin (1850–1933), the monetary economist, and John Dewey (1859– 1952), the influential philosopher, psychologist and educational reformer. After a brief term at the Bureau of the Census and two years teaching at Chicago, in 1903 Mitchell followed one of his former teachers, Adolph Miller, to the University of California at Berkeley where, apart from a few brief excursions, he stayed until 1912. During this time Mitchell produced Business Cycles (Mitchell 1913) a book which Arthur Burns (1952, p. 22) describes as “one of the masterpieces in the world’s economic literature”. Together with Business Cycles: The Problem and Its Setting (1927) and Measuring Business Cycles (1946, with Arthur Burns), these three books are Mitchell’s definitive work on the subject that still epitomizes his career, e.g., Klein (1983). Mitchell joined the faculty of Columbia University in 1913. Except for a brief period of government service at the end of WWI and three years as a lecturer at the New School for Social Research (1919–1921), Mitchell was a member of the faculty at Columbia until his retirement in 1944. Burns (1952) is a collection of papers on the importance and impact that Mitchell had for so many in the economics profession during his life. In addition to containing fitting tributes to Mitchell, Burns (1952) also contains such a wealth of information on subjects such as institutionalism and business cycle theory that it belongs in the category of a classic book in the history of economic thought. It was during the New School period that Mitchell was instrumental in organizing the NBER, where he served as Director of Research until he resigned in 1945. From the founding of the NBER, “the National Bureau was the focus of his intellectual interest, the emotional center of his own work, and the work responsibility that lay closest to his inner life” (Burns 1952, p. 102). The NBER was established with grants totaling $24,000 with which Mitchell was able to hire a small research staff to undertake the first major study on the size, growth, fluctuation and distribution of national income. The initial research staff for the national income study had three members: Willford King, Oswald Knauth and Frederick Macaulay. Though the published results of this study (Mitchell 1921–1922) appeared within three years, there were a number of follow-on business cycle projects generated by this initial

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effort. Among these special studies that got underway in the early 1920s was one on the cyclical fluctuations in bond yields and stock prices undertaken by Macaulay (Fabricant 1984).

Frederick Macaulay: The Academic and the Vernacular Unlike Mitchell who has been the subject of numerous detailed biographical studies, information on the life and times of Frederick Robertson Macaulay is scarce (Poitras 2007). In this regard, Macaulay was not unlike others in the vernacular realm. Macaulay also has some academic significance to the history of institutionalism, due to: his contributions to the NBER project; and, Macaulay (1938) that introduced the concept of ‘Macaulay duration’. However, these contributions did not resonate with the later academic Finance community of scholars. As a consequence, Macaulay receives little modern recognition. Frederick Robertson Macaulay was born in Montreal on 12 August 1882, the first born child of Henrietta and Thomas Bassett Macaulay (1860–1942);. making him a Canadian by birth, not Scottish or British as reported in some sources, e.g., Spears (2001); Society of Actuaries website (www.soa.org/duration.pdf). Both his grandfather, Robertson Macaulay (1833–1915), and his father were important figures in Montreal business and society. His grandfather served as the second President of the Sun Life Assurance Company of Canada from 1889–1906, resigning the position in favor of his son, T.B. Macaulay who served as the third president of Sun Life from 1906–1934. Though the Macaulay clan has ancestral roots in the Island of Lewis in the Hebrides, his grandfather was born in Fraserburgh, on the northeast coast of Scotland. From humble beginnings, he emigrated to Canada in 1854. Through hard work and his skills as an accountant he entered the life assurance business as a junior accountant with Canada Life Assurance in 1856. After sixteen years at Canada Life, rising eventually to be chief accountant, and a brief stint as Secretary of Mutual Life, in 1874 Robertson Macaulay assumed the position of Secretary at Sun Life. In 1877, his son, T.B. Macaulay joined Sun Life as a junior clerk. In 1880, at the age of twenty, T.B. Macaulay assumed the position of Actuary at Sun Life, the first person to hold such a position within the company. He held this position until 1889 when he assumed the position of Secretary. While Shiu (1990) does recognize that F.R. Macaulay’s father served for “many years as the chief actuary at Sun Life of Canada”, this attribution is decidedly incomplete. The contributions of T.B. Macaulay to the actuarial profession

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were such that he is one of only three Canadians in the Insurance Hall of Fame (www.insurancehalloffame.org). He was a charter member and fellow of the Actuarial Society of America and served as president of the Society from 1899–1901. Socially and politically, T.B. was “an important figure in Montreal’s closely knit tycoonarchy”. Under the leadership of T.B. Macaulay, Sun Life grew from a relatively small Canadian assurance company to become the largest assurance company in Canada with a presence in 55 countries by the mid-1920s (Schull 1971). He is credited with championing various innovations in assurance policy design, including the unrestricted policy and the automatic premium loan system. T.B. Macaulay also changed the practice of assurance company investment policy. Of particular importance to the history of equity securities, it was under his leadership that, according to Time magazine (October 24, 1932), Sun Life became the “world’s biggest investor in common stock”. As such, the father of Frederick Macaulay was at the forefront of the ‘cult of equity’ (Scott 2002) that engulfed the investment practices of insurance companies during the interwar period.1 Building on contributions to the ‘science of investments’, May (1912) marks the beginning of a recognition in the insurance industry that a properly diversified portfolio of common stocks can allow the achievement of average higher yields while mitigating the risk of capital loss due to price volatility.2 With such strong roots in Sun Life and the insurance business, there were undoubtedly strong family pressures for F.R. Macaulay to continue the family calling. Yet, this was not to be. Only his younger brother Douglas was to assume a position within the company, serving in capacities such as supervisor of the Group Assurance department in the early 1920s and later as Assistant Secretary in charge of construction projects. F.R. Macaulay graduated from Montreal High School and entered McGill University in 1900. After attending McGill for two years (1900–1901, 1901–1902) as an Arts student, Macaulay withdrew without graduating. He was to continue his education at Colorado College in Colorado Springs, transferring to the 1 Poitras (2007) quotes P. Bernstein regarding the personal equity security investment practices of T.B. Macaulay: “During the depression, when his bank loans secured by his personal equities were deeply under water, the banks still carried the loans because they wanted to continue with Sun Life’s business”. 2 Harold (1934, pp. 42, 43) traces the initial statement that common stocks are acceptable as long term investments to a statement made by William Hughes to a convention at the Institute of Actuaries in 1902, quoted in Raynes (1928). Harold observes: “Nothing of importance was done in the matter until 1912 when Professor Fisher and others suggested the theory, at least in part”.

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University of Colorado (CU) in Boulder in 1908, majoring in Economics and Law. He graduated with a BA in 1909, an MA in 1910 and an LL.B. in 1911. His MA in Commerce (Banking) featured a thesis titled, Money, credit and the price of securities. Macaulay attended law school while he was an undergraduate and a graduate student, which explains how he was able to complete his degrees almost simultaneously. While Colorado may seem an unusual educational destination for someone with the career path that was to follow, it is significant that, in 1906, CU founded a College of Commerce aimed at students wanting to combine higher education with preparation for the business world. As such, CU was one of the first institutions in the US, along with Harvard and Northwestern, to establish such a program. Though little is known of his activities in the period following his graduation, with his Master’s degree Macaulay was able to obtain university positions in economics at the University of Washington from 1915–1916 and as an assistant professor of economic theory and statistics at the University of California, Berkeley (UC) from 1916–1920. Significantly, alumni records at the University of Colorado indicate that in 1921, he was practising as an attorney at law in Berkeley, California with offices at 2442 Hiyard Avenue. It was during his time at Berkeley that Macaulay made the connection to W.C. Mitchell that was to have such an important impact on his future endeavours. Though Mitchell had left for a position at Columbia prior to Macaulay’s arrival at UC, his complementary research agenda and the academic network led Macaulay to decide to pursue a PhD under Mitchell at Columbia. Based on his published contribution to the first major research project undertaken at the newly formed NBER (Mitchell 1921–1922), in 1924 Columbia granted Macaulay a PhD in Economics. Upon arriving at Columbia, Macaulay was able to secure a position on the research staff of the NBER, a position that he held until the completion in 1938 of his special study on the cyclical behavior of interest rates. Because none of the staff of the NBER was paid more than a modest stipend, with senior staff being employed on a part-time basis, it was expected that the bulk of staff income would come from university teaching positions (Fabricant 1984, p. 31). To this end, from 1921–1926, Macaulay lectured at the New School for Social Research. His area of expertise combined with a growing network of contacts in the financial markets led Macaulay progressively into the business of financial consulting. In 1934, Macaulay joined with Allen M. Bernstein, the father of Peter L. Bernstein to form Bernstein–Macaulay Inc., a New York investment counsel firm. Macaulay served as vice-president of this firm until his retirement in 1961.

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In 1967, in a transaction that has been described as the first major deal of Sandy Weill, later to be head of Citicorp, Bernstein–Macaulay became a subsidiary of Carter, Berlind & Weill Inc. (shortly to become Berlind, Weill, Levitt & Cogan Inc. in 1968). Weill served as chairman of this firm from 1965–1984. During his tenure, the firm was subsequently acquired and became part of Hayden, Stone Inc.. Further transactions resulted in the firm becoming, in 1979, Shearson Loeb Rhodes, the second largest brokerage house in the US after Merrill-Lynch. In 1981, this firm was sold to American Express. Peter L. Bernstein (1919–2009) joined Bernstein–Macaulay in 1951 and assumed the position of CEO when his father died unexpectedly. He continued in this position until 1973 when he left the firm, by then part of Hayden, Stone to head Peter L. Bernstein, Inc. a financial consulting firm. The following year he participated in the founding of The Journal of Portfolio Management, one of the leading journals spanning the area between academic theory and vernacular practice. Cowles and Stock Market Forecasting Alfred Cowles III (1891–1984) is best remembered in modern times for his role in establishing the Cowles Commission (later Foundation) for Economic Research and for the 1871–1939 stock price index that became the basis for the important equity market benchmark S&P index launched in 1957 (Wilson and Jones 2002).3 Cowles is not typically identified with the institutionalist school, despite having similar philosophical goals. In particular, a primary motivation for Cowles to join forces with Irving Fisher and a group of other influential academic economists to form the Cowles Commission in 1932 was the desire to elevate economics into a more precise 3 Christ (1994) and Dimand (2009) discuss the early history of the founding of the Cowles Commission for Research in Economics. The Commission was founded in Colorado Springs in 1932, basically because the investment advisory firm run by Cowles was located in Colorado Springs. The Commission was formed primarily at the initiative of Cowles and Irving Fisher, president of the recently formed Econometric Society. The first edition of Econometrica in 1933 followed shortly after the Commission was founded. In 1939, the Cowles Commission moved from Colorado Springs to the University of Chicago. Jacob Marschak served as director from 1943–1948, when T. Koopmans succeeded to the position. For a combination of reasons, including some opposition to the Cowles Commission within the economics department at the University of Chicago and a desire to attract James Tobin to the directorship, in 1955 the Commission moved to Yale University and was renamed the Cowles Foundation. While a graduate student at the University of Chicago in the 1950s, Harry Markowitz was a member of the Cowles Commission.

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science using mathematical and statistical techniques. This is consistent with the general goals of institutionalism. Ironically, research developments associated with the Cowles Commission following World War II (WWII) were central to the demise of the ‘measurement without theory’ form of institutionalism as an intellectual force in modern economics, e.g., Weintraub (2002). Cowles has gone largely unrecognized in modern times for making other early contributions, particularly to the empirical validity of the efficient market hypothesis for the equity market. Cowles produced two seemingly conflicting contributions. Cowles (1933), updated in Cowles (1944), examines: “the attempts of two groups, 20 fire insurance companies and 16 financial services, to foretell which specific securities would prove profitable . . . [and] with the efforts of 25 financial publications to foretell the future course of the stock market”. The objective was to “lead to the identification of economic theories or statistical practices whose soundness has been established by successful prediction” (Cowles 1933, p. 309). Observing that the sample period predates Graham and Dodd (1934), the results are still quite remarkable (Cowles 1933, pp. 323, 324): 1. Sixteen financial services, in making some 7,500 recommendations of individual common stocks for investment during the period from 1 January 1928, to 1 July 1932, compiled an average record that was worse than that of the average common stock by 1.43 per cent annually. Statistical tests of the best individual records failed to demonstrate that they exhibited skill, and indicated that they more probably were results of chance. 2. Twenty fire insurance companies in making a similar selection of securities during the years 1928–1931, inclusive, achieved an average record 1.20 per cent annually worse than that of the general run of stocks. The best of these records, since it is not very much more impressive than the record of the most successful of the sixteen financial services, fails to exhibit definitely the existence of any skill in investment. 3. William Peter Hamilton, editor of the Wall Street Journal, publishing forecasts of the stock market based on the Dow Theory over a period of 26 years, from 1904 to 1929, inclusive, achieved a result better than what would ordinarily be regarded as a normal investment return, but poorer than the result of a continuous outright investment in representative common stocks for this period. On 90 occasions he announced changes in the outlook for the market. Forty-five of these predictions were successful and 45 unsuccessful.

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4. Twenty-four financial publications engaged in forecasting the stock market during the 4 years from 1 January 1928, to 1 June 1932, failed as a group by four per cent per annum to achieve a result as good as the average of all purely random performances. A review of the various statistical tests, applied to the records for this period, of these 24 forecasters, indicates that the most successful records are little, if any, better than what might be expected to result from pure chance. There is some evidence, on the other hand, to indicate that the least successful records are worse than what could reasonably be attributed to chance. While striking, even a casual observer will notice that the particular forecasting sample period, Jan. 1928 to June 1932 is particularly unusual. For this reason, the update provided in Cowles (1944) is of interest. Cowles (1944) does not replicate Cowles (1933). The sample of only 11 forecasters is much smaller. The four financial periodicals and seven financial services firms that are included also appear in Cowles (1933) making for a much longer January 1928 to July 1943 time series, effectively eliminating the questions raised about the 1928–1932 sample used in Cowles (1933). In addition, Cowles was able to obtain forecast data going back to 1903 for the individual forecaster that exhibited the best forecasting performance of the 11 forecasters over the 1928–1943 sample. Though the forecaster is not named, it is difficult to avoid the conclusion that the forecaster was Roger Babson.4 The reported results are (Cowles 1944, p. 214): (1) The records of 11 leading financial periodicals and services since 1927, over periods varying from 10 to 15 years, fail to disclose evidence of ability to predict successfully the future course of the stock market. (2) Of the 6904 forecasts recorded during the 15 year period, more than four times as many were bullish as bearish, although more than half of the period was occupied by bear markets, and stocks at the end were at only about two-thirds of their level at the beginning. (3) The record of the forecasting agency with the best results for the 15 years since 1927, when tabulated back to 1903, for the 40 years showed results 3.3 per cent a year better than would have been secured by a continuous investment in the stocks composing the Dow-Jones industrial average. Under present laws the capital-gains tax might wipe out 4 Some

Dow theorists argue that the forecasting series with the best record in Cowles (1944) originates with a spliced combination of Hamilton and Rhea predictions. As both Rhea and Cowles resided in Colorado Springs and were known to each other, there may be some basis for this claim. However, as the forecaster is not explicitly named in Cowles (1944), the identification of the forecaster is uncertain.

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Fig. 3.1 The index of performance in this case is the per cent by which the average of the compounded records of all forecasters is better or worse than the random forecasting record for each of the 17 major swings.

Notes: The curve in the upper half of the chart shows the monthly averages of Standard & Poor’s Index of 90 stocks except at terminations of bull markets where the highest of the daily averages are shown, and at termination of bear markets where the lowest of the daily averages are given. Source: Cowles (1944, p. 211).

most of this advantage. While prospects for the speculator are, therefore, not particularly alluring, statistical tests disclose positive evidence of structure in stock prices which indicates a likelihood that whatever success may be claimed for the very consistent 40 year record is not entirely accidental. The results supporting (1) are illustrated in Fig. 3.1. The decidedly more sympathetic tone towards the possibility of profitable stock market forecasting compared to Cowles (1933) is solidified by the closing statement: “A simple application of the ‘inertia’ principle, such as buying at turning points in the market after prices for a month averaged higher, and selling after they averaged lower, than for the previous month, would have resulted in substantial gains for the period under consideration”. The tenuous academic connection of Alfred Cowles III with the venerated and academically influential Cowles Commission reflects the sharp division that was beginning to emerge between vernacular and academic Finance. Cowles background was decidedly in the vernacular realm: the

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grandson of Alfred Cowles, Sr., founder of the Chicago Tribune, his father, Alfred Cowles, Jr., (1865–1939) also served as a manager and director of the Chicago Tribune. For a decade prior to the foundation of the Cowles Commission, Alfred Cowles maintained a private organization for statistical research on problems of investment and finance; partially in support of his activities managing the sizable financial assets associated with the Chicago Tribune fortune. At the time the Cowles Commission was founded, this advisory service was located in Colorado Springs. Despite spending considerable effort monitoring and heeding the advice of leading financial advisory services, Cowles was among those that suffered considerable losses in the equity markets during the 1929–1932 period. Deeply troubled by the losses, Cowles set about to establish stock market forecasting on a more scientific basis using mathematical and statistical methods (Christ 1994, pp. 30, 31). The Cowles Commission was the result of these efforts.

Durand and the Rise of Modern Finance Frederick Macaulay was of sufficient stature in the vernacular community to warrant selection to form an investment advisory firm, Bernstein–Macaulay, in 1934. At this point, the long promised effort that was to be Macaulay (1938) still was not near completion. In practice, Macaulay had few responsibilities within Bernstein–Macaulay and used the time and resources to finish the project. Peter L. Bernstein reports: “When he finally finished the book, Macaulay told my father he could continue to use his name, but he was tired of coming to an office every day and was going to retire” (Poitras 2007). Given his relatively limited duties in the investment counsel business, Macaulay was able to pursue some research activities. After leaving the NBER in 1938, he took up the position of research director with the Twentieth Century Fund for a study commissioned by the New York Stock Exchange on short selling. The final results of this study, Macaulay and Durand (1951), is Macaulay’s last published research contribution. The results of the study are somewhat anti-climatic as short selling was not found to significantly impact price, though some interesting individual transactions are identified. The connection between David Durand and Macaulay represents the final step in the demise of institutionalism within academic Finance. Like Macaulay, Durand was also a Columbia PhD (1941), attracted by the possibility of working with Mitchell. Earning his BA (1934) and MA (1938) from Cornell, Durand accomplished the significant academic

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achievement, prior to receiving his MA, of publishing a significant article on marginal productivity theory in the prestigious Journal of Political Economy (Durand 1937).5 Though Durand became a member of the NBER staff after Macaulay’s departure, Paul Samuelson recounts that, while at the NBER, Durand “pioneered the empirical study of how long-term bonds usually require a higher yield than short. Everyone understands that today, but he was the first to document it” (Szekely and Richards 2004). Given his considerable technical abilities, the NBER connection and the subsequent overlapping work on interest rates, it is not too surprising that Durand and Macaulay would undertake a joint project, such as that on NYSE short selling. Like so many at the time, Durand’s career was interrupted by WWII, where he served in the Naval Reserve, stationed in Hawaii and Guam. Following the war, Durand continued his work with the NBER and the Institute of Advanced Study at Princeton University where he became acquainted with Albert Einstein. Starting as a Research Associate in 1953, Durand obtained the position of Associate Professor at MIT in 1955 and professor in 1958, a position he held until his retirement in 1973. Durand played a recognizable role in the pre-history of modern Finance. For example. Just prior to joining MIT, at an NBER research conference Durand (1952) proposed the then unorthodox position that the financial goal of a firm is to maximize the investment value of the firm rather than to maximize income (Paulo 2003, p. 330). In addition, Modigliani and Miller (1958) mention Durand as contributing to the formulation of the MMI theorem. In an interview (Barnett and Solow 2000, p. 223), Franco Modigliani observed “listening to a paper by David Durand suggesting (and then rejecting) the so-called ‘entity theory’ of valuation, I gradually became convinced of the hypothesis that market value should be independent of the structure of financing . . . This result later became part of the proof of the ModiglianiMiller theorem”. Given the connection to MIT, strong quantitative training and initial insights into the emerging theories of modern Finance, Durand was a likely 5 As

evidence of quantitative background, Durand and Greenwood (1957) and Gumbel, et al. (1953) are two substantive contributions to mathematical statistics. Biographical information on Durand is available in a number of sources. The 6 March 1996 edition of Tech Talk, the official MIT newspaper, has a lengthy memorial by Enders Robinson, a close friend of Durand. Good coverage of available sources is given in Szekely and Richards (2005). See also Durand (1989) and Durand (1992) for more information on how Durand viewed his various contributions.

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candidate to be at the forefront of the emerging scientific movement. However, with such strong institutionalist roots, Durand was one of the few in a prestigious academic situation to question the rise of modern Finance, e.g., Durand (1959; 1968). As a consequence of this decision, Durand is best remembered today for the application of statistical methods to problems in corporate finance. Oddly enough, Durand (1957, p. 362) represents an important early criticism of discounted cash flow (DCF) valuation. More precisely, Durand make a significant connection between the St. Petersburg paradox and the use of DCF to value growth stocks: The moral of all this is that conventional discount formulas do not provide completely reliable evaluations. Presumably they provide very satisfactory approximations for high-grade, short-term bonds and notes. But as quality deteriorates or duration lengthens, the approximations become rougher and rougher. With growth stocks, the uncritical use of conventional discount formulas is particularly likely to be hazardous; for, as we have seen, growth stocks represent the ultimate in investments of long duration. Likewise, they seem to represent the ultimate in difficulty of evaluation. The very fact that the Petersburg Problem has not yielded a unique and generally acceptable solution to more than 200 years of attack by some of the world’s great intellects suggests, indeed, that the growth-stock problem offers no great hope of a satisfactory solution.

Szekely and Richards (2004–2005) revive the arguments in Durand (1957) to explain the crash of equity valuations for technology stocks during the market crash of 2000. In the history of equity security valuation, Durand symbolizes the end within academic Finance of concern with the vernacular problems of practical valuation and market forecasting. From Durand (1959) to Durand (1968), the resistance was considerable but the opposition was too overwhelming. Durand correctly observed that numerous claims being made by ‘the new finance’ were inflated. For example, regarding the claim that the emerging modern Finance approach was based on mathematical logic and supported by quantitative methods Durand (1968, p. 848) observes: What comes first to mind [in considering the difference between the new finance and the traditional], namely the use of mathematics and quantitative methods, will not stand a second thought. The quantitative approach is anything but new in finance; in the hands of actuaries, it dates back to the eighteenth century . . . The actuaries have . . . greatly contributed to the development of modern statistics, including hypothesis testing.

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Similar to Poitras (2000, esp. ch. 6, 2006), Durand finds a close connection between the early histories of finance and actuarial science. Such a connection was grossly inconsistent with the claims of ‘scientific revolution’ being made by the founders of the modern Finance school. Decades later on “the fiftieth anniversary of the publication of Harry Markowitz’s landmark paper, ‘Portfolio Selection’ ” Rubinstein (2002, p. 1042) would claim: With the hindsight of many years, we can see that this was the moment of the birth of modern financial economics. Although the baby had a healthy delivery, it had to grow into its teenage years before a hint of its full promise became apparent. What has always impressed me most about Markowitz’s 1952 paper is that it seemed to come out of nowhere.

The division of the academic Finance from the vernacular world of Finance was complete. Those wanting to keep faith with the vernacular world, such Durand, were irrelevant. 3.1.3

Lasting Insights: Graham, Dodd and Cottle (1962)

Even though a portion of Graham, Dodd and Cottle (1962) is material carried forward, unchanged from Graham and Dodd (1934), there is so much more in the 1962 edition that it can safely be considered as a separate text. To be sure, the themes of the two editions are consistent, but so were the themes that connected Withers (1910) with the 1934 edition. One of the features separating Graham, Dodd and Cottle (1962) is the substantive change in the approach to security analysis from the views advanced in the previous editions of 1951, 1940, and 1934. The change is attributed to a change in historical context (p. vi): Beginning sometime in 1955, our value standards and the actual market level parted company, and the gap has tended to widen through the ensuing years. Thus we are not able to proceed in 1960–1961 with the same comforting assurance as formerly that our standards are in accordance with both long-term and recent-term experience. In this respect we face a three-pronged dilemma, which we share with all serious-minded security analysts. If we persist in clinging to our old, highly conservative standards of common-stock appraisal, we risk not only the certain charge of old-fogeyism, but a real possibility of failing to recognize important changes in the underlying structure of common-stock values.

Gone is the overwhelming concern with the collapse of investor confidence associated with the pre-WWII period. In its place is a “confident appraisal of the market’s future on the general expectation of continued prosperity and growth” (p. 417).

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Even in the material carried forward, the changes between the 1934 and 1962 editions are more than cosmetic. In particular, where the 1934 edition presented a uniform notion of security analysis, the 1962 edition maintained: “we should acknowledge that there are some serious differences among practicing security analysts as to the basic approach to the selective function of security analysis” (p. 25). Speaking of the use of quantitative and qualitative information, the 1934 edition maintained (p. 34): Broadly speaking, the quantitative factors lend themselves far better to thoroughgoing analysis than do the qualitative factors. The former are fewer in number, more easily obtainable, and much better suited to the forming of definite and dependable conclusions. Furthermore, the financial results will themselves epitomize many of the qualitative elements, so that a detailed study of the latter may not add much of importance to the picture. The typical analysis of a security . . . will treat the qualitative factors in a superficial or summary fashion and devote most of its space to the figures.

The 1962 edition takes a decidedly different tone about the qualitative factors. Leaving the first two sentences unchanged, the 1962 edition says: “Furthermore, the financial results in themselves epitomize such qualitative elements as the ability of a reasonably long-entrenched management. This point of view does not minimize the importance of qualitative factors in appraising the performance of a company, but it does indicate that a detailed study of them — to be justified — should provide sufficient additional insight to assist significantly in appraising the company” (p. 86). Similarly, the 1962 edition advocates: “the weight given to financial material may vary enormously, depending upon the kind of security studied and basic motivation of the prospective purchaser” (p. 105). This emphasis on differences is not meant to imply that the texts are diametrically opposed. For example, on the distinction between speculation and investment the texts are still in agreement. Both editions italicize the statement: “An investment operation is one which upon thorough analysis, promises safety of principal and a satisfactory return. Operations not meeting these requirements are speculative” (1934, p. 54). Both texts explicitly recognize that security analysis has considerable limitations in speculative situations, e.g., “It is only where chance plays a subordinate role that the analyst can properly speak in an authoritative voice and accept responsibility for the results of his judgments” (1934, p. 26; 1962, p. 52). In other words, “the value of analysis diminishes as the element of chance increases”. Both the 1934 edition and the 1962 edition continues

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with a discussion about the benefits of holding a diversified portfolio of securities: “the element of diversification is counted upon to offset the recognized risk existing in individual securities” (p. 54). Insofar as fundamental analysis seeks to benefit from firm specific risks, it would seem that relatively undiversified portfolios would be more attractive. However, the diversification envisaged is much less than suggested by modern portfolio theory, more along the lines of an investment trust. In contrast to the vernacular orientation of earlier editions, the 1962 edition was substantively influenced by the emerging academic subject of modern Finance, the early rudiments of which were appearing at that time. There are discussions related to optimal capital structure (p. 548, 549) and impact of dividend payments on firm value. The discussion about dividends moves from the ‘greater benefits to stockholders from dividends’ in the 1934 edition to a more ambiguous view in the 1962 edition. There is also chapters dedicated to ‘newer methods for valuing growth stocks’ and ‘market analysis and security analysis’. The 1962 edition is also filled with copious footnotes that contain references to recent journal articles and trade publications. Where the 1932 edition examined fixed income investments and proceeded to common stocks, with a view of applying valuation principles for bonds to common stocks, the 1962 edition has a substantial examination of the principles of financial statement analysis before proceeding to fixed income securities and common stocks. On balance, there is much new material presented in the 1962 edition. Modern students of finance likely would not bother to read the original texts, relying instead on what a long list of journal articles propose as the ‘Ben Graham approach’. This approach is typically characterized by mechanical rules for security selection using selected financial ratios. Sometimes these rules are taken from the various editions of Graham and Dodd, in other cases from one of the editions of Graham The Intelligent Investor (1949, 1st ed.). For example, Oppenheimer (1981, p. 9) identifies four selection criteria for a defensive investor from the five editions of The Intelligent Investor. The rules differ only slightly from edition to edition. The rules from the 1973 edition are: (1) Some dividend paid each year since 1950; (2) the firm has at least $50 million in assets or annual sales and is in the upper 1/4 or 1/3 of its industry in size; (3) the security price does not exceed 25 times average earnings of the past seven years and does not exceed 20 times earnings over the last 12 month period; and, the equity at book value is at least 50% of the total market capitalization (for utilities this value is 30%). Oppenheimer also suggests criteria for the enterprising

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investor, e.g., market capitalization of common stock is two-thirds or less of current assets less total liabilities (including preferred stock). There are a number of other mechanical security selection criteria that have been attributed to the Graham and Dodd approach. A partial list would include: an earnings-to-price yield at least twice the AAA bond yield; a P/E ratio less than 40% of the highest P/E ratio the stock had over the past five years; a dividend yield of at least two-thirds the AAA bond yield; and, a stock price below two-thirds of tangible book value per share. In addition, Lowe (1994) provides a list of ‘Ben Graham’s investment principles’ that includes the following: be an investor, not a speculator; know the asking price; rake the market for bargains; regard corporate figures with suspicion; don’t stress out; don’t sweat the math; diversify, rule #1, minimum of 25% bonds, 25% stocks; diversify, rule #2, hold a large number of securities; when in doubt, stick to quality; dividends are a clue to value; defend your shareholder rights; be patient; and, think for yourself. Finally, armed with all this background, those seeking to undertake a security analysis need to consider the basic elements of fundamental analysis: profitability; stability; growth in earnings; financial position; dividends; and price history. Suggested valuation techniques for growth stocks differ substantively from the traditional approach to equity security valuation which has come to be identified as ‘value investing’. Graham and Dodd (1934) is justly recognized as a landmark text in the history of traditional equity security analysis. Much of this first edition appears, sometimes verbatim, in the fourth and final edition of this text, GDC. Being descended from a classic text from the ‘old Finance’ era, GDC shares the institutional and descriptive characteristics of that pedagogical approach. However, while there are hints of a drift towards the approach of modern Finance in GDC, the overall tone is still clearly from a different tradition. GDC typically proceed by employing a heuristic discussion of a particular topic, often illustrated with a number of practical examples using actual securities. Sometimes, usually where there is the potential for confusion in analyzing a particular situation, the discussion is followed by the statement of an investment principle. GDC is characterized by certain themes that permeate the analysis connecting GDC with earlier editions and other texts of traditional equity security analysis such as Dewing (1953) and Graham (1949). However, GDC is more than an expanded discussion of previous works, there are significant points of evolution and, on occasion, divergence. From Graham and Dodd (1934) to GDC, a key theme can be summarized as: “All security analysis involves the analysis of financial statements”

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(GDC, p. 105). In contrast, the growth stock approach focuses on the characteristics of the underlying business where analysis of financial statements play a subordinate role. This GDC viewpoint is qualified with the proviso: “the weight given to financial material may vary enormously, depending upon the kind of security studied and basic motivation of the prospective purchaser”. However, GDC (p. 88) are clear on the relative importance of ‘quantitative’ vs. ‘qualitative’ factors in security analysis. Quantitative factors are associated with statistical information from the income statement, balance sheet and additional data on factors such as capacity utilization, unit prices, costs, and so on. Qualitative factors include: the nature of the business; relative position of the company in the industry; physical, geographical, and operating characteristics; the character of management; the longer term outlook for the unit, industry and general business. The GDC approach to security analysis is fundamentally concerned with how quantitative and qualitative information is combined. On this point there is an apparent divergence of opinion across the various editions. Another central theme is the distinction between speculation and investment. This distinction is inherited directly from Graham and Dodd (1934) where the lessons of the stock market collapse of 1929–1933 and the ‘new era theory’ of common stock investing were still fresh in the air. Though concern with the ‘new era’ theory had been reduced to an historical discussion in GDC, the theme of investment versus speculation persisted: “An investment operation is one which upon thorough analysis, promises safety of principal and satisfactory return. Operations not meeting these requirements are speculative” (GDC, p. 49). This is an exact repetition of Graham and Dodd (1934, p. 54). GDC (e.g., pp. 51, 52) explicitly recognize that security analysis has considerable limitations in speculative situations. Security analysis is “an adjunct rather than . . . a guide to speculation. It is only when chance plays a subordinate role that the analyst can properly speak in an authoritative voice and accept responsibility for the results of his judgments”. By acknowledging limitations in the analysis of speculative securities, the range of common stocks and other securities to which the GDC techniques of security analysis apply is relatively narrow. More precisely, common stocks that have “too many uncertainties about [the] future to permit the analyst to estimate its earnings power with any degree of confidence” are speculative in nature because: “a common stock purchase may not be regarded as a proper constituent of a true investment program unless it is possible to show by some rational calculation that it is worth at least as much as the price paid for it”.

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Comparing GDC with earlier versions, it is apparent that the weight to qualitative factors in security analysis varies considerably. Graham and Dodd (1934, p. 430) maintain: “Quantitative data are useful only to the extent that they are supported by a qualitative survey of the enterprise”. In contrast, GDC (p. 86) maintain that quantitative factors are always an essential element of the analysis: Broadly speaking, the important quantitative factors lend themselves to much more precise consideration in appraising a specific company than do the qualitative factors. The former are fewer in number, more easily obtainable, and better suited to the forming of definitive conclusions. Furthermore, the financial results themselves epitomize such qualitative elements as the ability of a reasonably long-entrenched management. This point of view does not minimize the importance of qualitative factors in appraising the performance of a company, but it does indicate that a detailed study of them — to be justified — should provide sufficient additional insight to assist significantly in appraising the company.

A further level of ambiguity on this issue is achieved when GDC (p. 50) provide an additional criterion for investment: “An investment operation is one that can be justified on both qualitative and quantitative grounds”. This change in emphasis away from qualitative factors towards quantitative factors associated with financial statements was likely due to the substantially increased reliability and availability of this source of information due to historical developments such as the reform of securities laws that occurred around the time Graham and Dodd (1934) appeared. Another important theme in GDC carried forward from previous editions, but subjected to change, was the concept of ‘intrinsic value’. Whereas Graham and Dodd (1934, e.g., p. 17) emphasized the intrinsic value of a stock and provided heuristic methods for determining this ‘elusive concept’ based on examination of a range of factors such as the record of dividends and the ability of earnings to sustain the dividend, GDC (p. 435) adopted the discounted cash flow (DCF) model as the theoretical mechanism for determining the intrinsic value: The Valuation Process Briefly Described. The standard method of valuation of individual enterprises consists of capitalizing the expected future earnings and/or dividends at an appropriate rate of return. The average earnings will be estimated for a period running ordinarily between five and ten years. In the case of an issue valued as a “growth stock” the projection may be of a terminal year — e.g., four to five years hence — rather than a long term average. The capitalization rate, or multiplier, applied to earnings and dividends, will vary with the quality of

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the enterprise and will thereby give recognition to the longer-term profit possibilities which cannot be established with precision. Asset values become a significant factor in the appraisal only at the extreme ranges, where either the tangible assets are very low in relation to earnings power value or the net current assets alone exceed the earnings power value.

This approach leads GDC to identify the four basic components of common stock value: 1. Expected future earnings 2. Expected future dividends 3. Capitalization rates 4. Asset values. The influence of J.B. Williams on GDC is difficult to ignore. The GDC (pp. 438–441) approach to security analysis integrates the price estimates obtained from the DCF model with the ‘margin of safety’ principle and the benefits of diversification: “In our opinion, margin of safety — in the form of an excess of estimated intrinsic value over current market price — is a prerequisite to investing in secondary [and primary] shares”.6 Because the margin of safety is not a guarantee that any given stock will produce a loss, the diversification principle is also required: “A group of, say, twenty or more common stocks will usually average out the individual favorable and unfavorable developments. For this reason, the diversification or group approach is an integral part of the valuation concept itself”. GDC (p. 448) later clarify this number to between twenty and thirty stocks drawn from a list of not more than 100 ‘primary’ common stocks, i.e., large, prosperous and highly capitalized companies with a strong record of earnings. GDC suggest a further restriction on the amount invested in any one industry. The GDC recommendation that common stock portfolios contain ‘20 or more’ high grade common stocks that would be regularly adjusted is a distinct point of contrast with the recommendations of the growth stock approach to equity valuation and selection, e.g., Philip Fisher (1958) and Bohmfalk (1960).7 6 GDC do not use the words ‘primary’ and ‘secondary’ in the fashion that is conventional in modern Finance where a primary issue is a ‘new’ issue, such as an IPO for a common stock or a Treasury issue that has just been auctioned, and a ‘secondary’ issue is a previously issued security, such as the common stocks traded on the NYSE or Treasury bonds traded in the OTC market. For GDC (p. 3) a ‘primary’ stock issue is a ‘first line’ or ‘standard’ issue of ‘’large and prominent companies, generally with a good record of earnings and of continued dividends”. A ‘secondary’ issue refers to the more marginal common stock issues that have not obtained ‘primary’ quality. GDC estimate that about 80% of listed stocks and 90% or more of unlisted stocks belong in the secondary category. 7 The precise specification of the margin of safety is unclear. Recognizing that there is a target level of 20–30 stocks in a portfolio, presumably the margin of safety will change as the level of the market changes. When the market is ‘high’ there will be a greater proportion of fairly valued and overvalued stocks and it will be necessary to have a

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Though both the margin of safety and diversification concepts are carried forward from previous editions, there is a decided change in tone in GDC. For example, on the diversification principle, Graham and Dodd (1934, p. 320) state: “In our view, the purchase of a single common stock can no more constitute an investment than the issuance of a single policy on a life or a building can properly constitute insurance underwriting”. However, GDC (p. 55) substantially qualify this view: There is a well-known argument against diversification based on Andrew Carnegie’s maxim: “Put all your eggs in one basket and watch the basket”. We believe this counsel has an application to security investment but only within its strictest interpretation. An investor may concentrate heavily on the shares of one corporation provided that he has a personal connection with it — as an executive or a member of a controlling group. Many large fortunes have been built up over the years by such concentration. But where the close personal connection with the company is lacking that policy rarely works out well. When the choice is in fact a very good one, there is a tendency to sell out at a comparatively early stage in the long-term advance. Any other kind of choice will, of course, appear to be a mistaken one during periods of declining prices.

GDC (pp. 447–449) also recommend a form of ‘tactical asset allocation’ strategy where the composition of the investment portfolio would fluctuate between “an upper limit of 75 percent to be held in common stocks and a lower limit of 25 percent”. The proportion held in common stocks at any point in time would be “geared to the analyst-investor’s valuation of the DJIA, Standard & Poor’s Composite Index, or some other measure of the market”. In effect, GDC were advocates of index-tracking market timing strategies. In addition, GDC (pp. 446) recommend “the sale of holdings that appear definitely overvalued or replacement of less by more attractive stocks”. This implies a shorter holding period than the long-term buy-andhold horizon of Philip Fisher. GDC were intimately aware of the dramatic progression: in securities markets; in the professional practice of security analysis; and in the emerging theories of modern Finance that occurred between 1934 and 1962. Following J.B. Williams (1938), the acceptance and adoption of valuation lower margin of safety, say 10–15%, in order for there to be stocks that will qualify for selection as there will be ‘overvalued’ stocks that were purchased previously that now require selling. Similarly when the market is ‘low’ there will be a proportionately greater number of ‘undervalued’ stocks to buy and less ‘overvalued’ stocks in the portfolio to sell. This will require the margin of safety to be raised to, say, 25–30%, in order for the portfolio rebalancing exercise to avoid large fractions of portfolio value in cash.

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techniques for common stocks based on DCF modeling was explicitly recognized and rationalized. GDC (p. 416) acknowledge the changes that occurred in securities markets, particularly stock markets, during the 1950s, required “new points of view and standards of value”: Our philosophy and its related standards of value were derived primarily from the actual experience of stock investors (and speculators) during many decades prior to the 1950s. They were consistent with stock-market conditions existing at the time our previous editions were published. We think they proved a useful guide to investors from 1934 through 1954. But, . . . the latter half of the 1950s brought record high levels in stock prices and with them new points of view and standards of value. It is a difficult task to examine these new levels and standards as they exist at the beginning of the 1960s and to reach some conclusions as to their validity for investment purposes.

Consistent with the proposed use of DCF for common stock valuation, GDC (p. 434) criticize the observed practice of doing common stock valuations based on a “too abbreviated forecast of probable future earnings — covering generally only the next twelve months . . . value cannot soundly be established on the basis of earnings shown over a short period of time”. 3.2 3.2.1

Value Stocks and Growth Stocks Value Stocks Versus Growth Stocks

The distinction between value and growth stocks is fundamental to much of modern equity security valuation. Literally thousands of mutual funds investing in equity securities feature ‘value’ or ‘growth’ in the fund title to indicate the valuation and selection strategy. At least since Fama and French (1998), the distinction has also featured prominently in published contributions by modern Finance academics. Though the growth stock phenomenon was widely recognized by the end of the 1950s, the basic concept has origins that predate WWII. While growth stocks are not mentioned explicitly in Graham and Dodd (1934), Graham, Dodd and Cottle (1962) (GDC) (pp. 425, 426) recognized a distinct ‘growth stock approach’ to equity valuation and identify a 1938 report by an investment trust, the National Investors Corporation (NIC), that explicitly identified growth stocks as “the most effective medium in the field of common stocks”. This view was supported by “economic analysis and practical reasoning”. For NIC, growth stocks were “companies whose earnings move forward from cycle to cycle, and are only temporarily interrupted by periodic business depressions”. The modern disagreements over what constitutes a growth

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stock can be found in numerous contributions during the 1950s, e.g., Anderson (1955), Bernstein (1956), Kennedy (1959). GDC (p. 427) recommend the definition of Conklin (1958): “a ‘growth stock’ is a common stock which has recorded or gives promise of recording, a greater than average appreciation in market price over a span of several years”. On the historical evolution of common stocks, GDC (pp. 56, 57) observe: During the past half-century the investment and speculative characteristics of common stocks as a whole have undergone a series of changes, some of which are as subtle as they are important. Before World War I the typical common stock was basically speculative, for reasons related chiefly to the company itself. The capitalization structure was often top-heavy, the working capital inadequate, the management deficient in various respects, the published information sketchy and unreliable. The junior issue’s dividend history was nonexistent or erratic, its earnings action subject to wide fluctuations, and its market action to crass manipulation. Virtually, all these defects have been greatly ameliorated or abolished, as far as today’s representative common stocks are concerned.

GDC observe that the improvement in investment potential of common stocks led to “an upgrading in the public standing of common stocks generally”, leading to the mis-perception that many ‘speculative’ issues are actually of ‘investment’ quality. This mis-perception had been complicated by the rapid pace of technological change that created the ‘growth stock’ and led to more rapid erosion in the core business of certain ‘primary’ stocks due to an inability to adapt to the pace of change. This technological growth factor is not amenable to dependable prediction and, as a consequence, stocks in the growth category are ‘fundamentally speculative’. In contrast to Philip Fisher, GDC also maintain that the quality of the company alone is an insufficient indication of value without also considering the common stock price: “Strictly speaking, there can be no such thing as an ‘investment issue’ in the absolute sense, i.e., implying that it remains an investment regardless of price” (GDC p. 50). Though GDC is generally a more sophisticated and developed treatment of security analysis than Graham and Dodd (1934), there are a number of points where GDC failed to recognize the value contained in the earlier edition and dropped material that still had considerable insight. The discussion of the ‘new era’ theory is one of these cases. Graham and Dodd (1934, p. 307) provide the following description: During the post [WWI] war period, and particularly during the latter stage of the bull market culminating in 1929, the public acquired a

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completely different attitude towards the investment merits of common stocks. Two of the three elements [suitable and established dividend record and a satisfactory backing of tangible assets] lost nearly all of their significance and the third, the earnings record, took on an entirely novel complexion. The new theory or principle may be summed up in the sentence: “The value of a common stock depends entirely upon what it will earn in the future”. From this dictum the following corollaries were drawn: (1) That the dividend rate should have slight bearing upon the value. (2) That since no relationship apparently existed between assets and earning power, the asset value was entirely devoid of importance. (3) That past earnings were significant only to the extent that they indicated what changes in the earnings were likely to take place in the future. This complete revolution in the philosophy of common-stock investment took place virtually without the realization by the stock-buying public and with only the most superficial recognition by financial observers.

It is difficult for a modern observer of equity markets to read these words and not be struck by the similarity of the ‘new era’ theory to the common stock valuation philosophy appeared during the technology/dot.com bubble that started around 1995 and continued to early 2000, e.g., the ‘Gorilla Finance’ of Moore et al. (1999). Writing in the early 1960’s when concerns with the stock market collapse of 1929–1933 had largely faded from view, instead of a close examination of the ‘new era’ theory all GDC (p. 57) could muster was a concern about “the shift of investment emphasis from values established by the past record to values to be achieved solely by future growth . . . we are skeptical of the ability of all but the most gifted analysts to chart with precision the growth rate of a given company for many years ahead”. As astute observers of ‘real-time’ security markets, GDC were acutely aware of the growth stock phenomenon and of the implications that the views of growth stock proponents, such as Philip Fisher, had for the ‘Graham and Dodd’ approach to security analysis, e.g., Poitras (2005, ch. 7). An acknowledged limitation of the GDC approach is the inability to deal with ‘speculative’ securities. Technology driven growth stocks are viewed by GDC as ‘fundamentally speculative’. Despite this, GDC (p. 57) give considerable attention to the emergence and assessment of growth stocks propelled by “the rapid stepping up of technological change”: This has created opportunities for spectacular growth of profits for many companies, but it has also threatened the position of many others

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which have fallen behind in the technological race. To some degree these contrary occurrences can be projected well in advance by an unusually competent analyst who does some penetrating research of his own. But, broadly speaking, we think that modern technology has injected an important new factor in the affairs of many companies, which is not amenable to prediction and which for that reason must be recognized as fundamentally speculative.

While explicitly recognizing that “there have been investors capable of making [growth stock] selections with a high degree of accuracy and that they have benefitted hugely from their foresight and good judgment”, GDC (p. 426) question “whether or not careful and intelligent investors as a class can follow this policy with fair success”. For GDC, growth stocks present three related questions that require addressing: “First, what is meant by a ‘growth company’ ? Second, can the investor identify such companies with reasonable accuracy? Third, to what extent does the price paid for such stocks affect the success of the program?” GDC (pp. 425–433) give detailed attention to discussing these questions about growth stocks. The possibility of ‘growth industries’ is admitted with “aluminum, electronics, drugs, office equipment, paper, and some branches of chemical manufacture” being explicitly identified. Not surprisingly, GDC are unable to shed much light on the subject. According to GDC, growth stocks are difficult to define, difficult to identify and difficult to tell if the price is too high. The prognosis for growth stocks is cloudy: “if the analysis of growth stocks is pursued with skill, intelligence, consistency and diligent study, it should yield satisfactory results.” However, “it must represent the activity of a strong-minded and daring individual rather than investment in accordance with accepted rules and standards”. The incongruence between the ‘Graham and Dodd’ and the ‘growth stock’ approaches is apparent. It follows that, to get an accurate appreciation of equity security analysis and selection for growth stocks, a leading early ‘advocate’ of the approach, such as Philip Fisher, can be examined. 3.2.2

The Growth Stock Philosophy

Though the basic concepts of growth stock valuation in the trade has origins that predate WWII, among old Finance academics the growth stock phenomenon was widely recognized by the end of the 1950s, e.g., Clendenin and van Greave (1954) and Durand (1957). It was deductively demonstrated that applications of traditional discounted cash flow analysis

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to valuation of growth stocks created substantive problems, e.g., Durand (1957, p. 362): With growth stocks, the uncritical use of conventional discount formulas is particularly likely to be hazardous; for, as we have seen, growth stocks represent the ultimate in investments of long duration. Likewise, they seem to represent the ultimate in difficulty of evaluation . . . the growth stock problem offers no great hope of a satisfactory solution.

In the absence of a plausible solution to the equity valuation problem using discounted cash flow techniques, progress on valuation of growth stocks was confined largely to heuristic and anecdotal contributions contained in trade publications. Bohmfalk (1960, p. 122) observes: With growth stocks, the chief element of risk is a possibility of a change in the rate of growth of a company, and this possibly may be related to new technological developments or to a change in management. So the new growth stock philosophy demands some considerable technical competence on the part of the investor in appraising scientific enterprise and management.

Among the various growth stock prognosticators of this era, the contributions of Philip Fisher have been recognized for specific attention, e.g., Poitras (2005, ch. 7). To be clear, P. Fisher was not the originator of the ‘growth stock ’ approach. Rather, Fisher is selected based on largely anecdotal information on the performance of his privately managed equity portfolios. Fisher entered the investment industry somewhat later than Graham, though he did have substantive exposure to the ‘Great Bull Market of the 1920s’ having entered the fledgling Stanford Business School as a first year student in 1927–1928. Though he started his own investment firm, Fisher & Company in 1931, this venture was a from-scratch startup in San Francisco by a young entrepreneur with little market experience. While the appearance of Graham and Dodd (1934) solidified Ben Graham’s already considerable reputation in the New York financial community, by 1935 Fisher was just stabilizing his client list and achieving a small measure of success. It was not until the 1950s that Fisher rose to national prominence as a security analyst, a reputation that was solidified by Fisher (1958), a book that marks the beginning of systematic identification of the investment characteristics of growth stocks. Even though the investment philosophies of both Graham and Fisher were greatly influenced by events surrounding the Great Bull and Great Bear Markets of the late 1920s and early 1930s, there is a distinctly different flavour to their approaches to equity security valuation and investment strategy.

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The popularity of Fisher (1958) in the practical valuation of equity securities is due, at least partly, to the fashion in which the material is presented. Fisher was fond of providing point form summaries of his approach to investment analysis. In Fisher (1958), fifteen key questions are provided that need to be answered satisfactorily before a common stock is purchased. These questions, which are similar to those found in Fisher (1975) can be summarized as 1. Do the company’s products or services have sufficient market potential to make possible a significant increase in sales for at least several years? 2. Does the management have a desire and savvy to continue developing products or processes that will further increase total sales potential when the growth potential of current product lines has largely dissipated? 3. In relation to company size, how effective are the company’s research and development efforts? 4. Does the company have an effective and efficient sales organization? 5. Does the company have a viable profit margin? 6. What is the company’s strategy for maintaining or improving this profit margin? 7. Does the company have superior labor and personnel relations? 8. Does the company have superior relationships among the executives? 9. Does the company have strength and depth in its management structure? 10. Does the company have adequate cost analysis and accounting controls? 11. Are there other aspects of the business, specific to the industry, that will give the security analyst important clues to identifying if the company is outstanding in relation to its competition? 12. Does the company have an adequate short-range or a long-range profit outlook ? 13. Is there potential common stock dilution in the foreseeable future, i.e., will the growth of the company require additional equity financing that will dilute the existing common stockholders’ benefits from future anticipated growth? 14. Does the management willingly provide details about company activities when things are going well, but are reluctant to talk when troubles and disappointments occur? 15. Is the company management of unquestionable integrity and honesty ?

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By themselves, these questions are useful, if not overly revealing. The strength of Fisher (1958) is in the discussion and anecdotes that illustrate these various questions. In contrast to the Graham and Dodd (1934) view that “all security analysis involves the examination of financial statements”, it is apparent that Fisher is ‘focussed’ on the characteristics of a company. The general approach can be summarized in the quote: “I don’t want a lot of good investments; I want a few outstanding ones”. The essence of Fisher’s approach is captured in Table 3.1 that reports the price performance of eighteen stocks recommended in Fisher (1958) over the subsequent 26 months. Most attention is given to the remarkable ratio of the equally weighted average return to the return on the Dow Jones industrial average. While the Dow was able to gain a quite remarkable 40% over the less than two year period, Fisher’s stocks increased 2.82 times more at 113%. As 9 of the stocks are considered to have capitalization large enough to be sufficient for significant institutional trading and four more are close to that status, it is not possible to explain such results by claiming the Fisher portfolio achieved the returns due to a ‘higher beta than the market’. What a focus on the global portfolio performance obscures is biases in Fisher’s individual stock selection to companies in certain types of industries. Seven of the eighteen companies are either completely in or have significant exposure to the chemical industry, eight if the battery maker P.R. Mallory is included. Four companies had exposure to the fledging computer industry, five if Ampex is included because magnetic tape played a significant role in early computer storage. Stock groupings, such as resource companies, do not enter the mix. Though at the time still actively involved with his firm, Fisher (1980) was written when Fisher was well past the conventional age of retirement. The short monograph provides key points in Philip Fisher’s investment philosophy. The key points are summaries, but stressed with practical, hands-on discussion of the various points using examples from his personal experiences. The accompanying discussion is short and largely autobiographical. The first point deals with the elements of the 15 points from Fisher (1958) and the first three dimensions of Fisher (1975):8

8 The

four dimensions are: (1) superiority in production, marketing, research and financial skill; (2) the people factor; (3) essential characteristics of the business; and, (4) the current value of the stock, measured in a relative P/E sense. This leaves Fisher with four dimensions, used to structure the common stock selection strategy in Fisher (1975); 15 questions used to assess business characteristics from Fisher (1980); and eight points

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Table 3.1 Philip Fisher’s Eighteen Common Stocks Used as Examples in the 1958 Edition of “Common Stocks and Uncommon Profits” Twenty-Six Months Later. Price 9/20/57

Price 11/7/59

Per cent change

75 12 41 86

99 14 60 144 14

31 46 68

Dow

53.04

93 18

76

Du Pont General American Transportation

182 40 34

261 56 12

43 38

194.87 350.80 108 18

408 688 138 12

110 96 28

25 14

51

102

Motorola Companies approaching institutional stock status: Ampex

45 12

122

168

20

107 12

437

Texas Instruments Smaller companies: Beryllium Corporation

26 14

169 34

547

16.16

26 12

64

18 34

21 58

15

16

46 12

190

35

37 14

6

10

7 58

466.75

650.92

−24 113 40

Long established institutional stocks: Aluminum Corporation of America American Cyanamid Corning Glass

International Business Machines Rohm & Haas Union Carbide & Carbon Companies now attaining institutional status: Food Machinery & Chemical

Gladding, McBean Hewlett-Packard P.R. Mallory Huge potential profits at big risks: Elox Average of 18 stocks in this list Dow Jones Industrial Average Ratio of gains on the 18 stocks to the Dow Jones Industrial Average:

2.82

Notes: all stocks adjusted for stock splits and stock dividends; American Cyanamid and Elox eliminated from the Fisher & Co. portfolio during 1958; Hewlett-Packard was first offered in November 1957 at 16.

(1) Buy into companies that have disciplined plans for achieving dramatic long-range growth in profits and that have inherent qualities making it difficult for newcomers to share in that growth. in the investment philosophy, given in Fisher (1980) but synthesized from Fisher (1958, 1975). Only six of the eight are listed here.

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(2) Focus on buying these companies when they are out of favor; that is, when, either because of general market conditions or because the financial community at the moment has a misconception of its true worth, the stock is selling at prices well under what it will be when its true merit is better understood.9 (3) Hold the stock until either (a) there has been a fundamental change in its nature (such as a weakening of management through changed personnel), or (b) it has grown to a point where it no longer will be growing faster than the economy as a whole. Only in the most exceptional circumstances, if ever, sell because of forecasts as to what the economy or the stock market is going to do, because these changes are too difficult to predict. (4) Making some mistakes is as much an inherent cost of investing for major gains as making some bad loans is inevitable in even the best run and most profitable lending institution. The important thing is to recognize them as soon as possible, to understand their causes, and to learn how to keep from repeating the mistakes. (5) For those primarily seeking major appreciation of their capital, deemphasize the importance of dividends. The most attractive opportunities are most likely to occur in the profitable, but low or no dividend payout groups. (6) There are a relatively small number of truly outstanding companies. Their shares frequently cannot be bought at attractive prices. Therefore, when favorable prices exist, full advantage should be taken of the situation. Funds should be concentrated in the most desirable opportunities. Given this general background, Fisher provides a variety of directions, clarifications and explanations to aid in the identification and valuation of growth stocks. The desire to purchase targeted stocks as cheaply as possible is common sense and is found in virtually all analyses of securities trading and investment activities. The view is not unique to Fisher and GDC. Unlike GDC, Fisher does feel that if the company is good enough then buying 9 This

explicit statement by Fisher contradicts the perception in modern Finance that ‘growth’ investors bias purchases toward high P/E and, presumably, high P/BV stocks. Much like ‘value’ investors, ‘growth’ investors want to purchase the desired stocks as cheaply as possible. As illustrated, high P/E stocks are not desirable for “fresh purchase with new funds”.

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the common stock is recommended when it is fairly valued in line with the fundamentals. In advocating the use of intrinsic value and the margin of safety principle, GDC would seem to be in disagreement with this recommendation, per se, but this could be due to a difference in semantics. Fisher is using the P/E ratio to measure value, i.e., the fourth dimension, while GDC is using DCF to measure intrinsic value. Presumably, Fisher is implying that the growth in earnings from companies that have the strongest fundamentals is not being fully captured by the P/E. Where Fisher is saying the P/E fairly reflects fundamentals, GDC could say that the intrinsic value is low enough to qualify for purchase using the margin of safety principle. However, the difficulties of estimating the future cash flows for the types of companies Fisher’s first three dimensions identify may mean that GDC would not advocate a purchase. While there are possible interpretations that would have Fisher and GDC agreeing on criteria for purchasing common stocks, on the issue of when to sell there is unambiguous disagreement. GDC want to purchase common stocks that have the estimated intrinsic value more than the price by the margin of safety. These stocks are then held until an overvaluation is observed and then the stock is sold. In contrast, Fisher (1975, p. 43) is a long-term buy and hold investor in favor of retaining stocks “even though their prices seem too high. If the fundamentals are genuinely strong, these companies will in time increase earnings not only enough to justify present prices but to justify considerably higher prices”. For Fisher there are only a small number of companies that genuinely qualify for selection using the first three dimensions. Selling such companies because the price reflects an ‘overvaluation’ implies that there are similar companies available for purchase that are ‘undervalued’. Yet this is unlikely due to the small number of such companies. Parking the money from the sale in cash and waiting for a pull back in price requires illusive market timing skills: “it is my observation that those who sell stocks to wait for a more suitable time to buy back these same shares seldom attain their objective”. What specific criteria does Fisher propose for when to sell a successful stock? In addition to emphasizing “never sell the most attractive stocks you own for short-term reasons”, Fisher does recognize that, as companies grow, small companies that were efficiently run may fail to change management style to meet the different skill set that big companies need. The upshot is that, if management fails to grow as companies grow, shares should be sold. Fisher proposes a ‘three year rule’ for any new purchase. If the company has not achieved the objectives set out when the stock was purchased,

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then it is time to consider selling. Fisher basically wants to get in relatively early in the company growth cycle, accumulate during market down draft and hold onto the stock until the company has reached the point where future growth is problematic, always keeping a close eye on the first three dimensions. If the initial analysis is later found to be faulty, the position has to be unwound, but sufficient time has to be allowed for the company fundamentals to play out. From Graham and Dodd (1934, ch. 29) onward, the ‘Graham and Dodd’ approach has struggled with the importance of dividends: “From one point of view, the dividend rate is all-important; but from another and equally valid standpoint it must be considered an accidental and minor factor” (Graham and Dodd, p. 324). Similarly, GDC (p. 487) maintain: “The quality of common stock, which reflects itself in the multiplier applied to current or prospective earnings and dividends, is in most cases largely determined by the dividend record”. Yet, GDC (p. 488) are willing to accept: “that a fundamental difference may exist between the appropriate payout policy for average and subaverage companies and that for the exceptional growth issue”. Shareholders in growth companies will be better off if the company maintained a policy of complete retention of earnings. Recognizing the potential validity of the Miller and Modigliani (1961) argument on dividends, GDC observe that ‘synthetic’ dividend cash flows can be obtained by selling a fraction of the stock if desired. In addition, low or no dividend payout can have potential tax advantages for many stockholders due to the lower tax rate on capital gains vs. dividend income. Fisher recognizes that outstanding companies will often have a real need funds to finance expansion. As a consequence, Fisher identifies low dividend payout aspect of the growth stock profile. This view is also identified in modern Finance as being consistent with a desirable company characteristic advanced by ‘growth stock’ advocates such as Fisher. However, this aspect is not a necessary condition for Fisher (1975, p. 72): “As long as dividend policy is consistent, so that investors can plan ahead with some assurance, this whole matter of dividends is a far less important part of the investment picture than might be judged from the endless arguments frequently heard about the relative desirability of this dividend policy or that . . . dividend considerations should be given the least, not the most, weight by those desiring to select outstanding stocks”. Retained earnings can just as easily be used to “enlarge the inefficient operation rather than to make it better”. Allowances for increases in the capital stock can in some cases be achieved through depreciation rates.

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Portfolio composition is another key point of difference between growth stock proponents, such as Fisher, and traditional value investors, such as GDC. What is the optimal number of securities to own? On this point Fisher (1980) observes: “For individuals (in possible contrast to institutions and certain types of funds), any holding of over twenty different stocks is a sign of financial incompetence. Ten or twelve is usually a better number”. While Fisher does make allowance for ‘the costs of the capital gains tax’ impacting the time to achieve a ‘complete a move towards concentration’, the basic result is the same: “As an individual’s holdings climb toward as many as twenty stocks, it nearly always is desirable to switch from the least attractive of these stocks to more of the attractive.” Whereas GDC recommended holding 20–30 stocks which are rebalanced on a regular basis, Fisher maintains that for individual investors this number is so large as to be “a sign of financial incompetence”. There is some need to diversify across industries and in cases where the holdings are in venture capital or small cap situations. The bulk of these holdings will be of the long-term buy-and-hold variety. To adherents of the ‘efficient diversification’ approach of modern Finance, the approach of holding a narrow stable of winners will appear to be foolish and misguided. Yet, this approach is not unique to Fisher and can be found in other successful members of the trade. For example, Loeb (1935, 1965, p. 11) observes: “Diversification is a necessity for the beginner. On the other hand, the really great fortunes were made by concentration. The greater your experience, the greater your capability for running risks, and the greater your ability to chart your course yourself, the less you need to diversify”. Given this, Fisher does maintain that some degree of diversification across industries (and possibly countries) is essential. Hyperselective growth stock valuation and selection strategies, such as the Moore et al. (1999) gorilla game that preaches investment only in selected technology stocks, would not be advisable from Fisher’s growth stock perspective. The degree and extent of diversification is a slippery slope that marks a major point of divergence between the views of: modern Finance academics, GDC and related value investors, growth stock traditionalists, such as Fisher; and the modern growth stock proponents of the technology bubble. 3.2.3

The Warren Buffett Synthesis

Often described as the world’s greatest investor, Warren Buffett has developed an approach to equity valuation that synthesizes the traditional GDC ‘analysis of financial statements’ approach with the ‘focus on the company

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characteristics’ of the growth stock approach, e.g., Lowenstein (1995). Given the well known relationship between Buffett and Graham, the connection to the Fisher growth stock approach is apparent in various Buffett writings such as (Cunningham 2002, pp. 100, 101): Your goal as an investor should simply be to purchase, at a rational price, a part interest in an easily-understandable business whose earnings are virtually certain to be materially higher in five, ten and twenty years from now. Over time, you will find only a few companies that meet these standards — so when you see one that qualifies, you should buy a meaningful amount of stock. You must also resist the temptation to stray from your guidelines. If you aren’t willing to own a stock for ten years, don’t even think about owning it for ten minutes. Put together a portfolio of companies whose aggregate earnings march upward over the years, and so also will the portfolio’s market value.

While there is some overlap in the basic notions advanced by Graham and Fisher, it is on selecting appropriate points of emphasis and divergence that Buffett was able to arrive at a successful synthesis of the two approaches to equity valuation. For example, Graham proposed methods of determining whether common stock prices were selling below intrinsic value, emphasizing the use of financial statements. In contrast, Fisher is concerned with the characteristics of the business, emphasizing the quality of management and the company’s ability to generate sales and profits. Basic Buffett security selection dictums like searching for businesses with excellent management, focussing on a small number of core holdings (because there are only so many outstanding companies) and ‘buy a business not a stock’ are more echoes of Philip Fisher than Ben Graham, though Graham did make passing reference to these concepts as well. Buffett starts from the Graham and Dodd view that securities have an intrinsic value and that for a number of reasons, the prices of securities may not trade at intrinsic value creating trading opportunities. Following Williams (1938), Buffett advocates the use of the discounted cash flow model to estimate the intrinsic value. In order to overcome the difficulties of estimating the future cash flows, Buffett recommends examining only businesses that the analyst is capable of understanding: “You don’t have to be an expert on every company or even many. You only have to be able to evaluate companies within your circle of competence. The size of the circle is not very important; knowing its boundaries, however, is vital” (Cunningham 2002, p. 100). Once the cash flows have been determined, the margin-of-safety principle is used to decide whether the security is a

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buying opportunity. Because there are only a few companies that will meet the appropriate criteria, a Buffett portfolio for a retail investor will have few securities and be relatively inactive in trading. Examining the evolution of security analysis as reflected in the different editions of Graham and Dodd, it is apparent that the historical evolution of security markets has had a profound impact on the prescriptions of security analysis. For example, whereas in the pre-WWII period it was possible at various times to identify significant numbers of companies with common stock prices trading below the net current asset value per share, such companies are relatively uncommon in current US stock markets. Where such situations are available, this is, more likely than not, a situation that is to be avoided because the large balance of net current assets is likely being soldiered to stave off an impending sequence of negative earnings. While the views of GDC and Fisher may have provided considerable insight into securities markets of earlier times, there is no assurance that markets have not evolved beyond the lessons contained in those texts. This speaks to the importance of the Warren Buffett synthesis. Buffett has obtained his track record more recently and, as such, his prescriptions are more relevant to contemporary observers. To this end, Table 3.2 provides evidence on the performance of Berkshire Hathaway vs. the S&P 500 and Table 3.3 provides a listing of the companies in which Berkshire Hathaway currently has a substantial position. Hagstrom (1995, 2000) has summarized the ‘Buffett approach to investment’ into five principles. Though these principles do not do full justice to Buffett’s value investing prescriptions, e.g., Cunningham (2002), the basic structure is sound.10 These principles can be briefly summarized as 1. Do not follow the day-to-day fluctuations in the stock market. The market is a forum for buying and selling, not for precisely setting value. Investors need to be able to ignore significant short-term reductions in the value of a common stock. Follow the market only when the objective is to sell a stock at prices well in excess of intrinsic value. 2. Do not try to predict the direction of the general economy. If the stock market cannot be predicted, then how is it possible to predict the economy?

10 A

more expanded version of the thirteen “owner related business principles” plus one added principle underlying Buffett’s approach can be found in the Berkshire Hathaway annual report (2003, pp. 68–72).

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Table 3.2 Performance of Berkshire Hathaway Inc. versus the S&P 500. Annual percentage change In per-share book In S&P 500 with Relative value of Berkshire dividends included results Year (1) (2) (1)–(2) 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

23.8 20.3 11.0 19.0 16.2 12.0 16.4 21.7 4.7 5.5 21.9 59.3 31.9 24.0 35.7 19.3 31.4 40.0 32.3 13.6 48.2 26.1 19.5 20.1 44.4 7.4 39.6 20.3 14.3 13.9 43.1 31.8 34.1 48.3 0.5 6.5 (6.2) 10.0 21.0 10.5

10.0 (11.7) 30.9 11.0 (8.4) 3.9 14.6 18.9 (14.8) (26.4) 37.2 23.6 (7.4) 6.4 18.2 32.3 (5.0) 21.4 22.4 6.1 31.6 18.6 5.1 16.6 31.7 (3.1) 30.5 7.6 10.1 1.3 37.6 23.0 33.4 28.6 21.0 (9.1) (11.9) (22.1) 28.7 10.9

13.8 32.0 (19.9) 8.0 24.6 8.1 1.8 2.8 19.5 31.9 (15.3) 35.7 39.3 17.6 17.5 (13.0) 36.4 18.6 9.9 7.5 16.6 7.5 14.4 3.5 12.7 10.5 9.1 12.7 4.2 12.6 5.5 8.8 0.7 19.7 (20.5) 15.6 5.7 32.1 (7.7) (0.4) (Continued)

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Table 3.2

293

(Continued) Annual percentage change

In per-share book value of Berkshire (1)

Year 2005 2006 2007 2008 Compounded Annual Gain — 1965–2008 Overall Gain — 1964–2008

6.4 18.4 11.0 (9.6) 20.3% 362,319%

In S&P 500 with dividends included (2)

Relative results (1)–(2)

4.9 15.8 5.5 (37.0)

1.5 2.6 5.5 27.4

8.9% 4,276%

11.4

Notes: Data are for calendar years with these exceptions: 1965 and 1966, year ended 9/30; 1967, 15 months ended 12/31. Starting in 1979, accounting rules required insurance companies to value the equity securities they hold at market rather than at the lower of cost or market, which was previously the requirement. In this table, Berkshire’s results through 1978 have been restated to conform to the changed rules. In all other respects, the results are calculated using the numbers originally reported. The S&P 500 numbers are pre-tax whereas the Berkshire numbers are after-tax. If a corporation such as Berkshire were simply to have owned the S&P 500 and accrued the appropriate taxes, its results would have lagged the S&P 500 in years when that index showed a positive return, but would have exceeded the S&P 500 in years when the index showed a negative return. Over the years, the tax costs would have caused the aggregate lag to be substantial.

3. Buy a business, not its stock. A stock purchase can be viewed as though the entire business is being purchased. Four important elements apply to valuing the business: business characteristics, management, financial numbers and value. Business characteristics include: the business needs to be simple and understandable to the investor and the business needs a consistent operating history and favorable long-term prospects. The management has to be honest, capable and candid with shareholders. Management with a high fraction of personal wealth invested in a company, e.g., Buffett and Munger at Berkshire Hathaway, have a greater incentive to manage effectively. Key financial numbers to examine are return on equiyt, as opposed to earnings per share, profit margin and the ability to add value with retained earnings (return on additions to equity greater than cost of capital). 4. Buffett requires the intrinsic value to be greater than the market price by the margin of safety for a security to qualify as an eligible purchase.

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Table 3.3

Berkshire Hathaway Inc. Operating Companies.

Company

Employees

Berkshire Hathaway Homestate Companies Berkshire Hathaway Reinsurance Group Boat America Corporation

Company

Insurance Businesses 627 General Re Corporation 593

Kansas Bankers Surety Company 377 Medical Protective Corporation Central States Indemnity Co. 431 National Indemnity Primary Group GEICO 22, 249 United States Liability Insurance Group Insurance total Non-insurance Businesses Acme Building Brands 2, 307 Kirbya 266 Larson-Juhl Adaleta 310 The Marmon Groupd Altaquipa Applied Underwriters, Inc. 455 McLane Company Ben Bridge Jeweler 778 MidAmerican Energy Companyb Benjamin Moore 2, 467 MidAmerican Energy Holdings Companyb Borsheim’s Jewelry 204 MiTek Inc. The Buffalo News 846 Nebraska Furniture Mart Business Wire 520 NetJets 329 Northern Natural Gasb CalEnergyb a 579 Northern and Yorkshire Campbell Hausfeld Electricb a Carefree of Colorado 211 Northlanda Clayton Homes, Inc. 11, 998 PacifiCorpb 79 Pacific Powerb Cleveland Wood Productsa CORT Business Services 2, 773 The Pampered Chef CTB International 1, 079 Precision Steel Warehouse Dairy Queen 2, 362 Richline Group 70 Rocky Mountain Powerb Douglas/Quikuta Fechheimer Brothers 715 Russell Corporationc FlightSafety International 4, 482 Other Scott Fetzer Companiesa Forest River, Inc. 4, 461 See’s Candies Francea 104 Shaw Industries 34, 896 Stahla Fruit of the Loomc Garan 4, 563 Star Furniture H.H. Brown Shoe Group 1, 182 TTI, Inc.

Employees 2, 574 18 422 384 513 28, 188 648 1, 810 18, 000 16, 078 3, 150 654 1, 818 2, 712 7, 945 864 2, 444 107 3, 192 1, 224 814 194 2, 337 2, 180 4, 239 147 3, 000 28, 974 167 710 2, 782 (Continued)

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Table 3.3 Company

Employees

Halexa

126

Helzberg’s Diamond Shops HomeServices of Americab Iscar Johns Manville Jordan’s Furniture

2, 009 2, 602 10, 413 7, 280 1, 165

Justin Brands Kern River Gas Transmission Companyb Kingstona

911 164 162

295

(Continued) Company United Consumer Finance Companya Vanity Fair Brands, Inc.c Wayne Water Systemsa Wesco Financial Corp. Western Enterprisesa R.C. Willey Home Furnishings World Booka XTRA Non-insurance total Corporate Office

Employees 202 4, 819 153 13 360 2, 486 190 595 217, 876 19 246, 083

a

A Scott Fetzer Company. A MidAmerican Energy Holdings Company. c A Fruit of the Loom, Inc. Company. d Approximately 130 manufacturing and service businesses that operate within 11 business sectors. b

5. Manage a portfolio of businesses — act like a business owner rather than a stock trader. The implication is that being widely diversified is inconsistent with being able to manage so many businesses. In addition to these general principles, Buffett is credited with numerous interesting quotes such as: “It is just not necessary to do extraordinary things to get extraordinary results” and “As far as I am concerned, the stock market . . . is there only as a reference to see if anybody is offering to do anything foolish”. Despite all the reverence given to Buffett as the proto-typical value investor, it is apparent that individual investors would have difficulty pursuing the types of strategies that have brought considerable success to Berkshire Hathaway. For example, consider the “Acquisition Criteria” in Table 3.4 that is published annually in the Berkshire Hathaway annual report. This buy-a-business approach is reiterated in Buffett’s various writings. The following statement is contained in the Berkshire Hathaway (2003, p. 69) 2002 annual report: Our preference would be to reach our goal [of maximizing Berkshire’s average annual rate of gain in intrinsic value on a per-share basis] by directly owning a diversified group of businesses that generate cash and

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Table 3.4

Berkshire Hathaway Inc. Acquisition Criteria.

We are eager to hear from principals or their representatives about businesses that meet all of the following criteria: (1) Large purchases (at least $75 million of pre-tax earnings unless the business will fit into one of our existing units). (2) Demonstrated consistent earning power (future projections are of no interest to us, nor are “turnaround” situations), (3) Businesses earning good returns on equity while employing little or no debt. (4) Management in place (we cannot supply it), (5) Simple businesses (if there is lots of technology, we will not understand it). (6) An offering price (we do not want to waste our time or that of the seller by talking, even preliminarily, about a transaction when price is unknown). The larger the company, the greater will be our interest: We would like to make an acquisition in the $5–20 billion range. We are not interested, however, in receiving suggestions about purchases we might make in the general stock market. We will not engage in unfriendly takeovers. We can promise complete confidentiality and a very fast answer — customarily within five minutes — as to whether we are interested. We prefer to buy for cash, but will consider issuing stock when we receive as much in intrinsic business value as we give. We do not participate in auctions. Charlie and I frequently get approached about acquisitions that do not come close to meeting our tests: We have found that if you advertise an interest in buying collies, a lot of people will call hoping to sell you their cocker spaniels. A line from a country song expresses our feeling about new ventures, turnarounds, or auction-like sales: “When the phone do not ring, you will know it’s me”.

consistently earn above-average returns on capital. Our second choice is to own parts of similar businesses, attained primarily through purchases of marketable common stocks by our insurance subsidiaries. The price and availability of businesses and the need for insurance capital determine any given year’s capital allocation.

While it would be nice for individual investors to be able to search out companies and take a 100% interest, this is not practical for all but the select few investors (see Table 3.3 again). The detailed emphasis on business characteristics, which usually requires on-site visits and access to senior management, also makes it difficult for individual investors.11 In 11 For

example, in the 2002 Berkshire–Hathaway annual report (p. 4), Buffett recommends in reference to management: “to be a winner, work with winners”. While this is good advice for Buffett who is able to secure a golf game, weekend retreat or cosy dinner

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this regard and in the general approach to detailed fundamental analysis of the business, Buffett has much more in common with Philip Fisher than Graham and Dodd. Being a practitioner rather than an academic, the folksy writing style that characterizes Buffett’s published contributions often makes it difficult to untangle the analytical recommendations aimed at making 100% acquisitions from those associated with making fractional purchases of companies using common stock. However, this observation relates to the part of the Buffett synthesis that has a close connection to Philip Fisher, i.e., the economic analysis of the underlying business. Buffett’s approach to fundamental analysis also has a component that is closely related to Ben Graham. Whereas Philip Fisher concentrated on business characteristics, for the Graham and Dodd approach: ‘all security analysis involves the analysis of financial statements’. Unlike Fisher, who did not proceed much beyond the P/E ratio, profit margin and sales growth in the level of financial statement analysis, Buffett provides considerable insight into using financial accounting to identify investment opportunities (Cunningham 2002, p. 185): “In our own investing, we search for situations in which both [business analysis and financial statement analysis] give us the same answer”. Buffett’s insights into the use of accounting numbers in business valuation are generally unrecognized. Yet, this aspect of the Buffett synthesis may be the most impressive and useful to individual investors. Buffett explicitly recognizes the importance and limitations of accounting numbers (Cunningham 2002, p. 213): Accounting numbers, of course, are the language of business and as such are of enormous help to anyone evaluating the worth of a business and tracking its progress. Charlie and I would be lost without these numbers; they invariably are the starting point for us in evaluating our own businesses and those of others. Managers and owners need to remember, however, that accounting is but an aid to business thinking, never a substitute for it.

Because the most important source of information for Buffett’s views is the Annual Reports and Letters to Shareholders of Berkshire Hathaway, many of the comments are addressed to accounting aspects of that company. This means giving detailed attention to accounting for taxation, acquisitions and for different levels of ownership in the various companies that comprise the with virtually any major figure in American corporate management, it is little comfort to a small individual investor seeking to make a purchase in, say, U.S. Steel.

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Berkshire Hathaway holding company.12 However, there are also a number of general observations about accounting that appeal to a wider range of applications. Buffett recognizes the failings of conventional interpretations of accounting numbers and related valuation measures (Cunningham 2002, p. 218): “Common yardsticks such as dividend yield, the ratio of price to earnings or to book value, and even growth rates have nothing to do with valuation except to the extent they provide clues as to the amount and timing of cash flows into and from the business”. A common theme in Buffet’s writings is that reference to ‘growth’ and ‘value’ strategies reflect an ignorance of the valuation process. Growth can destroy value if the cash required to increase assets exceeds the cash generation of those assets in the future. For Buffett: The primary test of managerial economic performance is the achievement of a high earnings rate on equity capital employed (without undue leverage, gimmickry, etc.) and not the achievement of consistent gains in earnings per share. In our view, businesses would be better understood by their shareholder owners, as well as the general public, if managements and financial analysts modified the primary emphasis they place on earnings per share, and upon yearly changes in that figure.

Earnings are too readily manipulated by unscrupulous management or misinterpreted by naive investors. The use of GAAP accounting does not ensure a meaningful earnings number, only that the earnings number is calculated according to ‘generally accepted accounting principles’: “managers and investors alike must understand that accounting numbers are the beginning, not the end, of business valuation”. Buffett clearly states that the object is to maximize ‘economic earnings’ and not ‘accounting earnings’. This point is not original to Buffett. What Buffett brings to the table is the invaluable interpretations of an individual who has accumulated a remarkable record from understanding the difference. One example concerns ‘economic goodwill’ versus ‘accounting goodwill’: “You can live a full and rewarding life without ever thinking about Goodwill and its amortization. But students of investment and management should understand the nuances of the subject”. On this subject, writing in 1983 Buffett makes a veiled reference to the incorrectness

12 The

reference to holding company is intended in a descriptive and not a legal sense. The description of Berkshire Hathaway in the 10-K filing refers to an insurance company that owns a range of non-insurance related businesses.

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of the Graham and Dodd treatment of goodwill (Cunningham 2002, pp. 197, 198): My own thinking has changed drastically from 35 years ago when I was taught to favor tangible assets and to shun businesses whose value depended largely upon economic goodwill. This bias caused me to make many important business mistakes of omission, although relatively few of commission. Keynes identified my problem: “The difficulty lies not in the new ideas but in escaping from the old ones”. My escape was long delayed, in part because most of what I had been taught by the same teacher had been (and continues to be) so extraordinarily valuable. Ultimately, business experience, direct and vicarious, produced my present strong preference for businesses that possess a large amount of enduring Goodwill and that utilize a minimum of tangible assets.

Unlike accounting goodwill, which is ‘excess of cost over equity in the net assets being acquired’, economic goodwill is the capitalized value of the excess over market rates of return on net tangible assets. Both concepts are related to intangible assets, but in different ways. Economic goodwill provides a connection to the ‘earnings power value’ identified by proponents of ‘value investing’ (Greenwald et al. 2001, ch. 5). To illustrate the concept of economic goodwill, Buffett examines the purchase of See’s Candies in 1972, a basically debt free company that Berkshire Hathaway continues to own up to the present. The purchase price of this company was $25 million and the net tangible assets of the company was $8 million.13 Observing that the after tax earnings of See’s was approximately $2 million per year, it is apparent that the 25% return on assets represented more than just the market return earned on tangible assets. The excess return above what could be earned on the net tangible assets at prevailing market rates of return, capitalized at an appropriate discount rate, is the economic goodwill. See’s had intangible assets associated with reputation, consumer loyalty and quality of product. In contrast, accounting goodwill would depend on a combination of factors, i.e., the premium over book value of the price paid for the firm, adjusted for fair value revaluation of inventories and tangible assets, plus amortization of 13 Any

‘economic value’ calculation is subject to interpretation. The calculation of net tangible assets is no exception. A common convention is to use (cash + accounts receivable + inventory + property, plant and equipment) − (adjustments to reflect differences between the accounting value of the assets recorded on the balance sheet and the replacement cost of the assets).

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goodwill and adjustments for deferred taxes. The resulting number may, or may not, capture the implicit value of the intangible assets. Considerable discussion in value investing analysis is dedicated to the sources of ‘earnings power value’ associated with ‘assets plus franchise’. Businesses where the return on tangible assets is in excess of market rates of return are strong candidates for increased competition. This competition can arise in various forms, e.g., on the price side from competitors already in the market or from the entry of new firms. The end result is irresistible market pressures that force the return on assets to the market rate of return, or possibly below. What factors enable firms to resist these market pressures? Identifying sustainable sources of competitive advantage is the subject of numerous books and theories. A number of such sources of competitive advantage include: licenses, such as television or telecom broadcast rights; production efficiencies due to factors such as patents, specialized human capital or economies of scale; access to cheaper sources of capital, labor or other inputs; and the franchise factor associated with customer loyalty or acquired tastes.14 It is not surprising that arguably the most important franchise factor business, Coca-Cola, is also a major holding of Berkshire Hathaway. Another key difference between accounting and economic values identified by Buffett involves the treatment of depreciation. This is directly related to the concept of ‘owner’s earnings’ (Cunningham 2002, p. 211): ‘owner’s earnings’ . . . represent (a) reported earnings plus (b) depreciation, depletion, amortization, and certain other non-cash charges . . . less (c) the average annual amount of capitalized expenditures for property plant and equipment, etc. that the business requires to fully maintain its long-term competitive position and its unit volume.

Except in special cases, (c) will be difficult to estimate and, as a result, can only be a guess. However, for Buffett: “the owner’s earnings figure, not the [deceptively precise] GAAP figure, [is] the relevant item for valuation purposes — both for investors in buying stock and for managers in buying entire businesses”. Buffett cautions that the use of measures such as EBITDA to determine ‘cash flow’ will likely lead to ‘faulty decisions’. 14 Various

descriptions of the value investing approach, in general, and the Buffett approach to value investing, in particular, stress the key role played by the franchise factor as the source of long run corporate advantage and ‘monopolistic’ profit. However, while the franchise factor is of central importance in the many situations of sustainable competitive advantage, there are other sources that can also produce this result.

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Economic depreciation is not the same as amortization and this is another essential feature required to take into account in arriving at an estimate of intrinsic value. 3.3 3.3.1

Modern Finance and New Finance Conquering the Old Finance

Warren Buffett is an icon of modern vernacular Finance. While a range of similar views on vernacular equity security valuation could be presented, e.g., Peter Lynch (Lynch 1989, 1993) or Jim Cramer (2005, 2007), Buffett reflects the ‘best in breed’ among vernacular contributors. In contrast, starting from Markowitz (1952), modern Finance academics have developed an approach to equity valuation that diverges substantially from the approach of ‘old finance’. This divergence is founded on philosophical differences about the efficiency of markets. On the specific issue of equity valuation, vernacular finance practitioners are fundamentally concerned with weighing the various elements that determine specific risk of individual firms while modern Finance academics focus on the implications of market risk, maintaining that firm specific risk is too difficult to determine. Ultimately, resolution of differences between the disparate vernacular and academic approaches to equity valuation is not possible due to fundamentally different epistemological approaches to determining what constitutes knowledge. Referencing the vernacular contributions of old finance, Merton (1987, p. 150) describes ‘old finance’ as “an essentially loose connection of beliefs based on accounting practices, rules of thumb and anecdotes”. In contrast, modern financial economics features “rigorous mathematical theories and carefully documented empirical studies”. The battle for the academic high ground in Finance between institutionalists — representing the old finance approach — and the neoclassicals — representing modern Finance — was particularly vicious, even by academic standards. The opposition, it seems, was completely flattened and forgotten within academia. Any helpful ideas were rolled into the scientific movement express train that was modern Finance, e.g., Poitras (2007). As it played out, the wide gap between the ex ante claims advanced by the modern Finance movement and the actual ex post performance of the theories in the market place brings to mind another observation of Stigler (1965, p. 15): “we commonly exaggerate the merits of originality in economics . . . we are unjust in conferring immortality upon the authors of absurd theories while we forget the fine, if not particularly original, work of others”.

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While recognizing that the benefits of diversification had been identified long before, Markowitz (1999) emphasizes the contributions of Markowitz (1952, 1959): What was lacking prior to 1952 was an adequate theory of investment that covered the effects of diversification where risks are correlated, distinguished between efficient and inefficient portfolios, and analyzed riskreturn trade-offs on the portfolio as a whole.

Markowitz (1999) recounts that his motivation to develop a formal optimization model of the risk-return tradeoff for a portfolio of securities was inspired by a rejection of Williams (1938) where the rule guiding investment decisions was to “maximize the discounted . . . (expected) value of future returns”. For Williams, the value of a stock was the discounted expected value of future dividend payments. The resulting investment strategy called for selection of securities with the highest expected return. For Markowitz, the Williams approach to equity valuation decisions ignored benefits of diversification. Though Williams (1938) did deal with the impact of uncertainty, the approach suggested was to assign probabilities to possible future states and evaluate the expected value of the investment. Williams felt that diversification would result in an elimination of security risk premia, a view that does not deal adequately with security covariances. Due to a strong belief in the EMH, the notion that security analysis could enhance expected return is not permitted within the modern Finance framework. Markowitz (1999) reviews many contributions dealing with aspects of diversification, the risk–return tradeoff and the like appearing in the two decades before Markowitz (1952, 1959). The general assessment of prior contributions is that the discussion did not provide much beyond general terms and ‘did not clearly indicate why it is desirable’. As demonstrated by Rubinstein (2006), Dimand (2007) and others, this ignores the contributions of precursors such as Bruno di Finetti and Irving Fisher. To see this, consider the contribution by Fisher (1930) that receives no mention. In a discussion of “Taking Risk from Speculation” (pp. 204–207) Fisher clearly deals with the issue of diversification: A little reasoning permits of a startling corollary. It is this: If we can, by sufficient diversification in investments, get a greater certainty and thus run less risks from our speculation, then the more unsafe the investments are, taken individually, the safer they are taken collectively, to say nothing of profitableness, provided that the diversification is sufficiently increased.

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This paradox is derived directly from exploiting the old-fashioned fear of common stocks and the consequent refusal to deal in them, except well below their “mathematical value”.

What follows is a delightful discussion of the fair game model that is used to motivate the notion of the ‘caution coefficient’ — Fisher’s term for the cost of risk, a concept developed in Fisher (1906). Fisher measures the cost of risk as the difference between the expected value (‘mathematical value’) and the price that will be paid for the gamble: “a sound minded investor will pay less than the mathematical value for a chance to gain money on a risk. That is, he will trim the price by means of a ‘caution coefficient’ ” (p. 205). It is clear that Fisher was advocating the use of mean-variance expected utility functions to model investor choice: The “caution coefficient” becomes, in practice, greater and greater as the risk grows. If my chance of getting a dollar is a certainty, there would be no reduction on account of the caution factor. If it is like the chance of betting on “heads” or “tails”, the caution factor may trim the price of the chance down from fifty cents, in mathematical value, to say, forty cents for the chance to win the dollar. That is a reduction on account of caution to 20 per cent. But if one bets on two heads in succession, the reduction on account of caution would be correspondingly greater, so that instead of paying twenty-five cents, the mathematical value, the investor might insist on a reduction of more than 20 per cent to say, fifteen cents. It is both normal and proper that the higher the risk the cheaper the chance of winning can be obtained, compared to its mathematical value.

What remains is for Fisher to translate this risk–return tradeoff into a portfolio context. A key result of modern portfolio theory is that the market does not reward the total variability of a security’s return, only that part which cannot be eliminated in an efficiently diversified portfolio. Whether Fisher grasped this point is unclear from the key part of the discussion: Hence, the more risky the investment would be to a lone individual playing the game, the safer it is, if, by pooling in an investment trust with wide diversification in investment, the individual risk is thereby absorbed. For as the (individual) risk grows it can be constantly absorbed by corresponding increases in diversification. Thus the individual investor of the trust may gain more on the riskier investments, bought by the trusts at much less than their mathematical value, than if he played the market alone with less risky investments, but bought at much nearer their mathematical value.

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Fisher goes on to observe that the aggregate risk reducing benefits associated with increasing use of ‘investment trusts, investment counsels and other skilled means of diversifying’ contributed to the overall rise in stock prices during the 1920s. Fisher (1930, ch. 13) contains a number of other intellectual gems. For example, Fisher (p. 206) seems to anticipate what Markowitz was to do over two decades later: “This principle [of higher expected return for the same level of risk through diversification], so far as I know, never has been definitively formulated in the investment market”. Fisher directly ties the benefits of diversification to the ‘principle of constant inspection’. Portfolios have to be actively monitored — ‘rebalanced’ in modern terminology — in order to achieve the anticipated portfolio expected return. Bond portfolios require less monitoring than stock portfolios. Fisher explicitly identifies the value of ‘scientific appraisals of the stock market’ to increasing the value of stocks in general and spoke favorably about the benefits of what has come to be called ‘fundamental analysis’. Fisher recognizes the differences between the various entities using the moniker ‘investment trusts’ — some of which were “avowedly of the most speculative type . . . because they may heavily concentrate their holdings”. Finally, Fisher explicitly recognized the diversification benefits of holding foreign securities. From Markowitz to Fama A number of candidates are available for selection as the intellectual beginning of modern Finance. Numerous sourcess identify Markowitz (1952, 1959) as the starting point, e.g., Brealey (1991), Rubinstein (2002) and Markowitz (1999). In contrast, Rubinstein (2003) suggests an earlier beginning, tracing the roots back to Fisher (1906, 1907, 1930a) and Williams (1938). Rubinstein (2006) identifies the important role of di Finetti. Recognizing that the Markowitz approach was not widely recognized until after the contributions by W. Sharpe (Sharpe 1963, 1964), the contributions of Modigliani and Miller (Modigliani and Miller 1958; Miller and Modigliani 1961) (MM1;MM2) are arguably an appropriate starting point. This position is supported by a close reading of the literature at the time. For example, in launching a “hostile review” of MM1 (Bernstein 1992, p. 175), Durand (1959) represented a broad consensus of academic opinion at the time that MM1 appeared. Durand (1960) demonstrates that, at the time, the Markowitz model had not received the close scrutiny that was given to MM1. Initial criticisms of the evolving modern Finance approach included individuals that, at first glance, would seem to be predisposed to MM1, MM2, and the Markowitz approach, e.g., Durand (1957).

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As Rubinstein (2003) recognizes, the attribution of ideas to specific individuals is a difficult task, particularly where the individuals involved are no longer living. As such, the task of identifying the origins of modern Finance has been simplified significantly by Bernstein (1992) which provides a wonderful collection of first hand insights into the individuals involved at the beginnings of modern Finance in the 1950s and early 1960s. While it is tempting to push back to time line to individuals writing prior to this period, such as L. Bachelier, J.B. Williams and I. Fisher, there is too much of a temporal gap separating these contributors from the widespread recognition of the ‘bombshell assertions’ (Bernstein 1992, ch. 9) that modern Finance adherents used to supplant old finance from the core curriculum of business schools. In this interpretation, the modern Finance revolution begins with Modigliani and Miller (1958), gathers steam during the 1960s and reaches fruition by the middle of the 1970s. Though Markowitz (1952) appears at an earlier date, it is Markowitz (1959) that more appropriately fits into the time line suggested here. The selection of MM1 for the beginning date of the modern Finance revolution is not intended to imply that MM1 was the most theoretically significant of the early contributions. Bernstein (1992, p. 41) reflects the generally accepted view among modern Finance adherents about the relative significance of Markowitz’s contribution: The most famous insight in the history of modern finance and investment appeared in a short paper titled: “Portfolio Selection”. It was published in the March 1952 issue of the Journal of Finance, the only journal then in existence for scholars in the field. Its author was an unknown 25year old graduate student from the University of Chicago named Harry Markowitz.

Having said this, Bernstein proceeds to recognize a time line that supports the primacy of MM1: No one, including Markowitz, was aware that his paper would turn out to be a landmark in the history of ideas. Although his achievements would earn him a Nobel Prize in economic sciences 38 years later, the paper languished for nearly ten years after publication attracting fewer than twenty citations in the academic literature until after 1960. By that time, Markowitz had written his dissertation on the subject and had converted it into a full-length book.

In contrast to the slow acceptance of the Markowitz theory of portfolio optimization, MM1 gained almost instant notoriety.

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Markowitz (1952, 1959), ultimately, became the theoretical foundation for the ‘modern portfolio theory’ that is at the center of the modern Finance approach. In contrast, MM1 and MM2 did not make such a wide reaching contribution. This is, at least partly, due to the nature of the results being presented. MM1 demonstrated that, in perfect capital markets, the capital structure of the firm will be irrelevant to the market value of the firm, i.e., there is no optimal capital structure Similarly, MM2 demonstrated, again in perfect capital markets, that the dividend policy of the firm was also irrelevant to the market value of the firm. In the case of the firm’s capital structure, MM1 proposes that the market value of the firm (= market value of debt + market value of equity) is determined by the assets side of the balance sheet. The liabilities plus equity side of the balance sheet only determines the division of the asset cash flows between security claimholders. It is not possible to change the market value of the cash flows from the assets by reorganizing the division of those cash flows between claimholders. In addition to the basic demonstration that the value of the firm is determined by the assets side of the balance sheet, the MM1 argument also had to deal with investor preferences for a specific type of capital structure. Given the random behavior of asset cash flows, firms with more debt on the balance sheet will have a higher variability in the payments made to equity claims. While this would seem to indicate that the common stock in firms with higher debt levels is riskier and, as a consequence, will have a different market value than the common stock of an otherwise identical firm with a lower debt level, MM1 demonstrates that by engaging in borrowing or lending activities in conjunction with purchases of the common stock, individual investors are able to create a ‘synthetic capital structure’ for the firm that is consistent with the desired portfolio cash flow variability associated with holdings of the firm’s securities. Because the individual investor is able to synthetically achieve a desired capital structure through portfolio allocation, the market value of the firm’s debt and equity claims will not be priced to reflect differences in firm capital structure. MM2 follows lines similar to MM1. The dividend policy of the firm is irrelevant because individuals are able to create a synthetic dividend that is consistent with the individual’s desired dividend payout. From the firm’s perspective, dividend payments made to shareholders represent foregone retained earnings. In cases where retained earnings are insufficient to sustain the capital requirements needed to fund the firm’s growth, the dividend payments are recouped through new share issues. Where the dividend

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policy is lower than dictated by the firm’s capital requirements, then the excess retained earnings will be used to repurchase the firm’s common stock. Within this context, if the individual finds the firm’s dividend policy is lower than desired, then a fraction of the share holdings can be sold each period to obtain the desired level of ‘synthetic dividend’ cash flow. Similarly, if the dividend payout is higher than desired, the surplus can be used to purchase shares. While, over time, the number of shares outstanding will differ between otherwise identical firms with different dividend policies, the market value of the equity claims will be the same. As in MM1, this occurs because the value of the firm is determined by the assets side of the balance sheet. Though MM1 and MM2 did not go on to play a central role in the theoretical development of modern portfolio theory — the core of modern Finance — MM1 and MM2 did play a central role in the attack on old finance. Dividend policy and the capital structure of the firm are key concerns in traditional security analysis. The theoretical claim that such concerns are irrelevant is potentially devastating. More importantly, the irrelevance results were made by exploiting the analytical properties of perfect capital markets. The rational, maximizing individual operating in a ‘frictionless’ market environment — a central feature of the theorists that characterize modern Finance — represented a metaphor that was to prove irresistible compared to the institutionally and legally driven models of old finance. However, the topics that concerned MM1 and MM2 were focused largely on the central issues of old finance and did not play a crucial role in the evolution of the core theory of modern Finance. What early contributions did play a key role in the evolution of the core theory of modern Finance? The general consensus among modern Finance academics, e.g., Rubinstein (2002), is that at the head of the list are the seminal contributions that led to the capital asset pricing model (CAPM) and the market model: Markowitz (1952, 1959) and Sharpe (1963, 1964). In addition, as recognized in Markowitz (1999), Tobin (1958) can also be given some credit for containing the essence of the two fund separation result, albeit within the context of modeling the demand for money in a portfolio optimization framework. Markowitz (1999, p. 10) observes: “At a meeting with Tobin in attendance, I once referred to his 1958 article as the first capital asset pricing model”. Apparently Tobin did not accept this interpretation. In any event, while making an important contribution to monetary economics, Tobin (1958) did not have a similar impact on Finance. It was Sharpe (1963, 1964) that recognized the key revolutionary

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result: “the expected return on each security is linearly related to its beta and only its beta”. The core theory of modern Finance is not limited to the Markowitz mean–variance optimization framework and the CAPM. Running roughly in parallel with the development of these concepts was the work on the random character of stock market prices that culminated in Cootner (1965) and Fama (1965). While interesting in itself, this work also laid the foundation for the efficient markets hypothesis (EMH), and the modeling of stock prices (returns) as conditional expectations with information sets characterized as weak form, semi-strong form and strong form.15 This progression was aided considerably by Fama et al. (1969) which introduced a novel statistical methodology, based on cumulative abnormal residuals, that could be used to empirically test the semi-strong (and strong) form of the EMH. In turn, development of the EMH strengthened the argument for using the CAPM and Markowitz model. More precisely, under the EMH, it was not possible to use available information to earn systematic, risk-adjusted abnormal returns. This substantively undermined the basis for doing ‘old finance’ security analysis, strengthening the rationale for the elimination of diversifiable risk through portfolio optimization methods. While circa 1965 modern Finance was still in the process of evolving into a coherent package, Fama (1970) illustrates that by the end of the decade modern Finance had developed into something resembling a coherent whole. With the appearance of Fama (1976), Foundations of Finance, the revolution against old finance was largely completed, the corpus of modern Finance was solidified and the program of future research was well defined. In addition, by the mid-1970’s, attention of the modern Finance school was shifting to extending and exploring the seminal contribution of Black and Scholes (1973). Though a connection can be made between the CAPM and the Black–Scholes formula, it is difficult to meld the notion of pricing by arbitrage with that of pricing by expectation. Though there were substantive efforts to exploit the continuous time pricing technology used in Black and Scholes (1973) in the CAPM framework, e.g., Merton (1969, 1973a), a disconnect between these two streams of modern Finance survives to the present day.

15 Though Fama (1970) can be credited with popularizing the weak, semi-strong and strong form terminology, Fama credits the origination of these terms to a colleague at the University of Chicago, Harry Roberts.

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Modern Finance has adopted the rational, expected utility maximizing individual as the central abstraction upon which theoretical knowledge about security pricing can be obtained. Inductive methods — especially variants of regression analysis — are used to determine whether a particular version of a theoretical model is consistent with observed data. If the null hypothesis is not empirically supported, the model is restructured, typically by altering an assumption, and retested. While sharing this general epistemological approach, there have been three distinct tracks in modern Finance: the CAPM and Markowitz mean–variance portfolio optimization model; the EMH; and, the contingent claims pricing models that emerged following Black and Scholes (1973). Though there has been some complementarity between each of these tracks, each evolved somewhat differently and, as a consequence, modern Finance cannot be viewed as coherent doctrine of interlocking parts. Questioning of one part — such as the EMH being questioned by the ‘New Finance’ — does not necessarily involve questioning another part — such as contingent claims pricing models. The lack of initial coherence between the inductive EMH and the theoretical CAPM created a number of confusions that, at the time, puzzled those seeking to understand the emerging school of thought. Some of these confusions still survive to puzzle those being introduced to the dictates of modern Finance. This is illustrated by the use of the term ‘efficient frontier’ to define a central concept in the Markowitz approach. The ‘efficiency’ in this case is only loosely connected to the informational ‘efficiency’ that concerns the EMH or the Pareto ‘efficiency’ that arises in microeconomic theory. Similarly, the different tracks in modern Finance each lead to somewhat different implications for security analysis and selection. For example, while the CAPM leads to two fund separation as the appropriate investment strategy, contingent claims pricing technology suggests that dynamic portfolio insurance is an appropriate strategy. 3.3.2

Two Fund Separation and Exchange Traded Funds

At least as early as Roll (1977), it has been recognized that empirical testing of the key theories of modern Finance is frustrated by lack of a precise definition for the “market portfolio” and the “riskless asset”. A similar problem confronts any attempt to apply modern Finance theories to the valuation of equity securities. While a remarkable amount of effort has been dedicated to resolving definitional issues, the gains have been largely rhetorical. Empirical tests of, say, the CAPM would suggest that a broadly

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based stock index, such as the S&P 500, is a sufficient proxy for the market portfolio. This suggests that a passive equity index ETF, such as the SPY, is the appropriate market portfolio to hold in implementing two fund separation. The difficulties of incorporating foreign assets into the market portfolio can be handled by forming an appropriately weighted combination of foreign and domestic ETF’s, e.g., XIU for the TSX 60. A proxy for the long (short) riskless security can be obtained with a money market fund (margin account borrowing). As it turns out, this is only one of a number of possible empirical implementations of the logical results provided by modern Finance. Absent a belief that security analysis can enhance expected returns compared to selection of a passive equity index, empirical implementation of modern Finance theories focuses on the ‘top down’ asset allocation decision. Being ‘top down’, the asset allocation decision precedes the security selection decision. There are two basic components to this decision: strategic asset allocation; and, tactical asset allocation. Though the asset allocation concept also appears in various guises in vernacular Finance, attention has only recenlty been given to the practical asset allocation decision by modern Finance academics. In the process, it has gradually been recognized that conventional advice provided by professional investor advisors, personal financial planners and the like is inconsistent with the received theories of modern Finance such as two fund separation. Following Bernstein (1992) and Poitras (2005), this inconsistency is aptly referred to as ‘the interior decorator fallacy’. Strategic Asset Allocation Strategic asset allocation is a key first step that professional investment advisors take in the process of establishing new account parameters for unsophisticated investors, e.g., Bodie (1997). The new client is asked a range of questions regarding income level, risk tolerance, age, expected retirement age and the like. The types of questions asked are much the same across investment advisory firms. The end result is typically some target percentages for equity and fixed income holdings that will likely be slowly changed as the individual investor ages and the contribution levels to the portfolio change. This process is guided by the intuition that bonds are ‘safe’ and equities are ‘risky’. Investors approaching retirement with low levels of risk tolerance are directed to portfolios that are heavily weighted to fixed income while those investors that are younger and have a higher level of risk tolerance are funneled into portfolios more heavily weighted to

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equities. Despite the practical importance of such asset allocation strategies, Elton and Gruber (2000, p. 27) observe: “almost no attention has been paid [by academics] to examining advice regarding the asset allocation decision”. Canner et al. (1997) and Campbell and Viceria (2002) initiated a discussion about the inconsistency between central propositions of modern Finance, such as the capital asset pricing model and the two fund separation theorem, and the strategic asset allocation advice conventionally provided by professional investment advisors. In particular, the two fund separation theorem requires that the asset composition of the risky tangency portfolio — the market portfolio — is the same for all investors. In addition, differences in risk tolerance across investors are handled by altering the value weights allocated to the riskless asset and the risky tangency portfolio. Hence, the ratio of stocks to bonds associated with the market portfolio will not change across investors. This is inconsistent with the conventional strategic asset allocation advice of professional investment advisors. However, as Elton and Gruber (2000) illustrate, a range of qualifications are required to accommodate the various possible specifications of ‘modern portfolio theory’, which includes the two fund separation theorem as a special case. Included in these qualifications are: the specification of the riskless asset; whether short sales are permitted; and the number and type of risky assets permitted in the risky market portfolio. Despite being an integral part of the strategic asset allocation decision, little attention is given to the cash management element of that decision. For example, in the CAPM, which provides a theoretical basis for two fund separation, the cash management decision is modeled as a problem in riskless lending and borrowing. Yet, unless the investment horizon or rebalancing frequency of the portfolio is exactly equal to the term to maturity of the default-free, zero coupon fixed income security used as the riskless asset, then there will be a reinvestment risk associated with rolling the security over at maturity.16 In addition to confusions associated with specifying the riskless asset, there are also complications associated with the cash flow requirements of the portfolio over the investment horizon. The basic optimization model underlying the CAPM and two fund separation 16 This assumes that nominal returns are the variable of interest. If, as is common in modern Finance, the real return is the variable of interest, even a default-free, zero coupon fixed income security with maturity date equal to the investment horizon will be risky. Even though the nominal return will be certain, there is still purchasing power risk associated with inflation. This complication can be handled by using an inflation-indexed default-free fixed income security as the riskless asset.

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assumes that there is a fixed level of initial wealth that is invested at the beginning of the investment period. Depending on the specification of the optimization problem there may be rebalancing along the time path. In addition, in the consumption-investment form of the problem, allowance could be made for cash inflows or outflows along the time path, in the form of consumption and investment expenditures that can take positive or negative values. In a practical context, this leads to consideration of trading strategies concerned with buying along the time path, such as dollar cost averaging, e.g., Leggio and Lien (2003). Adherents of modern Finance have long recognized the practical limitations of the riskless asset concept, e.g., Roll (1978). This concept of ‘cash’ as a riskless security that pays the riskless rate of interest differs from actual ‘cash’ which is legal tender — Federal Reserve bank notes in the United States — that do not pay interest. Even this type of cash is subject to the erosion of purchasing power associated with price level inflation. Ignoring inflation, it is possible to view cash as a ‘riskless’ security but this requires the riskless rate of interest to be set equal to zero. Perhaps an interest bearing chequeable bank account is a more appropriate security to use as cash? What about using a money market mutual fund? Both of these securities feature changing interest rates, violating the CAPM condition that the security is riskless unless the frequency of interest rate changes equals the portfolio rebalancing frequency. In models with a fixed rebalancing frequency of, say, three months, then it is possible to use a three-month U.S. Treasury bill as the riskless asset. In any event, the issue of defining cash is a significant complication in assessing the appropriate cash management strategy to pursue. It is conventional in the modern Finance approach to unbundle the cash management decision from the asset allocation decision. There are a number of reasons given for this simplification. For example, the previous discussion illustrated the point that the cash management decision requires ‘cash’ to be defined. Even when an acceptable definition for the cash asset(s) is given, the cash requirements for the portfolio decision are usually given exogenously. Over time, there may be cash inflows to the portfolio from net labor income or cash outflows due to drawdowns during retirement. However, such cash flows do not typically impact the optimal solution to the theoretical investment decision problem in a transparent fashion. Theoretical interpretation usually involves making sense of intertemporal marginal rates of substitution, correlations between labor income and investment returns, rates of time preference and the like. To avoid such complications,

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it is conventional to simplify the cash inflow/cash outflow component of the portfolio decision by assuming that a lump sum of initial wealth is invested at the beginning of the investment horizon and is held until the end of the horizon. This framework can be adjusted to permit the initial lump sum to be invested over a sequence of time periods, as in dollar-cost-averaging strategies. Unbundling the cash management decision from the larger investment optimization problem permits a number of possible approaches to be pursued. Unfortunately, this unbundling does not necessarily lead to useful and practical recommendations. Following the theoretical approach used in economics, the optimal cash management solution will depend on the individual investor’s supply and demand for cash. The supply of cash will depend on the initial capital and, possibly, other factors such as the cash flow requirements, investment returns and labor income over the time path. The demand for cash will have three basic elements: precautionary demand; transactions demand; and speculative demand. Unfortunately, using this approach opens a hornet’s nest of conflicting opinions about: the specification of the different demand functions; the various definitions of money, from ‘high powered money’ to ‘near-money’ to ‘outside money’; the empirical properties of the possible demand function specifications and so on. Following Tobin (1958), the speculative demand for money can be modeled using much the same theoretical framework as that employed in the derivation of the Sharpe-Lintner CAPM. This approach reduces the solution of the cash management decision problem to that contained in the CAPM. In the CAPM framework, optimal holding of the riskless asset depends on a combination of investor risk attitudes and the spread between the riskfree rate and the expected return on the risky portfolio. When appropriate, this optimal holding is adjusted at each of the potentially diverse number of rebalancings that occur over the investment horizon. In practice, this process reduces to deciding the optimal method of purchasing risky assets over the rebalancing period (investment horizon). Cash assets are held as a buffer to support such purchases. A number of possible methods are available. Lump sum investing involves purchasing the desired asset allocation at the beginning of the rebalancing period (investment horizon). The disadvantage of this approach is that the purchase decision may occur at a time when the risky assets are selling at ‘high’ prices, somehow defined. In addition, the change in asset prices over time will cause the portfolio weights to deviate from the desired asset allocation. If no rebalancing is

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permitted along the path, or if the optimal lump sum allocation is 100% in risky assets, then the lump sum approach reduces to the buy-and-hold approach. In such cases, the tactical and strategic asset allocation decisions are identical. At least since Merton (1973) it has been recognized that the buy-andhold approach is generally sub-optimal. A widely recommended alternative approach to buy-and-hold is dollar cost averaging (DCA) where the investor makes a fixed dollar investment at regular intervals during the rebalancing period. The underlying rationale for DCA is that the risk of buying at a market high associated with lump sum investing is avoided. In addition, for risky assets with volatile prices, the larger number of shares purchased at low prices will more than offset the smaller number of shares purchased at high prices, resulting in a net gain. An alternative to DCA is value averaging where, instead of investing a fixed dollar amount each period, the size of the investment is set to maintain a constant increase in the value of the portfolio each rebalancing period. For example, assume the objective is to increase the portfolio value $100 per month (the rebalancing window). If the portfolio increases 5% in the first month, then investment in the second month would be $95 (+$105 = $200). If there is a 2% drop in the second month then the investment in the third month would be $104 (+196 = $300) and so on. Both value averaging and DCA are aimed at capturing the gains of ‘buy low, sell high’. Milevsky and Posner (2003) seek a theoretical resolution to the popularity of DCA among practitioners and individual investors. Working within a continuous time framework using Brownian bridges, Milevsky and Posner model DCA as a path dependent claim and develop a mathematical proposition that ‘proves’: “the expected return from . . . the DCA strategy — conditional on knowing the final value of the security will uniformly exceed the return from the underlying security for all sufficiently large volatilities”. In effect, DCA outperforms lump-sum investing. This leads to the conclusion that rational investors using DCA are working with target prices. This makes sense in the context of value investing, where adherents of DCA would be working with expectations based on calculated intrinsic values. In this framework, the more volatile is the underlying security price, “the greater is the benefit to dollar-cost averaging — conditional on knowing the final value”. This result is in sharp contrast to what has been generally accepted wisdom about DCA, based on Constantinides (1979) and later theoretical studies where DCA is shown to be a dynamically inefficient trading strategy, e.g., van Duffel et al. (2009).

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Table 3.5

Strategy

315

Annualized Excess Returns and Risk Measures, 1970–1999.

Mean

A. Asset: large stocks Lump sum 7.76 Dollar cost average 3.60 Value average 3.46 B. Asset: small stocks Lump sum 9.70 Dollar cost average 1.83 Value average 6.96 C. Asset: corporate bonds Lump sum 3.01 Dollar cost average 2.79 Value average −0.13 D. Asset: government bonds Lump sum 2.90 Dollar cost average 3.00 Value average −0.40

Std. dev.

Sharpe ratio

Sortino ratio

Upside potential ratio

16.18 8.88 9.38

0.48 0.41 0.37

4.95 4.46 3.73

2.93 3.46 3.28

22.84 12.17 13.35

0.42 0.15 0.52

4.49 1.87 4.93

4.02 3.44 3.93

11.91 6.85 5.22

0.25 0.41 −0.02

3.79 6.24 −0.34

5.69 6.19 4.60

12.33 6.71 5.96

0.24 0.45 −0.07

3.91 7.07 −1.15

4.87 4.78 5.20

Source: Leggio and Lien (2003).

Reconizing there are a diversity of ways to implement the ‘cash asset’, separation of the cash management decision provides further scope for defining the riskless asset used to implement two fund separation. The two fund separation result goes by a number of related names, such as the ‘portfolio separation theorem’, ‘two mutual fund theorem’ and the like, e.g., Ingersoll (1987, ch. 6), Elton and Gruber (1995).17 The essence of the two fund separation result is that all investors will hold combinations of only two portfolios, the market portfolio and the riskless security. In an equity valuation context, the market portfolio return is determined by the equity market and a proxy for the riskless rate would be the government bond yield. Hence, (domestic) two fund separation can be implemented using a combination of a passive value weighted equity index, e.g., SPY for domestic US or XIU for domestic Canada, and a long term 17 The ‘two fund separation’ terminology can be found in various sources. For example, Levy and Samuelson (1992, p. 1530) observe: “The Sharpe-Lintner CAPM can be derived by assuming either a quadratic utility function or normally distributed returns. In a multiperiod framework, the quadratic utility assumption also leads to the two-fund Separation Theorem, and hence implies the CAPM”.

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domestic government bond fund. With this interpretation, the change in the target percentages for equity and fixed income holdings suggested by professional investment advisors is consistent with changing risk preferences over time. However, if the riskless asset is determined by setting the term to maturity of the zero coupon government fixed income security equal to the rebalancing period, e.g., three month re-balancing, then the market portfolio will be composed of relatively stable proportions of the stock and bond funds, supporting the ‘interior decorator’ fallacy. In the purest form, the investment strategy decision associated with two fund separation is solely a strategic asset allocation decision: how is the total amount of invested capital divided between the riskless asset and the market portfolio. Because two fund separation is predicated on the assumption of market efficiency, it is not feasible to engage in tactical asset allocation where the proportions invested in the two funds varies according to market timing decisions. The investment strategy decision is based on the risk attitudes of the investor. While the composition of the market portfolio is fixed externally, the proportion of the portfolio held in the riskless asset can be either positive (lending) or negative (borrowing). If the proportion is negative then the investor has borrowed at the riskless rate and has a leveraged position in the market portfolio. The theoretical conditions required for two fund separation to apply are quite restrictive. If all other assumptions of the model are maintained, the basic two fund separation result is not affected by whether short sales are allowed. Given the assumed homogeneity of investors, the tangency portfolio is the market portfolio because all assets have to be held in equilibrium. Short sales of the riskless asset are used to move the investor along the capital market line (see Fig 5.1). Dropping the assumption that there is a riskless asset requires a zero beta portfolio to be determined as a substitute for the riskless asset. This will require a short sales assumption for the risky assets. Using the zero beta portfolio in place of the riskless asset, a version of the two fund separation theorem still holds with the additional implication that “all portfolios on the efficient frontier are a linear combination of any two other efficient portfolios” (Elton and Gruber 2000, p. 28). It follows that “any recommended portfolio must be a linear combination of any two other recommended portfolios”. The practical value of this recommendation is elusive. While it is possible to deal in some fashion with the riskless asset assumption, dropping this assumption and the short-sales-allowed

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assumption is sufficient to undermine the two fund separation theorem. Elton and Gruber (2000, pp. 28, 29) provide a summary of the implications arising from dropping the short sales allowed assumption: If short sales are not allowed, the nature of the efficient frontier changes. The two-fund [separation] theorem no longer holds. Securities enter and leave the efficient frontier at different risk–return tradeoffs. The points where they enter or leave are called corner portfolios. Securities may be held in zero weight for a range of risk tolerance and some assets are never held. Generally, the maximum return portfolio on the efficient frontier will consist of one asset and the minimum risk portfolio will consist of multiple assets. Thus, if short sales are not allowed and advisors are rational, any allocation recommendation should not be a linear combination of any two others unless all three lie at or between adjacent corner portfolios.

It follows that the practical implications of modern portfolio theory depend on the assumptions made to generate the results of interest. Depending on the assumptions made and the empirical return data used to determine the associated portfolio allocations, a range of possible specifications have to be considered in determining whether specific professional investment advice is consistent with the prescriptions of modern portfolio theory. The central impetus for Canner et al. (1997) was to develop tests of rationality consistent with modern portfolio theory that could be applied in assessing the validity of strategic asset allocation advice of professional investment advisors and financial planners. Though Canner et al. argue for the irrationality of a decrease in the ratio of bonds to stocks as investors risk tolerance increases, Elton and Gruber (2000, p. 40) demonstrate: “whether or not short sales are allowed, the sign of the relationship between the bond stock ratio and risk hypothesized in Canner et al. cannot be used as a rationality test”. In general, it seems that simple theoretical tests derived from modern portfolio theory are problematic and empirical properties of bond and stock returns have to be considered. Yet, once empirical properties are introduced this raises the problem of using ex post parameter estimates to determine the ex ante values required to make the strategic asset allocation decision. Ultimately, an underlying feature of this discussion is the implicit assumption that modern portfolio theory is the appropriate measure of rationality. Even if the epistemological approach of modern Finance is accepted, the various possible specifications of the model admit a range of sometimes conflicting strategic asset allocation prescriptions.

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What is Tactical Asset Allocation? In both vernacular and modern Finance, tactical asset allocation is a catchall expression that is aimed at capturing gains to market timing and portfolio rebalancing decisions. Tactical asset allocation strategies can take a variety of forms, e.g., Arnott (1998). A common format is reflected in Ragsdale and Rao (1994, p. 209): In tactical asset allocation, the central question is: Which asset class will provide superior future returns? Because relative returns are more important than absolute returns in this particular setting, many tactical asset allocators have focused on expected return premiums or spreads. As a practical matter, the most important comparison is that between stocks and fixed income (either bonds or cash) and the forecast on which the most effort is expended is the expected return for stocks. The comparison between stocks and fixed income is crucial because these are the two largest pools of assets in institutional portfolios. Stock return forecasts are important because, historically, stocks have provided the highest and most volatile investment returns.

In combination with government bond funds, ETF’s that track specific stock indexes are well designed for this approach to tactical asset allocation. Though a number of methods can be used to determine tactical asset allocation decisions, the basic procedure involves starting from a benchmark asset mix derived from the strategic asset allocation decision and then employing tactical methods to systematically deviate from the benchmark mix. Precisely how much deviation from the benchmark is permitted depends on the specifics of the fund being managed. Using the studies in Lederman and Klein (1994) as a guide, it appears that tactical strategies based on mean-variance optimization techniques are an important component of the class of available strategies. As portrayed in modern Finance, tactical asset allocation takes place prior to a security selection decision. As such, the composition of the market portfolio of risky assets is usually associated with a stock fund, such as the S&P 500, and a bond fund. The asset is identified with cash riskless. Following Fox (1999), this leaves two key elements in the tactical asset allocation decision: ‘the tilt’ and forecasting ability. The tilt is concerned with the allowable amount of deviation from the benchmark holdings of the risky assets. If the benchmark is, say, 60/40 stocks and bonds then a ‘full tilt size’ could be a 20% deviation, i.e., maximum values of 80/20 and 40/60. Fox uses this full tilt value in combination with a forecasting ability variable to simulate a range of tactical asset outcomes. Fox (1999,

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p. 46) describes some results of the simulation relationship: “In the long run, managers with forecasting ability of 60% or better will virtually never underperform the benchmark. For managers who have superior forecasting skill, increasing tilt size improves the entire range of possible return outcomes.” As with other tactical asset allocation studies, performance is measured relative to the benchmark portfolio. In a study of the tracking error that arises in tactical asset allocation, Ammann and Zimmermann (2001, p. 32) demonstrate that the higher returns to forecasting ability are not at the expense of benchmark tracking accuracy: “imposing fairly large tactical asset allocation ranges produces surprisingly small tracking errors”. Another element in the tactical asset allocation exercise is the rebalancing frequency.18 Fox (1999), for example, uses monthly rebalancing as do Ammann and Zimmermann (2001). Presumably, this fixed rebalancing interval is a restriction imposed by the requirements of the research design, rather than being reflective of actual fund manager practices. However, Fox (1999, p. 40) observes: “the relatively small size of the US [tactical asset allocation] universe. Other types of portfolio managers can be compared to fifty to eighty peers, each with a long investment history. [Tactical asset allocation] managers have many fewer counterparts and only a handful have long-enough observed histories for accurate assessment”. It would appear that the relevance of the tactical and strategic asset allocation approach is due more to the connection to modern Finance than to the practical importance of the approach in the fund management industry. As such, there is little guidance from practicing fund managers as to the appropriate rebalancing interval. Perhaps a daily or weekly tilt would apply for some funds while a quarterly or annual tilt would apply for other funds? Perhaps an irregular rebalancing interval is most appropriate but, if so, the process for determining a rebalancing point needs to be adequately specified. Though there are decided similarities with other approaches to investment strategy, the terminology ‘tactical asset allocation’ is intimately tied to strategic asset allocation and, in turn, to the modern Finance approach to equity security valuation and selection. As for similarities with other approaches, tactical asset allocation strategies can be contrasted with, say, the Dow theory where: the tilt is usually a ‘bang-bang ’ solution, i.e., 18 Among

others, Levy and Samuelson (1992) provide four sets of sufficient conditions for multi-period generalization of the single-period Sharpe-Lintner CAPM where investors are permitted to have diverse holding periods and rebalancing frequencies. In the multiperiod context, if portfolio rebalancing is not permitted then the CAPM and two fund separation do not hold, even in the restrictive case of quadratic utility.

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100% stocks during bull markets shifting to 100% cash during bear markets; the forecast is generated by interpreting the Dow theory signals; and the rebalancing period is determined by the movements of the market rather than by a fixed time interval such as monthly or quarterly. Within the conventional tactical asset allocation framework, industry rotation and country rotation strategies are considered to be too close to the realm of security analysis. There are some practical reasons for this. For example, certain institutional investors, such as pension funds and life insurance companies, have restrictions on holdings of foreign assets. A similar comment applies to the allowable tilt, where there are also various restrictions on the tilt imposed on institutional investors. The connection between security analysis and tactical asset allocation is explored in various sources, e.g., Poitras (2005, ch. 10); Brinson et al. (1991); Blake et al. (1999); Kritzman and Page (2002). When security analysis is eventually added to the process, there are a number of potential feedbacks into the tactical asset allocation decision that have to be considered. For example, the tracking error associated with deviations from the benchmark portfolio could become substantial if the actual risky assets are small collections of individual securities (or even individual securities), as opposed to broadly diversified passive index portfolios. Another potential feedback concerns the re-balancing frequency. Using, say, a monthly re-balancing interval would require that securities be purchased and sold on specific days while security analysis typically requires that transactions be determined by value calculations. In effect, the tilt is determined by the number and variety of securities that satisfies the security analysis selection criteria at a given point in time. It is not obvious how to integrate security analysis, which involves decisions about a significant number of individual securities, into the tactical asset allocation framework, where forecasts are made for a passive index. Despite the connections between tactical asset allocation and modern Finance, there is a lack of agreement among modern Finance adherents about the efficacy of the practice. To EMH purists, tactical asset allocation is another form of market timing strategy. Even when the potential for market timing is recognized, purists usually observe that the range of optimal changes in portfolio weights is much less than typically recommended by tactical asset allocators. For example, Samuelson (1990) observes: If you do have timing ability, flaunt it! But in the absence of Napoleonic pretensions to clairvoyance, your rational flauntings are more likely to involve switches of a few percent in your equity fraction around some

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optimal intermediate level rather than the swings from 100% in stocks to 10% in stocks that characterized many asset allocation systems . . .

The basic intuition behind the attack on tactical asset allocation is embedded in the terminology used by Samuelson (1990) to describe the practice: ‘across-time deviations from diversification’. Market timing requires the investor to temporarily deviate from the allocations that provide optimal, long-term diversification. Hence, unless there are sufficient gains in expected returns, tactical asset allocation will produce a sub-optimal amount of diversification resulting in a lower measured performance using, say, the Sharpe ratio. While this conclusion is strongest for iid returns and log utility, the basic result also carries through to other situations.

3.3.3

From Modern Finance to New Finance

While the ‘trente demoiselles de Geneve’ investment scheme is of historical interest, it is not possible to date the beginnings of modern Finance from this date. Not only is this date far removed from the institutional context of modern financial markets, the subject of modern Finance is much more than a collection of notions such as ‘the gains to portfolio diversification’. The various notions are connected by a philosophical approach — economic positivism — that unifies these notions to create a coherent and persuasive school of thought. The relevance of this school is clarified by considering the process by which modern Finance was able to supplant during the 1950’s and 1960’s the ‘old finance’ school epitomized by the ‘Graham and Dodd approach’ that emphasized individual equity security valuation and selection. By shifting focus onto the portfolio diversification problem, modern Finance argued for the elimination of the firm specific risk that was the stock in trade of the old finance adherents. In this process, a new philosophy of equity valuation and selection emerged. As discussed elsewhere, e.g., Poitras (2005, sec. 1.3), a range of philosophical issues need to be addressed in order to develop insight into the prevailing approaches to equity security valuation and selection. It was argued that modern Finance has an inherent philosophical bias that is reflected in both the rhetoric and the prescriptions of academics and, to a lesser extent, practitioners. This bias has resulted in a methodological approach to the subject that seeks to emulate the natural sciences. Yet, being concerned with variables that are the outcome of human interaction, Finance is inherently a human science. While the inductive methods of the natural

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sciences are necessary to the progress of knowledge in Finance, these techniques are insufficient in the human sciences. Knowledge about phenomena in the human sciences is not rigidly cumulative. Events are historical and, as such, require interpretation in the context of the times. The process of interpretation and prediction is complicated by having to deal with the ‘uncertainty’ of future events. Unlike the natural sciences, it is possible for writers of the past, working with less data and knowledge, to have insightful understandings of a specific phenomenon that compares favorably with the views of contemporary writers. This chapter has been concerned with developing the intellectual history of modern security analysis. This also required some selected discussion of financial history. The time line incorporates Graham and Dodd (1934), a text that is heavily influenced by the historical events which preceded its publication. Yet, the text stands as an example of how writers from a previous era, working with less data and ‘knowledge’, produce results that have a timeless quality. To be sure, Graham and Dodd (1934) has to be read in the context of the time the book was written as do other such books from that period, e.g., Keynes (1936). Given this, Graham and Dodd (1934) acts like a beacon that can be used to determine where modern Finance is now situated on the equity valuation landscape. As a consequence of recognizing the biases in modern Finance, even basic results such as ‘stock returns will outperform bond returns in the long run’ can be given a more useful interpretation in terms of predicting what type of valuation method to employ for identifying particular securities to purchase or sell. Haugen (1999a,b) provides a refreshing description of the academic evolution from the ‘old finance’ of Graham and Dodd to the world of modern Finance associated with modern portfolio theory, the CAPM and the EMH. Haugen proposes that the evidence against modern Finance, in terms of anomalies and the poor predictive ability of the models, is so strong that a ‘New Finance’ is emerging to replace modern Finance. For Haugen (1999b, p. 8), the New Finance represents the complete supremacy of the inductive method: And now Modern Finance begins to teeter. And a New Finance appears. Discard those theories that obviously have no predictive power. Discard the requirement that all explanations must be based on rational economic behavior. Look carefully at the data and measure accurately without preconception. Discard the tradition that you must model first without looking and then verify. Carefully measure behavior first, and

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then find reasonable and plausible explanations for what you see. Ascension of the ad hoc, expected return, factor model. The measure of any model’s relative merit: the unmined, out-of-sample, relative accuracy of its predictions.

For those unable to see whether this is sincerity or sarcasm, the next sentence is telling: “Go back to teaching students a craft rather than a religion”. For Haugen, the New Finance achieves complete supremacy for the inductive methods of the natural sciences. Putting aside some enthusiastic views concerning the emergence of the New Finance, Haugen (1999b, pp. 3–8) does give a useful analysis concerning the progression of Finance from the time of Graham and Dodd (1934) to the present. Haugen obtained his education in Finance in the early 1960s, “when modern Finance was relatively young and when the old finance was dying”. Accounting and law were the basic foundations of the old finance and the professors of the time were experts in those fields. The theme of the old finance was the analysis of financial statements and the nature of financial claims. Classic texts were Graham et al. (1951) and Dewing (1953). “Graham and Dodd spent most of their book showing us the painful process of adjusting accounting statements so that earnings and assets of different companies could be directly compared . . . In (Dewing), we learned the legal rights of financial claims — in great detail. We learned the laws relating to merger and acquisition as well as those governing bankruptcy and reorganization”. Haugen describes Graham and Dodd as ‘very dry stuff and not too interesting’. Dewing, on the other hand, made Graham and Dodd ‘look like a Stephen King thriller’. Haugen views the professors of the old finance as teachers of a craft. “As possible future financial executives, we needed to know the rules of the game if we had to merge or go bust, as well as the legal impediments on our firm’s behavior created by the financial claims that were there today or might be there tomorrow”. The time of Haugen’s graduate finance education, the early 1960s was ‘an interesting time indeed’ as modern Finance was breaking onto the academic scene, doing battle with and, eventually vanquishing the old finance. Though the birth of modern Finance can be traced to the portfolio optimization model of Markowitz (1952, 1959), the model was largely unnoticed until the emergence during the late 1950s and early 1960s of the other pillars of modern Finance: the Modigliani–Miller irrelevance theorems; the capital asset pricing model; and the efficient markets hypothesis. In contrast to the accounting and law foundations of the old finance, modern Finance was a product of financial

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economics. The central theme was that securities could be valued using models assuming rational economic behavior. The emergence of modern Finance represented a direct attack on the teachings of the old finance. Haugen (1999b, p. 6) observes: “The craft of finance and the teachings of my old professors had been rendered obsolete. It’s not nice to be obsolete. The professors of the old finance fought very hard to retain their relevance. The battles of this intellectual war are still recorded in the pages of the old issues of the Journal of Finance and the American Economic Review. But the professors of the old [Finance] lost most of these battles, and eventually they lost the war itself”. The winning of the rhetorical intellectual battle brought a wave of new professors into Finance programs, trained in graduate programs that emphasized theorizing using the assumption of rational economic behavior. The position of the proponents of modern Finance was buttressed by the emergence of option pricing theory: “Modern Finance took off. It became the dominant discipline in business schools, and it carried great influence in the real world”. Having gained a position of intellectual superiority, proponents of modern Finance actively promoted the paradigm. The intellectual history of modern Finance from the mid-1960s until the present makes for an interesting case study in the process by which knowledge is created in an academic environment. The developments are similar to those in economics where the assumption that economic agents are rational also became the central theme of economic theory, e.g., Kindleberger (1989, p. 29); Mirowski (1989), and Weintraub (2002). Even though rationality is only an assumption that may or may not be an accurate description of the world, Haugen, Kindleberger and others observe that the validity of the assumption was ‘intellectually enforced’ by the younger network of academics. This enforcement process took place in the journals and in the classrooms. Given the substantial investment of human capital that had been made by the younger network in the techniques and knowledge associated with the rational maximizing models, such enforcement activities are not surprising. However, as Haugen puts it (1999b, p. 7), “even when the mud is thick, truth always makes its way to the surface”. Haugen provides an interesting description of the enforcement process: Those who would dare to question the validity of the [modern Finance] paradigm — especially that of efficient markets — were summarily dismissed as gauche. Those who dared to publish papers contradicting the paradigms were ridiculed. Their studies were supposedly replete with bias. And their methods, of course, were naive.

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Their studies included only firms that survived the study period — survival bias. They used earnings numbers that may not have been publicly available at the time they bought the stocks — look-ahead bias. They spun the computer countless times until they got an interesting result — data mining. They did not take transactions costs into account. They did not risk adjust their returns. They did not test for statistical significance. Their results were not robust in different time periods. On and on . . .

Haugen is quick to point out that early studies critical of the paradigms of modern Finance did turn out to be on the mark: “But [were] summarily dismissed, in any case”. Haugen traces the emergence of the New Finance to the accumulation of theoretical and empirical results that challenged the main propositions of modern Finance, e.g., Kahneman and Tversky (1979), Lopes (1987), Tversky and Kahneman (1992), Statman (1995), and Levy and Levy (2002). New Finance is based on the theme of psychological explanations for inefficient markets.19 Though the connection between psychology and economics goes back at least to Katona (1951), the main empirical paradigm has been associated with inductive ad hoc factor models. The operative techniques are inductive methods from statistics and econometrics. There is a substantial overlap, if not a formal equivalence between Haugen’s New Finance and behavioral Finance, e.g., Shefrin (2000) and Akerlof and Shiller (2009). While Haugen’s description of the progress of modern Finance is helpful, the notion that there is a ‘New Finance’ emerging is suspect. It seems to be predicated on a misunderstanding of the economic positivism that underpins academic modern Finance albeit with a more inductive oreintation and less emphasis on the formal logic of model development or, more precisely, with emphasis on model development related to prospect theory, e.g., Tversky and Kahneman (1992). Ultimately, the New Finance is just an evolutionary, more inductive branch of the scientific movement associated with modern Finance. Even an individual as jaded as Haugen about the lack of vernacular appeal of modern Finance still clings to the belief 19 New Finance is theoretically based on psychological biases arising in prices. The following example of loss aversion is adapted from Kahneman and Tversky (1979). You currently own a stock that you purchased for $10,000 and has fallen to $2500. If you hold onto the stock there is a 75% chance the company will go bankrupt and the stock price will fall to zero, and there is a 25% chance the stock will recover to it’s original value. Based on an intuitive inspection of this decision, should you sell the stock today and lock in a loss of −$7500 or hold on? What is the expected value of the two transactions? The ‘gut instinct’ solution to the decision reflects loss aversion.

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that the inductive process will lead to an accumulation of knowledge that progressively uncovers the true nature of the subject. There are physical laws of nature governing financial activities. Given enough data, these laws can be identified and used to make valid enough predictions about optimal portfolios or security prices to be of significance in the vernacular world of Finance.

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PART II

Theories of Equity Security Valuation “The value of a share in a joint stock is always the price which it will bring in the market; and this may be either greater or less, in any proportion, than the sum which its owner stands credited for in the stock of the company.” Adam Smith (1723–1790), Wealth of Nations (1776, p. 232) “Academics . . . like to define investment ‘risk’ differently, averring that it is the relative volatility of a stock or portfolio of stocks — that is, their volatility as compared to a large universe of stocks. Employing data bases and statistical skills, these academics compute with precision the ‘beta’ of a stock — its relative volatility in the past — and then build arcane investment and capital-allocation theories around this calculation. In their hunger for a single statistic to measure risk, however, they forget a fundamental principle: It is better to be approximately right than precisely wrong.” Warren Buffett (1993), As quoted in Cunningham (2002, p. 82) “When you enter the stock market, you are going into a competitive field in which your evaluations and opinions will be matched against some of the sharpest and toughest minds in the business. You are in a highly specialized industry in which there are many different sectors, all of which are under intense study by men whose economic survival depends upon their best judgment. You will certainly be exposed to advice, suggestions, offers of help from all sides. Unless you are able to develop some market philosophy of your own, you will not be able to tell the good from the bad, the sound from the unsound.” John Magee, As quoted in Edwards and Magee (1992, p. viii) 327

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CHAPTER 4

Discounted Cash Flow Models 4.1

4.2

4.3

History of Equity Valuation Models 4.1.1 Equity Value in Partnerships . . . . . . . . . . . 4.1.2 The Emergence of Discounted Cash Flow Models 4.1.3 Rational Bubbles and Intrinsic Bubbles . . . . . A Variety of DCF Models 4.2.1 The Gordon Growth Model . . . . . . . . . . . . 4.2.2 Abnormal Earnings and Other Models . . . . . . 4.2.3 Simplified Discounted Dividend Valuations . . . 4.2.4 DCF Valuation of the COS Merger . . . . . . . . Basic Theory of Interest 4.3.1 Different Possible Definitions . . . . . . . . . . . 4.3.2 Examples of Fixed Income Valuation Problems . 4.3.3 Term Structure of Interest Rates . . . . . . . . .

. . 330 . . 333 . . 338 . . . .

. . . .

342 346 358 368

. . 375 . . 378 . . 382

Discounted Cash Flow Prior to J.B. Williams Macaulay (1938, pp. 130–132) makes the following observation: Because the good that the common stock offers to its purchaser is an expectation of future money payments, the relation of its present-money price to its future-money payments is as unmistakably an interest phenomenon as is the relation of the present-money price of a bond to its future-money payments. In the fullness of time the stock will have a ‘realized’ or ‘actual’ yield just as will the bond. And, though the stock makes no ‘promise’, as does the bond, and therefore has no ‘promised’ or ‘hypothetical’ yield, its price discounts estimated future payments as truly as does the price of a bond. (emphasis added)

Despite this recognition of using discounted cash flow methods to value common stocks, Macaulay objects quite strongly to the practicality of using such methods: The ‘assumption of payment’, which must be made before the promised or ‘hypothetical’ yield of a bond can be calculated . . . may, as we have seen, be a mere mathematical fiction for all except the highest grade of bonds. But, for common stocks it is not only a mathematical fiction but also an economic absurdity.

For Macaulay, the difficulty of estimating the cash flows generated by common stock prevented the practical application of discounting methods to value such securities. This skepticism is a useful backdrop to the following discussion on the use of discounted cash flow techniques. 329

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4.1 4.1.1

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History of Equity Valuation Models Equity Value in Partnerships

The problem of determining the value of an equity position in a business venture goes back to antiquity (Hecksher 1955, vol. 1). In particular, because transport of goods over long distance was expensive, arduous and risky, a number of merchants would often combine resources in a business venture to transport goods to and from a foreign trading location. Such ventures were common in the seaborne carry trade and usually were dissolved when the voyage was completed. The valuation problem involved the division of the terminal equity value into the shares determined by the contribution of each partner to the venture. For the seaborne trade, these shares were usually determined when the business venture was initiated. However, for more permanent ventures, such as a farm, wholesale business or a manufacturing facility, equity contributions might occur at different times. Equity valuation was required, not only when a share in a venture was sold or wound-up, but also in estate probate where more than one individual has a claim to the equity share of the deceased. A range of equity valuation problems are posed and solved in the commercial arithmetics that were used in training merchants in the 15th to 17th century reckoning schools (Swetz 1987; Poitras 2000, ch. 4) The Treviso Arithmetic (1478) is not a particularly memorable book from the standpoint of high theory. The primary relevance of the book is that it was the first printed book on commercial arithmetic and, more generally, on mathematics. As such, the book almost certainly provides a snapshot of the teachings that an unnamed maestri d’abbaco gave to the students of his reckoning school. The book is untitled and draws its name from being an arithmetic published in Treviso, a town in the Venetian republic, some 26 km northwest of Venice. Treviso was a town of some economic importance, being located about one day’s journey on the main trade route linking Venice with northern and central European centres such as Vienna and the German cities. Economic activity in Treviso was sufficiently robust that, as early as 1372, the town was capable of supporting a maestri d’abbaco (Swetz 1987, ch. 1). In the Treviso, three problems are given where simple interest rate methods are used to calculate the returns from partnership (Swetz 1987, pp. 138, 139). No other attention is given to any situations involving interest calculations to determine equity value. The first of these problems is an elementary application of the rule of three:

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Three merchants have invested their money in a partnership . . . Piero put in 112 ducats, Polo 200 ducats and Zuanne 142 ducats. At the end of a certain period they found that they had gained 563 ducats. Required is to know how much falls to each man so that no one shall be cheated.

The solution to the problem is uninteresting from a mathematical viewpoint.1 However, the problem is of interest in illustrating the general framework for practical partnership problems. In addition, the author is careful to implicitly observe that if all partners have funds invested for the same length of time, the solution to the problem is independent of the endpoint of the partnership. The second of the Treviso problems is more complicated in that the partners are permitted to be involved in the partnership for different time periods (Swetz 1987, p.143): Two merchants, Sebastino and Jacomo, have invested their money for gain in a partnership. Sebastino put in 350 ducats on the first day of January, 1472, and Jacomo 500 ducats, 14 grossi on the first day of July, 1472; and on the first day of January, 1474 they found that they had gained 622 ducats. Required is the share of each [man so that no one shall be cheated].

The proposed solution to this problem follows as an extension of applying the rule of three given in the first problem. As such, this is also a simple interest method of solution. Observing that the stated solution does not admit the possibility of compound interest provides considerable insight into the methods of calculation used in mercantile practice during this period. Considering the proposed solution in more detail requires knowing that 1 ducat = 24 grossi and 1 grossi = 32 pizoli. The solution to the problem proceeds by applying the rule of three which, in this case, involves expressing the two contributions in grossi, 8,400 grossi for Sebastino and 12,014 grossi for Jacomo with the addendum that ‘since Sebastino has had his share in 6 months longer than Jacomo, we must multiply each share by the length of its time’. Multiplying by 24 months gives Sebastino’s share as 201,600 and by 18 months gives Jacomo’s share as 216,252. Taking the sum of these two shares (417,852) for a divisor and applying the ‘rule of 1 The stated solution is for Piero, 138 ducats, 21 grossi, 11 pizoli and remainder; for Polo, 248 ducats, 0 grossi, 13 pizoli and remainder; and, for Zuanne, 176 ducats, 2 grossi, 7 pizoli and remainder. The Treviso proceeds to check the solution, so that ‘no one has been cheated’, by adding together the shares to verify that the total is 563 grossi.

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three’ gives the solution of 300 ducats, 2 grossi, 8 pizoli and a remainder for Sebastino and 321 ducats, 21 grossi, 13 pizoli and a remainder for Jacomo. The Treviso solution to the partnership problem does not involve the use of compound interest. Using semi-annual compounding, the inclusion of compound interest would involve solving:
r 4 r 3 14
14 1+ + 500 850 + 622 = 350 1 + 24 2 24 2 The solution of r = 34.694% requires the evaluation of a quartic equation. The associated shares would be 308.4 ducats (308 ducats, 9 grossi, 19 pizoli, and remainder) for Sebastino and 313.6 ducats (313 ducats, 14 grossi, 12 pizoli, and remainder) for Jacomo, a decidedly different result than the ‘just’ result proposed in the Treviso.2 Evidence that knowledge of compound interest calculations was common in the commercial practice of the 15th century, at least in the important financial centres such as Lyons, can be found in Chuquet’s Triparty. On the subject of compound interest, the Triparty makes explicit reference to the incongruity between the theoretically correct mathematical calculation and recommended commercial practice for calculating shares in partnerships reflected in the basic commercial arithmetics. The manuscripts contained in the Triparty are actually three main sections concerned with algebraic theory, and three other parts containing problems, a geometry and a commercial arithmetic. The latter is generally similar in content to the Treviso, reflecting the similarity in the study of commercial arithmetic throughout Europe. However, unlike the Treviso, the handling of compound interest is recognized directly (pp. 306–307): Three merchants formed a company, one of whom put in 10 ecus which remained there for the space of three years. The second put in 6 ecus 2 The third problem is a more complicated variation of the second: “Three men, Tomasso, Domenego, and Nicolo, entered into partnership. Tomasso put in 760 ducats on the first day of January, 1472, and on the first day of April took out 200 ducats. Domenego put in 616 ducats on the first day of February, 1472, and on the first day of June took out 96 ducats. Nicolo put in 892 ducats on the first day of February, 1472, and on the first day of March took out 252 ducats. And on the first day of January, 1475, they found that they had gained 3168 ducats, 13 grossi and 12 pizoli. Required is the share of each, so that one shall be cheated”. The solution procedure is an extension of the rule-of-three procedure used to solve problem 2. However, due to crediting Nicolo with three months full investment instead of only one month, “the solution stated does not satisfy the given conditions of the problem” (Swetz 1987, p. 147). Ignoring the remainders, the solution is given for Tomasso as, 1052 ducats 11 grossi and 8 pizoli, for Domenego, 942 ducats 3 grossi and 21 pizoli, and for Nicolo, 1173 ducats 22 grossi and 17 pizoli.

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which remained there for 7 years, and the third put in 8 ecus which remained there for four years. At the end of a period, 20 livres of profit was found. One asks how much comes to each, considering the money and the time that each has used it.

The answer proceeds with the usual application of the rule of three as in the Treviso. After presenting this method and the solution Chuquet states (p. 307): And the calculation is done, according to the style and opinion of some. And in order for such reckoning to be of value, it is necessary to presuppose that the principal or the capital alone has made a profit, and not the profit (itself). And inasmuch as it is not thus, for the profit and the profit on the profit made in merchandise can earn profit and profit on profit in proportion to the principal, from day to day, from month to month and from year to year, whereby a larger profit may ensue. Thus such calculations are null, and I believe that among merchants no such companies are formed.

Though the compound interest solution is not provided, Chuquet appears to hold that calculation of compound interest is fair practice in calculating the returns from partnerships of unequal duration.3

4.1.2

The Emergence of Discounted Cash Flow Models

The use of discounted cash flow (DCF) methods to value investments and real assets goes back centuries, e.g., Poitras (2000, ch. 4); Scorgia (1996); Lewin (1970, 2003); Smith (1967). The application of these techniques to the earliest issues of equity securities involved the use of valuation methods developed for fixed income securities to determine the ‘intrinsick’ value of the stock. Well into the 20th century, the dividend yield was considered to be the most important measure of equity security value, especially for investment grade stocks, e.g., Rutterford (2004). There were various reasons for this preference, including the absence of sufficiently accurate accounting information prior to reforms of the securities markets begun by passage in the United States of the Securities Act (1933) and the Securities and Exchange Act (1934) and the Companies Act (1948) in the United 3 A more precise specification of ‘such calculations’ is needed to determine the precise meaning of the statement. Though primary sources for the 15th century are scarce, if profit was paid on profit then such arrangements would be conducted outside the glare of public scrutiny for fear of ecclesiastic sanction.

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Kingdom.4 Dividends paid were the most visible and reliable source of information about firm performance. In addition, in the U.K. and Europe corporations tended to have high dividend payout ratios and a preference for raising capital for expansion from new share issues (Graham and Dodd 1934, p. 331), instead of having a lower dividend payout and reinvesting retained earnings to expand the business. The shortcoming with using fixed income methods to value common stock is that the dividend is not fixed over time. The historical transition from traditional fixed income valuation to discounted cash flow valuation is usually traced to a number of disparate contributions by actuaries, real estate appraisers, foresters, and engineers made in the mid19th century. These more advanced valuation methodologies permitted the future cash flows associated with the asset being valued to vary over time. These assets were associated with timber leases, forest land valuation, mining leases, growing or declining annuities and the like. There is some confusion over the priority of these contributions. For example, Gane (1968, p. 5) claims: “There can be no doubt that the concept of net present worth grew up over a considerable number of years, amongst foresters in Austria and Germany”. In the particular case of an equity security valuation, a U.K. mining engineer, William Armstrong (1811–1896), used discounted cash flow methods to value mining company issues and mining leases (Pitts 2001). Around this time actuaries also became interested in valuation for variable annuities. The appearance of the first Institute of Actuaries textbook (Sutton 1882) contained a section on variable annuities. Todhunter (1901) modelled the common stock price using a perpetuity with a constant growth rate, determining the pricing solution with an infinite number of dividend payments. This approach to equity valuation continued to attract attention until the 1960s, e.g., Clendenin and van Greave (1954), Durand (1957a), and Solodofsky (1966).

4 The

requirement introduced by the NYSE in the 1890s that traded firms provide financial statements was an early initial impetus to providing investors with accurate financial information, permitting the calculation of crude earnings numbers. While the securities laws of 1933 and 1934 were revolutionary, prior to this time U.S. investors still received considerably better accounting information than investors in other jurisdictions. The situation in the United Kingdom was decidedly murkier. It was not until 1976 that turnover numbers had to be fully disclosed (Toms and Wilson 2003). Until the Companies Act was passed in 1948, balance sheet information was clouded by the absence of a requirement to provide consolidated accounts (Rutterford 2004).

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While not directly concerned with DCF valuation, Smith (1924) (Common Stocks as Long-Term Investments) arguably marks the beginning of the transition from equity valuation based on dividend yields to equity valuation based on earnings. Providing detailed empirical evidence, Smith (1925, 1927) changed the perception of the importance of earnings relative to dividends. Prior to Smith, the convention was to measure the value of common stock relative to bonds: being the most junior of all securities with the greatest variability of cash flow common stock required the highest yield among the securities on offer from a given corporation. Smith demonstrated that the ex post returns on equities outperformed bonds due to the compounding effect on future dividends and future share prices of reinvesting “this increasing surplus in productive operation” (Smith 1925, p. 77). This view was well suited to U.S. companies which had benefited from strong economic growth over the 1866–1922 sample period that Smith examined. The superior presentation of accounting information by United States as compared to U.K. and European companies, e.g., in the reporting of consolidated versus unconsolidated earnings, also facilitated the use of valuations based on earnings as opposed to dividends (Figs. 4.1 and 4.2). The connection between equity valuation based on earnings and DCF valuation is that once reinvestment of retained earnings is recognized then the dividend is expected to rise over time with the share price. This

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Fig. 4.2

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The price-dividend ratio, 1871–1996. Source: Ma and Kanas (2004).

represents a significant change in the character of corporate finance which favoured distributing the bulk of earnings in dividend payments, leaving undistributed earnings in reserves designed to maintain the dividend payment in adverse conditions. Faced with favourable growth prospects, U.S. companies tended to have lower dividend payout ratios than firms in the United Kingdom and Europe that were often more mature and did not have the same type of need for capital to fund growth opportunities as those operating in the tariff-protected U.S. market. With high dividend payout and lower growth prospects, unconsolidated reported earnings were primarily used to measure the ‘dividend cover’, similar to the use of interest coverage ratios to value corporate bonds. Recognition that the dividend payment will increase over time led to theoretical contributions providing appropriate pricing models. For example, Guild (1931) developed a model of the share price using the sum of a finite period of constant growth in cash flow plus a terminal share value measured using the discounted value of a price/earnings multiple. While Guild (1931) was written for the investment trade, similar contributions were appearing in academic publications. Preinreich (1932) presented a model with a capital base that expands as earnings grow over a finite period. Significantly, Preinreich concludes: “only discounted cash flow techniques could value such growth firms correctly” (Rutterford 2004, p. 139). Despite the ability to model the price of equity claims using a discounted stream of growing dividends, the widespread recognition and acceptance of these methods by academics and some practitioners to value

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common stocks begins with the theoretical and empirical applications in John Burr Williams, The Theory of Investment Value (1938). The classic Graham and Dodd (1934) gives no explicit discussion or recognition of discounted cash flow valuation for equities, though in the final edition of Security Analysis, Graham, Dodd, and Cottle (1962), DCF methods are recommended to estimate intrinsic value without actually executing such a calculation. The basic notion advanced in Williams (1938) was that the present value for an equity security, such as a common stock, can be determined by discounting the future stream of expected cash inflows minus expected cash outflows at the appropriate rate of interest. The notion that “every stock price represents a discounted value of future dividends and earnings of that stock” (Fisher 1930, p. xxii) was well known by the time Williams (1938) appeared. What is significant about Williams (1938) is that the common stock valuation takes centre stage in the discussion. There is detailed discussion of how the distribution of company earnings into dividends and retained earnings impacted the future growth of both earnings and the balance sheet. While only simplistic growth assumptions are used, Williams (1938) devoted pages to actual valuations of companies such as General Motors. Recognizing that ‘investment value’ for Williams corresponded to ‘intrinsic value’ in Graham and Dodd (1934), Williams (1938) provided a promising and well-structured method of determining a numerical ‘intrinsic value’. The theoretical development of the basic discounted dividend model advanced in Williams (1938) reaches a climax with Durand (1957a) where a connection is made between the constant dividend growth version of the discounted dividend model and the St. Peterburg paradox. Though the constant dividend growth variant of the discounted dividend model is often attributed to Gordon (1962), as Durand (1957a, p. 351) observes this version of the model is given in Williams (1938). Durand (1957a) considers a number of theoretical nuances arising from the dividend discount model with growing dividends. Despite this long history, the eponym for the simplified DDM belongs to Myron Gordon (born 1920), currently Professor Emeritus at the University of Toronto. Because Gordon (1962) was concerned with the important practical problem of valuing companies in regulated industries, the formula provided a ‘killer application’ for the emerging capital asset pricing model to determine the unobservable discount rate for the stock. In recognition of the significance that the model played at that time, the constant dividend growth version of the discounted cash flow

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model is referred to as the ‘Gordon growth model’, e.g., Damodaran (1994, p. 99). 4.1.3

Rational Bubbles and Intrinsic Bubbles

To review the derivation of the basic DCF model, assume for the moment that the future is known with certainty and that perfect market assumptions apply. In the present context, this means there are no taxes and the term structure of discount rates is flat. Given this, consider the problem of determining the current price of a common stock by discounting the future cash flows. Assume that the stock to be valued is purchased at price P (0) and held for one period and then sold. This current price can be modeled as the discounted value for the sum of the dividend to be received in the next period (Div(1)) and the price P (1) received from selling the stock. Assuming the dividend is paid at the point the stock is sold: P (0) =

P (1) − P (0) Div(1) Div(1) + P (1) −→ k = + 1+k P (0) P (0)

This is the ‘basic valuation equation’, sometimes incorrectly referred to as the ‘absence of arbitrage’ condition. In effect, the (expected) return on the stock can be decomposed into two parts: the (expected) capital gain and the (expected) dividend yield. Dropping the assumption that future cash flows are known with certainty, leads to the result that k = E[RS ], the expected return on the stock. Accounting for randomness in the future cash flows by taking expectations conditional on information available at t = 0, the infinite horizon discounted dividend model is derived by making a progressive substitution for prices: E[P (1)] =

E[Div(1)] E[P (2) + Div(2)] E[P (2)] + E[Div(2)] −→ P (0) = + 1+k (1 + k) (1 + k)2

P (0) =

T  E[Div(t)] t−1

(1 + k)l

∞

+

 E[Div(t)] E[P (T )] −→ P (0) = (1 + k)T (1 + k)l t−1

The relevance of other perfect markets assumptions follows appropriately. For example, introducing taxes requires a distinction to be made between the stream of expected dividends and expected capital gain, which will be taxed at different rates. Combining this with differences in the relative riskiness for these two types of cash flows leads to the possibility that different discount rates might be required for dividends and capital gains. In

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addition, relaxing the assumption of a flat term structure of discount rates requires different k’s to be used to discount cash flows occurring at different points in time. Careful analysis of the substitution process involved in deriving the infinite horizon discounted dividend model reveals a problem: what if there are other variables that affect prices than just the discounted stream of future dividend payments? Then this component of the price will be ignored in the progressive substitution process and the proposed infinite horizon solution would be faulty. This theoretical difficulty is compounded by the empirical observation, initially advanced by Flood and Garber (1980), LeRoy and Porter (1981), and Shiller (1981) using the assumption of a constant discount rate, that the observed variation in stock prices was too volatile to be consistent with the infinite horizon discounted dividend model. The excess volatility hypothesis has subsequently generated an impressive collection of empirical articles that have explored a range of possible failings in the initial statement of the hypothesis, including Campbell and Shiller (1987), Evans (1991), Campbell and Kyle (1993), and McMillan (2007). Despite these considerable efforts, the basic empirical result still remains: the variability of common stock prices cannot be sufficiently explained by the variation in dividends. The appearance of the empirical ‘excess volatility hypothesis’ generated a demand for theoretical contributions that could explain this stylized fact. An initial step in this direction was the rational speculative bubble or ‘rational bubble’ proposed by Blanchard and Watson (1982). To motivate this approach, consider the discounted dividend model in continuous time:  T V (t, u) d(u) du (4.1) p(t) = V (t, T )p(T ) + t

where p(t) is the real (price index deflated) stock price observed at time t, p(T ) is the anticipated real stock price at time T , d(u) is the expected continuously paid real dividend over u ε(t, T ], and T is the terminal or maturity date for the valuation problem (T ≥ t ≥ 0). In this formulation, the set of valuation operators {V (t, T )} involves both discounting and expected value operations. The same set of valuation operators is applied to both prices and dividends. As illustrated above in discrete time, progressive substitution for p(T ) in (4.1) produces the infinite horizon, discounted-dividend model:  ∞ V (t, u) d(u) du = pF (t) (4.2) p(t) = t

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Convergence of the operator as T → ∞ is required for the satisfaction of a transversality condition: lim V (t, T ) p(T ) = 0

(4.3)

T →∞

This condition is needed to ensure that the stochastic difference equation identified by (4.1) will not have an infinite number of solutions, e.g., Craine (1993). In other words, (4.3) is a technical condition required for the solution to the pricing problem to be unique. The importance of the transversality condition can be seen by observing that it is possible the stock price p(t) has two components: p(t) = pF (t) + B(t), the ‘market fundamentals’ component pF (t) associated with the infinite stream of discounted future dividend payments and a rational bubbles component B(t), where pF (t) is given in (4.2) and B(t) can be any random variable that satisfies B(t) = V (t, T )B(T ). Because in this case p(t) incorporates both fundamental and bubble information, progressive substitution for p(T ) produces restrictions on the bubble component:  T V (t, u) d(u) du p(t) = pF (t) + B(t) = V (t, T )(pF (T ) + B(T )) +  = t

t

∞

V (t, u) d(u) du + V (t, T ) B(T )

In order for the transversality condition (4.3) to be satisfied, then an explosive bubble is ruled out. However, it is not enough to have B(T ) vanish in the limit as T goes to infinity. As initially demonstrated by Blanchard (1979), in order for B(t) = 0 and the current price to be determined solely by pF (t), it is necessary to rule out a ‘speculative, periodically collapsing bubble’. Following Evans (1991, p. 924), for stock price models: “Bubbles do not appear to be empirically plausible unless there is a significant chance that they will collapse after reaching high levels”.5 Considerable initial effort in the empirical analysis of rational bubbles was concerned with arriving at a correct formulation of the testable hypothesis. For example, Evans (1991) showed that the dynamics of a bubble 5 Various motivations can be provided for bubble behavior. Following Flood and Garber (1980), an explosive bubble is generated by the need for prices to increase at an increasing rate in order to compensate new entrants to the market for the ever increasing risk of a price collapse that will eventually occur at some later date in the future.

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could fool a testing strategy that involved comparing the stationarity properties of stock prices and dividends, as suggested by Diba and Grossman (1988), Hamilton and Whiteman (1985) and others. Accumulating empirical evidence against the ‘rational bubble’ model led to the introduction of ‘intrinsic bubbles’ by Froot and Obstfeld (1991). Because the intrinsic bubble component of the price also depends on dividends, the resulting relationship between the log of prices and dividends is non-linear. This nonlinearity hypothesis has received much more favourable empirical support, e.g., Ma and Kanas (2004). Non-linearity is now the norm in econometric studies of the relationship between stock prices and dividends, e.g., McMillan (2007), Balke and Wohar (2006, 2009). However, it is well known that non-linearity in the relationship between stock prices and dividends can be generated by a variety of observationally equivalent models, e.g., stochastic regime switching, temporal variation in the parameters of the dividend process and intrinsic bubbles all produce non-linearity. Balke and Wohar (2006, p. 55) provide the following summary of the empirical relationship between stock prices and dividends: “the data have difficulty distinguishing a stock price decomposition in which expectations of future real dividend growth is a primary determinant of stock price movements from one in which expectations of future excess returns are a primary determinant. The data cannot distinguish between these very different decompositions because movements in the price-dividend ratio are very persistent whereas neither real dividend growth nor excess returns are; most of the information about low-frequency movements in dividend growth and excess returns is contained in stock prices and not the series themselves . . . this inability to identify the source of the stock price movements is not solely due to poor power and size properties of our statistical procedure, nor does it appear to be due to the presence of a rational bubble”.

A quarter century after the excess volatility hypothesis first appeared, econometric explanations are still a work in progress. As indicated by the Balke and Wolhar (2006, p. 55) quote, there is an impasse in the line of empirical research that aimed to exploit properties of covariance stationary processes to decompose stock price movements: “The data cannot distinguish between . . . very different decompositions [of the stock price] because movements in the price-dividend ratio are very persistent whereas neither real dividend growth nor excess returns are”. Based on closer

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inspection of the ‘clean surplus’ equation, e.g., Lundholm (1995), it appears that cash dividends are not the most appropriate variable to use for cash flows in a given period if stock valuation is the objective. Rather, substituting earnings and book value for dividends has a stronger accounting foundation. It is also apparent that the ‘narrow dividends’ variable almost always employed in empirical bubble studies does not capture all cash flows contained in the ‘broad dividends’ variable defined by the clean surplus relationship, especially share repurchases (see Fig. 4.3). So even if dividends are to be used as the cash flow, the dividend variable that has been used is too ‘narrow’ to be consistent with clean surplus accounting. While the implications of the clean surplus relationship are well known to accountants, this point is only gradually being recognized by financial economists, e.g., De Angelo and De Angelo (2006) and Handley (2008). 4.2 4.2.1

A Variety of DCF Models The Gordon Growth Model

Despite impressions to the contrary, e.g., Cunningham (2002, p. 93), Williams (1938) did not originate the discounted cash flow model for security analysis. Rather Williams popularized acceptance of the approach.6 Prior to Williams, informed opinion was generally against the validity of the model for equity valuation, e.g., Macaulay (1938). What disturbed previous writers about this approach to common stock valuation was not the basic formulation but, rather, the difficulties of determining the future cash flows for stock. The application of discounted cash flow techniques to assess the value of stocks, where value is measured using a model price vs. market price, depends fundamentally on the forecasting of future payments. In textbook cases where the cash flows from the equity security are relatively predictable, then discounted cash flow techniques can provide a reasonable estimate for the intrinsic value of the security. Given this, where in the present common stock universe can such situations be commonly found? The motivation for the Gordon growth model (Gordon 1962) is to provide a simplification of the general form of the discounted dividend model (DDM), where determining the price involves evaluating the infinite sum of discounted dividends, a clearly impractical exercise. The Gordon growth 6 Williams

(1938, p. 6) states: “investment value [is] the present worth of the future dividends in the case of a common stock, or the future coupon and principal in the case of a bond”.

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Fig. 4.3 Equity Index Prices, Narrow Dividends (D1) and Broad Dividends, (D2), 1947–2000.

Source: Jiang and Lee (2005, p. 1481).

model permits the dividend to change over time according to the assumption: D(t + 1) = D(t)(1 + g), where g is the assumed constant growth rate in dividends. Dropping the expectation for ease of notation and substituting this result into the general form of the discounted dividend model

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produces the simplified DDM model or, other words, the Gordon growth model: ∞ ∞   Div(t) D(0)(1 + g)t = P (0) = t (1 + k) (1 + k)t t=1 t=1   1+g (1 + g)2 D(0)(1 + g) (1 + g)3 1+ + = + + ··· (1 + k) 1 + k (1 + k)2 (1 + k)3   1 D(1) D(0)(1 + g) 1+ for k > g = = 1+g (1 + k) k − g) 1 − 1+k By assuming that the dividend grows at a constant rate over time the Gordon growth model is able to provide a simple common stock valuation model: P (0) = D(1)/(k − g). The example that Macaulay provides refers to the situation where g → k which gives ‘a very high price level for stocks’. In the context of the Gordon growth model with g → k, Macaulay (1938) develops an interesting implication: If the dividends were $4(1.03), $4(1.03)2 , $4(1.03)3 , etc. . . . and if these dividends were discounted at 3 per cent per annum, the price of a share of the stock that was to pay the dividends, should be just four times the number of payments that were to be made; in other words, four times the number of years that the succession of dividends was to continue.

Though this result is relatively obvious from inspection of the original sum, this result is not so obvious from inspection of the D(1)/(k − g) formulation of the model where k > g is required for convergence of the perpetual sum. Over time, a number of developments of the basic Gordon growth model have appeared that introduce more complicated patterns for future dividend payments. For example, Malkiel (1963) has a two stage model where dividends grow at a constant rate for a finite number of years and then grows at a rate typical of other firms in the economy thereafter. Molodovsky et al. (1965) has a three stage model where dividends initially grow at a constant rate, then decline over a second period to be followed by a constant steady state dividend payment thereafter. While theoretically appealing, the two, three and multi-stage growth models lack practical applications in all but the most specialized situations. Due to the proliferation of parameters and terms, the formulas quickly get unwieldy. Useful simplifications of multistage growth models can be obtained for purposes of doing relative value analysis using P/E ratios, e.g., Leibowitz (1999, 2000).

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Clean Surplus Accounting The Gordon growth model makes the precise statement that common stock pricing depends on three variables: the dividend to be received next period, Div(1) = D(1); the expected return on the common stock, k; and the long term growth rate of dividends, g. In terms of expected returns the model maintains that: E[RS ] = k = (D(1)/P (0)) + g and (D(1)/P (0)) = (k − g). Returning to the ‘basic valuation equation’, this implies that the expected capital gain is equal to the expected growth rate of dividends. While this might seem to be quite unrealistic, it does have a reasonable interpretation. If the P/E ratio does not change over time, the growth rate in earnings will equal the growth rate in dividends if the dividend payout ratio does not change over time. Under these assumptions, g will be translated into the capital gain. Yet, if these assumptions are adopted, then the model can be manipulated to produce other interesting results that can be used to interpret widely used valuation measures. More precisely, assuming for the moment that the Gordon growth model is correct, it is possible to manipulate the model to provide precise statements for two important valuation measures, the price-earnings (P/E) ratio and the price-to-book value (P/BV ) ratio. In turn, these values can be used to provide an interpretation for g. To convert the Gordon model to P/E form requires the ‘clean surplus’ equation for earnings: E(t) = Div(t) + RE(t) = Div(t) + (BV (t) − BV (t − 1)), where E(t) is earnings available to common stockholders, RE(t) is the retained earnings and BV (t) is the book value of equity, all observed at time t and expressed on a per share basis. In keeping with currently accepted accounting practice, e.g., Bernstein (1989, p. 747), the clean surplus equation requires that all items involving gain or loss in income are accounted for in the period in which these items occur. In effect, E(t) is either paid out in dividends or is retained earnings and accounted for by changing the book value of equity. Though there are some accounting qualifications to this condition, the clean surplus equation is sufficient detail for purposes of equity security valuation. Letting b represent the dividend payout ratio (Div(t)/E(t)), i.e., b E(t) = Div(t), substituting this result into the Gordon growth model produces the simplified DDM P/E ratio: P (0) =

b E(0)(1 + g) P (0) b(1 + g) b E(1) = −→ = k−g k−g E(0) k−g

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The common practice of using the ‘forward’ P/E ratio (P (0)/E(1)) to measure the earnings multiple eliminates the (1 + g) term in the numerator. Taking the dividend payout ratio to be fixed over time produces: D(t + 1) = b E(t + 1) = b E(t)(1 + g) → E(t + 1) = E(t)(1 + g). In words, with a constant dividend payout ratio, the constant growth in dividends assumption translates into an assumption about the constant growth in earnings. To derive the price to book ratio involves observing that (E(t)/BV (t − 1)) = ROE (t), where ROE(t) is the return on equiyt at time t. (Though it is more conventional to use BV(t) in defining ROE(t), this definition will not be used here.) Making the appropriate substitution produces the simplified DDM P/BV ratio: E(1) b BV b ROE (1) P (0) (0) = = BV (0) k−g k−g

It follows that the price to book value ratio will depend on the dividend payout ratio, the ROE, the expected return on the stock and the growth rate in earnings. 4.2.2

Abnormal Earnings and Other Models

The failure of discounted dividend models, such as the Gordon model, to value most common stocks was not lost on accounting researchers (Lee 1999; Jiang and Lee 2005). From an accounting perspective, the dividend discount model is relatively naive as it ignores the variety of inter-relationships between accounting numbers that follow from the clean surplus relationship. As such, dividends in the clean surplus equation include not only conventional cash dividends but also other forms of cash payouts to shareholders (e.g., share repurchases, acquisitions). It is conventional for studies of the dividend discount model to use actual cash dividends paid, ignoring other forms of payments from earnings to shareholders. A number of different variations on the DCF model can be derived.7 Ohlson (1991, 1995) and 7 The

convention in accounting is to make a distinction between valuation methods that involve ‘cash flows’ and ‘accruals’. Using this distinction, discounted cash flow (DCF) techniques refer only to valuation methods that discount ‘cash flows’ such as free cash flow or dividends. Valuation methods such as the residual income method, which use accrual numbers, are not considered to be DCF techniques, e.g., Penman and Sougiannis (1998). While this distinction is useful in accounting studies, it is terminological overkill when the primary objective is discussing the valuation of equity securities. The operative cash flow in the residual income model, i.e., accounting earnings/net income, can be viewed either as a proxy for a cash flow or taken to be an accounting cash flow. In both cases,

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Feltham and Ohlson (1995) popularized the application of the clean surplus relationship, BV (t) = BV (t − 1) + E(t) − D(t) into the abnormal earnings form of the DCF model (English 2001, pp. 334–335):8 P (0) =

∞ ∞   D(t) E(t) − ∆BV (t) = t (1 + k) (1 + k)t t=1 t=1

= BV (0) +

∞  (ROE (t) − k) BV (t − 1) t=1

(1 + k)t

= BV (0) +

∞  AE (t) (1 + k)t t=1

where AE (t) = (ROE (t) − k)BV (t − 1) is the ‘abnormal earnings’ attributable to equity in period t and BV is expressed on a per share basis. A number of different titles have been given to the abnormal earnings model. Ritter and Warr (2002, p. 36) refer to this form the DCF model as the ‘residual income model ’ while Penman (2001, chap. 6) uses ‘residual earnings model ’.9 Ritter and Warr make numerous adjustments to the model to account for the impact of inflation and the use of accounting accruals. Dechow et al. (1999) and Callen and Segal (2004) provide a detailed examination of this model while Penman and Sougiannis (1998) compares this DCF model with the free cash flow and dividend discount variants. This formula has intuitive appeal because it relates the current price to the initial value of capital raised, reflected in BV(0) adjusted for the ability of the firm to earn more (or less) on invested capital (ROE) than the cost of maintaining the capital stock, as reflected in k. This formulation captures the idea that securities with superior investment potential create wealth (ROE > k) as opposed to destroying wealth (ROE < k). In practical applications it is often useful to work with the simplified residual income model, which corresponds to the Gordon growth model for discounted dividend valuation. One version of this model follows a cash flow is being discounted and the residual income model can be viewed as a DCF technique. This interpretation is used in what follows. 8 Similar to the discounted dividend model, there is a transversality condition on the convergence of book value in the limit that needs to be satisfied for the progressive substitution to have a unique solution. Jiang and Lee (2005) provide more detail on the derivation. 9 Elements of the residual income model can be found in early work by Preinreich (1938) and Edwards and Bell (1961). More recently, Peasnell (1981, 1982) made useful contributions. The more recent popularity of the residual income model is primarily due to its formalization by Ohlson (1991, 1995) and Feltham and Ohlson (1995) (see also Lee 1999).

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from manipulation of the DDM following substitution of the clean surplus equation: P (0) = =

P (1) + E(1) − ∆ BV (1) P (1) + D(1) = 1+k 1+k P (1) + E(1) − gB (1) BV (0) 1+k

ROE (1) − gB (1) → P (0) = BV (0) k−g

where gB corresponds to the growth in book value: BV (t + 1) = BV (t)(1 + gB (t + 1)). This formula captures the theoretical connection between the growth in earnings and the growth in book value. More precisely, except in special cases, both ROE and gB will be different and will vary over time. To see the connection between ROE and gB consider the following example: Initial values at t = 0: BV(0) = 100 g = 10% b = 0.6 At t = 1 : E(1) = 10 → D(1) = 6 RE (1) = 4 = ∆BV = BV (1) − BV (0) → BV (1) = 104 ROE (1) = E(1)/BV (0) = 10/100 = 10% gB (1) = ∆BV (1)/ BV (0) = 4/100 = 4% At t = 2 : E(2) = E(1)(1 + g) = 10(1 + g) = 11 D(2) = 6.6 RE (2) = 4.4 → BV (2) = 108.4 ROE (2) = E(2)/BV (1) = 11/104 = 10.58% gB (2) = ∆BV (2)/ BV (1) = 4.4/104 = 4.23% At t = 3 : E(3) = E(2)(1 + g) = 11(1 + g) = 12.1 D(3) = 7.26 RE (3) = 4.84 → BV (3) = 113.24 ROE (3) = E(3)/BV (2) = 12.1/108.4 gB (3) = ∆BV (3)/ BV (2) = 4.84/108.4 = 4.47%

=

11.16%

When the defined growth rate for earnings, g, is fixed and b > 0, this imposes a time path where earnings growth will exceed the growth in book value. It follows that the ROE (t) = {E(t)/BV (t − 1)} has to increase over time. The theoretical relationship for the growth in book values can be specified as RE (1) = (1 − b)E(1) = ∆BV (1) = gB (1)BV (0) → gB (1) = (1 − b)ROE (1) = (1 − b)

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(1 − b)(1 + g)E(1) (1 − b)E(2) 1+g = → gB (2) = gB (1) BV (1) (1 + gB (1))BV (0) 1 + gB (1)

Using the numbers from the example above 4.23% = {(1.1)(0.04)}/(1.04), which illustrates the evolution of the growth rate of book value. The simplified residual income model follows: E(2) gB (1)BV (0) gB (2)BV (1) E(1) + − + ··· − − ··· 1 + k (1 + k)2 1+k (1 + k)2  1+g gB (1) E(1) 1+gB (1) gB (1)(1 + gB (1)) − + = + 75 · · · BV (0) k−g 1+k (1 + k)2

P (0) =

Cancelling the powers of (1+gB ) gives the simplified residual income model:



b ROE (1) ROE (1) − gB (1) = BV (0) P (0) = BV (0) = k−g k−g For complete dividend payout, b = 1, this equals the Gordon growth model. Just as in the Gordon model, the result depends on a constant dividend payout. A useful manipulation of the abnormal earnings model follows from making a substitution for the dividend payout ratio, b, using the clean surplus relationship: D(t) = b E(t) = E(t)−(BV (t)−BV (t−1)). Observing that constant growth in dividends with a constant dividend payout gives BV (t) = (1 + g)BV (t − 1), it follows (English 2001, pp. 353–354):

g k BV (t − 1) E(t) − gBV (t − 1) =1− b= E(t) k E(t) Recalling that the definition for AE (t) requires, k BV (t−1) = E(t)−AE(t), the expression for b can be manipulated to get: 

 1 AE (t) b= k−g+g k E(t) Substituting this result into the P/E ratio expression associated with the Gordon growth model produces the abnormal earnings form of the P/E ratio:



  P (0) 1+g AE (1) g = 1+ E(0) k E(1) k−g Compared to the simple Gordon growth model formulation of the P/E ratio, by making the connection between P/E and the ability to generate ‘abnormal earnings’ this formulation is more revealing.

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Following Jiang and Lee (2005), the abnormal earnings model has a number of advantages over the DDM in estimating stock values. In particular, while the dividend process is too smooth to explain volatile stock prices, earnings and book value are considerably more volatile than dividends and, as such, have greater potential for explaining stock prices. Another more practical rationale for the abnormal earnings model is that, for many stocks, companies do not pay dividends significantly complicating application of the DDM. The earnings and book value inputs to the abnormal earnings model are both available even though dividends are not. Similarly, the abnormal earnings model makes direct use of the clean surplus accounting relationship while the ‘dividends’ used in the DDM are usually too narrow to be consistent. This lack of conceptual consistency extends to the interpretation of ‘dividend irrelvance’: “dividend policy irrelvance integrates naturally into the [abnormal earnings model]. The key is that dividends are paid out of book value but not out of current earnings. That is, residual income is invariant to changes in dividend policy” (Jiang and Lee 2005, p. 1468). Dividends and Share Repurchases Recognition of the clean surplus relationship led to empirical studies on the properties of ‘broad dividends’, effectively cash dividends and share repurchases. To this end, there are numerous studies of ‘narrow dividends’ that document an overall decline in aggregate dividend payout ratios since the 1950’s, marked by periods of persistence where the dividend payout ratio is relatively constant. This declining importance of dividends has been parallelled by an increasing importance of share repurchases. For example, using a sample of all industrial firms listed on the Compustat database, Jagannathan et al. (2000) find that from 1985 to 1996 the number of open market repurchase program announcements by U.S. industrial firms increased 650% from 115 to 755, with an announced value increase of 750% from $15.4 billion to $113 billion. Over the same period, dividends increased by a factor of just over two with aggregate dividends rising from $67.6 billion to $141.7 billion. Grullon and Michaely (2002), report an increase in the value of share repurchases from $1.5 billion to $194.2 billion over a 1972 and 2000 sample while dividends only rose from $17.6 billion to $171.7 billion. The study of share repurchases has progressed considerably as more and more firms have adopted this method of returning cash to shareholders, e.g., Stephens and Weisbach (1998), Jagannathan et al. (2000), Kahle (2002),

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Fig. 4.4 U.S. Dividend Payers, CRSP sample, 1926–1999. The number of CRSP firms in different dividend groups.

Note: The CRSP sample includes NYSE, AMEX, and NASDAQ securities with share codes of 10 or 11. A firm must have market equity data (price and shares outstanding for December of year t to be in the sample for that year. We exclude utilities (SIC codes 4,900-4,949) and financial firms (SIC codes 6,000–6,999). Payers pay dividends in year t: non-payers do not. The two subgroups of non-payers do not. The two subgroups of non-payers are firms (firms that do not pay in year t but did pay in a previous year). Source: Fama and French (2005, Fig. 1,p. 7).

and Lee and Rui (2007). At the time of the seminal work on corporate dividend policy by Lintner (1956), it was acceptable for corporate income to be effectively distributed among dividends, retained earnings, and taxes. Stock repurchases were not a practical part of the mix. But times have changed and, from the significant number of recent studies, a number of stylized facts have emerged. In particular, share repurchases and dividends are used at different times and by different types of firms. While dividends are typically paid by firms with a higher level of ‘permanent’ operating cash flows, firms using share repurchases tend to have higher ‘temporary’, non-operating cash flows. Both the cash flows and distributions from repurchasing firms tend to be substantially more volatile.

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Against this backdrop of increased usage of share repurchases, Ferris et al. (2009) examine the number of firms paying dividends in 1994 and 2007 for a sample of 25 countries and examine the global decrease in the percentage of firms that are dividend payers. Combined with the more detailed results in Fama and French (2001) on U.S. dividend payers for a 1926–1999 sample (see Fig. 4.4), some key developments are apparent. Recognizing that there has been a significant increase in the total number of firms over the period, the percentage of firms paying dividends has fallen over 30% in common law countries from 74% to 43% between 1994 and 2007, with a more modest reduction of 8% from 70% to 62% for civil law countries.10 The aggregate common law result brings these countries closer in line with the United States which saw dividend payers fall from 36% to 25%. Following a period in the 1970’s when the payers exceeded nonpayers, since 1980 the number of dividend non-payers in the United States has increasingly exceeded payers. The civil law countries, which include European firms other than those in the United Kingdom and Ireland and the important emerging markets of China and Brazil, even saw some increases in the percentage of dividend payers in smaller European countries such as Spain and Finland. The percentage of dividend paying firms in Germany fell from 71% to 46%, while the important sample of Japanese firms fell only from 88% to 86%. Given the secular decline in the importance of cash dividend payout relative to share repurchase programs, details on share repurchase activity increasingly assumes importance. For example, various studies observe that the increases in stock repurchases have been pro-cyclical. Examining the ongoing process of corporations substituting share repurchases for dividends, Grullon and Michaely (2002) provide evidence that firms are not simply cutting dividends and replacing them with repurchases. Rather, large dividend-paying firms are repurchasing stocks rather than increasing dividends, and that much of the growth in popularity of share repurchases is due to large dividend-paying firms. They report that although the dividend payout ratio of U.S. companies has been declining since the mid-1980s, the total payout ratio has remained more or less constant, which suggests that corporations have been substituting repurchases

10 Common law countries include the important equity markets of: Australia, Canada, Hong Kong, Malaysia, Singapore, South Africa, United Kingdom, and the United States. The civil law countries include the important markets of: France, Germany, Italy, Japan, Spain, Sweden, and Switzerland.

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for dividends. They also show the average dividend payout ratio fell from 22.3% in 1974 to 13.8% in 1998, while the average repurchase payout ratio increased from 3.7% to 13.6% during the same period. The connection of dividend payments with permanent cash flow and share repurchases with temporary, non-operating cash flows fits well with the traditional theory of dividends that originates with Lintner (1956). Based on a survey of corporate managers about the most important factors influencing dividend policy, Lintner found that the most important determinant of a change in the dividend payment is a change in company earnings that results in a dividend that is out of line with the firm’s target payout ratio. Firms seek to make only partial adjustments in the actual payout ratio toward the target payout ratio and are strongly averse to cutting the regular cash dividend payment. Hence, managers smooth dividends in the short run to prevent fluctuations in the dividend cash flow to shareholders. Lintner’s partial adjustment model for dividends can be formalized as: D(t) = D(t − 1) + λ(D∗ (t) − D(t − 1)) where λ ε[0, 1] is the speed of adjustment coefficient and D∗ (t) is the target dividend payment. The Lintner model of dividend payment behaviour has a number of testable hypotheses. One testable implication is that dividend decreases will be relatively rare and only be associated with historically poor performance. Similarly, following dividend decreases (increases), the bad (good) operating performance of the firm will continue. In more recent studies, this hypothesis has been formulated along the lines that dividend increases will be related to the permanent component of cash flow and not to the ‘temporary’ component of cash flows. Another implication of the Lintner model is that, due to the need for higher and more stable cash flows, dividend-paying firms will be larger than non-dividend paying firms. Strong empirical support for the Lintner model, in one form or another, has continued from the early cross-sectional work by Fama and Babiak (1968) to the recent survey work of Benartzi et al. (1997) and Baker et al. (2001). The aversion of firms to cutting dividends is understandable given the significantly negative stock market reaction to dividend cuts, e.g., Ghosh and Woolridge (1988) and Denis et al. (1994) both report an average stock price decline of about 6% on the three days surrounding the announcement of a dividend cut. This punitive market response to dividend decreases has been identified as an argument in favour of share repurchase programs where there is no commitment to initiate a new repurchase program when the old program expires. As such, stock repurchases are a sensible way for firms to pay out ‘temporary’ cash flows that have a high likelihood of

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not being sustainable. The typically favourable investor tax treatment for capital gains over dividend income is another argument in favour of share repurchases. The arguments in favour of share repurchases are so compelling that Black (1976) coined ‘the dividend puzzle’, e.g., Crockett and Friend (1988), Christie (1990), and Frankfurter (1999): why do firms use dividends to distribute corporate income and investors prefer this form of distribution when dividends are subject to double taxation? In the United States, the dividend puzzle has been largely resolved by the evolution of firm dividend policy. For example, Fama and French (2001) find that the percentage of firms paying cash dividends fell from 66.5% in 1978 to 20.7% in 1998 What has emerged more then three decades after Black introduced the dividend puzzle is that there is considerable heterogeneity in the dividend policy decision. This is particularly true if the scope of discussion includes international firms. Truong and Heaney (2007, p. 684, Table 3) demonstrate the importance across firms and countries of corporate ownership composition, particularly the presence of a large shareholder or shareholder group, to the determination of dividend policy. While not as significant an issue with U.S. stocks, in the Truong and Heaney sample of over 8000 firms from 37 countries, at least 50% of the firms had one shareholder or a shareholder group owning at least 25% of the equity in the firm, with the largest shareholder owning, on average, more than 30% of total voting shares. The PEG Ratio and Other Models The relationship between the P/E ratio and growth of the firm is a subject that receives attention in almost every introductory investments textbook, e.g., Bodie et al. (1999). The conventional starting point is the ‘present value of growth opportunities’ (PVGO) formulation of the P/E ratio. The simplifying, if somewhat confusing, assumption is made that there is benchmark ‘firm’ that is able to generate a constant stream of earnings into perpetuity that are fully paid out to common shareholders, i.e., b = 1. The value of this firm would be P (0)∗ = E(1)/k. The definition of the PVGO reflected in the stock price for any given firm follows appropriately as: P (0) = P (0)∗ + PVGO. Expressed as a P/E ratio, this formulation is: (P (0)/E(1)) = (1/k)[1 + (PVGO /P (0)∗ )]. Hence, the P/E ratio will be higher for firms with higher growth opportunities. Within this framework, it can be shown that g = ROE (1−b). Substituting into the Gordon growth model P/E ratio gives: (P (0)/E(1)) = (b/{k − (1 − b)(ROE)}). In this case, firms with higher ROE, which reflects growth opportunities,

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will have a higher P/E ratio. If accurate, these types of formulas would provide precise information about the relationship between P/E and growth opportunities. One application of the different formulas for the P/E ratio is to illustrate the behavior of the ‘PEG’ ratio, or P/E to growth rate ratio. This ratio is sometimes used as a crude rule of thumb to determine under/over valuation for a common stock. For example, a PEG rule could be formulated as: if the PEG ratio is less than one then the stock is undervalued because the ‘cost of growth’ as measured by the P/E is less than the actual growth. The AE form of the P/E can be used to show that this rule is difficult to apply in practice, even when simplifying assumptions are made, i.e.:   PEG 1 1 + g 1 + g AE (1) 1 P (0) = = + 100g E(0) 100 100 kg k E(1) k − g Scaling by 100 follows from recognizing that the PEG rule assumes the growth rate is expressed as a percentage whole number. It follows that if AE (1) = 0 because, say, the firm is in ‘competitive equilibrium’, then if k = g = 0.1 the PEG rule will be approximately correct. However, if k = g = 0.05, then the PEG will equal 4. Even without examining cases where AE (1) = 0, the PEG ratio rule can be seen to have significant limitations. There is not complete agreement about: what is to be considered a DCF model? To the capital budgeting purists, a DCF model discounts the net cash flows. In this case, the variable being discounted is cash flow and is to be interpreted in a cash accounting sense. Assuming that the only cash payments received by the buy-and-hold common stock investor are dividends, an assumption which ignores share repurchases, leads to the discounted dividend model and its variants, such as the Gordon model. As illustrated, it is possible to expand the DCF universe to include cash flows that involve accrual accounting numbers, as in the residual income models. At some point, a boundary is crossed and traditional manipulations of GAAP numbers no longer can capture the type of cash flow required. For example, use of unadjusted earnings is problematic in the valuation of REITs as GAAP accounting involves a number of non-cash expenses, such as depreciation and amortization, that make little sense where the value of the assets is usually appreciating. As a consequence, REIT associations, such as REALPAC in Canada and NAREIT in the United States, recommend the use of ‘funds from operations’ as the appropriate cash flow measures for firms in the REI industry.

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Instead of starting with available accounting numbers to determine relevant cash flow numbers, it is possible to start with the characteristics of the desired cash flow and work backward to assemble a useful proxy from the accounting numbers. This is the basis of the ‘economic free cash flow’ model proposed by Warren Buffett. In its purest form,the appropriate variable to discount is economic profit — the net payment to invested capital after allowance for the economic cost of factors expended in the production process, including the opportunity cost of investment capital. In accrual form, this is the basis of the abnormal earnings model. However, there is a heterogeneity in the amount and type of distortion in the relationship between ‘true economic value’ and the reported accrual value. Recognizing that economic profit cannot be observed directly, the analytical problem is to fashion a proxy from available accounting numbers, using a combination of accrual and cash flow accounting. The most widely used proxy for economic profit is ‘free cash flow’. Being a non-GAAP number, there is no standardized definition currently in use. Examining a sample of U.S. firms that voluntarily report free cash flow (FCF) information in 10-Q and 10-K filings, Adhikari and Duru (2006) find cash flow from operations-based — as opposed to net income-based — definitions of FCF are most commonly used. Within the group of firms reporting CFO-based FCF, Adhikari and Duru were able to identify seven different types of adjustments made to arrive at the reported FCF number. Compared to a matched sample of non-disclosing firms; firms disclosing FCF estimates tended to be less profitable; more leveraged; have lower credit ratings and higher dividend payout. Even for firms that view FCF as an important enough non-GAAP number to warrant reporting in the annual SEC filings, FCF definitions vary widely. While this does limit the immediate comparability of FCF disclosures across firms, it also reflects the difficulties in arriving at a specific measure of economic profit. For purposes of valuing common stock using free cash flow, the relevant pricing model is the free cash flow to equity model While seeking to provide a more representative cash flow measure, there is conflicting academic evidence on whether these techniques are successful at achieving that objective. The free cash flow to equity model (FCFE) aims to measure the return to equity above the amount required to maintain existing production levels; or, alternatively, to keep the firm on a particular growth path. To derive the FCFE DCF model, observe that the cash flow in this case is free cash flow to the firm, adjusted for net debt payments. Discounting of these

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cash flows leads to the general and simplified forms of the FCFE DCF model : ∞  FCFE (t) FCFE (1) → P (0) = P (0) = t (1 + k) k − gf t=1 where FCFE (t) is expressed on a per share basis and gf is the expected growth rate in free cash flow. Recognizing that constant growth in dividends with a constant dividend payout does not ensure that FCFE will also grow at the same rate, it is possible to assume that FCFE grows at a constant rate gf such that FCFE (t) = FCFE (t−1)(1+gf ), this produces the simplified free cash flow valuation model: P (0) = {FCFE ∗ (0)(1 + gf )}/{k − gf }. While it may be possible to assume g = gf under certain assumptions, given the higher relative variability in free cash flow, this is an unlikely situation. There is a fundamental difficulty with using FCF to measure the ‘true cash flow’ or economic profit. There is no assurance that the cash amount spent on capital expenditures in a given period and the amount required to keep the firm on the assumed growth path will be the same. It is not even clear which items to include in the capital expenditure item. Room for improvement is indicated. The search for a measure of economic profit is not restricted to its uses in the valuation of equity securities. In particular, the management consulting industry is fundamentally concerned with corporate performance measurement for purposes such as setting executive compensation levels. To this end, Stern Stewart Management Services introduced the economic value added (EVA) measure (Stewart 1991). The EVA approach is conceptually the same as measures proposed by a number of other major management companies, such as the ‘Economic Profit Model’ of McKinsey & Company (Copeland et al. 1996). EVA-type models require a large number of possible adjustments; in the case of EVA more than 250 adjustments to accounting information are possible, though no more than 15 adjustments are usually of material significance (Bacidore et al. 1997). As described by Copeland et al. (1996, pp. 149, 150), the economic profit model and EVA-type models are an advance over DCF valuation using FCF because these measures can be used for understanding a company’s performance in any single year, while free cash flow fluctuates too much to be useful. For example, tracking a company’s progress by comparing actual and projected free cash flow, is too difficult because free cash flow in any year is determined by highly discretionary investments in fixed

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assets and working capital. Management delays or accelerates investments for various reasons. To target free cash flow in a given year at the expense of long term value creation is problematic. The basic idea behind the EVAtype models is that a company is worth more or less than its invested capital only to the extent that it earns more or less than its weighted average cost of capital. So the premium or discount relative to invested capital must equal the present value of the company’s future economic profit. For purposes of equity valuation, the logic of the EVA-types models raises the question: are these approaches as superior to other DCF approaches and other valuation techniques as the proponents claim? Unfortunately, the promise of superior performance for EVA as a security analysis tool compared to traditional measures such as net income does not have much empirical support. For example, Clinton and Chen (1998) found that other traditional accounting measures, such as P/E, EPS and ROA, tracked stock returns more reliably than EVA. More recently, Cordeiro and Kent (2001) considered whether analysts that adopted EVA outperformed other analysts in forecasting future EPS and found “no significant relationship between EVA adoption and security analyst forecasts of future firm EPS performance”. Biddle et al. (1997, 1998) find similar results. For example, Biddle et al. (1997) conclude: “earnings [are] more highly associated with returns and firm values than EVA, residual income, or cash flow from operations. Incremental tests suggest that EVA components add only marginally to information content beyond earnings . . . these results do not support claims that EVA dominates earnings in relative information content, and suggest rather that earnings generally outperform EVA”. Similar results are reported by Kyriazis and Anastassis (2007).

4.2.3

Simplified Discounted Dividend Valuations

It is not too difficult to inspect the simplified DCF models of stock valuation, such as the Gordon growth model, and dismiss these models based on superficial analysis of the model structure. For example, without simplifying assumptions such as ‘constant growth’ the model is difficult to implement due to the larger number of terms that have to be estimated and calculated. Where the simplifying assumption of constant growth in dividends (earnings) is used, the empirical behaviour of dividends (earnings) does not support the assumption that dividends (earnings) grow at a constant rate over time. In addition, the market practice of low or no cash dividend payout would seem to argue against straight forward application of DCF

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models where the cash flows are defined as ‘narrow’ as opposed to ‘broad’ dividends. There are problems with obtaining estimates of k; there are problems with obtaining estimates of D(1), and so it goes. However, adherents to Friedman’s ‘positivist’ approach would argue it does not follow that just because the assumptions of a model seem impractical or unrealistic, that the model is necessarily invalid. Before dismissing the model out of hand, it would be appropriate to examine the performance of the model in practice. Strong advocates of the simplified DDM model, such as Damodaran (1994), explicitly recognize essential characteristics of firms required for the Gordon growth model to be used for screening companies in order to produce adequate valuations. Damodaran identifies a number of the essential characteristics: a firm growth rate that is comparable to or lower than the nominal growth in the economy; the firm has a readily identifiable dividend-payout policy that is expected to continue into the future; and, the dividend payout of the firm has to be consistent with the assumption of stability, since stable firms generally pay substantial dividends. Damodaran (1994, p. 103) optimistically estimates the average payout for large stable firms in the United States at about 60%. Large utilities, such as SW Bell, and high capitalization companies, such as Exxon, qualify as examples of a ‘large stable firm’. Dresdner Bank, a German company, is used as an example of a large stable foreign company. Calculating the Inputs There are many subtle features that have to be resolved to do a simplified DCF valuation using the Gordon growth model. Consider the cost of equity k. It is conventional to estimate k using a form of the capital asset pricing model (CAPM): ki = E[Ri ] = r + βi {E[RM ] − r}. To be operational this requires values for r, βi and E[RM ]. In portfolio management applications of the CAPM, it is conventional to use a short-term interest rate, such as the 3 month Treasury bill rate, for the riskless interest rate (r). The maturity of the Treasury bill would be equal to the rebalancing frequency of the portfolio. However, application of the CAPM to determining the stock price using the Gordon growth model poses a different problem for defining the riskless interest rate. Following Damodaran (1994), the riskless security is identified “by matching the duration of the riskfree security with the duration of the asset being analysed”. As a consequence, in the estimating the CAPM it is appropriate to use the longest maturity government bond available which, for the United States, is the 30 year Treasury bond.

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Another input required to use the CAPM is the risk premium on the market, {E[RM ] − r}, also known as the equity risk premium or equity premium. Some method is required to estimate this variable. Being an unobservable variable, it is difficult to determine the most appropriate procedure to estimate the expected return. However, the importance of the equity premium to modern Finance has generated a large number of studies attempting such an estimate (Oyefeso 2006). Using an 1889–1978 sample, Mehra and Prescott (1985) estimated an equity premium value of around 6% for US data and argued that the size of the ‘equilibrium’ equity risk premium was too large, marking the beginning of the ‘equity premium puzzle’ in modern Finance.11 If correct, this puzzle has to sort out whether expected returns are too high or the risk-free rate is too low (Weil 1989) or both. Unfortunately, there is a considerable lack of both a theoretical and empirical consensus about the equity premium, e.g., Kocherlakota (1996). As Pastor and Stambaugh (2001, p. 1207) observe: the equity premium remains “one of the most important but elusive quantities in finance”. What is the correct value to use for the equity premium in DDM valuations? Using Ibbotson Associates (1995) data, Brealey and Myers (1996), a widely used corporate finance textbook, reports an equity premium of between 8.2%–8.6% for the U.S. market in 1995. This value is at the extreme end of the range of empirical estimates. The original estimate of Mehra and Prescott (1985) examined the average annual yield on the Standard and Poors 500 Index and found this was seven per cent over the period 1889–1978. Using an average yield for short-term debt of less than one per cent, the average equity premium of 6% is achieved. This estimate is also high. For a 1870–1989 sample, Shiller (1989) suggests an average equity premium of 4.3% for the U.S. market. Expanding the search to international markets, using a 1985–1998 sample Claus and Thomas (2001) find equity premia as low as 3% for Canadian, French, German, Japanese, U.K. and U.S. stock markets. Similarly, Dimson et al. (2002) find the following equity risk premia over the entire 20th century: France 7.7%; Switzerland 4.3%; Denmark 2.8%; Canada 4.6%; Unietd Kingdom 4.9%; and United States 5.8%. In Damodaran (1994), the equity premium was estimated by using the difference of the annualized geometric means for the S&P Composite stock

11 This

is not to imply that the roots of the equity premium originate with Mehra and Prescott (1985). Such views can be found in Smith (1925) and, as demonstrated by Dimand (2007), were of interest of Irving Fisher.

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market index (10.08%) and the Treasury bond rate (4.58%) — values in brackets being the estimates over a 1926–1990 sample. The difference of 5.5% is used as the equity risk premium to estimate the cost of equity from the CAPM that, in turn, is used as the discount rate (k) in the Gordon model. As discussed in Sec. 1.2.1, the difference of the geometric means is smaller than the difference of the arithmetic means (12.13% − 4.90% = 7.23%). The rationale for this choice is stated as: “where cash flows over a long time horizon are discounted back to the present, the geometric mean provides a better estimate of the risk premium” (p. 22). Consistency would appear to require that geometric averages be used to estimate g but, despite recognition of this point, an arithmetic average is often used, e.g., Damodaran (1994, p. 68). A search for the ‘best practices’ approach to implementing the Damodaran’s Six DCF Valuation Myths Damodaran (1994, simplified DCF models leads to pp. 2–4) Damodaran (1994) where the implementation of the Gordon model and To be taken into account when assessing the validity of the DCF other types of DCF models reaches technique. These myths are: a relatively sophisticated stage of 12 evolution. Aswath Damodaran is a “Since valuation models are quantitative, valuation is objective”. professor at the Stern School of Business at New York University (NYU) “A well-researched and well-done specializing in executive education valuation is timeless”. and the author of a number of books “A good valuation provides a prealong these lines. Given the justcise estimate of value”. around-the-corner proximity of the “The more quantitative a model, NYU business school campus to Wall the better the valuation”. Street, it is likely than many individ“The market is generally wrong”. uals in the New York financial community have been directly exposed “The product of a valuation — to these ideas and have used, or the value — is what matters, the attempted to use, the models in pracgeneral process of valuation is not tical situations. Damodaran (1994) important”. goes carefully over the appropriate 12 Damodaran

(1994) is of interest because of the intensive examination of the discounted dividend approach to DCF valuation. As such, Damodaran differs from other sources in the depth of coverage. Useful textbook level overviews of the different approaches to DCF analysis are available in a number of sources, e.g., Palepu et al. (2000) and Weston et al. (2001).

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procedures for estimating the discount rate, the cash flows and the growth rates. This background is then used to implement the dividend discount model and the free-cash-flow-to-equity discount model. Valuation results are provided for the common stocks of the firm types where the DCF model would be most likely to work. Example 1: Exxon Damodaran (1994) illustrates the use of the DDM for Exxon (now XOM), a large stable firm that is not a utility. The following information is provided in the valuation: Exxon: Valuation date May 1993 Common Stock Price: $65.00 1992 earnings per share: $3.82 (% of earnings paid out as dividends 74%) 1992 Dividend : ($3.82)(0.74) = $2.83 Earnings and dividend growth: 6% a year between 1988 and 1992 (expected to grow at same rate in long term) Beta for Stock : 0.75 30 year T-Bond rate: 7% Cost of equity = 7% + 0.75 × 5.5% = 11.13% Value of equity per share = 2.83 × 1.06/(0.1113 − 0.06) = $58.47. The estimated value and the observed stock price are sufficiently close according to Damodaran, indicating that considerable pricing slippage is expected even when the DDM valuation is useful. Damodaran (1994) does not clarify whether Exxon was selected more-or-less at random from the available group of ‘large stable non-utility’ firms, or whether Exxon was selected because the Gordon growth model produced the most plausible price estimate from a group of such estimates. The choice of Exxon as an example of a large stable firm suitable for application of the Gordon growth model seems misplaced because of the sensitivity of Exxon’s earnings to developments in the oil sector. Poitras (2005, p. 241) provides an updated DDM valuation of Exxon, now Exxon-Mobil (XOM), for March 2003. The beta was relatively unchanged at 0.91 but the long Treasury bond rate had fallen to 5.375%. Solving for the cost of equity using the 5.5% long-run risk premium on the market gives: 10.38% = 5.375% + 0.91(0.055). Observing that for 2000–2003 dividends increased from 0.83 to 0.88 to 0.91 cents per share

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Fig. 4.5

363

XOM Ten-year chart, February 1997–February 2007.

(2.68% dividend yield in 2003), gives a growth rate of g = 4.4%. Dividend growth is used in favour of the more variable earnings growth. Using earnings over the three years, the dividend payout is less than 50%. Evaluating the Gordon growth model estimate of the price of the stock gives: (0.91)(1.044)/(0.1038 − 0.044) = 15.89. This does not compare favorably to the observed stock price of $34.37. Raising the growth rate to 5.4% (or lowering the market risk premium by 1/0.91%) only raises the price estimate to $19.08. Solving for the growth rate that is consistent with the observed price gives g = 7.7%. As evidenced in Figs. 4.5–4.6, the DDM did not perform well in predicting the future price movement of XOM. The evidence of substantial overvaluation in March 2003 is brutally denied by the remarkable 237% increase the stock price had achieved by February of 2008. Similarly, the 1994 assessment that the stock was fairly valued failed to miss a doubling of the stock price over a similar future interval. This is unfortunate because it would be difficult to find a more stylized example of a large, stable company. Formed in November 1999 by the merger of Exxon and Mobil, ExxonMobil (XOM)

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Fig. 4.6

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XOM snapshot (08 February 2008). Source: www.globeinvestor.com

is the world’s largest company by revenue (US$404.5 billion for 2007); by market capitalization (US$517.92 billion on 20 July 2007); and the most profitable, posting the largest annual profit by a U.S. company (US$40.6 billion) with a record quarterly net income for Q4 of 2007 ($11.7 billion). Due primarily to the dramatic increase in oil prices from 2003–2008 g > k for XOM, illustrating the difficulties of applying the DDM to companies where the future cash flows depend substantially on commodity prices — in the case of XOM, the price of crude oil. Example 2: SBC/ATT The original Gordon model (Gordon 1962) was developed for valuation of companies in regulated industries. At that time, these types of companies

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Fig. 4.7

365

S&P 500 1993–2007.

included telephones and public utilities. The regulation of rates provided these companies with stable and relatively predictable cash flows. With this historical application in mind, a more modern application of the Gordon growth model to Southwestern Bell is illustrated in the procedure followed by Damodaran (1994): Southwestern bell : Valuation Date: May 1993 Common stock price: $78.00 1992 earnings per share: $4.33 (% of earnings paid out as dividends: 63%) 1992 dividend: ($4.33)(0.63) = $2.73 Earnings and dividend growth: 6% a year between 1988 and 1992 (expected to grow at the same rate in the long term) Beta for the stock : 0.95. 30 year T-bond rate: 7% Cost of equity = 7% + 0.95 × 5.5% = 12.23% Value of equity = $2.73 × 1.06/(0.1223 − 0.06) = $46.45

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It is also possible to take the stock price as given, in this case $78.00, and to solve for g from the Gordon model as 8.43% (Damodaran 1994, p. 103). This is interpreted as the expected growth rate embedded in the current price which is 2.43% higher than the estimated historical growth rate. Updating the Damodaran (1994) valuation for Southwestern Bell is complicated. The world of regulated utilities that followed the breakup of AT&T in 1984, found one of the ‘baby bells’, Southwestern Bell Telephone Company, being managed by Southwestern Bell Corporation (SBC). In 1995, SBC decided to change its corporate name to SBC Communications, Inc. and aided by passage of the Telecommunications Act of 1996, proceed to acquire Pacific Telesis Group in 1997, Southern New England Telecommunications in 1998, and Ameritech in 1999. By 2002, SBC had integrated all the operating companies, and ‘SBC’ emerged as a national telecommunications brand. On 18 November 2005, SBC Communications merged with AT&T Corp. and changed its name to AT&T Inc. The period from the breakup of AT&T to the reintegration of SBC and AT&T was marked by remarkable technological and regulatory changes in the telecommunications industry. The stable, regulated hard line business has been replaced by a sometimes fiercely competitive jungle of alternative technologies and sophisticated consumers. The inability to accurately determine model inputs makes application of the DDM impractical in this case. Valuing Foreign Stocks How does Damodaran use the Gordon growth model to value a foreign stock? As another case of a ‘stable large firm’, Damodaran (1994, p. 105) selects what was at the time the second largest German bank, Dresdner Bank. Dresdner bank : Valuation Date: July 1993 Common stock price: 408 DM 1992 earnings per share: 34.05 DM (% of earnings paid out as dividends: 47.6%) 1992 dividend: (34.05)(0.476) = 16.21 DM Earnings and dividend growth: 5% a year between 1983 and 1992 (expected to grow at the same rate in the long term) Beta for the stock : 0.87. 10 year German bond rate: 6.42%

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Before the cost of equity can be calculated, a number of issues need to be addressed. In particular, the equity risk premium for a German stock cannot be measured relative to a U.S. stock market index. A German index is required. To this end, Damodaran uses 3.5% as the risk premium for the German DAX stock index over bonds. It follows Cost of equity = 6.42% + (0.87 × 3.5%) = 9.45% Value of equity per share = 16.21DM × 1.05/(0.0945 − 0.05) = 383.01DM Similar to the Exxon and SW Bell estimates, Damodaran obtains a relatively close estimate of the observed stock price for Dresdner using the Gordon growth model. No attention is given to substantive problems such as determining the U.S.$ return or reconciling the need to use different equity premia in an internationally diversified portfolio. Damodaran’s favorable, if relatively limited, application of the discounted dividend model to specific stocks is supported by Sorensen and Williamson (1985) which provides an ex ante application of the dividend discount model to 150 stocks in the S&P Composite Index. Valuation using a form of the dividend discount model was done in December 1980 and the stocks were held for two years with the result that stocks identified as ‘undervalued’ significantly outperformed ‘overvalued’ stocks. Further evidence in support of using the dividend discount model to identify undervalued stocks is provided by Haugen (1990) which examines the 1979–1991 performance of a fund that used the dividend discount model to select undervalued stocks. Over the 1979–1991 period, the quintile of stocks judged by the fund to be most undervalued using the dividend discount model outperformed the most overvalued by 1253% to 434%. Damodaran (1994, p. 124) concludes: “The dividend discount model outperforms the market over five-year time periods, but there have been individual years when the model has significantly underperformed the market”. This empirical evidence in favour of the dividend discount model can be contrasted with the mountain of unfavourable evidence provided by the studies on rational and intrinsic bubbles. A resolution of the seeming conflict between these disparate results can be found in Williams (1938, p. viii): “the present worth of future dividends, [is] of practical importance to every investor because it is the critical value above which he cannot go on buying or holding, without added risk”. Studies of bubbles typically track the ability of aggregate dividends to explain aggregate stock prices and find that dividends do a poor job. Advocates of the dividend discount

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model depend on this result and use fluctuations in the pricing relationship to determine trading opportunities in individual equity securities. The properties of aggregate stock prices during periods of bubble behaviour, which are central to empirical analysis of rational and intrinsic bubbles, are of limited interest to discounted dividend investors who would see most equities as grossly ‘over-valued’ during these periods. Ultimately, dividend discount models may perform well, not because the valuations are accurate, but because companies that pay stable and increasing dividends include many outstanding companies. Recognizing that dividends reduce the funds available for investment, it is logical that high dividend payout will be accompanied by weaker future earnings growth than for comparable firms that have lower dividend payout. Yet, cross-sectional studies on the relationship between dividend payout and future earnings growth show that high-dividend-payout companies tend to experience stronger, not weaker, earnings growth in the future. Zhou and Ruland (2006) find the positive association between dividend payout and future earnings growth to be “robust to alternative measures of payout and earnings, sample composition, mean reversion in earnings, the effects of particular industries, time periods, and share repurchase”.13 4.2.4

DCF Valuation of the COS Merger

A key observation of the ‘value investing’ or fundamental analysis approach is that the market value of a security can, at any time, differ from the ‘intrinsic value’ that reflects the appropriately discounted future cash flows. According to the value investing approach, the equity security price will eventually reflect intrinsic value creating a trading opportunity when the spread between intrinsic value and market price is sufficiently wide enough. A DCF valuation of Canadian Oil Sands Limited (COS) based on the COS share of the Syncrude project produces an estimate for the intrinsic value of the traded equity security (COS.UN). Such a valuation, done in 2000, was contained in the Joint Information Circular prepared for the 2001 merger of two trusts that were merged to form COS. As a closer inspection of this DCF valuation reveals that extending DCF valuation beyond the simply DDM case can be a challenging task even for a simple equity security valuation such as COS.UN. Significantly, the DCF valuation methodology relies on the estimation of a single DCF value or, in more sophisticated treatments, 13 See

chapter 8 for more details on Canadian Oil Sands Limited.

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an estimate of the mean of a unimodal distribution for the discounted cash flows is determined together with an estimate of the associated standard deviation. Valuation of a resource company such as COS depends fundamentally on the price that will be received for the commodity being produced at the time the commodity will be sold. Though the valuation process for a resource company is not theoretically complicated, considerable confusion is created by the relationship between the current price of the commodity and the equity security price of a resource company producing that commodity. For example, the runup in gold prices during 2002 was not accompanied by corresponding increases in the prices of the common stocks of gold mining companies such as Barrick Gold Corporation (ABX). Similarly, the DCF value for the COS share of the Syncrude project will depend on assumptions made about the impact of the future time path of the oil price on the equity security value (Fig. 4.8). What was the estimated DCF value of the COS share of the Syncrude project in 2000? Table 4.1 provides a summary of a DCF analysis for the value of the Syncrude project, with cash flows calculated before taxes, prepared by the reputable firm of Gilbert Laustsen Jung and Associates. The estimated reserves for the Syncrude project vary depending on whether proved (3.28 billion barrels), proved plus 50% probable (4.276 billion barrels) or proved plus probable (5.271 billion barrels) reserve

Fig. 4.8

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COS unit price 1999–2004.

Summary of DCF Valuation of Syncrude and COSL, 2000.

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Table 4.1 09:31:30.

Summary of Reserves and Present Value of Estimated Future Net Cash Flow Combined working interest Net after crown royalty (Mmbbls)

Present value of estimated future net cash flow before income taxes Undiscounted

10%

12%

15%

20%

($millions) 3,280 4,276 5,271

713 929 1.146

611 787 962

$10,368 13.769 17.171

$2,470 2,756 3,043

$2,063 2,208 2,353

$1,647 1,657 1,668

$1,233 1,130 1,027

3,280 4,276 5,271

713 929 1.146

604 781 958

$13,853 18.419 22.985

$3,807 4,466 5,124

$3,223 3,680 4,138

$2,603 2,861 3,119

$1,958 2,033 2,108

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Source: COS Management Information Circular, 2000.

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Escalated Prices and Costs Proved . . . . . . . . . . . . . . . . . . . . . Proved plus 50% probable . . Proved plus 50% probable . . Constant Prices and Costs Proved . . . . . . . . . . . . . . . . . . . . . Proved plus 50% probable . . Proved plus 50% probable . .

Gross reserves (Mmbbls)

Valuation of Equity Securities

Gross project reserves (Mmbbls)

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estimates are used. In Table 4.1, the COS share of these reserves is calculated at 21.7%. From this point the importance of various assumptions in the discounting calculation, such as future costs and oil prices, are apparent (see Table 4.2). Based on the approximately 57 million trust units outstanding from 1999–2002 (see Table 4.3), a value of about $19.50 per trust unit (= ($5.124 million) ∗ (21.7) ∗ (57 million)) is determined using constant prices and costs, with a 10% discount rate. Remembering that the DCF valuation was done in 2000 well prior to the 2001 merger date when unit prices were around $25, the most optimistic estimated DCF is consistent with unit prices at the beginning of 2000, a year when average unit prices were well over $30. Proponents of the relative value approach to security analysis argue that DCF analysis is impractical for ‘combat finance’ because the estimated intrinsic values are too dependent on assumptions. It is argued that, in the hustle and bustle of professional security analysis, it is impractical to spend significant amounts of time exploring and debating various assumptions that go into a DCF analysis when‘reasonable’ assumptions can become widly inaccurate as events unfold. Table 4.2 provides a useful illustration of this observation in the detailed assumptions made to provide the various DCF estimates in Table 4.1. For example, the constant price and costs case assumes a future SCO price of C$43.60 for Edmonton delivery. In addition to assuming zero inflation, the constant cost case also embeds implicit assumptions about the $US/$C exchange rate and spread between the U.S.$ WTI crude oil and SCO prices. Though not stated, an exchange rate of 0.645 produces a constant Edmonton SCO price into the future of about U.S.$28 (ignoring transport costs from the plant gate to Edmonton). In considering the usefulness of a particular DCF valuation, the process of preparing the valuation can have relevance. Confronted with a known traded market value for an equity security, DCF valuation can be an exercise in determining assumptions that support the current valuation. In effect, a DCF target is established and then assumptions are made to generate future cash flows consistent with that target. This is a possible explanation for the escalating prices and costs case in Table 4.1 where escalated prices and costs are not actually assumed. For example, the U.S.$ WTI price is assumed to fall from 2001–2004 and then rise thereafter. The U.S.$/C$ exchange rate is assumed to rise to 0.72 by 2008 and stay at that level thereafter, effectively U.S.$31.40 per barrel. All this leads to the question: were the DCF estimates of intrinsic value given in Table 4.1 useful for assessing whether the current market price of COS units is over or under valued? Subsequent

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Assumptions for 2000 COS DCF Valuation.

09:31:30.

The constant price assumptions reflects a reference posting for light sweet crude oil at Edmonton of $43.60 Cdn/bbl. zero inflation and an Alberta Reference Gas Price of $8.75 per MCF for natural gas. In the escalated price assumption evalution. the Gilbert Laustsen Jung 1 April 2001 price forecast was used: Exchange rate $U.S./$Cdn

West Texas intermediate at cushing U.S.$/bbl

Light sweet crude oil at Edmonton $Cdn/bbl

Alberta average natural gas price $Cdn/MMbtu

1.5% 1.5% 1.5% 1.5% 1.5% 1.5% 1.5% 1.5% 1.5% 1.5% 1.5% 1.5%

0.645 0.066 0.670 0.680 0.690 0.700 0.710 0.720 0.720 0.720 0.720 0.720

27.25 24.00 22.00 21.00 21.25 21.75 22.00 22.25 22.50 23.00 23.25 +1.5%

41.25 35.25 31.75 29.75 29.75 29.75 29.75 29.75 30.25 30.75 31.25 +1.5%

7.90 5.90 5.15 4.30 4.20 4.10 4.05 4.05 4.10 4.20 4.25 +1.5%

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Reference postings of light, sweet crude oil at Edmonton were adjusted to a Syncrude Sweet Blend price at plant gate by deducting $1.00/bbl. beyond 2004 to account for the increased competition from other oil sands developments.

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2001 . . . . . . . . . . . 2002 . . . . . . . . . . . 2003 . . . . . . . . . . . 2004 . . . . . . . . . . . 2005 . . . . . . . . . . . 2006 . . . . . . . . . . . 2007 . . . . . . . . . . . 2008 . . . . . . . . . . . 2009 . . . . . . . . . . . 2010 . . . . . . . . . . . 2011 . . . . . . . . . . . Thereafter . . . . .

Inflation

Valuation of Equity Securities

Year

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Table 4.2

($ thousands, except as indicated)

COS Statistical Summary, 1998–2003. 2001

2000

1999

1998

932,063 514,912 38,235 11,936 9,047 7,418 67,832 94,750 (135,165) 17,422 (2,246) — 307,922 3.87 272,851 3.43 169,885 2.00 785,587

715,302 308,877 19,392 7,378 7,355 5,812 38,737 55,091 (2,956) 5,413 — 275 269,928 4.72 326,444 5.71 114,655 2.00 403,203

663,053 327,116 17,794 52,540 8,381 4,243 20,326 60,451 23,538 1,852 — 420 146,392 2.58 226,908 4.00 156,121 2.75 179,514

665,495 276,231 7,198 124,830 9,497 2,083 13,495 55,235 5,588 1,584 — 660 169,094 2.98 232,635 4.10 132,562 2.34 110,441

468,488 216,105 5,961 9,471 7,847 2,128 11,231 66,019 (11,541) 1,286 — 660 159,321 2.81 206,418 3.64 71,820 1.27 163,202

328,653 219,432 5,622 120 3,878 2,148 13,174 57,266 13,604 867 — 660 11,882 0.22 81,368 1.51 18,900 0.35 107,715

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2003

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09:31:30.

Net revenues Operating costs Non-production costs Crown royalties Administration Insurance Interest, net Depreciation and depletion Foreign exchange loss (gain) Income and Large Corporations Tax Future income tax recovery Dividends on preferred shares of subsidiaries Net income Per Trust unit ($) Funds from operations Per Trust unit ($) Unitholder distributions Per Trust unit ($) Capital expenditures

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Table 4.3

(Continued)

373

($ thousands, except as indicated) 09:31:30.

2001

2000

1999

1998

1,070 1,810 3,240 66,793

676 N/A 1,794 49,806

694 N/A 1,808 48,508

713 N/A 1,831 44,145

598 N/A 1,830 48,456

597 N/A 1,847 45,497

38.23 21.12 0.49 16.62

39.35 16.99 0.41 21.95

37.46 18.48 2.97 16.01

41.15 17.14 7.75 16.26

26.50 12.22 0.54 13.74

19.93 13.21 0.01 6.71

5.2 40.4 20.2 87,195

1.2 29.1 31.3 57,684

1.2 25.9 18.3 56,779

0.5 12.0 20.8 56,750

0.5 11.4 22.4 56,750

1.9 20.9 2.1 54,000

45.70 32.26 45.69 45,417

44.85 33.28 38.05 33,296

41.95 29.25 38.50 20,360

33.00 23.50 29.10 12,673

25.90 16.90 24.90 8,657

24.50 14.00 16.80 9,657

prior to the 5 July 2001, merger date represent Athabasca Oil Sands Trust, the surviving entity.

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∗ Data

2003

Valuation of Equity Securities

Reserves (million bbls, net to COS) Proved reserves Proved and probable reserves Resource (includes proved and probable reserves) Average daily sales (bbls) Operating netback ($/bbl) Average realized sales price Operating costs Crown royalties Netback price Financial ratios Net debt to cash flow (times) Net debt to total capitalization (%) Return on average Unitholders’ equity (%) Number of Trust units outstanding (in thousands) $/Unit prices∗ High Low Close Trading volume (thousands of Trust units)∗

(Continued)

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375

market events did find the assumptions to be sufficiently inaccurate as to misrepresent the potential for the dramatic increase in unit prices that did occur (see Fig. 8.11). 4.3

Basic Theory of Interest

The discounted cash flow methods used in equity valuation are based on valuation methods initially developed for fixed income securities. In turn, with few exceptions preferred shares are appropriately valued as fixed income securities. Historically, the fixed income characteristics of common shares were important elements in equity valuation. As such, the basic theory of interest has relevance to the use of discounted cash flow to value equity securities. Recognizing that an adequate treatment of fixed income security valuation lies well outside the boundaries of equity security valuation, some topics of relevance have to be skipped in the tradeoff between brevity and completeness. In particular, no discussion is provided of the duration concept. Poitras (2005, p. 213, 214) demonstrates the basic result for the duration of a common stock by using the Gordon growth model to solve for the elasticity of stock price with respect to changes in the expected return on the stock. This produces a solution for the duration of common stock comparable to the duration of a perpetuity. 4.3.1

Different Possible Definitions

The number of possible definitions for ‘the interest rate’ is unexpectedly large. In practice, there is not even a single interest rate for the same type of fixed income security, such as Treasury bonds, as there are different interest rates associated with the various maturities and coupons. Perhaps the most important interest rate in fixed income analysis is the yield to maturity. In a DCF context, this interest rate is a special case of the internal rate of return, the interest rate that equates the discounted value of the future net cash flows to the value of the initial investment. There are also interest rates associated with the convention used to calculate the interest rate, such as the simple interest rate, annual percentage rate (APR), effective interest rate and continuously compounded interest rate. Other interest rate definitions include: coupon interest rate; zero coupon interest rate; and current yield. This list is not exhaustive. In analyzing the term structure of interest rates, the spot interest rate (implied zero coupon interest rate) and implied forward (interest) rate are essential definitions. Each of these definitions has relevance to specific DCF valuation problems.

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Yield to Maturity Perhaps the most widely used definition for ‘the interest rate’ is the yield to maturity. Although the yield to maturity can be used as the interest rate for a range of fixed income securities, the most important practical application is, arguably, to describe the interest rate for a bond. For a bond valuation problem where the bond pays annual coupons and is being valued on the issue date or a coupon payment date, the annualized yield to maturity (y) is obtained by solving:   T  C M + PB = t (1 + y) (1 + y)T t=1 In this formulation, T is the number of annual coupon payments remaining to be paid on the bond, (T = term to maturity in years), C is the annual coupon payment, M is the par value of the bond which is repaid at maturity and PB is the price of the bond. Because the calculation assumes that future coupon cash flows can be reinvested at the stated y, it follows that y is only a promised yield to maturity. In other words, reinvestment of coupons at the promised yield is required in order for the bond to actually earn the stated yield if the bond is held to maturity. As such, the yield to maturity is an ex ante forecast of the ex post realized yield. When C = 0, the bond is referred to as a pure discount or zero coupon bond. If held to maturity, a default and option free zero coupon bond will have the promised yield to maturity equal to the realized yield. In practice, the formula given for the price of an annual coupon bond is useful for pedagogical purposes. Only a relatively small number of bonds, e.g., Eurobonds, pay annual coupons. Most government-issued bonds, such as those issued by the U.S. Treasury, pay coupons semi-annually. The quoting convention in the financial press is to express the coupon as the sum of the coupon payments made in one year. For example, the 11.75% coupon U.S. Treasury bond maturing in November 2014 pays a $5.875 coupon every six months for a bond with a par value of $100. Valuing the semi-annual coupon bond on an issue date or coupon payment date, the valuation formula is   2T  C/2 M + PB =   2T y t 1 + y2 t=1 1 + 2 The sum is now over 2T because there are now two payments per year (T is term to maturity measured in years). The convention of dividing the

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(annualized) yield to maturity by 2 creates a situation where the yield on annual coupon bonds is not directly comparable to the (annualized) yield to maturity calculated from this formula. The effective rate of interest is used to reconcile this difference. The yield to maturity provides a measure that can be used to compare relative value across different types of bonds. For example, convention in the bond market is to execute trades using prices. Due to the variation in term to maturity and coupon, it is difficult to assess bond value by comparing prices. The yield to maturity provides a method to compare value across bonds. The simple rule of thumb for using yield to identify value is: “All other things equal, choose the bond with the highest yield to maturity”. However, if all things are equal, then efficient pricing requires that the yields will be the same. Hence, the yield to maturity can be used as a measure to assess bonds that have one or more features that are different. This leads to the notion of what Fabozzi (1989) refers to as ‘traditional yield spread analysis’ where the difference in yield for bonds with different features, e.g., different levels of default risk but the same term to maturity, is used as a measure of relative value. Current Yield and Dividend Yield There are so many different approaches to calculating interest rates that it is not practical to give a detailed account of each method. Though not used much in recent years, prior to the advent of computerized calculations, the current yield was a commonly quoted approximation to the yield to maturity for bonds. In the form of the ‘dividend yield’, the current yield is still the most common measure for valuing preferred stocks. The ‘current yield’ is defined as Current Yield = CY = (Annual Coupon or Dividend Paid)/(Bond or Stock Price) = C/PB . The relationship between the current yield and the yield to maturity for a bond is useful to illustrate for pedagogical purposes. When PB = M , the bond sells at par, then CY = y. When PB > M , for premium bonds CY > y with the difference increasing as the bond has a greater premium. When PB < M , for discount bonds CY < y with the difference increasing as the bond has a greater discount. For a zero coupon bond, CY = 0. In general: CY = T

C

C t=1 (1+y)t

+

M (1+y)T

09:31:30.

 T −1  M → CY (1 + y)t + = (1 + y)T P B t=0

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Some special cases follow, e.g., for T = 1: M CY + = (1 + y) → y = CY + PB For T = 2: CY (1 + y) +

M = (1 + y)2 → y = CY + PB

M −1 PB



M −1 PB (1 + y)



As T increases, the size of the deviation shrinks to the point where, for a perpetuity: C CY =
 = y C y

i.e., when T goes to infinity, the current yield equals the yield to maturity. This solution extends traditional yield spread analysis to preferred stock valuation. 4.3.2

Examples of Fixed Income Valuation Problems

The history of interest rate calculations stretches back centuries, e.g., Poitras (2000, Chs. 4 and 5), Scorgia (1996), Lewin (1970; 2000). In this history, the use of worked examples has played an important pedagogical role in illustrating concepts. An early example of the sophistication of such problems can be found in Witt (1613): A oweth to B £1200 to be paid in 6 yeares, in 12 equall payments, viz. at the end of each halfe yeare £100. They agree to cleare this debt in 3 yeares, in 6 equall payments, viz. at the end of each halfe yeare, one payment. The Question is, what each payment ought to be, reckoning interest after the rate of 10 per cent per ann. and int. upon int.

A conventional solution to this problem can be determined by equating the discounted value of the annuity stream of £100 for 12 half-year periods with the discounted value of £C for 6 half-year periods and solving for C. The exact solution requires recognizing Witt’s practice of using (1 + r)T /2 instead of the modern convention of (1 + r/2)T to discount the T period cash flow. More precisely, the solution can be determined by solving: 100 100 100 + ···+ + 1/2 (1 + r) (1 + r)6 (1 + r) =

C C C + ···+ + 1/2 (1 + r) (1 + r)3 (1 + r)

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 1 1 − r r(1 + r)6 

1 1 − = C{1 + (1 + r)1/2 } r r(1 + r)3

= 100{1 + (1 + r)1/2 }

Solving this for r = 0.10 gives the solution stated by Witt of £175.13145 or £175. 2s. 7d. Yet, Witt is able to show that this solution can be obtained as 100 +

100 = £175. 2s. 7d. (1 + r)3

Lewin (1970, p. 126) describes the method Witt uses to arrive at this solution as ‘extremely elegant’. Though no longer used for government financing activities, during the early years of government finance perpetuity issues were commonly used. The perpetuity is still of theoretical interest today. What is a perpetuity? A perpetuity is a security that offers to pay a fixed or variable coupon, at regular intervals, forever (in perpetuity). If the coupon is variable, then it is referred to as a floating rate perpetuity. Almost all perpetuities issued in recent years have been floating rate perpetuities, e.g., the floating rate perpetuities issued by financial institutions in the Euromarkets during the 1980s. The most well known perpetuity is a consol, originally issued by the British government in the 18th and early 19th century, which pays a fixed coupon. This perpetuity was so named because it originated from the consolidation of a number of different types of government debt issues, i.e., consol is a short form for consolidated debt issue. Consol issues traceable back to these early debt operations are still traded on the English stock exchanges. The perpetuity is more than a historical curiousity. The pricing formula for this security is of theoretical value, if only to illustrate a geometric series. Consider deriving the pricing formula for such a security when coupons are fixed and paid annually: ∞ 

C (1 + y)t t=1

 1 1 C 1 1+ + ··· = + (1 + y) (1 + y) (1 + y)2 (1 + y 3 )

P perp =

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Recall:

1 = 1 + x + x2 + x3 + x4 + · · · for |x| < 1. 1−x   1 C C perp = = ∴ P 1 (1 + y) 1 − (1+y) y

It can be immediately verified that, when coupons are fixed and paid quarterly, the perpetuity has the same pricing formula. Because quarterly coupons are paid sooner than annual coupons, this result may seem odd. However, this result can be explained when it is observed that the annual and quarterly coupon perpetuities will sell for different prices. Hence, even though the pricing formulas are the same, the yields will not be the same. Another interesting result occurs for the default free floating rate perpetuity where the coupon is variable (floating) and equal to the current interest rate times the par value of the perpetuity, i.e., C = yM . It follows that this perpetuity will always sell at par because the coupon will adjust to keep the price of the perpetuity equal to par. This was the idea behind the floating rate perpetuities issued in the Euromarkets during the 1980s. Prior to Basel I, because financial institutions regularly came to the market to reissue short maturity debt. Issuers could save on financing costs by offering a security that has a floating coupon. Similarly purchasers saved on commissions and other costs associated with rolling over short-term debt issues. However, this analysis depends on the level of default risk staying relatively constant. In the face of actual default risk shocks that led to the collapse of this market during the 1980s, market makers were forced to absorb large amounts of these securities at falling prices. The losses incurred led to a collapse of the market for this type of security and the subsequent shift to preferred share issues encouraged by Basel I and II capital requirements for depository institutions. One interesting extension of the fixed coupon perpetuity pricing formula occurs with the pricing of fixed coupon, fixed term annuities. The basic formula for pricing such an annual pay annuity can be stated as:

 

T  $A 1 1 $A 1 − 1 − = = $A PV A = (1 + y)t y y(1 + y)T y (1 + y)T t=1 where $A is the annual coupon payment, y is the applicable interest rate, and T is the term over which the annuity payment is received. This general pricing formula appears in numerous guises, such as in consumer loans for automobiles, house mortgages and the like. In these applications, the payment frequency is monthly. By observing that the cash flow stream

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from a fixed term annuity can be conceived as a perpetual annuity minus a perpetuity that starts at T + 1 (valued at T ) the perpetuity formula can be used to reexpress this sum as a single closed form expression, i.e.: PV =

     T $A $A 1 1 $A $A − 1 − = = y y (1 + y)T y (1 + y)T (1 + y)t t=1

In effect, the price of a fixed coupon annuity with maturity at T is equal to the price of a perpetuity minus the present value of a perpetuity that starts at T + 1 (with price taken at T ). In contrast to perpetuities that are something of an oddity in modern fixed income markets, much of the modern focus and discussion of fixed income securities is concerned with bond valuation. Various quirks can arise in bond pricing problems. One useful example arises with using the same yield to maturity to value bonds with different coupon payment frequencies. For example, consider the following problem: a bond offers eight annual coupon payments of $8 and will repay its face value of $100 at the end of eight years. You observe that other similar bonds have yields to maturity of 10%. How much is this bond worth? If the coupons are paid semi-annually, how much is the bond worth? To solve this basic problem, let C = $8, M = $100, and the term to maturity (T ) be T = 8: PBA = $8

8  t=1

PBSA = $4

1 $100 + = $8 (5.335) + $100 (0.467) = $89.38 (1.1)t (1.1)8

16  t=1

1 100 + = $4 (10.84) + $45.80 = $89.16 (1.05)t (1.05)16

where PBA is the price of the annual coupon bond and PBSA is the price of the semi-annual bond. The impact of increasing the coupon payments can be established with the following two problems: if these bonds have coupon payments of $12 annually, how much is the bond worth? If the coupons are paid semiannually how much is the bond worth? These questions can be solved as: PBA = $12 (5.335) + $46.70 = $110.72 and PBSA = $6 (10.84) + $45.80 = $110.84. To assess the impact of increasing the term to maturity, compare these bond prices with the 8% coupon prices calculated with 10 years to maturity. Do the same for the bonds with the 12% coupon. What do you observe about the relationships between the prices? Solving for the bond prices gives for C = $8, T = 10, y = 0.10, PBA =

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$8 (6.145) + $38.60 = $87.76 and PBSA = $4 (12.46) + $37.70 = $87.54. Similarly, for C = $12, T = 10, y = 0.10, PBA = $12 (6.145) + $38.60 = $112.34 and PBSA = $6 (12.46) + $37.70 = $112.46. This series of bond valuations illustrates the pricing differences that arise for discount and premium bonds. This illustration requires some definitions to be introduced. A ‘straight bond ’ requires a stream of fixed coupon payments paid at regular intervals plus a ‘return of principal’ at maturity that involves a payment on the maturity date equal to the stated par value (M ) of the bond. If no coupons are offered the bond is said to be a zero coupon or pure discount bond. If the price of the bond PB > M , then the bond is referred to as a premium bond. This occurs when the annual coupon payment C satisfies: (C/M ) > y, i.e., the coupon rate exceeds the yield to maturity on the bond. If the price of the bond PB < M , then the bond is referred to as a discount bond and (C/M ) < y. If PB = M , the bond sells at its par value, then (C/M ) = y and the bond is referred to as a par bond. In the bond valuation solutions, it can be observed that, for discount bonds with the same yield but different term to maturity, PB10 < PB8 . For premium bonds, with the same yield but different term to maturity, PB10 > PB8 . Shorter term bonds have higher prices when the bonds sell at a discount and longer term bonds sell at higher prices when the bonds sell at a premium. For discount bonds, with the same term to maturity and yield to maturity: PBSA < PBA . This result seems counter-intuitive because the semi-annual bond pays the coupon sooner than for the annual bond. For premium bonds, with the same term to maturity and yield to maturity: PBSA > PBA . All these results are somewhat misleading because with the same C and T a semi-annual coupon bond will always be preferred to an annual coupon bond, because a portion of the cash flows are received sooner. Hence, the semi-annual bond will sell for a higher price, and lower stated yield to maturity. 4.3.3

Term Structure of Interest Rates

In situations involving coupon bonds, the relationship between term to maturity and the yield to maturity for the set of available bonds is referred to as the yield curve. Different yield curves can be identified for different types of bonds, e.g., the corporate bond yield curve or Treasury bond yield curve. As will be discussed below, analysis of ‘the yield curve’ poses a range of problems. For example, bonds with the same term to maturity may have different coupons and, as a consequence, different yields. This leads

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to the introduction of the abstract relationship between term to maturity and the spot interest rate (implied zero coupon interest rate) referred to as the term structure of interest rates. These definitions are not always adhered to in various texts and financial newspapers where the terminology ‘term structure of interest rates’ can be used synonymously with ‘the yield curve’. However, the concepts are only equivalent if the yield curve is flat, i.e., the yield to maturity is equal across maturities. Spot Interest Rate (Implied Zero Coupon Interest Rate) As with any internal rate of return calculation, the yield to maturity has a number of limitations. One limitation involves applying the same interest rate to discount cash flows occurring at different points in time. This approach would only be valid if yield curves were flat, i.e., yields were the same for all terms to maturity. Casual inspection of real world bond markets reveals that near term cash flows are usually discounted at lower interest rates than longer term cash flows. This limitation leads directly to the concept of the spot interest rate or, more descriptively, the implied zero coupon interest rate (implied zero rate). Whereas there is a yield to maturity that can be calculated for every bond, the implied zero coupon interest rate applies to the term to maturity. There is an implied zero coupon interest rate for every fixed income payment date. For example, when the U.S. Treasury issued 30-year bonds, there were at 60-implied zero coupon interest rates that could be calculated, one for each of the 60 coupon payment dates. To see the connection between the implied zero rate and the yield to maturity, consider the following valuation formulas for bonds with annual coupons:    T  T   C C M M + + = PB = t T t (1 + y) (1 + y) (1 + z ) (1 + zT )T t t=1 t=1 Recognizing that the implied zero rate or spot interest rate (zt ) is the interest rate applicable to cash flows occurring at time t, it follows that valuation with implied zero rates values the bond by treating each of the cash flows (coupon payments and return of principal) as zero coupon bonds. The price of the bond is then calculated as the sum of the prices of the zero coupon bonds, valued using the implied zero rate applicable to single cash flows for that term to maturity, i.e., the price of the bond is the sum of the appropriately discounted zero coupon bond prices. For default free (riskless)

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zero coupon bond prices, the spot interest rate (implied zero rate) is equal to the yield to maturity. While each bond has an associated yield to maturity, each coupon payment date will have an implied zero rate. To make sense of such an interest rate, it is necessary to abstract from default risk and other features. Hence, the implied zero rates are extracted from the relevant default free bond prices, i.e., the U.S. Treasury debt issues are used to extract the implied zero rates for the U.S. debt market. Though it would be conceptually possible to use the observed interest rates for zero coupon bonds, such as the rates for U.S. Treasury strip securities (STRIPS), for the implied zero rates, this raises a number of difficulties. Sundaresan (2002, p. 231) specifically addresses this point: “It should be stressed that strips are not implied zeroes. Strips are traded securities directly subject to demand and supply. Implied zeroes are estimated pure discount functions derived from the prices of coupon-paying Treasury securities”. As such, implied zeroes provide a benchmark for assessing the relative richness or cheapness of Treasury securities. Fabozzi (1989, pp. 192, 193) identifies three reasons why stripped Treasury securities are not an adequate substitute for implied zeros: problems of liquidity in the Treasury strips market; maturity preferences in specific segments of the Treasury strip market may cause mispricing of certain maturities; and, differences in the tax treatment of stripped Treasuries and coupon Treasury bonds. Sundaresan (2002, pp. 237–241), Mason et al. (1995, pp. 48–55) and others demonstrate that, while not dramatically different, U.S. Treasury strip rates do differ empirically from implied zero rates calculated from U.S. Treasury coupon bonds.14 While each bond has an associated yield to maturity, each coupon payment date will have an associated implied zero coupon interest rate. As such, the method for calculating the implied zero rate differs from the method for calculating the yield to maturity. Mathematically, the yield to maturity calculation for a bond with T coupon payments involves one equation with one unknown. A bond with T coupon payments would have T unknown spot rates. This requires T equations to determine the T unknowns. Because the market used to calculate implied zero coupon rates is the US Treasury coupon bond market, a bootstrap technique is needed to extract the spot

14 For the specific dates examined, both these sources report that implied zero and strip rates are approximately equal at short maturities with implied zeros being slightly below strip rates at intermediate maturities and strip rates being well below the implied zero rate at long maturities.

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interest rates from the observed coupon yields. A bootstrap is the name given to a generic algorithm that uses a stepwise solution procedure to arrive at the solution for a number of unknowns. In particular, the first step solves for the first unknown using one equation with one unknown. This solution is then used to solve a second equation that is specified with the first unknown (now solved) and the second unknown. These two solutions are then used to solve the third equation that is specified with the first two unknowns (now solved) and the third unknown. This procedure continues until all the unknowns are solved. Calculation of Implied Zero Coupon Interest Rates The term structure of interest rates is concerned with the empirical relationship between term to maturity and the implied zero coupon rates calculated from the default free coupon bond market.15 Because implied zero rates are not directly observed, it is necessary to estimate these variables from observed coupon bond prices. This involves bootstrapping spot interest rates from coupon bond prices. The bootstrapping technique, e.g., Fabozzi (2000) and Sundaresan (2002), is an iterative process for calculating implied zero coupon interest rates (spot interest rates) from observed coupon bond rates. The process requires the observed yields for coupon bonds of each relevant term to maturity along the yield curve. In practice, spot rates would typically be extracted from the yield curve for federal government bonds, Treasury bonds in the United States or Government of Canada bonds in Canada. Because these types of bonds pay semi-annual coupons, precision requires that the bootstrap be executed at semi-annual intervals. In certain cases, exactly precise implied zeros are not required. If this is the case, then it is possible to achieve computational simplifications by proceeding under a number of assumptions. In particular it is possible to reduce the number of computations by a factor of two by assuming that the observed government bond prices are for annual coupon bonds. Another simplification can be achieved by taking the nearest available bond instead of estimating a par bond yield curve. To see how this simplified calculation 15 The

‘term structure of interest rates’ terminology can also be used to refer to implied zero coupon rates derived from bonds with default risk, e.g., Bierwag et al. (1992) refer to the duration of bonds from different term structures where the term structures differ due to default risk. However, where further qualification is not given, the term structure of interest rates refers to default free securities.

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process works, consider the example in Poitras (2002, p. 250) that involves solving for the Canadian spot interest rates from quotes obtained from the Globe and Mail for 28 August 1994. This involves picking the following bills/bonds from the available maturities: 1 year tbill z1 = 0.0720 6.5% 1 August 1996 P2 = 97.505 (y2 = 0.07887) 7.5% 1 July 1997 P3 = 98.225 (y3 = 0.08197) 6.5% 1 September 1998 P4 = 93.350 (y4 = 0.08474) 7.75 1 September 1999 P5 = 96.800 (y5 = 0.08542) These bonds were selected because they were closest to the required maturity dates. Two possible bootstrap solution techniques are available: the direct approach and the par bond approach. The direct approach involves using the observed price and coupon to solve for the spot interest rate. Solving for z2 : 97.505 = 6.5/(1 + z1 ) + 106.5/(1 + z2 )2 Using this method, z2 = 0.0792. For the par bond approach, use the result that when the stated yield to maturity equals the C/M then the bond sells at par: 100 = 7.887/(1 + z1 ) + 107.887/(1 + z2 )2 Using this method z2 = 0.0791428. The difference of 0.6 of a basis point is due to a combination of the assumption that the bond pays annual coupons, i.e., a semi-annual yield is used as an annual yield, and to the difference between the actual maturity date (August 1) and the required maturity date (August 28). Calculating the spot rates out to five years, it is evident that the differences involved are generally small: Par bond: z3 = 0.082423 z4 = 0.0854697 z5 = 0.0861374 Price/Coupon: z3 = 0.08232 z4 = 0.08595 z5 = 0.08630 Even for the five year implied zero, the difference is only 1.7 basis points. Observe that when the yield curve slopes up, as in this case, the implied zero curve will be above the yield curve. Similarly, when the yield curve slopes down, the implied zero curve will be below the yield curve. When the yield curve is flat, then both curves will be equal. This relationship follows mathematically from observing that the yield to maturity acts as a form of geometric average of the spot rates.

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Spot Rates and Implied Forward Interest Rates The implied forward interest rate (implied forward rate) has a number of possible uses in theoretical modeling. This interest rate concept is an extension of the breakeven interest rate associated with comparing a rollover investment strategy with a buy and hold strategy. To see this, consider the following comparison involving a two period, two portfolio model where zi is the zero coupon yield on a bond maturing i periods from now, zi,j is the (i − j) period interest rate starting at t = i and maturing at t = j, e.g., z1,2 is the one period interest rate that starts at t = 1 and ends at t = 2: Portfolio A: Buy and hold a two-year zero coupon bond. If the initial investment is $1 the return at the end of 2 years is (1 + z2 )2 Portfolio B: Buy and mature a one year zero coupon and use the proceeds to purchase another one year zero coupon bond, one year in the future. If the initial investment in this portfolio is $1 then the expected return at end of year two is (1 + z1 )(1 + E[z1,2 ]) Portfolio A is referred to as the buy and hold portfolio and Portfolio B as the rollover portfolio. To derive the breakeven interest rate, assume that the expected returns on the two portfolios are equal, then: (1 + z2 )2 = (1 + z1 )(1 + E[z1,2 ]) It follows that the breakeven expected interest rate can be calculated as (1 + E[z1,2 ]) =

(1 + z2 )2 (1 + z1 )

Using this result, the correspondence between the breakeven interest rate and the definition of the implied forward rate f1,2 follows appropriately: f1,2 = E[z1,2 ]. (The notation for the implied forward rate differs across the various textbooks on the subject, i.e., there is no generally accepted notational convention.) The use of {zi } to define {fi,j } is intentional. In the absence of representative zero coupon interest rates, implied forward rates are calculated using spot interest rates. The extension of the definition of an implied forward rate from the two period case to the n period case follows appropriately. For example, consider the one year implied forward interest rate that will

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apply from period t to t + 1. This is given by (1 + ft,t+1 ) =

(1 + zt + 1 )t (1 + z)t

+ 1

It is also possible to define implied forward rates applying to the interest rates longer than one year. For example, the five year implied forward interest rate between t = 5 and t = 10 can be calculated using the ten- and five-year spot rates:  (1 + z10 )10 (1 + f5,10 ) = 5 (1 + z5 )5 Similarly the implied forward rate for a three year zero coupon bond that starts at t = 2 and matures at t = 5, using the two-and five-year spot rates, is specified:  (1 + z5 )5 (1 + f2,5 ) = 3 (1 + z2 )2 Given this, the general formula for the implied forward interest rate is specified:  (1 + zt·k )t·k (1 + ft,t+k ) = k (1 + zt )t It follows that an observed yield curve for, say, n maturities will produce (n − 1) + (n − 2) + · · · + 1 = (n(n − 1))/2 implied forward rates.

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CHAPTER 5

Stochastic Theories of Equity Value 5.1

5.2

5.3

Foundations of Modern Finance 5.1.1 Basics of Mean–Variance Portfolio Analysis . . . . 5.1.2 Separation, the CAPM, and the Market Model . . Ergodicity and Asset Pricing Theories 5.2.1 A Brief History of Ergodic Theory . . . . . . . . . 5.2.2 Uncertainty and the Ergodic Hypothesis . . . . . . 5.2.3 Ergodicity in Economics and Financial Economics Bifurcation and Multimodal Densities 5.3.1 The Phenomenological Approach . . . . . . . . . . 5.3.2 Transition Density Decomposition . . . . . . . . . 5.3.3 Bifurcation and the Quartic Exponential Distribution . . . . . . . . . . . . . . . . . . . . . .

. 390 . 406 . 416 . 419 . 430 . 435 . 440 . 451

Modern Finance and Equity Valuation In order to be implemented in practice, the equity valuation methodology proposed by modern Finance academics requires knowledge of parameters from ex ante return distributions. In particular, the parameters required for the capital asset-pricing model (CAPM) are the means, variances, and covariances of the ex ante return distributions for the equity securities and market index of interest. Empirical implementation of such valuation models involves use of ex post estimates of the relevant ex ante distribution parameters. Estimators are chosen to have desirable statistical properties such as unbiasedness and consistency. Yet, despite decades of effort, there is little evidence that ex post optimal portfolios have similar ex ante performance. A range of explanations and apologies have been provided for this unexpectedly poor performance. This chapter demonstrates that fundamental theoretical difficulties can be traced to the pervasive use of time reversible ergodic stochastic processes. This assumption permits the use of a single ex post sample path to estimate the parameters of the ex ante stationary distribution for the ensemble of possible future time paths. In contrast, time irreversible ergodic processes can provide a viable explanation for some unexplained behavior of equity prices. Such processes can account for the erratic forecasting properties of parameter estimates from conventional models, excess volatility in stock prices relative to the underlying fundamentals, and the anecdotal claims regarding ex ante valuation accuracy achieved using technical analysis. 389

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5.1 5.1.1

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Foundations of Modern Finance Basics of Mean–Variance Portfolio Analysis

Many of the essential analytical tools used in mean–variance portfolio analysis can be found in the results for linear combinations of random variables from mathematical statistics. One basic result is the following, e.g., Freund (1971, p. 195): Theorem: Moments of Linear Combinations of Random Variables If X(1), X(2), . . . , X(N ) are random variables and a1 , a2 , . . . , aN are constants and Y = a1 X(1) + a2 X(2) + · · · + aN X(N ) then: E[Y ] =

N


ai E[X(i)]

i−1

var[Y ] =

N


a2i var[X(i)] + 2





i=1

ai aj cov[X(i), X(j)]

i>j

where the double sum over i > j extends over all values of i and j, from 1 to N , for which i > j. Derivation of var[Y ] requires the observation that cov[X(i), X(j)] = cov[X(j), X(i)]. One immediate corollary is that if cov[X(i), X(j)] = 0 for all i and j where i
= j, i.e., the random variables are all independent, and a1 = a2 = · · · = aN = 1/N then var[Y ] has the property: N 
2 lim var[Y ] = lim ai var[X(i)] = 0 N →∞

N →∞

i=1

This result has applications in insurance where the random variables are policy payouts and the ai are the fraction of the portfolio of policies attributable to policy i. Extending these results to portfolios follows immediately from identifying the random variables as the returns on individual securities held in a given portfolio, i.e., let X(i) = Ri for all i. The definition of the portfolio expected return follows: Definition: The expected return on the portfolio E[Rp ] is the value weighted sum of the expected returns on the individual securities, the E[Ri ]: E[Rp ] =

k
i=1

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wi E[Ri ]

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where k is the number of securities in the portfolio. To calculate the value weights, wi : $Ai wi = k i=1 Ai

where

k


wi = 1

i=1

with $Ai being the dollar value invested in security i and the sum over all $Ai being the total amount of money invested in the portfolio. As a simple example, consider having $1 million invested in a portfolio of two securities, and there is $500,000 in each security, then each wi = 0.5. As a slightly more complicated example consider the following problem: At the beginning of the year, Joe Investor owned four securities in the following amounts A, 100 shares, B, 400 shares, C, 200 shares, and D, 200 shares. The current prices of the securities are A = $12.50, B = $17.50, C = $25, and, D = $50. In one year’s time, Joe expects the prices to be: A = $25, B = $20, C = $30, and D = $55. What is the expected return on Joe’s portfolio for the year? The solution to this problem is determined by calculating the total value invested as 100(12.50)+400($17.50)+200($25)+200($50) = $23, 250. This permits the calculation of the value weights: wA = 1, 250/23, 250 = 0.054; wB = 0.301; wC = 0.215; wD = 0.430. The expected return on the portfolio can now be calculated as: E[Rp ] = 0.054(E[RA ])+0.301(E[RB ])+ 0.215(E[RC ]) + 0.430(E[RD ]) = 0.054(1.00) + 0.301(0.143) + 0.215(0.2) + 0.430(0.1) = 0.183 (or 18.3%). The other key element in the mean–variance portfolio model is the standard deviation of portfolio returns. As with calculating the risk for individual securities, calculations are done for the variance and the standard deviation is determined by taking a square root. The standard deviation, as opposed to the variance, is of the appropriate measure of risk because it is in the same units as the expected returns. However, calculations are done using the variance. Definition: The standard deviation of portfolio returns, σp is the square root of the variance of portfolio returns var[Rp ] ≡ σp2 . Various equivalent forms for the portfolio variance formula are available: var[Rp ] ≡ σp2 ≡

k k



wi wj σij ≡

i=1 j=1

≡

k
i=1

wi2 σi2

+2

k


wi2 σi2 + 2

i=1 k k

j=1 i=1,i>j

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wi wj σij ≡

k


wi wj σij

i>j k
i=1

wi2 σi2 + 2



i>j

wi wj σij

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where cov[Ri , Rj ] = σij . In the double sum expression, when i = j the covariance is a variance. These expressions can be further manipulated by making further substitutions using the definition for ρij , the correlation coefficient between Ri and Rj , i.e., cov[Ri , Rj ] = σij ≡ ρij σi σj . It is easiest to understand these results for the case where k = 2, when there are only two securities in the portfolio. In this case: σp2 = w12 σ12 + w22 σ22 + 2w1 w2 σ12 = w12 σ12 + (1 − w1 )2 σ22 + 2w1 (1 − w1 )ρ12 σ1 σ2 Similarly for three assets in the portfolio: σp2 = w12 σ12 + w22 σ22 + w32 σ32 + 2{w1 w2 σ12 + w1 w3 σ13 + w2 w3 σ23 } When there are k securities in the portfolio, the resulting portfolio variance will contain k variance terms and {k(k − 1)}/2 covariance terms. Further substitutions can be made using the definition for the correlation coefficient and the restriction that the sum of the value weights equals one. Having the formula for the variance of portfolio return permits the ready identification of an important special case of an optimum portfolio: the minimum variance portfolio, the portfolio that has the smallest risk in the set of all possible portfolios. The formula for this portfolio can be derived by minimizing var[Rp ] with respect to the choice variables, the value weights for each of the individual securities, subject to the restriction that the sum of the value weights be equal to one. In the simple case of the minimum variance portfolio for two securities, using the result that w1 + w2 = 1: σp2 = w12 σ12 + (1 − w1 )2 σ22 + 2w1 (1 − w1 )σ12 dσp2 = 2w1 σ12 − 2(1 − w1 )σ22 + 2(1 − 2w1 )σ12 = 0 dw1 w1∗ =

σ22 − σ12 σ12 + σ22 − 2σ12

This result demonstrates that the minimum variance portfolio will be a combination of the two securities and not just be fully invested in the security with the lowest risk. The intuition behind the portfolio diversification problem can be illustrated with the following artificial situation: assume that all the securities in the market have the same expected return of 10% and the same standard deviation of security return of 15% with the covariance between all security returns being 0.02. Construct an equally weighted portfolio containing

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393

N securities. While the expected return on this portfolio will be 10%, the variance of the equally weighted portfolio containing N securities will be σp2 =

N N

σi2 σij + 2 < 0.15 2 N N2 i=1 i>j

While the expected return is a linear combination of the individual security expected returns, the same result does not apply to the variance. This property of the variance for a linear combination of random variables is an essential ingredient in portfolio optimization models. Recall the result stated previously where, if the random variables are uncorrelated, then the variance of an equally weighted linear combination will go to zero as N goes to infinity. What happens to the portfolio expected return and standard deviation of this portfolio as N gets large? Because it is assumed that all standard deviations are the same, there are N equal terms in the first sum and, because the covariances have been assumed to be equal, there are N (N − 1) terms in the second sum and the portfolio variance reduces to   σij 1 σi2 σi2 2 + N (N − 1) 2 = + 1− σij σp = N N N N As N → ∞, the first term goes to zero and the portfolio variance is reduced to the covariance. To get this result, N must be very large. Even for portfolios containing, say, 100 securities, there is still some contribution to variance from the σi . As noted, when the covariance between all available securities is zero (independent returns), the standard deviation of the portfolio will go to zero as N gets large. This simple example provides a pedagogical basis for illustrating the gains to diversification. Examining the variance of the equally weighted portfolio described above, the (σi2 /N ) term applies to the specific risk associated with the individual securities, where the σi2 for each of individual security are associated with individual firm specific risks. Because this component of portfolio variance goes to zero as the number of securities gets large, it is appropriately described as diversifiable risk. The (1−(1/N ))σij term is associated with the covariance between security returns. Because this source of portfolio risk does not go to zero as N goes to infinity, it is appropriately described as non-diversifiable risk. It follows that the portfolio standard deviation can be decomposed into the sum of diversifiable risk and non-diversifiable risk. Hence, the risk associated with any portfolio of securities equals the sum of the diversifiable risk and non-diversifiable risk for that specific portfolio. ‘Efficiently diversified’ portfolios have eliminated diversifiable risk.

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As securities are added to the equally weighted portfolio, the risk of the portfolio is reduced until the lower bound provided by non-diversifiable risk is reached. However, the amount of risk reduction decreases as the number of securities in the portfolio increases to the point where there is no more firm specific risk that can be eliminated. The lower bound on portfolio risk, associated with the non-diversifiable risk, is due to the covariance between security returns. Modern portfolio theory expends considerable theoretical effort in developing the capital asset-pricing model (CAPM) where individual security returns depend on a combination of the riskless interest rate and the covariance of the individual security return with the return on the market portfolio. In this model, it is the non-diversifiable risk, referred to as systematic risk, that is compensated with higher expected return. Hence, there is a tradeoff between systematic risk and expected return. Because firm specific risk (unsystematic risk) can be eliminated in an efficiently diversified portfolio, the security market will not reward this source of risk with higher expected return. The Optimization Model The mean–variance portfolio optimization model is a central paradigm of modern Finance. The essence of the model is captured in the following quadratic optimization problem, e.g., Elton and Gruber (1995) and Luenberger (1998):1 min var[Rp ] =

{wi }

k k



wi wj σij

i=1 j=1

subject to E[Rp ] =

k


wi E[R] = cn

i=1

for cn {c0 , c1 , c2 , . . .} where c0 = cmv

and

k


wi = 1

i=1

where k is the number of risky securities or assets available for investment, E[Ri ] is the (conditional) expected return on security or asset i, E[Rp ] is the 1 The σ ij term is interpreted as being a covariance when i
= j and as a variance when i = j. Because the basic optimization problem is quadratic, it follows that the optimal solutions will take the form of an ellipse or a parabola. Consider the case where the {wi } are restricted to be non-negative, then the solution will be an ellipse. At any given target level of expected return, there will be two values of σ which solve the optimization problem. In evaluating the solutions, it is conventional to ignore the optimal solution which has the lower level of E[R] and consider only the portfolios which have the higher E[R] for a given σ.

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expected return on the portfolio, cmv is the return on the minimum variance portfolio, and var[Rp ] is the variance of portfolio return. In this model, the {wi } are the value weights, the fraction of the total value of the portfolio invested in each asset. Though it is conventional to develop the model under the assumptions of perfect capital markets (see Box 5.1), it is possible, even desirable, to impose additional restrictions on the optimization problem. One such additional restriction is wi ≥ 0 for all i. This restriction prevents short selling of securities. Without this restriction, all or almost all securities will be held in some form, either long or short. With the short selling restriction, the resulting estimates of optimal portfolio weights will have many securities that have value weights equal to zero. Box 5.1. Perfect Capital Markets Assumptions. What Are Perfect Capital Markets? Various presentations of perfect capital markets are available, with different versions emphasizing elements which are of importance to the argument at hand. One particularly complete set is provided in Haley and Schall (1979). A.1 Costless Capital Markets: No capital market transactions costs (including commissions and bid/offer spreads), no government restrictions which interfere with capital market transactions, and the costless ability to make financial assets infinitely divisible. A.2 Neutral Taxes: There are no personal or corporate taxes. A.3 Competitive Markets: There are many perfect substitutes for all securities of a firm at any point in time and there is no discrimination in the pricing of these securities such that any security can be acquired at the same market price by all investors. In addition, firms and investors are price takers in investing, borrowing and lending activities. A.4 Equal Access: Investors and firms can borrow, lend and issue claims on the same terms. This assumption requires that borrowing and lending rates be equal. A.5 Homogeneous Expectations: All capital market participants have the same expectations about relevant random variables. A.6 No Information Costs: Firms and individuals have the same available information and this information is acquired at zero cost. A.7 No Costs of Financial Distress: Firms and individuals incur no costs of financial distress or bankruptcy such as legal costs and disruption of operations. This assumption does not rule out the possibility of bankruptcy.

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The quadratic optimization problem is to determine the value weights for each security which minimize the variance of the return on the portfolio, subject to a target level of expected return. Because there is range of possible expected returns that can be chosen, the solution to the optimization problem will be a set of portfolios, each with its own set of optimal weights. This set of optimal portfolios is typically referred to as the efficient frontier. Other terms such as efficient set (Fama 1976), portfolio possibilities curve (Elton and Gruber 1995) and mean–variance efficient locus (Ingersoll 1987) are also used. There are a number of solution methodologies that can be used to solve quadratic optimization problems. A simple iterative method involves initially solving the minimum variance problem. The resulting optimal minimum variance weights are used to identify cmv . This value is used to specify c1 = cmv + ε, where ε(> 0) is specified according to the desired precision required in the solutions. Using c1 it is now possible to solve the Lagrangian problem for the next portfolio along the frontier. This process continues for c2 = cmv + 2ε, c3 = cmv + 3ε and so on until the desired efficient frontier is determined. With the short sales constraint, the maximum ci is given by having all funds invested in the highest returning security. Without the short sales constraint, the efficient frontier can be extended indefinitely. Because the underlying problem is quadratic, there will be two ‘optimal’ solutions, one of which is ignored because it will have higher risk for the same expected return. The number of variations that have emerged from this basic model is staggering.2 Initially, implementation of the model was impeded by the large number of parameters required to make the model operational. In addition to the k individual asset returns, E[Ri ], there are k variances, σi2 , and {k(k − 1)}/2 covariances which have to be estimated from past data. Even if these parameters are available, the model is only capable of generating a set of mean–variance optimal portfolios, the efficient frontier. Additional structure is needed to select a specific portfolio from the set of optimal portfolios. Tobin (1958), Sharpe (1963, 1964), and others handled this problem by introducing a riskless asset. This permits the investor to form portfolios which combine the riskless asset with an efficient frontier portfolio. In this fashion, the investor is able to achieve the same level of expected return as that generated by an efficient frontier portfolio, again with a lower level of risk. Effectively, the addition of a riskless asset transforms the investment

2 Markowitz

(1999) reviews the historical development of the model.

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opportunity set from a convex function, the efficient frontier, to a set of linear functions, the capital allocation lines. In general, where there are many possible securities available for inclusion in the portfolio, solution of the efficient set from the optimization problem is complicated. For purposes of illustration, it convenient to assume that there is only two risky securities. In this case it is possible to derive the efficient frontier directly, permitting basic concepts to be illustrated. So, assume you are considering creating a portfolio combining a stock fund composed of large stocks (S) and a bond fund (B). The statistics for these funds are E[R], large stock fund = 12%, bond fund = 5%; σ, large stock fund = 15%, bond fund = 8%. For ease of calculation, assume the correlation coefficient between the funds is zero. It is now possible to calculate E[Rp ] and σp for all possible portfolios, starting from 0% invested in the stock fund (ws = 0) and going to 100% (ws = 1), in increments of 20%. This produces: ws

E[Rp ] (%)

σp (%)

0 0.2 0.4 0.6 0.8 1.0

5.0 6.4 7.8 9.2 10.6 12

8.0 7.07 7.68 9.55 12.11 15

Plotting these values in {E[R], σ} space produces the efficient frontier. From these values, it is apparent that an investment of 100% in the bond fund (ws = 0) does not make sense because portfolios with values such as ws = 0.2 and ws = 0.4 both provide a higher portfolio expected return with a lower level of portfolio risk. Recalling that the returns were assumed to be independent, the portfolio weights, E[Rmv ], and σmv for the minimum– variance portfolio are ws =

σs2

σb2 0.082 = = 0.2215 → wb = 0.7785 2 + σb 0.152 + 0.082

It follows that E[Rmv ] = 0.0655 and σmv = 0.0706. Suppose the number of securities available for selection in the portfolio included a third fund composed of small stocks which has E[R] = 15% and σ = 0.20. How would you derive the efficient frontier for portfolios combining the three funds? Attempting to use the method of direct calculation that worked for the two security case is no longer possible. The two security

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case reduced to solving for one weight because it was possible to substitute out the other weight using the constraint that the sum of the weights equals one. Hence, there was no optimization problem to solve as there was only one effective weight. Barring trivial cases, when there are three or more securities the optimal weights have to be determined by solving the first order conditions of the optimization problem in order to identify how much of a given frontier portfolio is invested in each security. Ingersoll (1987) discusses the relevant solution procedure.

Capital Allocation Lines: Introducing a Riskless Asset The efficient frontier specifies a set of portfolios that achieve optimal combinations of the available risky assets. In order to provide a practical guide to portfolio selection, some method is required to identify a specific portfolio from the efficient frontier. Observing that the efficient frontier is a convex relationship between E[R] and σ for portfolios of risky assets, by introducing a risk free asset it is possible to produce a linear set of available portfolios. In particular, when a riskfree asset is introduced a range of portfolios can be identified which are not available with risky assets alone. What is the riskfree asset? This depends on the investment horizon or the portfolio rebalancing period. The riskfree asset must be free of default risk, have no coupons to reinvest (this would create coupon reinvestment risk), have maturity equal to the investment horizon and be denominated in domestic currency. For U.S. investors, it is typical to use the three month Tbill rate as the riskfree interest rate. Though it is conventional to proxy the riskfree asset with a three month U.S. Treasury bill, some presentations, e.g., Damodaran (1994), argue that the U.S. Treasury long term bond yield is appropriate. The problem of specifying the riskfree asset will be explored in more detail shortly. The riskfree asset permits the creation of portfolios which combine the riskfree asset with a risky portfolio located on the efficient frontier (see Fig. 5.1). In (E[R], σ) space, the line connecting the riskfree rate with a point on the efficient frontier is referred to as a capital allocation line (CAL). (This terminology is used in Bodie, Kane and Marcus 1999). There are as many capital allocation lines as there are portfolios on the efficient frontier. Each point on a given capital allocation line defines a range of possible portfolios which combine the riskfree asset and an efficient portfolio composed of risky assets. Along a given capital allocation line connecting the riskfree rate, r, with an efficient portfolio A, the expected return

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399

EFFICIENT FRONTIER CAL E[R]

Wr = -1.0 wA = 2.0

Borrowing Expected Portfolio Return %

Wr = -0.5

Wr = 0.0 wA = 1.0 Lending Wr = 0.5

r

Wr = 1 wA = 0 σ Standard Deviation of Portfolio Return

Fig. 5.1

Effect of borrowing and lending on risk and expected return.

(E[RR ]) and standard deviation (σR ) of a portfolio combining the efficient frontier portfolio and the riskfree asset can be specified: E[RR ] = wr r + (1 − wr )E[RA ] 2 2 σR = wr2 σr2 + (1 − wr )2 σA + 2wr (1 − wr )σrA 2 = (1 − wr )2 σA → σR = (1 − wr )σA

The result for the variance of the portfolio follows because the risk-free asset has no risk or covariance because it is risk free. Some care has to be taken in interpreting the weight wr . Though the notation w is used, this weight is not associated with the wi weights for the various efficient frontier portfolios. The wr weight is the fraction of the portfolio in the riskfree asset and (1 − wr ) = wA is the fraction held in the efficient portfolio (A). When 1 ≥ wr ≥ 0, this implies that the portfolio involves a positive investment in both the riskfree asset and the efficient portfolio. In Fig. 5.1, this condition is applicable to all the portfolios lying on the portion of the CAL between r and A. At r, wr = 1 (wA = 0) and at A on the efficient frontier wr = 0 (wA = 1). When wr ≤ 0, this implies that

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the riskfree asset is held short, i.e., the investor is borrowing at the riskless rate. This is equivalent to saying that, in addition to investment of the original capital, the investor has also borrowed money at the riskfree rate and has purchased additional units of the risky portfolio A. For example, if the investor has $1 million of original capital to invest and wr = −0.5 (wA = 1.5), then the investor has borrowed an additional $500,000 and has used this money to purchase an additional $500,000 of A. Portfolios where wr ≤ 0 lie to the right of the efficient frontier on the CAL. The key point to recognize is that the presence of the riskfree asset permits the investor to attain portfolios which are not available using risky assets alone. The Capital Market Line and Market Equilibrium To this point, the problem of picking an individual portfolio from the set of efficient frontier portfolios has not been solved. A convex set has been replaced by a set of CAL’s, each of which has a theoretically infinite number of possible portfolios. What has been demonstrated is that, with a riskfree asset, it is possible to specify (E[R], σ) tradeoffs that are unattainable with risky assets alone. In order to identify the best CAL and the appropriate portfolio to select on that CAL, it is conventional to introduce the mean– varance expected utility function: EU [R] = E[R] − b var[R]. As depicted in Fig. 5.2, the mean–variance EU function defines a preference ordering over the (E[R], σ) space. Movements in a northwest direction indicate increasingly higher levels of expected utility. It follows that the CAL which is just tangent to efficient frontier will attain the highest level of expected utility and the tangency of that CAL with the highest EU curve will be the specific portfolio that maximizes EU. This importance of this particular CAL is recognized specifically by referring to it as the capital market line (CML). As it turns out, the slope of the capital allocation line for any efficient portfolio X will be of interest in identifying the properties of the capital market line. Observing that the rise of the CAL is E[Rx ] − r and the run from the origin is σx it follows that the slope of any CAL is (E[Rx ] − r)/σx . Using this result, the equation of the capital allocation line for X becomes: E[R] = r +

E[Rx ] − r σR σx

Refer to Fig. 5.2 describing the indifference curves in (E[R], σ) space for a risk averse investor. Because utility increases as the slope of the capital allocation line increases, the rational investor will achieve the maximum level of utility by selecting the capital allocation line with maximum slope,

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Fig. 5.2

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401

Expected Utility Map for Risk Averse Mean-Variance Preferences.

i.e., the CAL that is just tangent to the efficient frontier set. Under perfect market assumptions, the CAL that is just tangent to the efficient frontier set represents the highest level of utility. This tangency portfolio is the portfolio which represents the market equilibrium. With the additional theoretical apparatus provided by the capital asset pricing model (CAPM) it can be demonstrated that the tangency portfolio associated with the capital market line is the market portfolio. To illustrate the process of identifying a specific portfolio, refer back to the stock/bond fund portfolio discussed previously. Assume that a riskfree asset is available with r = 3%. By maximizing the slope of the CAL, the weights for the tangency portfolio are given to be wS = 0.561 and wB = 0.439. For these weights, E[RM ] = 0.0893 and σM = 0.0912 where M indicates the tangency portfolio. Observing that the slope of CML is (0.0893 − 0.03)/0.0912 = 0.65, the equation of the capital market line can be specified as: E[RR ] = 0.03 + 0.65σR . Now, suppose the investor’s indifference map is given by the expected utility function: EU [R] = E[R] − {3.25 var[R]}. Recognizing that var[R] = ((1 − wr )σM )2 and E[RR ] = wr r + (1 − wr )E[Rx ], the process of maximizing EU [R] gives wr = −0.096 as the optimal holding for the riskless asset. This implies that, for the specified mean–variance expected utility function, the optimal solution involves a solution on the CML to the right of the tangency with the efficient frontier. It can be verified that alternative values of the risk

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aversion parameter b give: b = 5, wr = 0.2875; b = 3, wr = −0.01786; and, b = 2, wr = −0.78125. Criticism of Mean–Variance Portfolio Analysis While the mean–variance portfolio model has considerable theoretical appeal, there are a number of substantive problems that arise in implementing the model. One obvious problem concerns the large number of parameters that have to be estimated, e.g., Lummer and Riepe (1994). Even if this problem can be overcome, attempting to capture the gains, out-of-sample, has proved to be illusive, particularly when international assets are permitted to be part of the set of available securities. In practice, the use of ex post (in-sample) data to estimate the relevant parameters of the ex ante (out-of-sample) distribution creates numerous problems, not the least of which is instability in both the mean and variance–covariance parameter estimates. This is especially the case where expected returns are of interest. As pointed out by Eaker, et al. (1991): “The problem with including returns in the portfolio selection decision is that such portfolios generally perform poorly in out-of-sample tests.” The mean–variance portfolio model is a central tenet of modern Finance. Much like another central tenet, the efficient markets hypothesis, enthusiasm for the mean–variance portfolio model within Finance has evolved considerably. In recent years the model has been subjected to substantial critical scrutiny, e.g., Fisher and Statman (1997). The first wave in the assault on the mean–variance approach can be attributed to Jorion (1985, p. 265), which describes the problems emphatically in the context of internationally diversified portfolios: Mean–variance analysis has serious shortcomings which are too often ignored . . . Perhaps the most serious defect in the classical (portfolio) approach is the poor out-of-sample performance of the optimal portfolios. Performance measures always deteriorate substantially outside the sample period, and the supposedly optimal choice is sometimes dominated by a naive method . . . . Another problem is the instability in the optimal portfolio: the proportions allocated to each asset are extremely sensitive to variations in expected returns, and adding a few observations may change the portfolio distribution completely. Also, optimal portfolios are not necessarily well diversified. Often a corner solution appears, where most of the investments are zero and large proportions are assigned to countries with relatively small capital markets and high average returns.

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As it turns out, this attack is somewhat overstated. However, the basic point remains: ex post estimates of expected returns, based on arithmetic or weighted average estimators, can be unreliable estimates of future returns. Relative to estimates of variances and covariances, numerous empirical studies dating back to Jorion (1985) and Eun and Resnick (1988) demonstrate that estimates of expected returns are considerably more unstable over time. Empirically, the parameter instability problem has a number of implications. For example, ex ante results concerning the return on a given portfolio may vary significantly from sample to sample. Jorion (1985) examines the out-of-sample performance of the two ex post optimal internationally diversified portfolios identified by Grubel (1968) and Levy and Sarnat (1974), together with two ‘naive’ portfolios, the equally weighted and market value weighted. As measured by the Sharpe ratio, Jorion found that over the next investment horizon, the ex ante performance of the two mean–variance efficient portfolios was inferior to the performance of the naive equally weighted portfolio. Jorion (1985) also provides evidence that, in estimating ex post returns, longer sampling windows, e.g., five years for monthly data, provides superior ex ante forecasting when compared with shorter sampling windows, e.g., one year of monthly data. The difficulty with longer sampling windows is that it takes a longer time interval for the estimates to react to changing market conditions.3 In addition to the length of the sampling window used to determine the relevant parameter inputs, the presence or absence of short-selling has been found to be fundamental in assessing the performance of mean–variance efficient portfolios. Even though the early studies implicitly assumed short selling was not permitted, at least since Jorion (1985) it has been recognized that odd results can be obtained when short selling is permitted. For example, Jorion reports results for the time series properties of the optimal weight on domestic assets in the ex post tangency portfolio. A considerable amount of short selling is indicated at various times, as much as −2.4 times the total principal value of the portfolio at one point in 1978. For many types of investor situations, e.g., pension funds, life insurance companies, this amount of short selling would be unacceptable and unobtainable. 3 Such is the reason for using moving sampling windows instead of using all the data available. For example, 100 years of monthly data produces estimates of the arithmetic average which would not be affected by an additional observation. Hence, the optimal weights would not change over time.

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Evidence on portfolio composition with short selling restrictions, e.g., Glen and Jorion (1993), indicates a dramatic narrowing of the number of assets held in the portfolio is likely, amplifying the concentration of a given portfolio in a small number of assets. Somehow, proponents of the model believe that the out-of-sample prediction problems can be resolved by improving the estimation methods that are used. This still leaves the problem of identifying the appropriate portfolio from the set of mean–variance efficient portfolios. Following Sharpe and others, the efficient frontier portfolio to be selected is that portfolio associated with the capital allocation line which is just tangent to the efficient frontier, i.e., the portfolio associated with the capital market line. This tangency portfolio can be determined by solving the following optimization problem, e.g., Eun and Resnick (1994): max {wi }

E[Rp ] − r σp

subject to

k


wi = 1

i=1

where r is, as before, the riskfree interest rate. On theoretical grounds, the tangency portfolio is the ex ante mean–variance-expected-utility optimizing risky portfolio. Even though the precise combination of riskless asset and risky tangency portfolio for any given investor requires specification of the relevant parameters for the investor’s mean–variance expected utility function, the optimal risky portfolio has been determined. Given the ex post estimates of the relevant means, variances and covariances, the optimality problem is solved and the resulting tangency portfolio will represent the optimal, in-sample portfolio. Whether this in-sample optimality translates into superior out-of-sample performance is an open question. The answer to this question becomes even more complex when foreign assets are admitted into the asset universe. In particular, the domestic currency return on a foreign asset depends on a combination two random variables: the return denominated in foreign currency terms; and, the change in the exchange rate. The correlation coefficient between foreign and domestic asset returns will tend to be lower than the correlations coefficient between domestic assets, making foreign assets excellent candidates for diversification. However, as illustrated in Goetzmann et al. (2005, p. 20), the correlations of U.K., U.S., French, and German monthly equity market returns have changed dramatically over the available 1872–2000 sample period. For example, the correlation between US and French monthly equity returns for 1946–1971 (1972–2000) period was −0.02 (0.414). Using

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the same sub-samples, the U.S. and U.K. correlation increased from 0.182 to 0.508. In contrast to the modern period, the correlations between equity market returns on investment over the 1872–1914 sample associated with the “average investment trusts” confirms the empirical basis of the “geographical distribution of risks”. As Lowenfeld (1909) observed The fact that whilst the world’s trade is constantly expanding, the share of each separate nation in it is constantly altering is the fundamental principle of our geographical method of equalizing risks. For it follows that if an investor widely distributes his own capital over the earth’s surface, local depression in one quarter will be counter-balanced by the local trade activity in another quarter. Further, it also follows, if an investor’s capital is sufficiently large to enable him to purchase investments representative of every trading centre in the world, that the world’s perpetual trade expansion will automatically increase the realisable capital value of his investments year by year.

Compared to an average correlation among major markets of 0.475 for 1972–2000, the correlation was 0.102 (0.155) for the 1872–1889 (1890–1914) sample. In the modern context, the higher geographical correlations make returns more dependent on global trade expansion. Despite the considerable attention paid to the risk diversification benefits of foreign assets, it is the possibility of significantly higher ex ante and, in some cases, ex post returns than those on offer for domestic assets that drives the bulk of the demand for offshore equity securities. This creates real difficulties for the ex ante performance of mean-variance optimal portfolios. In Eun and Resnick (1994), for example, the difficulties associated with estimating expected returns results in the minimum variance portfolio having generally superior ex ante performance compared to the ex post optimal tangency portfolio. The difficulties in using ex post estimates to proxy for ex ante expected returns is increased significantly for foreign securities compared to domestic securities due to the additional currency risk. The impact of currency risk is also observed in the home country bias observed in investment portfolios in different countries. Though currency risk can be hedged with currency derivatives, this is not common practice among individual investors. While this is partly due to having position sizes smaller than minimum contract sizes for exchange traded derivatives, the amount to hedge is complicated by the amount of currency hedging that individual firms are also doing.

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Separation, the CAPM, and the Market Model

Two Fund Separation The combination of mean–variance expected utility, perfect markets and the CML provides the basis for a version of the two fund separation property : in market equilibrium, rational risk averse investors will hold portfolios which combine the risk free asset with the tangency portfolio. The precise combination of the risk free asset and the tangency portfolio will depend on the risk preferences of the individual investor. The CML result does not provide any information about how to determine the return on individual assets, or any portfolio of assets which is not efficient. The CML also does not provide specific information about the asset composition of the tangency portfolio. This information is provided by the capital asset pricing model (CAPM). If the CAPM is incorporated, then it can be shown that the tangency portfolio will be the market portfolio. In this case, the two fund separation property says that, in market equilibrium, rational risk averse investors will hold portfolios which combine the riskfree asset and the market portfolio. Two fund separation provides the theoretical basis for a persuasive and implementable investment strategy. This strategy requires a strong belief in efficient markets. If markets are efficient then the gains to individual security selection strategies, using either fundamental or technical analysis, will be illusory. The decision problem facing the rational investor is to determine what fraction of invested capital to hold in the risky market portfolio — effectively a fixed, open ended, value weighted, passively managed index fund — and what fraction to hold in the riskless asset. Investors with high levels of risk tolerance will leverage up, by borrowing at the riskfree rate, and purchase more of the market portfolio. Investors with moderate to low levels of risk tolerance will have positive investment weights for both the riskfree asset and the market portfolio. Though this perfect markets result requires some adjustment to account for market imperfections, e.g., differences between lending and borrowing rates, the basic intuition survives in tact. As pointed out by Roll (1977), the main practical ambiguities lie with the specification of the riskfree asset and the market portfolio. The CAPM provides a method for determining the expected return, E[Ri ], for any asset i, not just for portfolios on the efficient frontier. The CAPM is an ex ante model that can be expressed as E[Ri ] = r + {E[Rm ] − r}βi

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where E[Rm ] is the expected return on the market portfolio and βi is a measure of the systematic risk of asset i. In words, the CAPM can be expressed as: the expected return on asset i = risk free rate + systematic risk premium for asset i. A key variable in the CAPM is β which is specified as cov[Rp , Rm ] σi,m = 2 βi = 2 σm σm 2 where σm is the variance of the return on the market portfolio. Some examples of mechanical calculations that can be done with CAPM are: assume that the rate of return on the market E[Rm ] = 0.15 and r = 0.05 and βi = 1.5 then the expected return on asset i is E[Ri ] = 0.05 + (0.15 − 0.05)(1.5) = 0.20; assume that E[Ri ] = 0.1, E[Rm ] = 0.105 and βi = 0.9 then the riskfree rate r is 5.5%; assume that E[Ri ] = 0.2, E[Rm ] = 0.15 and r = 0.10, then βi = 2. Beta is applicable not only for individual securities but also for a portfolio of securities. The following useful result can readily be derived: the beta of a portfolio, βp is the value weighted sum of the individual betas (the βi s). This follows because the CAPM holds for any asset, including individual assets as well as portfolios of assets. Recognizing that the CAPM will hold for the efficient portfolios on the efficient frontier, the CAPM can be used to show that the tangency portfolio in the CML is the market portfolio. To demonstrate this result, assume that the CAPM is true. If the tangency portfolio is the market portfolio, the CML provides the result:

E[RR ] = r +

E[Rm ] − r σR σm

where m refers to the market portfolio. Using the result that σR = (1 − wf )σm this can be rewritten: E[RR ] = r +

E[Rm ] − r (1 − wr )σm = r + {E[Rm ] − r}(1 − wr ) σm

If the CAPM is true then it will hold for any portfolio along the CML. If the market portfolio is the tangency portfolio for the CML then E[R] = wr r + (1 − wr )E[Rm ] and evaluating β gives: β=

cov[{wr r + (1 − wr )E[Rm ]}, E[Rm ]] cov[E[R], E[Rm ]] = 2 2 σm σm =

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Substituting this result back into the CML shows that the CAPM and CML are equivalent when the tangency portfolio is the market portfolio. The relationship between the CAPM and the CML can be expressed in a linear form in (E[R], β) space. This linear relationship is the security market line (SML). While the CAL and CML provide a linear relationship in (E[R], σ) space between total risk, as measured by standard deviation, and expected return, the SML provides a linear relationship between systematic risk, as measured by β, and expected return. The equation for the SML can be derived by identifying two points on the line: the risk-free rate where βf = 0 and E[Ri ] = r and the market portfolio where βm = 1, E[Ri ] = E[Rm ]. It follows that the slope is (E[Rm ] − r). From this the equation for the SML can be stated: E[Ri ] = r + (E[Rm ] − r)βi . Hence, the SML is the graphical representation of the CAPM. A useful pedagogical application of the SML is to describe whether a particular equity security is over or underpriced relative to its measure of systematic risk. As illustrated in Fig. 5.3, points above the SML have an E[R] that is higher than warranted for the associated β and, as a consequence, represent underpriced securities. The instability of alpha and beta estimates from the market model make this method of valuing equity securities generally inapplicable for vernacular Finance purposes. THE SECURITY MARKET LINE E[R]

UNDERPRICED SECURITY

E(Rm)

SML

MARKET RETURN

r OVERPRICED SECURITY

β=1

Fig. 5.3

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β

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The Capital Asset Pricing Model The Markowitz model of mean–variance portfolio optimization is concerned with the behavior of an individual investor selecting securities for inclusion in an optimal portfolio. Practical application of this model is complicated by the large number of parameters that have to be estimated and the associated complexity of the solutions as the number of securities is increased. The CAPM provided a theoretical mechanism for handling this problem. Using the CAPM, the problem of estimating the optimal weights for the individual assets in the tangency portfolio is replaced with a method of identifying the predetermined set of weights associated with the market portfolio. Though the notion of a ‘market portfolio’ is somewhat nebulous, in practice it has been interpreted to be a widely diversified value-weighted portfolio of common stocks such as the S&P 500, e.g., Damodaran (1994). This all raises the need to examine the derivation of the CAPM in more detail. In the years since the CAPM was introduced by Sharpe (1964), Lintner (1965), and Mossin (1966) considerable effort has been given to extending and expanding the basic model. The basic CAPM, also referred to as the one factor or single index model, is derived under perfect markets assumptions. The process of extending and expanding has been largely concerned with relaxing these assumptions. Unlike the partial equilibrium approach of the mean–variance portfolio model, the CAPM is a general equilibrium model. It is this feature that permits the CAPM to go beyond the basic portfolio structure to make statements about the expected returns for individual assets. General equilibrium requires market clearing conditions for all assets to be satisfied. To accomplish this, the CAPM relies on the assumption the investors are homogeneous, possessing the same expectations about the means and variances of returns and the same investment horizon. All investors are assumed to have the same form of mean–variance expected utility function. Much of the derivation of the CAPM follows the mean–variance optimization procedure. The homogeneity assumption is invoked after the riskfree rate is introduced and the optimality of the tangency portfolio is established. Because investors are homogeneous and market clearing is required, it must be that the tangency portfolio is the market portfolio. Fama (1976, pp. 274, 275) describes the logical argument: a market equilibrium requires a market-clearing set of prices; a market equilibrium requires that, in aggregate, investors demand them in

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the proportions in which they are outstanding. Given the nature of the efficient set when there is risk-free borrowing and lending, this marketclearing condition means that a market equilibrium is not attained until the one tangency portfolio that all investors try to combine with risk-free borrowing or lending is a portfolio of all the positive variance securities in the market, where each security is weighted by the ratio of the total market value . . . of all its outstanding units to the total market value of all outstanding units of securities. In short, a market equilibrium is not reached until the tangency portfolio . . . is the value-weighted version of the market portfolio . . . A market equilibrium — a set of security prices that clears the securities market and a value of [the risk-free rate] that clears the borrowing-lending market — requires that the tangency portfolio be the market-weighted version of the market portfolio.

This last step, the identification of the tangency portfolio with the market portfolio, follows immediately from the investor homogeneity assumption. In the derivation of the CAPM, this step is something of an afterthought. The key parts of the CAPM relate to developing the relationship between the expected return on a given asset and the expected return on an efficient portfolio. This derivation requires one useful result associated with linear combinations of random variables:4

var[Rp ] =

k k



wi wj σij =

i=1 j=1

=

k


k


 wi 

i=1

k


 wj σij 

j=1

wi cov[Ri , Rp ]

i=1

Given this, the derivation of the CAPM proceeds by solving the Lagrangian arising from the mean–variance portfolio model: max L = var[Rp ] − 2λ1 {wi }

 k
i=1

wi E[Ri ] − c¯n

 − 2λ2

k


wi − 1

i=1

This optimization problem will produce k first order conditions associated with the {wi } together with two additional first order conditions for the constraints to produce a system of k + 2 equations.

4 The

general approach in the following discussion is adapted from Fama (1976).

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For jth security, the first order condition provides: k


wi cov[Ri , Rj ] − λ1 E[Rj ] − λ2 = 0

i=1

As the ordering of the securities is arbitrary, this result can be equated with the first order condition for the first security to obtain: k


wi cov[Ri , Rj ] − λ1 E[Rj ] =

k


i=1

wi cov[Ri , R1 ] − λ1 E[R1 ]

i=1

The next step involves multiplying both sides by wj and summing over j. This affects the right and left hand sides differently. The left hand side produces: k
j=1

wf

k


wi cov[Ri , Rj ] − λ1

i=1

k


wj E[Rj ] = var[Rp ] − λ1 E[Rp ]

j=1

The right hand side produces:  k k k


wj wi cov[Ri , R1 ] − λ1 E[R1 ] = wi cov[Ri , R1 ] − λ1 E[R1 ] j=1

i=1

i=1

This result follows because there is no j on the right hand side and, as a result, the sum of the weights equals one and has no impact. Observing that the weights apply to a mean–variance efficient portfolio, i.e., Rp is on the efficient frontier, manipulating the right and left hand sides produces the result:  k 1
E[R1 ] − E[Rp ] = wi cov[Ri , R1 ] − var[Rp ] λ1 i=1 =

1 (cov[R1 , Rp ] − var[Rp ]) λ1

What remains is to determine λ, which is the Lagrange multiplier associated with the impact of changes in the target level of portfolio expected return on the variance of the portfolio. When there is a riskfree rate, the λ for the tangency portfolio can be determined as:   d var[Rp ] dσp σp d var[Rp ] = = 2σp 2λ1 = dE[Rp ] dσp dE[Rp ] E[Rp ] − r Substituting this λ result back into the prior equation and manipulating gives the CAPM.

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Nothing in this derivation demonstrates that the tangency portfolio is the market portfolio. This result is obtained from the logical argument about market clearing with homogeneity of consumers. In a sense, two fund separation, where the rational investor holds combinations of the market portfolio and the riskless asset, is too strong a condition. A more appropriate result would be a partial equilibrium result where the rational investor holds combinations of a mean–variance efficient portfolio and the riskless asset. But this would require the mean–variance efficient portfolio to be determined, falling back to the problems associated with complexity, number of parameters to estimate, estimator forecasting error and the like. That the CAPM assumptions make proponents of modern Finance uncomfortable is implicit in the following quote from Elton and Gruber (1984, p. 273): the final test of a model is not how reasonable the assumptions behind it appear but how well the model describes reality . . . many assumptions [may be] objectionable. Furthermore, the final model is so simple the reader may well wonder about its validity . . . despite the stringent assumptions and the simplicity of the model, it does an amazingly good job of describing prices in capital markets. The real world is sufficiently complex that to understand it and construct models of how it works, one must assume away those complexities that, hopefully have only a small (or no) affect on its behavior. As the physicist builds models of the movement of matter in a frictionless environment, the economist builds models where there are no institutional frictions to the movement of stock prices.

These words reflect the relationship between the philosophical foundation of modern Finance and the CAPM. While acceptable in an academic context, the claim about “amazingly good job of describing prices” is not supported in the world of vernacular Finance where forecasting future equity prices is of central importance. The Market Model Because the CAPM is an ex ante model it depends on expected returns and other unknown values that are not directly observable or testable. The statistical representation of the CAPM which is testable is known as the market model. The market model is a bivariate regression model of the form: Rit = αi + βi Rmt + eit

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where Rit is the observed return on asset i at time t, Rmt is the observed return on the market portfolio at time t, αi and βi are statistical parameters to be estimated and eit is the asset specific error which is assumed to obey the statistical properties for ordinary least squares regression. For the market model the ordinary least squares (OLS) assumptions (dropping the t subscript for convenience) are: E[ei ] = 0, the firm specific error has mean zero; E[ei Rm ] = 0, the firm specific risks are uncorrelated with the market return; E[ei ej ] = 0 for i not equal to j, the firm-specific risks for different securities are uncorrelated; in addition, it is assumed that the ei are iid random variables. The additional assumption of normality of ei facilitates hypothesis testing. With these assumptions, ordinary least squares can be used to estimate the coefficients αi and βi . The market model is sometimes referred to as the single index model, e.g., Elton and Gruber (1995). Taking expected values for the market model gives for any t: E[Ri ] = αi + βi E[Rm ] because E[ei ] = 0 If the CAPM is true, it follows that αi = (1 − βi )r, (βi has the same interpretation as cov[Ri , Rm ]/var[Rm ]). This interpretation for α depends on the riskless rate being a constant. While this assumption is correct in onestep-ahead decision making, it is problematic when estimating parameters in a time series. To account for changes in r over time, the market model is often expressed in risk premium form, by subtracting the observed riskless rate, in any given period, from the observed returns: Rit − rt = αi + βi [Rmt − rt ] + uit where ui is also a firm specific risk with ordinary least squares properties. In this form, taking expectations and assuming that the CAPM holds gives αi = 0 and βi with the same interpretation. Beta is a measure of systematic or market risk. It provides information on how the stock return reacted historically when the market portfolio return changed. Beta estimates are reported at a number of websites, such as www.bloomberg.com. For βi > 1 (high beta), when the return on the market portfolio changes, the return on the stock will tend to change by more than the return on the market portfolio. Stocks with higher than market betas are considered to be aggressive. When the market is expected to move up, shifting into stocks with high beta is indicated. In the US market, examples of high beta stock groups occur in industries such as trucking,

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consumer durables, construction and air transport. For βi < 1 (low beta) when the return on the market portfolio changes, the return on the stock will tend to change by less than the return on the market portfolio. Stocks with lower than market betas are considered to be defensive. When the market is expected to move down, shifting into stocks with low beta is indicated. In the U.S. market, examples of low beta stock groups occur in telephone stocks, in utilities, breweries and food producers/distributors. Alpha is an asset specific measure which indicates the excess return that the security earned beyond that warranted by the risk premium captured by the security’s beta. For the market model expressed in risk premium form, positive alpha indicates that the stock outperformed the market, after adjusting for systematic risk. Negative alpha indicates that the stock underperformed the market, after adjusting for systematic risk. The market model provides a useful simplification for determining the betas and alphas for a portfolio from the alphas and betas of the individual securities: E[Rp ] =

k


wi E[Ri ] =

i=1

=

k


wi αi +

i=1

k


wi {αi + βi E[Rm ]}

i=1 k


βi E[Rm ] = αp + βp E[Rm ]

i=1

In other words, the alpha and beta for the portfolio are the value weighted sums of the individual portfolio alphas and betas. The market model can also be used to demonstrate that portfolio diversification leads to the elimination of unsystematic or firm specific risk leaving only systematic risk as the determinant of portfolio variance. If the market model is true then the variance for individual security returns reduces to 2 + σe2i σi2 = βi2 σm

Similarly, the covariance between the security returns becomes: 2 σi,j = βi βj σm

These results follow from the assumptions made in the market model. Substituting these results into the formula for the portfolio variance,

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σp2 gives: σp2 =

k


2 wi2 βi2 σm +

i=1

=

k
i=1

k k



wi2 σe2i +

2 wi wj βi βj σm +

i=1 j=1

k
i=1




2 wi wj βi βj σm

i>j

wi2 σe2i

Observing that the variance of the market portfolio is a common term in the double sum, it is possible to do some factoring:   k  k k  


2 wi βi wi βi σm + wi2 σe2i σp2 =   i=1

j=1

i=1

Using the result that the beta of the portfolio is the value weighted sum of the individual security betas, the following simplification is available for the portfolio variance: 2 + σp2 = βp2 σm

k


wi2 σe2i

i=1

σp → βp σm

as k → ∞ and wi ⇓

The term involving βp is the systematic or market related risk. It depends only on the composition of the portfolio and the variance of the return on the market. The second term involves only firm specific or unsystematic risk. To show the impact of diversification on both systematic (market) risk and unsystematic (firm specific) risk, observe that the first term involving the beta of the portfolio is not much affected by increases in the number of securities in the portfolio. The second term involving the firm-specific risks is directly affected by the number of securities in the portfolio. Take the case of an equally weighted portfolio where wi = 1/N . In this case, as the number of the securities in the portfolio increases the firm-specific risks are reduced at the rate of (1/N 2 ), which is converging to zero quite rapidly. This follows from observing that when the firm specific risk has been eliminated then the last term on the rhs of the last equation is zero. Taking square roots and observing that the portfolio beta is the weighted sum of the individual security betas provides the required result. However, because there are a large number of securities in a portfolio, this does not mean that the firm specific risks are eliminated. Rather, the elimination of firm specific risk depends on reducing the value weights attached to each

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security as N increases. For example, if w1 = 0.5 for a particular security, and this value does not change as the number of securities in the portfolio increases, then the firm specific risk associated with that security is not eliminated as the number of securities in the portfolio increases. 5.2 5.2.1

Ergodicity and Asset Pricing Theories A Brief History of Ergodic Theory

The Encyclopedia of Mathematics (2002) defines ergodic theory as the “metric theory of dynamical systems. The branch of the theory of dynamical systems that studies systems with an invariant measure and related problems”. This modern definition implicitly identifies the birth of ergodic theory with proofs of the mean ergodic theorem by von Neumann (1932) and the pointwise ergodic theorem by Birkhoff (1931). These early proofs have had significant impact in a wide range of modern subjects. For example, the notions of invariant measure and metric transitivity used in the proofs are fundamental to the measure theoretic foundation of modern probability theory (Doob 1953; Mackey 1974). Building on Kolmogorov (1933), a seminal contribution to probability theory, in the years immediately following it was recognized that the ergodic theorems generalize the strong law of large numbers. Similarly, the equality of ensemble and time averages — the essence of the mean ergodic theorem — is necessary to the concept of a strictly stationary stochastic process. Ergodic theory is the basis for the modern study of random dynamical systems, e.g., Arnold (1998). In mathematics, ergodic theory connects measure theory with the theory of transformation groups. This connection is important in motivating the generalization of harmonic analysis from the real line to locally compact groups. From the perspective of modern mathematics, statistical physics or systems theory, Birkhoff (1931) and von Neumann (1932) are excellent starting points for a history of ergodic theory. Building on the ergodic theorems, subsequent developments in these and related fields have been dramatic. These contributions mark the solution to a problem in statistical mechanics and thermodynamics that was recognized 60 years earlier when Ludwig Boltzmann (1844–1906) introduced the ergodic hypothesis to permit the theoretical phase space average to be interchanged with the measurable time average. From the perspective of modern financial economics, the selection of the less formally correct and rigorous contributions of Boltzmann are a more auspicious beginning for a history of the ergodic hypothesis. Problems of interest in mathematics are generated by a range of subjects,

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such as physics, chemistry, engineering and biology. The formulation and solution of physical problems in, say, statistical mechanics will have mathematical features which are unnecessary in, say, economics. For example, in statistical mechanics, points in the phase space are often multidimensional functions representing the mechanical state of the system, hence the desirability of a group-theoretic interpretation of the ergodic hypothesis. From the perspective of Finance and economics, such complications are largely irrelevant and an alternative history of ergodic theory that captures the etymology and basic physical interpretation is more revealing than a history that focuses on the relevance for mathematics. This arguably more revealing history begins with the formulation of the problems that von Neumann and Birkhoff were able to solve. Mirowski (1989, esp. ch. 5) establishes the importance of 19th century physics in the development of the neoclassical economic system advanced by Jevons, Walras and Menger during the marginalist revolution of the 1870s. As such, neoclassical economic theory inherited essential features of mid-19th century physics: deterministic rational mechanics; conservation of energy; and the non-atomistic continuum view of matter that inspired the energetics movement later in the 19th century.5 It was during the transition from rational to statistical mechanics during the last third of the century that Boltzmann made the contributions that led to the transformation of theoretical physics from the microscopic mechanistic models of Rudolf Clausius (1822–1888) and James Maxwell (1831–1879) to the macroscopic probabilistic theories of Josiah Gibbs (1839–1903) and Albert Einstein (1879–1955).6 Coming largely after the start of the marginalist revolution in economics, this fundamental transformation in theoretical physics and mathematics had little impact on the progression of mainstream economic 5 In rational mechanics, once the initial positions of the particles of interest, e.g., molecules, are known, the mechanical model fully determines the future evolution of the system. This scientific and philosophical approach is often referred to as Laplacian determinism. 6 Boltzmann and Max Planck were vociferous opponents of energetics. The debate over energetics was part of a larger intellectual debate concerning determinism and reversibility. Jevons (1877, pp. 738, 739) reflects the entrenched determinist position of the marginalists: “We may safely accept as a satisfactory scientific hypothesis the doctrine so grandly put forth by Laplace, who asserted that a perfect knowledge of the universe, as it existed at any given moment would give a perfect knowledge of what was to happen thenceforth and for ever after. Scientific inference is impossible, unless we may regard the present as the outcome of what is past, and the cause of what is to come. To the view of perfect intelligence nothing is uncertain”. What Boltzmann, Planck and others had observed in statistical physics was that, even though the behavior of one or two

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theory until the appearance of contributions on continuous time finance in the 1970s.7 The deterministic mechanics of the energistic model was well suited to the subsequent axiomatic formalization of neoclassical economic theory which culminated in notions fundamental to modern Finance: the von Neumann and Morgenstern expected utility approach to modeling uncertainty and the Bourbaki inspired Arrow-Debreu general equilibrium theory, e.g., Davidson (2007) and Weintraub (2002). Having descended from the deterministic rational mechanics of mid-19th century physics, defining works of neoclassical economics, such as Hicks (1939) and Samuelson (1947), do not capture the probabilistic approach to modeling systems initially introduced by Boltzmann and further clarified by Gibbs.8 Mathematical problems raised by Boltzmann were subsequently solved using tools introduced in a string of later contributions by the likes of the Ehrenfests and Cantor in set theory, Gibbs and Einstein in physics, Lebesque in measure theory, Kolmogorov in probability theory, Weiner and Levy in stochastic processes. Boltzmann was primarily concerned with problems in the kinetic theory of gases, formulating dynamic properties of the stationary Maxwell distribution — the velocity distribution of gas molecules in thermal equilibrium. Starting in 1871, Boltzmann took this analysis one step further to determine the evolution equation for the distribution function. The mathematical implications of this analysis still resonate in many subjects of the modern era. The etymology for ‘ergodic’ begins with an 1884 paper by Boltzmann, though the initial insight to use probabilities to describe a gas system can be found molecules can be completely determined, it is not possible to generalize these mechanics to the describe the macroscopic motion of molecules in large, complex systems, e.g., Brush (1983, esp. ch. II). 7 This ignores developments in econometrics that commenced in the 1950s. These developments were concentrated on discrete time models that featured additive errors with strictly stationary distributions. In other words, probabilistic implications were incorporated by solving a deterministic model and then adding an error to the postulated theoretical relationship. This static probabilistic approach to modeling uncertainty has difficulty determining the non-linear dynamics that are captured by models associated with statistical mechanics. 8 As such, Boltzmann was part of the larger: “Second Scientific Revolution, associated with the theories of Darwin, Maxwell, Planck, Einstein, Heisenberg and Schr¨ odinger, [which] substituted a world of process and chance whose ultimate philosophical meaning still remains obscure” (Brush 1983, p. 79). This revolution superceded the: “First Scientific Revolution, dominated by the physical astronomy of Copernicus, Kepler, Galileo, and Newton, . . . in which all changes are cyclic and all motions are in principle determined by causal laws”. As such, the irreversibility and indeterminism of the Second Scientific Revolution replaces the reversibility and determinism of the First.

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as early as 1857 in a paper by Clausius and in the famous 1860 and 1867 papers by Maxwell.9 The Maxwell distribution is defined over the velocity of gas molecules and provides the probability for the relative number of molecules with velocities in a certain range. Using a mechanical model that involved molecular collision, Maxwell (1867) was able to demonstrate that, in thermal equilibrium, this distribution of molecular velocities was a ‘stationary’ distribution that would not change shape due to ongoing molecular collision. Boltzmann aimed to determine whether the Maxwell distribution would emerge in the limit whatever the initial state of the gas. In order to study the dynamics of the equilibrium distribution over time, Boltzmann introduced the probability distribution of the relative time a gas molecule has a velocity in a certain range while still retaining the notion of probability for velocities of a relative number of gas molecules. Under the ergodic hypothesis, the average behavior of the macroscopic gas system, which can objectively be measured over time, can be interchanged with the average value calculated from the ensemble of unobservable and highly complex microscopic molecular motions at a given point in time. In the words of Weiner (1939, p. 1): “Both in the older Maxwell theory and in the later theory of Gibbs, it is necessary to make some sort of logical transition between the average behavior of all dynamical systems of a given family or ensemble, and the historical average of a single system”.

5.2.2

Uncertainty and the Ergodic Hypothesis

In aiming to achieve a scientific approach, positivists are fundamentally concerned with the quantification, measurement and empirical verification

9 There are many interesting sources on these points which provide citations for the historical papers that are being discussed. Cercignani (1998, pp. 146–150) discusses the role of Maxwell and Boltzmann in the development of the ergodic hypothesis. Maxwell (1879) is identified as “perhaps the strongest statement in favour of the ergodic hypothesis”. Brush (1974) has a detailed account of the development of the ergodic hypothesis. Gallavotti (1995) traces the etymology of “ergodic” to the ‘ergode’ in an 1884 paper by Boltzmann. More precisely, an ergode is shorthand for ‘ergomonode’ which is a ‘monode with given energy’ where a ‘monode’ can be either a single stationary distribution taken as an ensemble or a collection of such stationary distributions with some defined parameterization. The specific use is clear from the context. Boltzmann proved that an ergode is an equilibrium ensemble and, as such, provides a mechanical model consistent with the second law of thermodynamics. It is generally recognized that the modern usage of ‘the ergodic hypothesis’ originates with Ehrenfest and Ehrenfest (1912).

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of hypotheses. As a key assumption in the application of statistical methodology to time series data, ergodicity lies at the philosophical core of modern Finance. This statement captures the thrust of the strong criticisms that Davidson (1991, pp. 132, 133) and others make about the economic foundations of modern Finance: “Acceptance of the presumption of an ergodic economic environment is often rationalized by the necessity of developing economics as an empirically based science. Indeed, Samuelson has made the acceptance of the ‘ergodic hypothesis’ the sine qua non of the scientific method in economics”. In Finance, ergodicity plays a fundamental role in converting ex post logical relationships, such as the CAPM or Markowitz mean–variance diversification models, into ex ante empirical prescriptions. It is an essential component of the efficient markets hypothesis and is the driving force behind the fascination with the risk–return tradeoff and the equity risk premia, e.g., Mehra and Prescott (1985), Kocherlakota (1996) and Constantinides (2002). Formal Definitions Ergodicity is a property of stochastic processes. Formally, a stochastic process can be defined: Definition: Let {X(t)} be a family of random variables indexed by the linear (index) set
, where t ε
. Then {X(t)} is said to be a stochastic process.

In Finance, the terms stochastic (random) process and time series are often used interchangeably, though it is possible for the index set to refer to some linear variable other than time. Following Karlin and Taylor (1975, p. 32), “a stochastic process may be considered as well defined once its state space, index parameter and family of joint distributions are prescribed”. Similar approaches can be found in other sources, e.g., Dhrymes (1974, p. 383): “The probability characteristics of a stochastic process {X(t)} are completely specified if we determine the joint density function of a finite number of members of the family of random variables comprising the process”. Heuristically, the theory of stochastic processes describes the behavior of random variables, the X  s, over time, t ε . Conventionally, a random variable is a function that maps from a prespecified domain, or sample space, to some portion of the real line, 1 . In the theory of stochastic processes, a single realization of X defines a sample path starting at, say, X(0) and ending at X(T ). When the distribution of X is continuous, there are an infinite number of such possible sample paths. In order to make

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reference to individual sample paths, it is necessary to further introduce another indexing variable for X, ξ ε Ξ. This index allows individual samples paths or ‘states’ of X to be identified. It follows that X(ξ, T ) would refer to the time t = T observation from a single sample path in {X(t)} that starts at X(0) and ends at X(T ) and {X(ξ, T )} would be the set of all X(ξ, T ) at t = T . The ξ ε Ξ index makes it possible to define the operation of summing over the ξ at any time t = T . Such operations are relevant to identifying the properties of one of the joint distributions of the {X(t)} at a single point in time. In certain financial applications, e.g., where X refers to a security price, X takes values only on the positive, half line. In this case as well as when the X values are allowed to assume any value along the real line, it is conventional to assume that there is a zero probability of X being equal to plus or minus infinity. When t is fixed at a given point, X(t) has the conventional interpretation of a random variable, with associated (one-dimensional) probability density function. In contrast, the ergodicity assumption is concerned with using the X(ξ, t), X(ξ, t+1), X(ξ, t+2) · · · X(ξ, T ) observations from a single sample path to estimate the parameters of the joint distributions defining the {X(t)}. Specification of the stochastic process for X requires specification of the joint density functions that relate X  s at different points in time: the joint densities provide a probabilistic specification of how X evolves over time. This potentially complicated mapping can involve various combinations of discrete or continuous observations on X and t. In many empirical applications of stochastic process theory, the objective is to rationalize how to use past and present observations on X(t) (t ≤ 0) to predict future values (t > 0). A classical example of this type of reasoning in Finance is: “Stock returns will outperform bond returns in the long run”. Based on past realizations of the time series of returns on stocks and bonds, a prediction is made about the future path for returns. The task of prediction is difficult because the past and present X(t) represent only one realization of the process, i.e., there is only one observed sample path. Yet, for any given t ε  the joint probability densities can be used to specify an infinite number of future possible paths for X(t). Theoretically, an assumption is required to permit the statistics for the joint probability densities, i.e., the means, variances and other parameters, to be calculated from a single realization of the process. The requisite assumption invokes some form of ergodicity for the stochastic process.

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To visualize how an ergodicity assumption works, choose a given starting value for a stochastic process, X(0). From this starting point, the (continuous) joint probability distributions of the stochastic process define an infinite number of possible future paths for X(t). Between t = 0 and t = T each of these paths will start at X(0) and reach some point X(ξ, T ) at time T . It is now possible to take a ‘large number’ of the points for these paths at T and calculate an arithmetic mean of the {X(ξ, T )}. Setting N to be a large number this gives: N 1
¯ X(ξ, T ) X[N, T] = N ξ=1

The set of X defined by the ξ is referred to as the ensemble of time paths. Ergodic theorems are concerned with the conditions under which M (T ), the arithmetic average calculated from an individual time path from t = 1 to t = T , converges to the same limit (mean value) as the ensemble average taken at T . More precisely, for t measured discretely: M (T ) =

T T 1
1
¯ X(t|ξ = a) = X(t|ξ = a) ↔ X[N, T] T t=1 T t=1

Being concerned with the convergence properties of the arithmetic mean, ergodic theorems are closely related to the strong and weak laws of large numbers, e.g., Feller (1957, ch. X). Laws of Large Numbers An important convergence property of the arithmetic mean of the ensemble of time paths is given by the strong law of large numbers. Under certain conditions, such as stationarity of the stochastic process, the process is ergodic and the strong law also applies to time averages. More precisely, if the {X(ξ, T )} are independently and identically distributed (i.i.d.) with mean |µ| < ∞, the strong law of large numbers for the ensemble average states:   ¯ T] = µ = 1 P r lim X[N, N →∞

where µ is the population mean of {X(ξ, T )}, i.e., µ = E[X(ξ, T )]. In words, the strong law states that, for a random sample of iid {X(ξ, T )} observations, the sample mean will converge to the population mean with probability 1. This is purely a convergence property of the mean,

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no restriction is imposed on the variance or higher moments. Because {X(ξ, T )} is iid, it follows that µ = E[X(ξ, t)]. The weak law of large numbers is so-called because it deals with convergence in probability. A process which converges with probability one will also converge in probability, but not conversely. Applied to the ensemble averages, the weak law of large numbers requires: ¯ T ] − µ| > ε} = 0 lim P r{|X[N,

N →∞

where, for large enough N , ε can be chosen to be an arbitrarily small positive number. A key result, due to Khinchine (Khintchine), is that if {X(ξ, T )} or, more generally, {X(ξ, t)} is a sequence of independently, identically distributed random variables with a finite mean µ, then this sequence will obey the weak law. The difference between the strong and weak law relates to the type of convergence which is imposed. By imposing convergence with probability one, the strong law applies to the properties of the arithmetic average as N increases to the limit. In using convergence in probability, the weak law only applies to the arithmetic average at the limit. In modern presentations, the strong and weak laws apply to the properties of the arithmetic mean. Where additional conditions are imposed on the variance and, possibly, higher moments, then attention shifts to the central limit theorems which provide information not only about the mean but also the distribution of the sequence. In particular, by imposing additional restrictions to those required for the strong law, the central limit theorem can be used to estimate the size of the discrepancy between the arithmetic average and the population mean.10 This is accomplished by demonstrating that the distribution of the arithmetic average is asymptotically normal. The central limit theorem is a development on Chebyshev’s inequality which states: P r{|X(ξ, T ) − µ| ≥ θ} ≤

σ2 θ2

where σ 2 = E[(X(ξ, t) − µ)2 ] and θ is a given constant. In this form, Chebyshev’s inequality provides a relationship between the variance of a 10 Reference

to ‘the’ central limit theorem is somewhat misplaced as there are numerous varieties of central limit theorems which vary according to the initial assumptions imposed, e.g., Feller (1966, ch. VIII). Reference to the central limit theorem is to the general result which establishes the conditions under which sums of independent random variables are asymptotically normally distributed.

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distribution and the probability for the size of observed deviations from the mean. Feller (1966, p. 219) observes: “Chebyshev’s inequality must be regarded as a theoretical tool rather than a practical method of estimation. Its importance is due to its universality, but no statement of great generality can be expected to yield sharp results in individual cases”. The use of the variance to specify Chebyshev’s inequality is an essential component of the result. However, if it is assumed that the random variable X(ξ, T ) is strictly positive, as is the case where X refers to a security price, then it is possible to derive a form of the inequality that does not involve the variance, i.e.: E[X(T )] P r{X(ξ, T ) ≥ α} ≤ α where α > 0 is a given constant. This form of Chebyshev’s inequality illustrates the extensions that are possible where X can be restricted to be positive. The central limit theorem goes well beyond Chebyshev’s inequality to make a precise statement about the form of the probability distribution which, in turn, can be used to provide a practical estimate of the size of the deviation of the arithmetic average from the mean (|µ| < ∞) of the distribution, in terms of the distribution’s standard deviation (0 < σ < ∞). More precisely, at any arbitrary time t = T : Central Limit Theorem Let {X(ξ, T )} be a sequence of independently, identically distributed random variables with µ = E[X(ξ, T )] and σ 2 = E[(X(ξ, T ) − µ)2 ]. Then for every fixed β at time T :    β ¯ √ X[N, −u2 1 T] − µ j. This definition directs attention to the ergodic unit shift transformation: U ∗ Ψ[x(t)] = Ψ[U ∗ x(t)] = Ψ[x(t + 1)].15 Because this transformation is measure preserving, the replication property of strictly stationary distributions is captured.16 Recognizing the possibility that there may be other ergodic transformations than the unit shift, a connection between nonstationarity and nonergodicity is recognized: “Nonstationarity is a sufficient, but not a necessary condition, for nonergodicity” (Davidson 1991,

15 That the unit shift transformation implies stationarity is apparent from the definition: A stochastic process is strictly stationary if all its finite-dimensional probability densities are invariant against time shifts. In other words, strict stationarity requires time homogeneity. This transformation is applicable to gambling-type situations where the probability distribution of the outcome, e.g., head or tail, is the same for all replications. This requires the distribution of the initial x(0) to be identical to the distribution for x(t) and permits objective relative frequencies to be used to estimate parameters such as the mean. 16 There are ergodic theorems for transformations that are not measure preserving, e.g., Hurewicz’s ergodic theorem (Halmos 1949, p. 1017). In this case, special weighted replace equally weighted averages, passively averages and the weighted sums are shown to converge to a finite limit. Such transformations are not considered here and, as a consequence, all ergodic transformations considered are measure preserving.

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p. 332). Limit cycles are given as an example of a stationary stochastic process that is nonergodic.17 In turn, nonstationarity is identified with path dependence and structural breaks. Beyond this point, the discussion is less clear. The possibility that certain ergodic transformations, more complicated than the unit shift transformation, are consistent with structural breaks is unrecognized. The reasons that limit cycles can be stationary but not ergodic is unexplored.18 There is the distinct impression that Post Keynesians maintain the class of ‘real world’ processes can not be formally specified because such processes are nonstationary. The post-Keynesian critique is rooted in the insights of The General Theory. These insights include recognizing the distinction between fundamental uncertainty and objective probability for wealth accumulation and liquidity preference. It is unlikely that Keynes gained much exposure to Birkhoff (1931) and von Neumann (1932) or the substantive extensions and applications that appeared in the years following these contributions. As a consequence, the definition of ergodic theory in Post Keynesian thought lacks formal precision, e.g., “There is no reason to presume that structures will remain stable; the economic system is nonergodic” (Dow 2005, p. 387). Ergodic theory is implicitly seen as another piece of the mathematical formalism inspired by Hilbert and Bourbaki and captured in the Arrow–Debreu general equilibrium model of mainstream economics. Yet, the 19th century statistical mechanics that inspired ergodic theory is grounded in real world problems; in particular, Birkhoff (1931) and von Neumann (1932) formally solved the Boltzmann problem of incorporating dynamic phase transitions — from gas to liquid and from liquid to solid — where the mechanical model governing the ergodic process changes abruptly. Though there are a variety of ergodic transformations

17 This position is adopted in other sources, e.g., Dunn (2001, p. 573): “One must be careful not to conflate the concepts of stationarity and ergodicity. A stochastic process is stationary if the estimates of time averages do not vary with the period under observation. Since some stationary processes are nonergodic, that is, limit cycles, nonstationarity is not necessary for nonergodicity. But since all nonstationary processes are nonergodic nonstationarity is a sufficient condition”. 18 The failure of limit cycles to be ergodic can be generalized to the case where ‘dynamical systems possessing periodic orbits are never ergodic’ (Wightman 1971, p. 20). This is because a periodic system retains information about the initial condition as t goes to infinity, violating the ergodicity requirement. Stationarity in this case, which holds only for certain parameter values, is sometimes referred to as periodic stationarity to distinguish this case from the conventional strictly stationary case where processes are required to be ergodic.

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that incorporate such possibilities, the Post Keynesian critique only considers transformations that do not allow for such possibilities. 5.3 5.3.1

Bifurcation and Multimodal Densities The Phenomenological Approach

The distributional implications of boundary restrictions, derived by modeling the random variable as a diffusion process subject to reflecting barriers, have been studied for many years, e.g., Feller (1952,1954). The diffusion process framework is useful because it imposes a functional structure that is sufficient for known partial differential equation (PDE) solution procedures to be used to derive the relevant transition probability densities. Wong (1964) demonstrated that with appropriate specification of parameters in the PDE, the transition densities for popular stationary distributions such as the exponential, uniform, and normal distributions can be derived using Sturm-Liouville (SL) methods. Following Karlin and Taylor (1981), the transition probability density function U (= U [x, t|x0 ]) is associated with the random (economic) variable x at time t that follows a regular, time homogeneous diffusion process with a state space that is either a possibly infinite open interval Io = (a, b : ∞ ≤ a < b ≤ ∞), a finite closed interval Ic = [a, b : −∞ < a < b < +∞], or the specific interval Is = [0 = a < b = ∞).19 Assuming that U is twice continuously differentiable in x and once in t and vanishes outside the relevant interval, then U obeys the forward equation (e.g., Gihhman and Skorohod 1972, pp. 102–104): ∂U ∂ ∂2 {A[x]U } = (5.1) {B[x]U } − ∂x2 ∂x ∂t where B[x](= 1/2σ 2 [x] > 0) is one half the infinitesimal variance and A[x] is the infinitesimal drift of the process. B[x] is assumed to be twice and A[x] once continuously differentiable in x. Being time homogeneous, this formulation permits state, but not time, variation in the drift and variance parameters. The specific problem of deriving the transition probability density for a diffusion process starting at an interior point x0 > 0 with constant parameters A[x] = µ(≤ 0) and B[x] = 1/2σ 2 subject to a regular, fixed lower 19 A diffusion process is ‘regular’ if starting from any point in the state space I, any other point in I can be reached with positive probability (Karlin and Taylor 1981, p. 158). This condition is distinct from other definitions of regular that will be introduced: ‘regular boundary conditions’ and ‘regular S-L problem’.

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reflecting barrier at x = 0 is well known (e.g., Cox and Miller 1965). Because the process can reach but not pass below the barrier this imposes a restriction on the density to integrate to 1 over the specific interval Is = [0, ∞) or the open interval Io = (0 < a < b < ∞), depending on singularities at x = 0 in B[x] arising from, say, natural boundary restrictions. Differentiating with respect to time the condition that the density integrate to 1 over the state space then switching the order of integration and differentiation, permits the forward equation to be substituted for the time derivative. Letting U = U [x, t|x0 ] = U [x, t] for ease of notation, evaluating the remaining integral gives the reflecting boundary condition: ∂ {B[x]U [x, t]}|x=0 − A[0]U [0, t] = 0 (5.2) ∂x In effect, reflecting barriers can be represented as first derivative restrictions at the boundaries, in this case a lower boundary at x = 0. The drift term is required in the boundary condition to ensure conservation of probability. When the drift is zero, (5.2) reduces to the ‘flux zero’ condition. More generally, if the diffusion process is subject to upper and lower reflecting boundaries that are regular and fixed (−∞ < a < b < ∞), the “Sturm-Liouville problem” involves solving (5.1) subject to the separated boundary conditions:20 ∂ {B[x]U [x, t]}|x=a − A[a]U [a, t] = 0 (5.3) ∂x ∂ {B[x]U [x, t]}|x=b − A[b]U [b, t] = 0 (5.4) ∂x And the initial condition:  b U [x, 0] = f [x0 ] where f [x0 ] = 1 (5.5) a

and f [x0 ] is the continuous density function associated with x0 where a ≤ x0 ≤ b. When the initial starting value, x0 , is known with certainty, the 20 The

classification of boundary conditions is typically an important issue in the study of solutions to the forward equation, e.g., Berg and McGregor (1966). Important types of boundaries include: regular; exit; entrance; and natural. Also important in boundary classification are the properties of attainable and unattainable; whether the boundary is attracting or non-attracting; and whether the boundary is reflecting or absorbing. In the present context, only regular, attainable, reflecting boundaries are being considered in Sec. 5.2 with a few specific extensions to other types of boundaries being incorporated in Sec. 5.3. In general, the specification of boundary conditions is essential is determining whether a given PDE is self-adjoint The presence of the drift term in the boundary condition is required to ensure that the density integrate to one or, in the terminology of Feller (1952), that the boundary condition be norm preserving.

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initial condition becomes the Dirac delta function: U [x, 0] = δ[x − x0 ] and the resulting solution for U is referred to as the ‘principal solution’. Recognizing time homogeneity of the process eliminates the need to explicitly consider the location of t0 , for ease of notation it is assumed that t0 = 0. In practice, solving (5.1) combined with (5.3)–(5.5) requires a and b to be specified. While a and b have ready interpretations in physical applications, e.g., the heat flow in an insulated bar, determining these values in economic applications can be more challenging. Some situations, such as the determination of the distribution of an exchange rate subject to control bands, are relatively straight forward. Other situations, such profit distributions with arbitrage boundaries or output distributions subject to production possibility frontiers, may require the basic S-L framework to be adapted to the specifics of the modeling situation. In general, solving the forward Eq. (5.1) for U subject to (5.3), (5.4) and some admissible form of (5.5) is difficult, e.g., Feller (1952) and Risken (1989). In such circumstances, it is expedient to restrict the problem specification to permit closed form solutions for the transition density to be obtained. Wong (1964) provides an illustration of this approach. The PDE (5.1) is reduced to an ODE by only considering the non-trivial stationary distributions arising from the Pearson system.21 More precisely, the processes considered obey:  b f [x0 ] U [x, t|x0 ] dx0 = Ψ[x] lim U [x, t|x0 ] = t→∞

a

where only the principal solution (f [x0 ] = δ[x − x0 ]) is considered. Restrictions on the stationary distributions Ψ[x] are constructed by imposing the fundamental ODE condition for the unimodal Pearson system of distributions: e1 x + e0 dΨ[x] = Ψ[x] dx d2 x2 + d1 x + d0 The transition probability density U can then be reconstructed by working back from a specific closed form for the stationary distribution using known results for the solution of specific forms of the forward equation. In this procedure, the d0 , d1 , d2 , e0 and e1 in the Pearson ODE are used to specify the relevant parameters in (5.1). The U for important distributions that 21 Johnson and Kotz (1970, ch. 1) has a helpful introduction to the Pearson system of distributions.

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fall within the Pearson system, such as the normal, beta, central t, and exponential, can be derived by this method. The solution procedure employed by Wong (1964) depends crucially on restricting the PDE problem sufficiently to apply classical S–L techniques. Using S–L methods, various studies have generalized the set of solutions for U to cases where the stationary distribution is not a member of the Pearson system or U is otherwise unknown, e.g., Linetsky (2005). While the conventional method is to employ an eigenfunction expansion solution, Veerstraeten (2004) demonstrates that a more revealing solution is provided for the special case where B[x] and A[x] are constants if the Green’s function is used to solve the S–L problem.22 In order to employ the separation of variables technique used in solving S–L problems, (5.1) has to be transformed into the canonical form of the forward equation. To do this, the following important function has to be introduced:23    x A[s] ds r[x] = B[x] exp − a B[s] Using this function, the forward equation can be rewritten in the form (see Appendix):   ∂U ∂U 1 ∂ p[x] + q[x]U = (5.6) r[x] ∂x ∂x ∂t where p[x] = B[x]r[x]

q[x] =

∂A ∂2B − ∂x2 ∂x

Equation (5.6) is the canonical form of Eq. (5.1). The S–L problem now involves solving (5.6) subject to appropriate initial and boundary conditions. 22 In Veerstraeten (2004), the use of Green’s functions is implemented by using a transformation that achieves the PDE form: gUxx = Ut where the subscript denotes partial differentiation. A Laplace transform is then used to eliminate the time derivative. It is well known that using Laplace transforms to determine closed form solutions is usually restricted to the constant coefficient case because, without constant coefficients, the solution to the transform would involve another differential equation and nothing substantive is achieved by doing the transform. Hence, while Veerstraeten (2004) produces an insightful solution, more general cases require a different solution procedure if the Green’s function solution is used to determine the transition probability density. 23 Following Karlin and Taylor (1991, pp. 194, 195) and Linetsky (2005, p. 437) r[x] can be interpreted as B[x] times the ‘scale density’.

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Because the methods for solving the S–L problem are ODE-based, some method of eliminating the time derivative in (5.1) is required. The eigenfunction expansion approach applies separation of variables, permitting (5.6) to be specified as U [x, t] = e−λt ϕ[x] where ϕ[x] must satisfy the ODE:   dϕ 1 d p[x] + [q[x] + λ]ϕ[x] = 0 r[x] dx dx

(5.7)

(5.1 )

Transforming the boundary conditions involves substitution of (5.7) into (5.3) and (5.4) and solving to get: d {B[x]ϕ[x]}|x=a − A[a]ϕ[a] = 0 dx d {B[x]ϕ[x]}|x=b − A[b]ϕ[b] = 0 dx

(5.3 ) (5.4 )

Significant analytical advantages are obtained by making the S–L problem ‘regular’ which involves assuming: [a, b] is a closed interval with r[x], p[x] and q[x] being real valued and p[x] having a continuous derivative on [a, b]; and, r[x] > 0, p[x] > 0 at every point in [a, b]. ‘Singular’ S–L problems arise where these conditions are violated due to, say, an infinite state space or a vanishing coefficient in the interval [a, b]. The separated boundary conditions (5.3) and (5.4) ensure the problem is self-adjoint (Berg and McGregor 1966, p. 91). The S–L problem of solving (5.6) subject to the initial and boundary conditions admits a solution only for certain critical values of λ, the eigenvalues. Further, since Eq. (5.1) is linear in U , the general solution for (5.7) is given by a linear combination of solutions in the form of eigenfunction expansions. Details of these results can be found in Hille (1969, ch. 8), Boyce and Di Prima (2001) and Birkhoff and Rota (1989, ch. 10). When the S–L problem is self-adjoint and regular the solutions for the transition probability density can be summarized in the following: Proposition I: The regular, self-adjoint Sturm–Liouville problem has an infinite sequence of real eigenvalues, 0 = λ0 < λ1 < λ2 < · · · with: lim λn = ∞

n→∞

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To each eigenvalue there corresponds a unique eigenfunction ϕn ≡ ϕn [x]. Normalization of the eigenfunctions produces:  −1/2 b

Ψn [x] =

a

r[x]ϕ2n dx

ϕn

The ψn [x] eigenfunctions form a complete orthonormal system in L2 [a, b]. The unique solution in L2 [a, b] to (5.1), subject to the boundary conditions (5.3)–(5.4) and initial condition (5.5) is, in general form: U [x, t] =

∞


cn ψn [x]e−λ0 t

(5.8)

n=0

where

 cn =

a

b

r[x]f [x0 ]ψn [x]dx

This Proposition provides the general solution to the regular, self-adjoint S–L problem of deriving U when the process is subject to reflecting barriers. The Proposition demonstrates that having a discrete spectrum permits a representation for the transition probability density in the summation form of (5.8).24 However, while useful, (5.8) is not immediately revealing because time is allowed to vary over [0, ∞]. The issue of decomposing U into time dependent and time independent components is addressed in the following section. 5.3.2

Transition Density Decomposition

By providing an appropriate foundation, Proposition I facilitates the derivation of the general form of U for the regular, self-adjoint S–L problem. This section demonstrates that for this problem U can be decomposed into two components: a limiting equilibrium stationary density which is independent of time and the initial condition; and, a power series of transient terms that are time, boundary and initial condition dependent but with zero net density. In many econometric applications, the assumption of stationarity permits the Ψ[x] distribution to be used directly as the likelihood function. This implicitly assumes that only the limiting behavior of U as t → ∞ is relevant. The impact of the transient component is ignored. In a sampling 24 Birkhoff

and Rota (1989, p. 337) demonstrate that the regular S–L problem has a spectrum that is always discrete and has eigenfunctions that are (trivially) square-integrable. These eigenfunctions will be orthogonal with respect to the weight function r[x].

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context, this can be rationalized by standardizing the variables and assuming the transient components will average out to leave only the asymptotic behavior of a stationary process. Using the S–L approach, theoretical results on the U ’s associated with different types of boundary restrictions can be derived and the implications for, say, testing theory can be formulated by examining the shape and i.i.d. behavior of the relevant distributions and proposing appropriate adjustment factors for confidence intervals. Being in the form of an eigenfunction expansion, (5.8) cannot be readily applied to the types of closed form distributions typically encountered in econometrics. Further simplification is required. This leads to the following result:25 Proposition II: Density Decomposition Under the conditions required for Proposition I, the transition probability density function for x at time t (U ) can be expressed as the sum of a stationary limiting equilibrium distribution that is linearly independent26 of the boundaries and a power series of transient terms that are boundary and initial condition dependent: U [x, t|x0 ] = Ψ[x] + T [x, t|x0 ]

(5.9)

where Ψ[x] =  b a

r[x]−1 r[x]−1 dx

(5.10)

Using the specifications of λn , cn , and ψn from Proposition I, the properties of T [x, t] are defined as: T [x, t|x0 ] =

∞


cn e−λn t Ψn [x] =

n=1

with

 a

b

T [x, t|x0 ]dx = 0

∞ 1
−λn t e ψn [x]ψn [x0 ] r[x] n=1

and

(5.11)

lim T [x, t|x0 ] = 0

t→∞

Proposition II permits (5.9) to be combined with appropriately specified (5.10)–(5.11) to analyze the distributional implications of reflecting barriers. The distributional impact of the boundary restrictions enter through 25 In the following Proposition Ψ[x] is proportional to the ‘speed density’ given in Karlin and Taylor (1981, p. 195). R 26 This excludes the affect of the normalizing constant: b r[x]−1 dx. a

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T [x, t](= T [x, t|x0 ]). From the restriction on T [x, t] in (5.11), the total mass of the transient term is zero. The transient acts to redistribute the mass of the stationary distribution, thereby causing a change in shape. The specific degree and type of alteration depends on the relevant assumptions made about the parameters and initial functional forms. A key feature of the Proposition is that (5.11) is in the form of a discrete spectrum.27 Because the power series given in (5.11) involves powers of exp[−λn ], from Proposition I it follows that for given t the terms in the sum will decrease as n → ∞. This property and the discrete spectrum significantly simplifies the calculation of the transient T [x, t] in practical applications. To see the implications of Proposition II, consider the variety of boundary independent stationary densities Ψ[x] generated by appropriate choices of A[x] and B[x]. A range of results are available in Wong (1964), Borodin and Salminen (2002), Veerstraeten (2004), and Linetsky (2005). A benchmark solution is given by the Brownian motion, constant coefficient case where A[x] = µ(
= 0) and B[x] = 1/2σ 2 . Evaluating (5.10) gives the solution as (e.g., Veerstraeten 2004):    2µ  exp 2µ 2µ 2µ exp σ2 (x − a) σ2 x    2µ  = 2   Ψ[x] = 2 (5.12) σ exp 2µ σ exp 2µ σ2 b − exp σ2 a σ2 (b − a) − 1 There is no convention for a specific closed form to use for expressing this case. For example, Linetsky (2005) simplifies this solution by setting σ 2 = 1 and a = 0. In either form, Ψ[x] is a scaled exponential density. If µ = 0, the exponential density reduces to a uniform density: Ψ[x] = 1/(b − a). The uniform stationary density is intuitive: if the reflecting boundaries are constant and the process has no drift then as t → ∞ each point in the state space will be equally likely. It follows that the exponential stationary distributions are a consequence of the sample paths drifting to the upper (A[x] > 0) or the lower (A[x] < 0) boundary and ‘bouncing off’. These solutions can be contrasted with Wong (1964) where the stationary exponential density Ψ[x] = exp[−x] corresponding to the Pearson system {dΨ/dx} = −Ψ[x] is used but the specific interval Is = [0, ∞) is required due to the density having to integrate to one over the state space. 27 Hansen et al. (1998, pp. 12, 13) recognize the importance of having solutions with a discrete spectrum and provide a sufficient general condition required for this result: “finite first moment with the stationary density in natural scale”. This condition will always apply where there are reflecting barriers. The well-known result that a discrete spectrum is possible with certain singular diffusion problems arising with natural boundaries is also identifed.

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The simplicity of the closed form stationary density component, Ψ[x], of the transition density in the Brownian motion, constant parameter case does not carry over to the transient component. Following Borodin and Salminen (2002, pp. 121, 122), the simplest constant parameter solution selects the principal solution (delta function initial √ condition), sets the drift to zero (uniform stationary), B[x] = 1(σ = 2), and Ic = [0 ≤ x ≤ 1] (Ψ[x] = 1). This produces the power series of transient terms which using (5.11) defines the eigenvalues (λn = n2 π 2 ) and eigenfunctions √ (ψn = 2 cos nπx), i.e.: ∞
2 2 exp[−n π t] cos[nπ x] cos[nπ x0 ] T [x, t|x0 ] = 2 n=1

This ‘simplest’ solution can be used to illustrate the implications of altering the specification of the S–L problem. In particular, the drift zero, principal 1/2σ 2 prosolution with Ic = [0 ≤ x ≤ L] (Ψ[x] = 1/L) and B[x] =  2 2 2 2 duces eigenvalues (λn = ((n π σ )/2L ), eigenfunctions (ψn = (2/L) cos [(nπx)/L]) and the solution: ∞   nπ ! 2
n2 π 2 σ 2 nπ ! x cos x0 exp − t cos T [x, t|x0 ] = L n=1 2L2 L L Both the interval length and dispersion value act to scale the simple solution. This formulation permits the impact on T [x, t] of increasing the interval length for given t to be assessed. This result can also be used to illustrate the analytical significance of having a process with zero drift. To see the importance of drift specification, consider the principal solution where Ψ[x] is given by (5.12) with Ic = [a, b], A[x] = µ(
= 0) and B[x] = 1/2σ 2 . The U for this case has been derived in the context of exchange rates distributions with target rate bands (Svensson 1991; de Jong 1994). Formal treatments of the Brownian motion, constant parameter solution are available in Linetsky (2005) and, using the alternative Green’s function approach, in Veerstraeten (2004): # ∞ " exp σµ2 (x − x0 )
σ2 π2 exp[−λn t] T [x, t] = (b − a) λn (b − a)2 n=1      µ(b − a) x−a x−a + × n cos nπ sin nπ b−a σ2 π b−a      µ(b − a) x0 − a x0 − a + sin nπ × n cos nπ b−a σ2 π b−a

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where the eigenvalues are λn = (µ/2σ 2 ) + ((σ 2 π 2 n2 )/2(b − a)2 ) and the eigenfunctions retain both the sin and cos terms from the general solution. It is apparent that processes possessing a non-zero drift pose increased analytical complications associated with solving variable coefficient PDE’s. This substantial increase in the complexity of the solution for the transient component in the constant coefficient case does not bode well for finding ready to implement solutions in more complicated cases. This intuition about increased complexity is confirmed by Linetsky (2005) where the Sturm-Liouville problem is solved for the U associated with an Ornstein-Uhlenbeck (OU) process. In this case, the drift is state dependent A[x] = κ(χ − x) with κ > 0 and χ the long run mean of x (b > χ > a). The infinitesimal variance is constant with B[x] = 1/2σ 2 . Evaluating (5.10) for these values gives the solution of the stationary distribution as (e.g., Linetsky 2005, p. 447): √ 2κ n[z] Ψ[x] = σ N [β] − N [α] √ √ √ 2κ 2κ 2κ z= (x − χ) α = − (χ − a) β = (b − χ) σ σ σ where n[·] and N [·] are the standard normal density and the cumulative standard normal distribution function, respectively. The process of determining the eigenfunctions is decidedly more complicated (Linetsky 2005, pp. 447–449), involving functions not commonly encountered in econometrics. More precisely, changing variables to transform the forward equation into Weber–Hermite form permits solutions involving Weber–Hermite parabolic cylinder functions, which are related to Kummer confluent hypergeometric functions available in standard software packages, e.g., Mathematica.28 The solutions require derivatives of the Kummer functions to be evaluated numerically leading to solutions involving digamma functions. The worked solution for the eigenfunction expansion of U in this case is available in Linetsky (2005, p. 449). Beyond Regular Boundaries The previous discussion demonstrates that, despite having the theoretical advantage of a discrete spectrum, imposing regular reflecting barriers on 28 Whittaker and Watson (1963) is a useful source on Kummer and other transcendental functions.

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the state space for the forward equation quickly leads to analytical complexity in actually deriving the eigenfunction expansion for the transition probability density. These disadvantages need to be tempered by considering the alternatives to imposing reflecting boundaries. Consider the well known solution (e.g., Cox and Miller 1965, p. 209) for U involving a constant coefficient standard normal variate Y (t) = ({x − x0 − µt}/σ) over the unbounded state space Io = (∞ ≤ x ≤ ∞). In this case the forward Eq. (5.1) reduces to: 1/2{∂ 2U/∂Y 2 } = ∂U/∂t. By evaluating these derivatives, it can be verified that the principal solution for U is 

(x − x0 − µt)2 U [x, t|x0 ] =  exp − 2σ 2 t σ (2πt) 1



and as t → −∞ or t → +∞ then U → 0 and the stochastic process does not possess a non-trivial stationary distribution. In effect, if the process runs long enough then U will evolve to where there is no discernible probability associated with starting from x0 and achieving a given point x.29 The absence of a stationary distribution raises a number of practical problems, e.g., unit roots. Imposing regular reflecting boundaries is a certain method of obtaining a stationary distribution and a discrete spectrum (Hansen and Schienkman 1998, p. 13). Alternative methods, such as specifying the process to admit natural boundaries where the parameters of the diffusion are zero within the state space, can give rise to continuous spectrum and raise significant analytical complexities. At least since Feller (1952), the search for useful solutions, including those for singular diffusion problems, has produced a number of specific cases of interest. However, without the analytical certainty of the S–L framework, analysis proceeds on a case by case basis. One possible method of obtaining a stationary distribution without imposing both upper and lower boundaries is to impose only a lower (upper) reflecting barrier and construct the stochastic process such that positive (negative) infinity is non-attracting, e.g., Linetsky (2005) and A¨ıt-Sahalia (1999). This can be achieved by using an OU drift term. In contrast, Cox and Miller (1964, pp. 223–225) use the Brownian motion, constant coefficient forward equation with x0 > 0, A[x] = µ < 0 and B[x] = 1/2σ 2 subject to the lower reflecting barrier at x = 0 given in (5.2) to solve for both the U and the stationary density. The principal solution is solved using the 29 More precisely, the probability U [x, ∞|x ] is associated with the set of time paths that 0 start from x0 and achieve an ending in the given volume element dx as t → ∞.

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‘method of images’ to obtain: 1 U [x, t|x0 ] = √ σ 2πt



 exp −

(x − x0 − µt)2 2σ 2 t



 4x0 µt − (x − x0 − µt)2 + exp − 2σ 2 t      x + x0 + µt 1 2µ 2µx √ 1 − N + √ exp σ2 σ t σ 2πt σ 2 

where N [x] is again the cumulative standard normal distribution function. Observing that A[x] = µ > 0 again produces U → 0 as t → +∞, the stationary density for A[x] = µ < 0 follows: ψ[x] =

2|µ| exp − σ2



2|µ|x σ2



Though x0 does not enter the solution, combined with the location of the boundary at x = 0, it does implicitly impose the restriction x > 0. From Proposition II, T [x, t|x0 ] can be determined as U [x, t|x0 ] − Ψ[x]. Following Linetsky (2005), Veerstraeten (2004), and others, the analytical procedure used to determine U involved specifying the parameters of the forward equation and the boundary conditions and then solving for Ψ[x] and T [x, t]. Wong (1964) uses a different approach, initially selecting a stationary distribution and then solving for U using the restrictions of the Pearson system to specify the forward equation. In this approach, the functional form of the desired stationary distribution determines the appropriate boundary conditions. While application of this approach has been limited to the restricted class of distributions associated with the Pearson system, it is expedient when a known stationary distribution, such as the standard normal density, is of interest. More precisely, let  2 x 1 √ , exp − Ψ[x] = 2 2π

I0 = (−∞ < x < ∞)

In this case, the boundaries of the state space are non-attracting and not regular. Solving the Pearson equation gives: dΨ[x]/dx = −xΨ[x] and a

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forward equation of the OU form: ∂U ∂2U ∂ xU = + ∂x2 ∂x ∂t The principal solution for this unrestricted equation is  2
∞ exp[−nt] −x 1 U [x, t|x0 ] = √ exp Hn [x0 ]Hn [x] 2 n=0 n! 2π where Hn [x] are the Hermite polynomials, e.g., Kendall and Stuart (1963, p. 155), and the solution for the (discrete spectrum) T [x, t] is given by taking the sum from n = 1. Following Wong (1964, p. 268) Mehler’s formula can be used to express the solution for U as   1 −(x − x0 e−t )2 exp U [x, t|x0 ] =  2(1 − e−2t ) 2π(1 − e−2t ) Given this, as t → −∞ then U → 0 and as t → +∞, U achieves the standard normal ergodic distribution. The ergodic normal distribution is an example where a discrete spectrum is obtained without imposing boundaries on the state space. Another example is given by Wong (1964, pp. 268, 269) where the stochastic process has a state space Is = [0 ≤ x < ∞) and a discrete spectrum involving Laguerre polynomials with a stationary density of the form: 1 xa e−x = exp{α ln[x] − x} Ψ[x] = Γ[α + 1] Γ[α + 1] and forward equation:30 ∂2 ∂U ∂ [(α + 1 − x)]U = [xU ] − ∂x2 ∂x ∂t where the gamma function Γ[α + 1] has α > −1. This process is significant in having x dependence on the infinitesimal variance and a solution for U involving Laguerre polynomials that can be solved in closed form. Linetsky (2005) provides results for affine diffusion processes where the coefficients of the forward equation are given by B[x] = 1/2σ (x − l) with the shift parameter l < 0 and A[x] = κ(χ − x) with the same parameter restrictions as for the OU process. When subjected to to a lower reflecting barrier (because ∞ is non-attracting) the affine diffusion also has a discrete spectrum. However, a closed form solution is unavailable.31 30 The drift coefficient follows from observing d ln[Ψ]/dx = (α − x)/x where the drift is specified as A[x] − (dB[x]/dx) = (α − x) → A[x] = (α − x) + 1 (Cobb 1978). 31 Following standard convention, a closed-form solution is available if, and only if, at least one solution can be expressed in terms of a bounded number of well-known functions.

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Generalized Pearson Systems The results in Wong (1964), Linetsky (2005), Veerstraeten (2004), and related studies apply directly to the transition probability densities associated with the unimodal Pearson system. Generalizing this approach to allow more flexibility in the shape of the stationary distribution can be achieved using a higher order exponential density, e.g., Fisher (1921), Cobb et al. (1983), and Crauel and Flandoli (1998). Increasing the degree of the polynomial in the exponential comes at the expense of introducing additional parameters resulting in a substantial increase in the analytical complexity of the transition density spectrum. As a consequence, the generalized Pearson distributions typically defy a closed form solution for the transition densities. However, at least since Elliott (1955), it has been recognized that the solution of the associated regular S–L problem will still have a discrete spectrum, even if the specific form of the eigenfunctions and eigenvalues in T [x, t|x0 ] are not precisely determined (Horsthemke and Lefever 1984, Sec. 6.7). Inferences about transient stochastic behavior can be obtained by examining the solution of the deterministic non-linear dynamics. In this process, attention initially focuses on the properties of the higher order exponential distributions. To this end, assume that the stationary distribution is a fourth degree or ‘general quartic’ exponential: Ψ[x] = K exp[−Φ[x]] = K exp[−(β4 x4 + β3 x3 + β2 x2 + β1 x)] where: K is a constant determined such that the density integrates to one; and, β4 > 0.32 Following Fisher (1921), the class of distributions associated with the general quartic exponential admits both unimodal and bimodal densities and nests the standard normal √ as a limiting case where β4 = β3 = β1 = 0 and β2 = 1/2 with K = 1/( 2π). The generalized Pearson ODE restriction for the quartic exponential takes the form: e3 x3 + e2 x2 + e1 x + e0 dΨ[x] = Ψ[x] dx g[x] These well-known functions are defined to be the elementary functions, including the error function, gamma function and the general hypergeometric functions. Solutions which involve infinite series, limits, and continued fractions are not consistent with closed forms. 32 In what follows, except where otherwise stated, it is assumed that σ = 1. Hence, the condition that K be a constant such that the density integrates to one incorporates the σ = 1 assumption. Allowing σ
= 1 will alter either the value of K or the β’s from that stated.

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In this case, the generalization occurs because the degree of the ‘shape polynomial’ in the numerator has been increased from one to three. It is possible to further generalize to a stationary distribution with a k (>4) degree exponential. With correct selection of parameters, the quartic exponential density is sufficient to capture the implications of stationary bimodality; a higher degree polynomial is needed if the possible number of stationary modes is greater than two. The implications of generalizing the Pearson system by increasing the degree of the exponential is apparent from the ODE restriction. In the Pearson system, g[x] = d0 + d1 x + d2 x2 is a polynomial of degree at most two in x that depends on the particular specification of the stationary or transition density desired. The classification of Pearson system of stationary distributions into the various Types I–VII follows the specification of the degree of the polynomial g[x] (Johnson and Kotz 1970, pp. 9–14). Extending this approach to the generalized Pearson system, when g[x] is a constant there is a family N of distributions that include the standard normal and the quartic exponential densities, instead of a single distribution defined by the standard normal that is the limiting case of all Pearson distribution types. Permitting g to be a linear transformation of the form d1 x restricts the admissible xε{0 < x < ∞). In particular, a stationary distribution of the form: ψ[x] = KG exp −[g0 ln[x] + g1 x + g2 x2 + g3 x3 ] produces the family of gamma densities that nest the Pearson Type III. Allowing g[x] = d2 x2 produces the inverse gamma family nesting the Pearson Type V; and, setting d1 = d2 = 1 and g[x] = x(1 − x) produces the beta family nesting the Pearson Type I. Each of these families requires an appropriate version of the exponential stationary distribution to correspond with the desired g[x] in the generalized Pearson ODE (Cobb et al. 1983). In specifying the generalized Pearson system, the additional complications introduced by the higher degree polynomial in the numerator of the ODE augments the concern with different solutions of the quadratic polynomial in the denominator that arises with the Pearson system. To avoid complicated solutions for the generalized Pearson ODE involving ratios of polynomials in x, it is expedient to focus attention on the non-linearity in the drift and away from state dependence of the infinitesimal variance. In effect, enhancing precision in the estimation of distributional shape comes at the expense of incorporating state dependence in the variance. This

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induces a fundamental shift in the conceptual approach to modelling random behavior using diffusion processes. Consider the problem of modeling the drift and diffusion parameters for the short term interest rate process, e.g., Stanton (1997). Following Ait-Sahalia (1996) the preferred approach to empirically determining these parameters has been to fit a flexible, nonlinear functional form for each parameter, such as θ3 B[x; β] = β1 x + xβ2 x The generalized Pearson ODE suggests that such ‘flexibility’ is misleading. Consistent with this observation, Chapman and Pearson (2000) argue against the flexible, non-linear function form approach to capturing nonlinearity in the drift of short-term interest rates due to multicollinearity between the drift and diffusion coefficients. Similarly, Hurn and Lindsay (2002) address the multicollinearity problem by employing orthogonal Legendre polynomials and find estimation of the non-linear drift function depends crucially on “specification of the drift in terms of orthogonal constituents” (p. 563). Hence, permitting state dependence of both the drift and volatility imposes significant restrictions on the parameters of the stationary distribution. Despite being recognized as early as Fisher (1921) as the class of distributions for which the efficiency of the method of moments coincides with maximum likelihood, generalized Pearson distributions such as the quartic exponential density have been mostly ignored in econometrics in favor of processes, such as affine diffusions, that feature state dependence of the infinitesimal variance. Where diffusions from this class are used, as in the ‘double- well’ diffusion process in Ait-Sahalia (1999): A[x; θ] = θ0 + θ1 x + θ2 x2 +

dX(t) = (X(t) − X(t)3 )dt + dW (t) where dW (t) is a Weiner process, the parametric flexibility needed to fit the non-linearity in the drift is ignored.33 While the double-well process does have a symmetric bimodal stationary density, the a priori restrictions on the non-linear drift term are apparent from the specification of the generalized Pearson ODE. The analytical advantage of setting the infinitesimal variance to a constant is to enhance fitting of the shape polynomial for the stationary 33 Ait-Sahalia

(1999) also considers a diffusion with non-linear drift (α0 + α1 X(t) + α2 X(t)2 + α3 X(t)−1 ) and state dependent infinitesimal variance (σX(t)p ). This complicated process could be readily transformed into the family G by setting p = 1, and changing 1/X to ln[X] in the drift. Conceptual advantage can be gained by adding a cubic term in the drift, e.g., (Cobb 1981, p. 76).

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distribution. The restrictions imposed by the double well process produce a quartic exponential distribution that is bimodal and symmetric about zero. The parameter restrictions imposed are too severe to be representative of actual economic time series. 5.3.3

Bifurcation and the Quartic Exponential Distribution

The stationary distribution of the double well process is a special case of the symmetric quartic exponential distribution: Ψ[y] = KS exp[−{β2 (x − µ)2 + β4 (x − µ)4 }] where

β4 ≥ 0

where µ is the population mean and the symmetry restriction requires β1 = β3 = 0. To see why the condition on β1 is needed, consider change of origin X = Y − {β3 /4β4 } to remove the cubic term from the general quartic exponential (Matz 1978, p. 480): Ψ[y] = KQ exp[−{κ(y − µy ) + α(y − µy )2 + γ(y − µy )4 }] where γ ≥ 0 The substitution of y for x indicates the change of origin which produces the following relations between coefficients for the general and specific cases: κ=

8β1 β42 − 4β2 β3 β4 + β33 8β42

α=

8β2 β4 − 3β32 8β4

γ = β4

The symmetry restriction κ = 0 can only be satisfied if both β3 and β1 = 0. Given the symmetry restriction, the double well process  further requires −α = γ = σ = 1. Solving for the modes of Ψ[y] gives ± {|α|/(2γ)} which reduces to ±1 for the double well process, as in Ait-Sahlia (1999, fig. 6B, p. 1385). As illustrated in Fig. 5.4, the selection of ai in the stationary density Ψi [x] = KQ exp{−(0.25x4 −0.5x2 −ai x)} defines a family of general quartic exponential densities, where ai is the selected value of κ for that specific density.34 The coefficient restrictions on the parameters α and γ dictate that these values cannot be determined arbitrarily. For example, given that β4 is set at 0.25, then for ai = 0, it follows that α = β2 = 0.5. ‘Slicing across’ the surface in Fig. 5.4 at ai = 0 reveals a stationary distribution that is equal to 34 A number of simplifications were used to produce the 3D image in Fig. 5.4: x has been centered about µ; and, σ = KQ = 1. Changing these values will impact the specific size of the parameter values for a given x but will not substantively change the appearance of the density plots.

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Fig. 5.4 Family of stationary densities for Ψi [x] = Ko exp{−(0.25x − 0.5x2 − ai x)}. ∗ Each of the continuous values for ai signifies a different stationary density. For example, at ai = 0 the density is the double well density which symmetric about zero and with modes at ±1.

the double well density. Continuing to slice across as ai increases in size, the bimodal density becomes progressively more asymmetrically concentrated in positive x values. Though the location of the modes does not change, the amount of density between the modes and around the negative mode falls. Similarly, as ai decreases in size the bimodal density becomes more asymmetrically concentrated in positive x values. While the stationary density is bimodal over ai ε {−1, 1}, for |ai | large enough the density becomes so asymmetric that only a unimodal density appears. For the general quartic, asymmetry arises as the amount of the density surrounding each mode (the sub-density) changes with ai . In this, the individual sub-densities have a symmetric shape. To introduce asymmetry in the sub-densities, the reflecting boundaries at a and b that bound the state space for the regular S–L problem can be used to introduce positive asymmetry in the lower subdensity and negative asymmetry in the upper sub-density. Solving the forward equation to obtain a closed form for the transition density of a diffusion process with a quartic exponential stationary distribution is confounded by the presence of the cubic non-linearity in the numerator of the generalized Pearson ODE and in the forward equation term: ∂ {A[x] U [x, t]} ∂x

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Except in the special generalized Pearson cases such as the family G of gamma densities, also permitting state variation in B[x] renders the forward equation for higher order exponential densities unsolvable in closed form. To obtain information about T [x, t|x0 ], attention focuses on solving the non-linear dynamics of the deterministic equation associated with the drift term. For the symmetric quartic exponential, these deterministic dynamics can be described by the pitchfork bifurcation ODE: dx = −x3 + ρ1 x + ρ0 dt where ρ0 and ρ1 are the ‘normal’ and ‘splitting’ control variables, respectively (e.g., Cobb 1978). While ρ0 has significant information in a stochastic context, this is not usually the case in the deterministic problem so ρ0 = 0 is assumed. Given this, for ρ1 ≤ 0, there is one real equilibrium ({dx/dt} = 0) solution to this ODE at x = 0 where “all initial conditions converge to the same final point exponentially fast with time” (Crauel and Flandoli 1998, p. 260). For ρ1 > 0, the solution bifurcates into three equilibrium solu√ tions x = {0, ± ρ1 }, one unstable and two unstable. In this case, the state space is split into two physically distinct regions (at x = 0) with the degree of splitting controlled by the size of ρ1 . Even for initial conditions that are ‘close’, the equilibrium achieved will depend on the sign of the initial condition. It is well known that the introduction of randomness to the pitchfork ODE changes the properties of the equilibrium solution, e.g., (Arnold 1998, sec. 9.2). It is no longer necessary that the state space for the principal solution be determined by the location of the initial condition relative to the bifurcation point. The possibility for randomness to cause some paths to cross over the bifurcation point depends on the size of σ which measures the non-linear signal to white noise ratio. Of the different approaches to introducing randomness (e.g., multiplicative noise), the simplest approach to converting from a deterministic to a stochastic context is to add a Weiner process to the ODE. Augmenting the diffusion equation to allow for σ to control the relative impact of non-linear drift versus random noise produces the ‘pitchfork bifurcation with additive noise’ (Arnold 1998, p. 475) which in symmetric form is dX(t) = (ρ1 X(t) − X(t)3 ) + σdW (t) While capable of sustaining the common approach in econometrics based on a one-to-one correspondence between invariant Markov forward measures

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and stationary distributions, the dynamics of the pitchfork process captured by T [x, t|x0 ] have been ‘forgotten’ (Arnold 1998, p. 473). Bifurcation and the Ex Ante/Ex Post Dilemma The significance of the ex ante/ex post distinction was recognized as early as Myrdal (1939), though only in connection with the more general problem of determining aggregate savings and investment equilibrium (Meacci 2009). As Shackle (1967, pp. 242, 243) observes: it is the level of incomes which moves in search of an equilibrium between (designed ex ante) saving and (designed ex ante) investment . . . when there is a disparity, a disequilibrium, between the two ex ante quantities, there will almost inevitably follow one period later, that is, so soon as this disparity is revealed, ex post, a set of decisions by business men to change designed general output, and thus aggregate income.

For purposes of equity security valuation, the ex ante/ex post distinction applies to the use of past data to forecast future values, especially for equity prices and those variables that drive equity prices. The single ex post observed sample path used to estimate parameters of the transition density is the outcome of decisions made using ex ante distributions that can differ substantively from the ex post distribution. In particular, if the future time paths for the ensemble of sample paths are of long enough duration, there will almost certainly be differences in the ex ante and ex post distributions. That ex ante and ex post distributions are equivalent in stochastic theories of equity value associated with modern Finance is due to the usually unstated assumption of time reversible ergodic processes. Despite the importance of the assumption of ergodicity, a sufficiently accurate definition of an ergodic process has not been provided. More precisely, if the stock price observations are generated by time irreversible ergodic processes, then the calculation of time averages based on a sufficiently long enough set of past data cannot, by definition, provide a statistically reliable estimate of the state space averages that will be observed in a sufficiently distant future calendar time. In the case of a time irreversible bifurcating process, there is a non-linearity in the ex ante drifts that cannot be captured by statistics calculated from a single sample path. While a single ex post sample path will typically appear to be a unimodal density, the ex ante stationary distributions are bimodal. The precise location and density associated with each mode is subjectively determined and depends on the anticipated

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time to bifurcation. In other words, the type of reversible ergodic stochastic processes commonly encountered in mainstream academic Finance are less capable of representing the ex ante stochastic behavior of equity prices than irreversible, bifurcating ergodic processes. Significantly, a type of fundamental uncertainty is inherent in bifurcating processes as illustrated in the selection of ai in Fig. 5.4. A semantic connection can be established between the subjective uncertainty about encountering a future bifurcation point and, say, the possible collapse of an asset price bubble due to a change in Keynesian convention about market valuations. Examining the quartic exponential stationary distribution associated with a bifurcating ergodic process, it is apparent that this distribution nests the Gaussian distribution as a special case. In this sense, the bifurcating process represents a stochastic generalization of the mainstream stochastic theory of equity price behavior. By construction, ergodic bifurcating processes become unstable due to the mean being non-linear in time, with degree and timing of the instability being uncertain at t = 0. Following Shackle, once the surprise generated instability has been assimilated the ‘standstill effect’ ends with the formation of new ex ante distributions. While the ex post process at any point in time is given, the ex ante distributions can vary depending on changes in subjective perceptions and the like. A specification of the uncertainty critique based on decomposing the transition probability density of an ergodic one-dimensional diffusion process subject to regular upper and lower reflecting barriers is seemingly inconsistent with the spirit of Keynes (1936), Shackle (1958), or Davidson (2003, 2007). In contrast to Shackle, the use of diffusion processes involves additive probability and the phenomenological approach involves the solution of differential equations. Uncertainty appears, not with some portion of the total probability that is not allocated, but rather with the determination of the amount of the total ergodic density allocated to subdensities associated with the different modes. The problem of using the time path for a single ex post realization to estimate the parameters of the ex ante ensemble of future time paths is questioned when the ex ante stationary density is captured by using bimodal or multi-modal stationary densities such as the quartic exponential. As such, estimates of means and variances have less meaning than Shackle’s approach of identifying the ‘best’ or ‘worst’ that can happen associated with the modes of the ex ante distribution. The use of bifurcating stochastic processes involves a number of fundamental differences with conventional time reversible processes. Because multimodality implies a mean process that is non-linear in time, the

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variation in the ex ante process originates with changes in mean values, not changes in variance and covariance. At least since Shiller (1981), the ‘excess’ variation in stock prices compared to variation in the underlying fundamentals has puzzled academics. This ‘excess’ variation can be explained using: ex ante processes with mean values that are non-linear in time; and, observing that the ex post sample path is only a single realization of the ensemble of possible ex ante paths between t = 0 and t = T . In order to efficiently recover information about the distribution of the mean value process, only in special cases is it feasible to introduce time variation in the volatility parameter. This follows because the generalized Pearson conditions have to be satisfied in order to recover information about the functional form of the underlying stationary distribution from the solution to the forward equation. Following Ford (1993, pp. 690,691), Shackle has a number of theoretical insights about decision making under uncertainty applicable to the interpretation of time irreversible processes: it is not possible “to construct a dynamic model of an economic system except for one period at a time”; “at the outset of the ensuing period market participants would form new expectations, not necessarily linked to anything which had gone before”; and economics cannot be a predictive science as it is built on concepts of “mechanical, non-expectational time”. This leads to the following interpretation of the decision problem: at a particular t = 0 with X(0), the two modes for the ensemble of ex ante time paths reflect the possibilities of continued prosperity or market collapse. This is consistent with Shackle’s theory that individuals concentrated on the ‘best’ and ‘worst’ that can happening in making decisions under uncertainty (Ford 1993, p. 696). Observing the ai evolves over time to capture change in subjective expectations of prosperity or collapse, changes in ai can be seen to roughly correspond to Shackle’s ‘degrees of potential surprise’. Appendix: Preliminaries and Proofs Preliminaries on solving the Forward Equation Due to the widespread application in a wide range of subjects, textbook presentations of the Sturm–Liouville problem possess subtle differences that require some clarification to be applicable to the formulation used in this chapter. In particular, to derive the canonical form (5.6) of the Fokker– Planck equation (5.1) observe that evaluating the derivatives in (5.1) gives:   2   ∂U ∂ B ∂U ∂B ∂A ∂2U − A[x] + U= − B[x] 2 + 2 ∂x ∂x ∂x ∂x2 ∂x ∂t

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This can be rewritten as   1 ∂ ∂U ∂U P [x] + Q[x]U = r[x] ∂x ∂x ∂t where P [x] = B[x]r[x]

∂B 1 ∂P =2 − A[x] r[x] ∂x ∂x

Q[x] =

∂2B ∂A − 2 ∂x ∂x

It follows that 1 ∂P 1 ∂r ∂B B[x] ∂r ∂B = − 2 P [x] = 2 − A[x] − ∂x r[x] ∂x r ∂x ∂x r[x] ∂x This provides the solution for the key function r[x]: 1 ∂B A[x] 1 ∂r − =− → ln[r] − ln[k] = − r[x] ∂x B[x] ∂x B[x]    x A[s] ds r[x] = B[x] exp − B[s]



x

A[s] ds B[s]

This r[x] function is used to construct the scale and speed densities commonly found in presentations of solutions to the forward equation, e.g., Karlin and Taylor (1981) and Linetsky (2005). Another specification of the forward equation that is of importance is found in Wong (1964, Eq. 6, 7):   dθ dθ d B[x]ρ[x] + λρ[x]θ[x] = 0 with b.c. B[x]ρ[x] =0 dx dx dx This formulation occurs after separating variables, say with U [x] = g[x]h[t]. Substituting this result into (5.1) gives: ∂h ∂2 ∂ [A g h] = g[x] [B g h] − 2 ∂x ∂x ∂t Using the separation of variables substitution (1/h){∂h/∂t} = −λ and redefining g[x] = ρθ gives:     d d d d B g − A g = −λg = B[x]ρ[x]θ[x] − A[x]ρ[x]θ[x] = −λρθ dx dx dx dx Evaluating the derivative inside the bracket and using the condition {d/dx}[Bρ] − Aρ = 0 to specify admissible ρ gives:     d d d d d θ (Bρ) + Bρ θ − Aρθ = Bρ θ = −λρ[x]θ[x] dx dx dx dx dx which is Eq. (5.6) in Wong (1964). The condition used to define ρ is then used to identify the specification of B[x] and A[x] from the Pearson system. The associated boundary condition follows from observing the ρ[x] will

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be the ergodic density and making appropriate substitutions into the boundary condition: d ∂ {B[x]f [t]ρ[x]θ[x]} − A[x]f [t]ρ[x]θ[x] = 0 → [Bρθ] − Aρθ = 0 ∂x dx Evaluating the derivative and taking values at the lower (or upper) boundary gives: dBρ dθ[a] + θ[a] − A[a]ρ[a]θ[a] = 0 dx dx   dB[a]ρ[a] dθ[a] + θ[a] − A[a]ρ[a] = B[a]ρ[a] dx dx

B[a]ρ[a]

Observing the expression in the last bracket is the original condition with the ergodic density serving as U gives the boundary condition stated in Wong (1964, Eq. 7). Proof of Proposition II35 (a) ψn has exactly n zeroes in [a, b] Hille (1969, p. 398, Theorem 8.3.3) and Birkhoff and Rota (1989, p. 320, Theorem 5) shows that the eigenfunctions of the Sturm–Liouville system (5.1 ) with (5.3 ), (5.4 ) and (5.5) have exactly n zeroes in [a, b]. More precisely, since it assumed that r > 0, the eigenfunction ψn corresponding to the nth eigenvalue has exactly n zeroes in (a, b). b ψ [x]dx = 0 (b) For ψn = 0, a n Proof: For ψn = 0 the following applies:

  d 1 d [B[x]ψn ] − A[x]ψn λn dx dx   b d 1 [B[x]ψn ]|x=b − A[b]ψn [b] ψn [x]dx = λ dx n a  d − [B[x]ψn ]|x=a + B[a]ψn [a] = 0 dx ψn =

Since each ψn [x] satisfies the boundary conditions. 35 The

essence of this proof is due to John Heancy.

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(c) For some k, λk = 0. Proof: From Proposition 1: U [x, t] = Since

b a

∞


dk e−λk t ψk [x]

k=0

U [x, t]dx = 1 then: 1=

∞


ck e−λk t



k=0

b

a

ψk [x]dx

But from part (b) this will = 0 (which is a contradiction) unless λk = 0 for some k. (d) λ0 = 0 Proof: b From part (a), ψ0 [x] has no zeroes in [a, b]. Therefore, either a ψ0 [x]dx > 0 b or a ψ0 [x]dx < 0. It follows from part (b) that λ0 = 0. (e) λn > 0 for n
= 0. This follows from the strict inequality conditions provided in Proposition 1 and in part (d). (f) Obtaining the solution for T [x] in Proposition 2. From part (d) it follows: d {[B[x]ψ0 [x, t]]x − A[x]ψ0 [x, t]} = 0 dx Integrating this equation from a to x and using the boundary condition gives: [B[x]ψ0 [x, t]]x − A[x]Ψ0 [x, t] = 0 This equation can be solved for ψ0 to get:   x A[s] ds = C[r[x]]−1 ψ0 = A[B[x]]−1 exp a B[s] Therefore: ψ0 [x] =

 a

b

−1/2 −2

r[x]C [r[x]] 2

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where

C = constant

[r[x]]−1 C[r[x]]−1 =  b [ a r[x]−1 dx]1/2

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Using the definition in Proposition I and observing that the integral of f [x] over the state space is one it follows:   b r[x]−1 1 f [x]r[x]  b dx =  b c0 = 1/2 a [ a r[x]dx] [ a r[x]dx]1/2 r[x]−1 ∴ c0 ψ[x] =  b [ a [r[x]]−1 dx] (g) The Proof of Proposition 2 now follows from parts (f), (e) and (b).

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CHAPTER 6

Technical Analysis Demystified 6.1

6.2

6.3

What is Technical Analysis? 6.1.1 Different Forms of Technical Analysis . . . . . 6.1.2 Conceptual Foundations of Technical Analysis 6.1.3 New Finance and Mystical Finance . . . . . . . Traditional Technical Analysis 6.2.1 The Dow Theory . . . . . . . . . . . . . . . . . 6.2.2 Charting and Moving Average Systems . . . . 6.2.3 Chart Patterns . . . . . . . . . . . . . . . . . . 6.2.4 Contrarian and Contrary Opinion Strategies . . Recent Developments in Technical Modeling 6.3.1 Relative Strength . . . . . . . . . . . . . . . . . 6.3.2 Momentum and ‘Price Rate of Change’ . . . . 6.3.3 Oscillators and MACD . . . . . . . . . . . . . .

. . . 462 . . . 464 . . . 476 . . . .

. . . .

. . . .

483 495 499 509

. . . 514 . . . 518 . . . 522

The ‘New’ New Finance New Finance is a euphemism for behavioral finance, an approach based primarily on theoretical results aimed at explaining empirical anomalies in security prices. Following Kahneman and Tversky (1979), these theories are derived from psychological biases that appear in human behavior. Consistent with the positivist approach, logical explanations are provided for empirical results that are inconsistent with the efficient markets hypothesis (EMH). While recognizing that there are anomalies in prices, New Finance is not too concerned with demonstrating that observed anomalies can be used to generate abnormal returns. This is the preserve of the ‘New’ New Finance. The progress of this ‘movement’ has been remarkable, encompassing even the key publication outlets of modern Finance, e.g., Zhu and Zhou (2009). The research agenda is outlined in Friesen et al. (2009): “At present, we lack theoretical models that can explain the presence of pattern-based trading rules, though several empirical studies suggest that such rules may be profitable.” Is it possible that the last vestige of the EMH — weak form efficienty — is falling?

461

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6.1

What is Technical Analysis?

6.1.1

Different Forms of Technical Analysis

Much like ‘fundamental analysis’, ‘technical analysis’ suffers from an oversimplified interpretation given to this body of techniques. For many years, adherents of modern Finance maintained the empirical evidence against technical analysis was overwhelming. For example, Malkiel (1990, p. 133) claims: Technical rules have been tested exhaustively by using stock price data on both major exchanges, going back as far as the beginning of the 20th century. The results reveal conclusively that past movements in stock prices cannot be used to foretell future movements. The stock market has no memory. The central proposition of charting is absolutely false, and investors who follow its precepts will accomplish nothing but increasing substantially the brokerage charges they pay.

Yet, in a remarkable about-face, this ‘overwhelming’ evidence has been contradicted and the prevailing academic view now seems to be: “Most recent studies investigating return predictability have concluded that security returns are predictable from information that investors can easily obtain” (Beller et al. 1998). It is not difficult to find similar views, e.g., Brock et al. (1992), Lo and MacKinlay (1999), Siegel (1998, ch. 17), and Savin et al. (2007). Despite this accumulating evidence, some modern Finance stalwarts still maintain that consistently profitable trading rules have not yet been demonstrated and the results are likely due to ‘data snooping’ and the like, e.g., Bessembinder and Chan (1998), Sullivan et al. (1999) and Ready (2002).1 Much like fundamental analysis, technical analysis is an important, diverse and sometimes complicated approach to the evaluation of both equity securities and commodity derivatives that has been overly simplified in traditional tests of the ‘weak form’ efficient markets hypothesis. The methods and procedures involved in taking a body of ‘technical information’ and translating that information into an evaluation of whether a stock 1 The

production of empirical results on technical analysis in modern Finance provides an interesting illustration of McCloskey’s ‘conversations among academics’. For example, a recent listing of eighteen studies, largely from the core journals of modern Finance, that provide either direct or indirect empirical support for technical analysis can be found in Lo et al. (2000, p. 1706). This list does not include the numerous studies outside the core journals of modern Finance, i.e., outside the conversation among strong adherents of modern Finance, that also provide support for technical analysis.

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is correctly valued does not necessarily correspond to conventional methods of testing whether, on average, changes in a particular type of technical information is rapidly translated into prices. The perception that technical analysis is an alternative and competitive approach to fundamental analysis is also inaccurate. Much of technical analysis is concerned with market timing and speculative trading, not with investment based on the long term prospective yield of the security. Certain types of technical analysis may be used in conjunction with fundamental analysis, e.g., as a guide to market timing for determining when to purchase securities that have been identified using fundamental analysis. Some forms of technical analysis can be theoretically rationalized in terms of fundamentals, such as the intra-day interaction between market liquidity and order flow. Even the precise dividing line between technical and fundamental analysis is unclear, with some ‘technical’ trading rules exploiting information that would best be characterized as fundamental. The boundaries of technical analysis can be defined with reference to the type of information that is being used in the specific trading rule or valuation model. More precisely, technical analysis involves the use of ‘market generated data’ as inputs. This includes: current and past security prices; aggregations of these prices into market and sector indexes; total volume; up/down volume and ratios or differences for the number advancing issues to number of declining issues (e.g., the advance/decline line); implied volatilities for put and call options; relationships among bond yields, such as the ‘confidence index’ published by Barron’s; odd lot trading volume; and short sales positions in aggregate or by type of trader (specialist vs. odd lot). It is possible to extend the set of information to include other more circumspect types of ‘market generated’ data, e.g.: mutual fund cash positions; credit and debit balances with brokerage firms; insider trading transactions (revealed through SEC filings such as Form 4); and, investment advisory opinions. Technical analysis involves the processing of these sources of information into valuation or market timing decisions about securities. In some cases the processing is cursory, in other cases the processing is quite sophisticated. Technical analysts are often referred to as ‘chartists’, e.g., Siegel (1998, p. 240), Lo et al. (2000, p. 1705). Though many types of technical analysis employ charts, this reference confuses the method of analysis with the type of information being analyzed and the type of signal that is expected. Though widely used by technical analysts, charts are neither necessary or sufficient for technical analysis. Even when charts are being

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used, there are a range of possible techniques that can be employed. For the same set of data, different charting techniques may produce different trading signals. Some types of charting techniques are aimed at specific sampling intervals, e.g., point-and-figure charts are often used to analyze intra-day price movements while moving average charts are applied to, say, time series of daily or monthly prices. Ultimately, charts are only visual aides. It is always possible to translate the information in a chart to mathematical or statistical expressions, though this may be difficult to accomplish in many cases, e.g., Treynor and Ferguson (1985). It is unfortunate that by stressing the connection of technical analysis with charting the theoretical foundation for the general approach is overlooked. Taken as a whole, technical analysis is much more than an atheoretical reading of the ‘tea leaves’. Technical analysis is a vast subject containing so many contributions that it is not possible in this chapter to provide more than a brief overview. Such an overview has to deal with selecting topics for examination. The subject has not been static. For example, classic texts, such as Edwards and Magee (1966), do not deal with numerous concepts such as oscillators and stochastics that have risen to popularity since the early 1970s and now form the grist of various on-line sites featuring technical indicators. In addition, significant contributions to the subject span both the commodity and securities markets. Initially, key contributions to technical analysis, such as the Dow theory, were concerned with stock markets. Over time, the emphasis on speculative trading of derivative securities in commodity markets resulted in many essential sources on technical analysis, e.g., Kaufman (1978), being concerned with trading in commodity derivative markets. In turn, the rapid development of day trading in stocks, enhanced execution ability, and the dramatic drop in transactions costs associated with on-line trading and the growth of ETNs has created a resurgence of contributions concerned with stocks, e.g., Elder (1993) and Blau (1995). Those interested in the current state of theory are advised to examine a number of the excellent websites featuring the ‘technical’ approach, e.g., www.marketscreen.com, www.futuresource.com or clearstation.etrade.com. 6.1.2

Conceptual Foundations of Technical Analysis

Astrological Beginnings Technical analysis is based on an investment philosophy which does not believe in the efficient markets hypothesis. Where the strong believers in

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EMH have an intellectually appealing conceptual foundation based on a unifying theoretical framework, there is a buffet of competing theories that provide the conceptual foundation for technical analysis. Certain technical theories have mathematical roots that stretch back centuries, such as the Fibonacci numbers used in the Elliott wave theory. Ehrenberg (1928) relates what is perhaps the earliest known application of technical analysis on the Antwerp exchange during the 16th century where the emergence of liquid financial and commodity markets created the potential for significant gains or losses from speculation, e.g., Poitras (2009). It was difficult for merchants actively involved in the bill or commodity markets to avoid the implications of rapid price changes on the exchange: “dealing in commodities in Antwerp [was] a risky business for anyone not able to follow the market from hour to hour and even for those who did so” (Ehrenberg 1928, p. 240). The pressing need for merchants to predict price movements created the preconditions for the emergence around 1540 of an interesting early version of technical analysis based on astrology (Ehrenberg 1928, pp. 240–242). The originator of this security market forecasting system was one Christopher Kurz, an astrologer from Nuremberg. The Tuchers, among the most prominent merchant families of that time, were his most important clients. According to Ehrenberg (p. 240), around this time: astrological prognostications flourished in the Netherlands; there were prophecies of every kind which were reproduced in print. Christopher Kurz had puzzled out an astrological system by which he could foretell prices. He praised his invention to the Tuchers, mixing sober business statements with fantastic combinations in a way that seems absurd to use, but which probably at the time gave quite a different impression . . . Lienhard Tucher made marginal notes on the reports that Kurz sent which prove that he read them carefully and did not fail to observe the prognostications.

Acknowledging that ‘trade in spices needs great foresight’, Kurz claims to have a system for forecasting the prices of pepper, ginger and saffron a fortnight ahead. To quote from one of Kurz’s reports to Tucher (quoted in Ehrenberg 1928): I sought it three years but until this year found it not. I think God hath given it to me. I have observed it for the space of a year. Yet I will not boast myself of it, till I myself have observed it for yet a time longer with mine own eyes and have traced it out. Yet I doubt not, it is well founded . . . In the same manner I have known how to show for the matter as touching cinnamon, nutmegs and cloves . . . likewise with bills can one

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happen on many a good chance. As ye have often noted in my writings to you how great an alteration is there here day by day in bills on Germany, Venice, or Lyons, so that in the space of eight, ten, fourteen or twenty days with other folks’ money, a man may make a profit of 1, 2, 3, 4, 5, or more per cent., with such there is here each day great business on the Bourse. On these also have I my experiment so that I may foretell not only from week to week the Strettezza and Largezza (tightness or ease in money), but also for each day and whether it shall be before midday. I have, however, nigh forgot this again, since I have found you so reluctant.

The similarities of Kurz’s claims with those often advanced by modern technical analysts are striking. Though there has been some progress towards precision in specifying trading rules associated with New Finance theories, modern technical analysis has generally been characterized by vagueness in making precise statements about how specific technical trading rules generate future price predictions. For example, concepts such as ‘support and resistance levels’ are used even though competing technical analysts often identify different support and resistance levels when confronted with the same data. Similar observations can be made about chart patterns, such as ‘head-andshoulders’ and ‘W-bottoms’. Technical analysts have little ex post difficulty identifying such patterns successfully in charts for past price data but exhibit considerable ex ante disagreement when asked to identify such patterns to use in predicting future price behaviour. There is a widespread tendency for traditional technical analysts to claim a special ability in interpreting available data which is, somehow, intuitive enough to be incapable of precise formulation. The correspondence between Kurz’s astrological system and modern technical analysis can be captured by examining the four point conceptual scheme of Levy (1966) adopted in Francis (1983, p. 434) which provides a rough characterization of the ‘basic assumptions of [traditional] technical analysis’: 1. Market value is determined solely by the interaction of supply and demand. 2. Supply and demand are determined by numerous factors. These factors can be both rational and irrational. Included in these factors are those of importance to fundamental analysts, as well as moods, sentiment, guesses and blind faith. The market is a mechanism for weighing each of these factors on a continuing basis.

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3. Though there are minor fluctuations in the market, stock prices have a tendency to move in trends that persist for appreciable lengths of time. 4. Changes in trend are the result of shifts in supply and demand. These shifts, no matter what factors determine the shift, can be detected sooner or later in analysis of market action and used to forecast future price movements. Interpreting ‘chart patterns’ to be ‘astrological chart patterns’ reveals an interesting, if somewhat whimsical, connection between Kurz’s 16th century astrological system for predicting future security price movements and the methods used in modern technical analysis. It also provides a foundation for a classification of technical methods into three general groups: traditional technical analysis, based on chart formations and moving average methods; New Finance, based on generalizing modern Finance to incorporate pricing anomalies using psychological predictions about investor behavior; and, mystical finance encompassing a range of technical theories, from the universal to the ephemeral, that cannot be justified by traditional or New Finance methods, e.g., the Elliott wave theory. Keynes, New Finance, and the EMH As evidenced by Akerlof and Shiller (2009, esp. ch. 11), it is gradually being recognized that the connection between the EMH and New Finance explanations of technical trading can be traced back to Keynes, especially Chapt. 12 of the General Theory. For Keynes, the EMH is a convention. This is an important observation because in the Keynesian model, “conventions are essentially shared rules of behavior that enable individuals to take actions in situations where the future results of these actions are unknowable . . . though the future may be unknowable the existence of conventions and the belief that they will be maintained provide a basis for decision making under uncertainty” (McKenna and Zannoni 1993, pp. 402, 403).2 The weakness of the EMH as a convention is that the actual security 2 While

it is tempting to extend the discussion to notions of individual liberty and freedom, this would take the discussion too far afield. However, it is worth observing at this point that this concept of uncertainty “requires a social matrix for its existence” (McKenna and Zannoni 1993, p. 405). This is almost diametrically opposed to the neoclassical approach, of which the modern portfolio theory is an extension. In this approach, decisions are absolute and social conventions and institutions are not required to situate the optimal solution, which is conceived to be immutable.

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prices are not being determined with reference to the long-term prospective yield. Rather prices are being determined “as the outcome of a large number of ignorant individuals” and misguided professional investors and speculators. This produces a stock market that, when confidence in the convention is ‘less plausible than usual’, is “subject to waves of optimistic and pessimistic sentiment, which are unreasoning and yet in a sense legitimate, where no solid basis exists for a reasonable calculation” (p. 154). Such fluctuations are so pervasive that “the energies and skill of the professional investor and speculator are mainly occupied . . . not with making superior long-term forecasts of the probable yield of an investment over its whole life, but with foreseeing changes in the conventional basis of valuation a short time ahead of the general public” (p. 154). This reference to convention has deep philosophical implications that cannot be ignored. Conventions are the result of social interaction, what McKenna and Zannoni (1993) pedantically refer to as the social matrix (the cultural context within which individuals exercise their freedom). As a consequence of the EMH being a convention, the extent of the violent fluctuations in the market depend on the temporal state of the social matrix. In other words, the institutional, social and historical context will impact the security pricing process. The same event occurring at different times may produce a violent fluctuation in pricing in one period and have no impact at another time. Uncertainty is created by the infinite number of future outcomes which are possible at a given point in time. The specific outcome which occurs “is the result of individual choice in the context of social interaction . . . It is not the case that the far distant future is sometimes more knowable than at other times. It is always simply unknowable. What does change . . . is the meaning people choose to attach to this fact, and hence the manner in which people’s behavior responds to this uncertainty” McKenna and Zannoni (1993, p. 403). It is evident from his personal and professional investment practices that Keynes is not among the full fledged dis-believers in the EMH and, as a result, can not be considered in the same camp as the technical analysts. Yet, there is substantive misgivings about the success of fundamental analysis: “Investment based on genuine long-term expectation is so difficult today as to be scarcely practicable. [An investor] who attempts it must surely lead much more laborious days and run greater risks than [an investor] who tries to guess better than the crowd how the crowd will behave; and given equal intelligence, he may make more disastrous mistakes ... It needs more intelligence to defeat the forces of time and our ignorance of the future than

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to beat the gun” (p. 157). Besides, there is more excitement in the chase after speculative profit: “... life is not long enough; – human nature desires quick results, there is a peculiar zest in making money quickly, and remoter gains are discounted by the average man at a very high rate” (p. 157). The reliance on the social matrix is one element of the Keynesian approach that is worrisome to neo-classical economists and, in the present context, presumably also to modern portfolio theorists. Yet, to be relevant to present day security markets, this material has to be reworked to fit the contemporary social matrix. Conventions, which are so important for decision making under uncertainty, depend fundamentally on the social matrix. In this vein, Keynes was writing at a time that was different in many ways from the world of today. There has certainly been substantive changes in financial markets since the time of the General Theory. Perhaps the world has changed enough that the investor motivated by long-term expectations has come to predominate, inducing an EMH convention which is more stable and less susceptible to violent fluctuation? Putting aside for the moment the empirical evidence to the contrary provided by the high tech/dot com/NASDAQ 5000 stock bubble of 2000 or the slow motion global crash of 2008–2009, what suggestions would Keynes have for those seeking to employ a security valuation strategy based on fundamental analysis? It is difficult to deny that the ‘zest’ for quick profit is any less vigorous today than in times gone by. It is also still the case that (p. 157): “The game of professional investment is intolerably boring and overexacting to anyone who is entirely exempt from the gambling instinct”. The investor who would seek to engage in fundamental analysis, i.e., “an investor who proposes to ignore near-term market fluctuations” and purchase a security on the basis of long-term prospective yield, is advised of the need for ‘greater resources for safety’ and not to “operate on so large a scale, if at all, with borrowed money”. All these potential difficulties are compounded by the following prediction (p. 158): “If I may be allowed to appropriate the term speculation for the activity of forecasting the psychology of the market, and the term enterprise for the activity of forecasting the prospective yield on assets over their whole life, it is by no means always the case that speculation predominates over enterprise”. Unfortunately, this hopeful statement is followed by: “As the organization of investment markets improves, the risk of predominance of speculation does, however, increase”. If this prediction is correct, fundamental analysis is likely to be even more difficult today than at the time of the General Theory.

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Old Finance and Technical Analysis The current debate over the merits of technical analysis can be traced back to the beginnings of modern Finance in the late 1950s and early 1960s. Prior to this time, the potential benefits of technical analysis were generally acknowledged by many practitioners, though the subject was largely disparaged by adherents of ‘old finance’ due to the emphasis on speculative trading strategies.3 Technical analysis, in some form or other, has been practiced in European securities market at least since the 16th century (Poitras 2000). Nison (1996) finds evidence for the use of candlestick chart technical analysis in 18th century Japanese commodity markets. Brock et al. (1992, p.1731) observe: “In the United States, the use of trading rules to detect patterns in stock prices is probably as old as the stock market itself”. Prior to the widespread availability of detailed and accurate financial statement information about publicly traded companies, market generated data were often the most important source of information about a security. The introduction of the NYSE stock ticker in 1867 marks the beginning of an important technological advance that brought ‘tape reading’ into the lexicon of mainstream society. Prior to this time, the barriers to information transmission made the analysis of market generated data largely the preserve of those able to directly observe trading at the exchange.4 Though a definitive intellectual history of technical analysis is yet to be written, the origin of traditional technical analysis is usually traced to the late nineteenth century when Charles Dow originated the Dow–Jones Industrial Index.5 Together with his successor at the Wall Street Journal, William Peter Hamilton, Dow was an active promoter of technical analysis 3 Wyckoff (1933, p. 105) quotes a newpaper reporter from the 1920s bemoaning ‘unwarranted market declines’ caused ‘by purely mechanical interpretation of a meaningless set of lines’ on ‘charts of professional stock traders’. 4 A similar revolution happened in the last decade of the 20th century with the impact of computing and telecommunications technology on global securities trading. The substantive impact of these technological factors on the programmed trading driven market crash of October 1987 marks a symbolic beginning to this revolution. The inability of regulators to deal with events such as the emergence of global ETN’s and the growth of the OTC derivatives market can be traced to a regulatory failure to anticipate the implications of the fundamental technological changes impacting securities markets. 5 There are a number of sources that do pay some attention to the history. For example, Kaufman (1978, chs. 12, 13) provides considerable background on the important, if unrecognized, individuals in the history of technical analysis such as: R.N. Elliot, developer of the ‘Elliot Wave Principle’ based on Fibonnaci numbers, during the mid-1930s; the various systems developed by William Gann, starting in the mid-1930s and continuing until the 1950s; William Dunnigan, originator of ‘the thrust method’, during the

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based on market averages. These developments by Dow and Hamilton were not produced in isolation. As evidenced in Wyckoff (1910), other notions commonly used in modern chart reading, such as resistance and support levels, were in use around that time. Graham and Dodd (1934, p. 608) recognize that ‘technical study’ had “increased immensely during the past ten years. Whereas security analysis suffered a distinct and continued loss of prestige beginning about 1927, chart reading apparently increased the number of its followers even during the long depression”. These followers of chart reading were to be found in significant numbers in Wall Street. Graham and Dodd identify a number of references for these techniques including: Gartley (1934), which provides a development of moving average techniques examined in Gartley (1930); Schabacker (1930), which Kaufman (1978) describes as outstanding and a ‘must read’; and Rhea (1932) which is still an essential source for examining the Dow theory. Graham and Dodd (1934) and later editions up to and including Graham et al. (1962) took a dim view of ‘market analysis’ which included technical analysis as a significant subset. A number of logical arguments were advanced against this approach. Though the connection was not recognized, the Graham and Dodd position against technical analysis was supported by statistical evidence, which started to accumulate during the 1950s, that security price changes were serially uncorrelated.6 These statistical studies were broadly interpreted as being strong evidence against technical analysis. Though some adherents of modern Finance have recently claimed that this interpretation of the evidence was incorrect (e.g., Lo et al. 2000; Jegadeesh and Titman 2001), at the time enthusiasm for the evolving efficient markets paradigm of modern Finance outweighed the answers to the common sense question: if technical analysis is incapable of generating abnormal returns, why are so many technical analysts employed by the securities industry?7 early 1950s; Eugene Nofri, originator of the ‘congestion-phase system’; Chester Keltner, originator of the ‘minor trend rule’, during the late 1950s. 6 The statistical attack on technical analysis by academics can, arguably, be traced back to Cowles (1934) where the performance of the Hamilton version of the Dow theory is examined. Cowles found that returns from the Dow theory lagged the market which is inconsistent with the claim that the Dow theory can be used for market timing. Brown et al. (1998) reconsider Cowles’ results and observe: “Cowles compares the returns obtained from Hamilton’s market timing strategy to a benchmark of a fully invested stock portfolio. In fact, the Hamilton portfolio, as Cowles interprets it, is frequently out of the market. Adjustment for systematic risk appears to vindicate Hamilton as a market timer”. 7 While there are a significant number of technical analysts on Wall Street, the preponderance of analysts are of the fundamental persuasion.

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In the process of making a headlong rush to judgment, modern Finance was quick to dismiss conceptual arguments supporting the foundations of technical analysis. Levy (1966) and Francis (1983) are not the only statements of the conceptual framework for traditional technical analysis. Following Murphy (1999), the framework can be reduced to three propositions: market movements discount all relevant information; prices move in trends; and, history repeats itself.8 Though reference is made to ‘all relevant information’ being incorporated into prices, hiding in the background is a view of equity security pricing that is decidedly contrary to the view contained in the Graham and Dodd approach. For example, Edwards and Magee (1966, p. 5) observe: It is futile to assign an intrinsic value to a stock certificate. One share of United States Steel, for example, was worth $261 in the early fall of 1929, but you could buy it for only $22 in June 1932. By March 1937, it was selling for $126 and just one year later for $38 . . . This sort of thing, this wide divergence between presumed value and actual value, is not the exception; it is the rule; it is going on all the time. The fact is that the real value of a share of United States Steel common is determined at any given time solely, definitely and inexorably by supply and demand which are accurately reflected in the transactions consummated on the floor of the New York Stock Exchange.

Though not as sophisticated as the model of stock pricing proposed by Keynes (e.g., Poitras 2002a), technical analysts recognize that both rational and irrational factors can impact market prices. The resulting trading strategies are generally consistent with the ‘anticipation approach’, as opposed to the ‘intrinsic value’ approach, to security valuation. For Graham and Dodd (1934, p. 608), technical analysis is part of the more general subject of ‘market analysis’ that seeks to predict the ‘short-term behavior of the stock market’, as opposed to the ‘long-term market considerations’ that are the basis of the intrinsic value approach. Two approaches to market analysis are identified. One approach uses ‘all sorts of economic factors’, including general and specific business conditions, short-term interest rates, political considerations and so on. The other approach “finds the material for its predictions exclusively in the 8 Kaufman (1978, p. 192) provides the following quote from R.N. Elliot, originator of the Elliot wave theory, that describes the epistemological approach of technical analysis: “Even though we may not understand the cause underlying a particular phenomenon, we can, by observation, predict the phenomenon’s recurrence”.

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past action of the stock market”, i.e., technical analysis. “The underlying theory of [this] approach may be summed up in the declaration that ‘the market is its own best forecaster’ ”. While it is always theoretically possible to reconstruct chart analysis in terms of mathematical or statistical equations, this will typically be difficult to do without the aid of computing power. Writing prior to the widespread introduction of mainframe computers, Graham and Dodd observe that technical analysts “generally studied [the behavior of the market] by means of charts on which are plotted the movements of individual stocks or of ‘averages’ ”. As consequence, Graham and Dodd refer to technical analysis as ‘chart reading’ and to technical analysts as ‘chartists’. Though not fully descriptive, this terminology has carried forward into the modern lexicon. The Feedback Effect The arguments advanced by Graham and Dodd (1934, p. 609) against technical analysis are 1. Chart reading cannot possibly be a science. 2. It has not proved itself in the past to be a dependable method of making profits in the stock market, at least not one available to the general public. 3. Its theoretical basis rests on faulty logic and also upon mere assertion. 4. Its vogue is due to certain advantages it possesses over haphazard speculation, but these advantages tend to diminish as the number of chart students increases. These arguments are carried verbatim into later editions. The intuition underlying each of these points is presented. All four points revolve around an observation that can be characterized as the ‘feedback problem’. This problem is illustrated in a discussion of the first point: If [technical analysis] were a science, its conclusions would be as a rule dependable. In that case, everybody could predict tomorrow’s or next week’s price changes, and hence every one could make money continuously by buying and selling at the right time. That is patently impossible. A moment’s thought will show that there can be no such thing as a scientific prediction of economic events under human control. The very “dependability” of such a prediction will cause human actions which will invalidate it. Hence thoughtful [technical analysts] admit that continued success is dependent upon keeping the successful method known only to a few people.

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There are two key observations being made here. One observation deals with the inherent unpredictability of events under human control. This is the essence of the epistemological problem confronting the human sciences. The other point has to do with the need to keep successful technical analysis systems secret in order to prevent a ‘feedback problem’ where trading on a successful system by large numbers of traders eliminates the profitability.9 But if successful systems are secret, how can such systems be tested to assess ex ante profitability? Graham and Dodd recognize that security analysis is not immune to the inherent unpredictability of events under human control. Yet, there are differences (GDC, p. 714): The past earnings of a company supply a useful indication of its future earnings — useful, but not infallible. Security analysis and [technical] analysis are alike, therefore, in the fact that they deal with past data that are not conclusive as to the future. However, we are inclined to the view that for the typical analyst the so-called “fundamental” information for investment-quality shares — sales, earnings, asset and capital data, etc. — lends itself to more meaningful interpretation than does [technical] information. Moreover . . . there is the added difference that the security analyst can protect himself by a margin of safety that is denied to the [technical] analyst.

This emphasis on the margin of safety is not the only difference. The longer time horizon of fundamental analysis looks beyond the near-term horizon that is reflected in the ‘consensus’ forecast embedded in current stock prices generated by “the analysis and advice supplied in the financial district [that] rests upon the near-term business prospects of the company considered”. In GDC, there is explicit recognition of the possibility that the feedback problem could also affect the intrinsic value approach. However, compared to the longer-term buy-and-hold intrinsic value approach, the reliance of technical analysis on near-term trading intensive techniques means that “the expense of trading weights the dice heavily” against this approach.

9 Practicing technical analysts are well-aware of the feedback problem. Consider the following statement from the Dow theorist, Richard Russell (Du Bois 2000): “I began publishing the Primary Trend Index (PTI) in 1971. It’s a compilation of eight components that measure only market action. There’s no subjective interpretation involved. I prefer not to name the components. If everybody followed the same ones in the same way, the PTI would lose its usefulness”.

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In addition to the logical objections presented by the feedback problem, Graham and Dodd observe that there is nothing in the structure of technical analysis that ensures adequate performance (GDC, pp. 714, 715): You may learn a great deal about the technical position of individual stocks by studying charts of their past market performance, but the question is whether you learn enough to predict the future with sufficient accuracy to operate profitably over time in the stock market. In other words, does the information which you derive from the past market action of individual issues prove valuable often enough for you to invest profitably in common stocks?

The Levy (1966) and Francis (1983) four point conceptual foundation for technical analysis could be accepted without any assurance that sustainable and profitable strategies could be identified and pursued. While there may be certain situations where technical analysis provides ‘really convincing cases’, such cases are not the norm: “such precise signals apparently occur at wide intervals, and all too often the chart configurations are such that chart readers ‘find themselves adrift on a sea of ambiguities’ ”. The Graham and Dodd (1934, p. 615) objections to technical analysis extend to all forms of market analysis that seek to profit from making near-term predictions of common stocks: We are skeptical of the ability of the analyst to forecast with a fair degree of success the market behavior of individual issues over the near-term future — whether he bases his predictions upon the technical position of the market or upon the general outlook for business or upon the specific outlook for individual companies.

Despite arguing for the absence of a scientific approach to such market analysis, Graham and Dodd were not able to shake the observation that such activities are widely used in the investment industry. This perception increased from edition to edition reaching the conclusion (GDC, p. 716): The more intelligent chart students recognize these theoretical weaknesses, we believe, and take the view that market forecasting is an art that requires talent, judgment, intuition, and other personal qualities. They admit that no rules of procedure can be laid down, the automatic following of which will ensure success. Hence the widespread tendency in Wall Street circles toward a composite or eclectic approach, in which a very thorough study of the market’s performance is projected against the general economic background and the whole is subjected to the appraisal of experienced judgment.

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While recognizing that the prevalence of market analysis in Wall Street circles implicitly supported the possibility of profitably pursuing such an approach, Graham and Dodd still left no room for the possibility of a systematic, quasi-scientific technical analysis. 6.1.3

New Finance and Mystical Finance

Revival of Technical Analysis? In recent years, modern Finance has revisited the possibility that there may be something in technical analysis beyond being a convenient punching bag for the efficient markets hypothesis. Consistent with the economic positivism that drives this approach, the process of ‘empirical verification’ has guided this change. For example: “statistically significant evidence has been presented from momentum profits” (Chan et al. 2000); “a systematic and automatic approach to technical pattern recognition using nonparametric kernel regression . . . provide[s] incremental information and may have some practical value” (Lo et al. 2000); “trading strategies that buy past winners and sell past losers realize significant abnormal returns . . . relative strength profits cannot be attributed to lead-lag effects that result from delayed stock price reactions to common factors” (Jegadeesh and Titman 1993); “momentum profits have continued in the 1990s, suggesting that the . . . results were not the product of data snooping bias” (Jegadeesh and Titman 2001); “Hamilton’s [Dow theory] timing strategies actually yield high Sharpe ratios and positive alphas for the period 1902–1929 . . . Neural net modeling to replicate Hamilton’s calls provides interesting insight into the Dow Theory” (Brown et al. 1998). This change of location for the boundaries of modern Finance requires some reworking in the classification of ‘technical analysis’ theories. In modern Finance, evidence in favor of certain types of technical analysis has been accompanied by a range of other statistical studies that have questioned the empirical validity of the efficient markets hypothesis. The scope of these studies includes evidence for: pricing anomalies, such as the January effect and the small firm effect, e.g., Dimson et al. (2002); serial correlation in returns, e.g., Campbell et al. (1997) and Lo and Mackinlay (1999); value stocks outperforming growth stocks, e.g., Fama and French (1998); and, various aspects of behavioral finance such as a bias to buying winners and selling losers, e.g., Shefrin and Statman (1984); De Bondt

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and Thaler (1985, 1987), Shefrin (2000), and Akerlof and Shiller (2009).10 Confronted with ‘statistically significant evidence’, a natural reaction for a positivist is to rethink the prevailing theory and construct new theories that explain the stylized empirical facts. This reaction has given particular impetus to the development of behavioral finance or New Finance that seeks to explain deviations from market efficiency in terms of investor psychology. While strong prior beliefs still leads those with attachments to the prevailing theory to question the statistical results in favor of the new theories, claiming the results are due to ‘data-snooping’ or ‘data-mining’, others have proceeded cautiously down the new path, as evidenced in Jegadeesh and Titman (2001): “The evidence provides support for the behavioral models, but this support should be tempered with caution”. To those not well-versed in the theories of modern Finance, discerning the distinction between technical analysis and modern Finance is something of a quandary. Technical analysis is concerned with using market-generated data to predict future price behavior. Yet, core theories of modern Finance, such as the capital asset pricing model (CAPM) and the Markowitz mean– variance optimization model, also use market generated data to form ‘optimal portfolios’. Practical implementation of, say, the Markowitz mean– variance optimization model requires the analyst to examine the time series of returns for the securities of interest together with a proxy for the risk free interest rate and the market portfolio, e.g., Eun and Resnick (1994). ‘Optimal’ portfolios are obtained by solving a quadratic optimization problem using ex post estimates of the means, variances and covariances of security returns. To the uninitiated, this is not substantively different than a technical analyst using the Dow theory, combined with a moving average system, to select a portfolio of speculative trading opportunities. Both approaches examine market generated data to identify equity security investment opportunities. However, the CAPM is decidedly unlike technical analysis in being derived from a coherent theory of equilibrium pricing.

10 The empirical evidence on the profitability of selling losers and buying winners is gathered from samples using returns that are generated over shorter time horizons, say one month, producing ‘under reaction’ for periods up to one year. For returns generated over longer horizons, say a year or more, ‘over reaction’ is reported where buying losers and selling winners becomes profitable.

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Though there has been various attempts to extend the core theory of modern Finance to incorporate a range of other ‘factors’, e.g., Jagannathan and Wang (2002), modern Finance has not yet proposed methods for determining which factors to include in ‘the model’ that are not immune from the criticisms of data-snooping and ad hocery. In some cases, the factors that have been selected for inclusion have corresponded to measures that are widely used in the relative value analysis commonly practiced by “Wall Street” security analysts, e.g., Fama and French (1998). However, there is still an absence of a well-developed theoretical foundation for, say, the inclusion of ‘value factors’ in asset pricing models or for the apparent success of momentum strategies. By abandoning the strong belief in efficient markets and shifting the focus onto the identification of securities that generate abnormal returns, modern Finance is operating on a different battlefield. The various anomalies that have been identified may be ex post fictions that cannot be used to produce ex ante abnormal returns. The upshot is that the efficient markets hypothesis cannot be readily abandoned by practitioners of modern Finance. It is essential to the philosophical foundation upon which the edifice of this scientific movement is constructed. It is the ‘Keynesian convention’ that is used to deal with the uncertainty arising in equity security valuation, e.g., Poitras (2002a). By adopting this convention, modern Finance is able to avoid the logical contradiction of technical analysis: how can the market discount all relevant information and prices still follow trends? Why is the trend not considered to be part of ‘all relevant information’ ? Technical analysts avoid this logical contradiction by claiming specialized expertise in identifying the trends while refusing to reveal the forecasting system that is being used to identify the trend due to fear of the feedback effect. Academic researchers cannot take refuge in this approach because norms of scientific analysis require at least the appearance of verification through replication. Alternative Explanations Technical analysis has not been without adherents in the modern Finance academic community. At least since Treynor and Ferguson (1985), it has gradually been recognized that equity prices may have stochastic properties that lead to the possibility of technical trading rule profits. More recently, Lo and Hasanhodzic (2009) provide a more-or-less favorably disposed presentation of this aspect of the vernacular Finance approach with interviews detailing the background and insights of thirteen fairly prominent technical analysts. This belated realization of the possibility that ‘there

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might be something in technical analysis’ is unfortunate as there were credible scientific studies available around the time the efficient market hypothesis (EMH) was being formulated indicating there may be alternative explanations with better explanatory power than the EMH. These studies are both theoretical, as with Shackle (1949–1950; 1952) on non-additive probability, and empirical, as with Cowles and Jones (1937) and the associated interpretation by Rose (1951) on the ‘stickiness of prices’ as arising from ‘rumor in the stock market’. Rose (1951) describes the empirical situation: If we inspect a graph of stock prices, we will observe that they do not fluctuate entirely at random in pursuing the course of the business cycle. Rather, the prices will move apparently at random for a while, and then exhibit a sudden spurt, either up or down, for several days. These spurts are the graphic manifestations of the factor of stickiness.

This behavior is consistent with the presence of more ‘sequences and reversals’ than for a purely random process as empirically observed by Cowles and Jones (1937) for both individual stocks and the Cowles market index for a number of different sampling frequencies, e.g., daily, monthly. An additional empirical result is also reported: there is statistically more sequences than reversals. In an odd connection to R. Elliott and the golden ratio, this resulted in a ratio of approximately 62% reversals to sequences for the important monthly sampling frequency. Though this exact result was later revised by Cowles (1960) to correct for some deficiencies in Cowles and Jones (1937) identified by Holbrook Working, the conclusions regarding the preponderance of ‘sequences and reversals’ and the associated use of inertia strategies to identify profitable market timing opportunities was unchanged. If correct, the preponderance of sequences over reversals has implications for the accuracy of an ex ante bifurcating process as a description of the ex post time path. Using the ‘standstill effect’ of a surprise event, Shackle (1952) is able to generate such a result theoretically where the speed of reaction to downside moves is faster than for upside moves. The time reversible stochastic processes conventionally used by modern Finance academics to formulate the EMH have difficulty producing such a result even with considerable ad hoc calibration. The time irreversible bifurcating process also needs to resort to ad hoc restrictions to achieve the result, e.g., by introducing an asymmetry into the method to reset the theoretical ex ante decision problem following the occurrence of a bifurcation. Given the other similarities between time irreversible bifurcating processes and the general theoretical features of Shackle’s framework, it appears that

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such properties of stochastic price behavior are more readily described by non-additive probability notions. The implications of using time reversible stochastic processes extend beyond theoretical considerations to include empirical testing. A number of different statistical tests can be used for determining if the randomness requirements of the EMH are satisfied. Time reversible processes permit the testing of periodicity properties. As a consequence, testing for unit roots and serial correlation are common in statistical studies of the EMH. After appropriate adjustment, e.g., converting price changes to returns, tests determine whether some simple transformation of price changes is serially uncorrelated. What has emerged from these tests is a profound concern with the higher moments of the ex post distribution — skewness and kurtosis. Various statistical techniques, ranging from EGARCH to Markov switching models, have been assembled to capture the unpleasant distributional properties that have been consistently and repeatedly observed in financial market data. Similar to Cowles and Jones (1937) and Rose (1951), empirical tests employing time irreversible processes explore the relationship between changes in the non-linear mean value process and the presence of sequences and reversals in the ex post data. R.N. Elliott and Mystical Finance Mystical Finance encompasses technical theories that lie outside the boundaries of traditional technical analysis and New Finance. Relevant theories that lie outside these very wide boundaries all have a mystical character, as evidenced in the most important component of modern Mystical Finance: the Elliott wave theory. Christopher Kurz, the 16th century astrologer from Nuremberg that advised the Tuchers about future prices on the Antwerp bill market, is arguably a fitting candidate to be the father of Mystical Finance. Another, much earlier candidate, could be Thales, the Greek philosopher. Aristotle in The Politics reports that somehow (!) Thales was able to predict a bumper crop for olives in his locale and was able to take leases on all available olive presses at low prices well before the crop materialized, e.g., Poitras (2009a). When the bumper crop materialized, Thales was able to make a fortune, subleasing the presses at high prices. Whatever the origins, the essence of these theories is aptly described by the title of the last book by R.N. Elliott (1871–1948): Nature’s Law–The Secret of the Universe (1946; Prechter 1994). The line between traditional technical analysis and Mystical Finance is blurry. For example, basic elements of the Elliott wave theory are derived

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from the Dow theory which is a central concept in traditional technical analysis. Triangles, wedges and rectangles, price formations that play a key role in the Elliott wave theory, have corresponding notions in the Dow theory and other forms of traditional technical analysis, e.g., Frost and Prechter (1990, p. 165). Where mysticism appears is in the next step: connecting the method of analysis with a divine reality, God, Absolute of Nature or some other such universal construct. “Elliott discovered that the ever-changing path of prices reveals a structural design which in turn reflects a basic harmony found in nature. From this discovery, he developed a rational system of market analysis” (Frost and Prechter 1990, p. 17). Where Elliott was concerned with the universal element of the cyclic movements in the US stock market, Kurz connected price movements in the Antwerp bill market with the astrological movements of heavenly bodies. Instead of the mysticism of astrology, Elliott substitutes ‘Nature’s Law’ which is based on the Fibonacci sequence (Elliott 1946, p. 229): All human activities have three distinctive features — pattern, time and ratio — all of which observe the Fibonacci Summation Series. Once the waves can be interpreted, the knowledge may be applied to any movement, as the same rules apply to the price of stock, bonds, grains, cotton, coffee and all other activities previously mentioned.

For Elliott the Fibonacci sequence is: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. “The sum of any two adjoining numbers equals the next higher number. For example 3 + 5 = 8. The waves of every movement coincide with these numbers”. From this observation, Elliott is able to construct some predictions about the behavior of stock market prices or, more precisely, stock market indexes. Elliott did not give much concern to the stock market until quite late in life. His main academic contribution prior to this time was Tea Room and Cafeteria Management (Elliott 1926). It was Rhea (1932), The Dow Theory, that sparked Elliott’s initial interest in predicting the market. As such, Elliott can be considered an offshoot of the Dow theorists. In contrast to Hamilton, Rhea advocated using the Dow theory to predict secondary as well as primary trends in the equity market. Prechter (1994, p. 50) observes that Elliott’s: essential path of inquiry, i.e., looking for patterns in aggregate stock price movement, was undoubtedly directed initially by exposure to tenets of the Dow Theory. However, Elliott’s ultimate discovery was all his own, as over a period of several years he painstakingly uncovered the Wave Principle of market behavior by studying empirical evidence.

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The impact of Rhea and the additional input of Elliott is apparent in the following table which depicts a complete stock market cycle conforming to the Elliott wave theory (Frost and Prechter 1990, p. 21): Subdivisions of Cycle degree Cycle Primary waves Intermediate waves Minor waves

Bear market

Bull market

Complete cycle

1 3 13 55

1 5 21 89

2 8 34 144

One full stock market price cycle is composed of one bear and one bull cycle. The bear cycle is composed of three primary waves followed by the bull cycle that has five primary waves. And so it goes, conforming to the dictates of the Fibonacci sequence. One of the strong predictions of the Elliott wave theory deals with the ratio of terms in the Fibonacci series. In particular, if the series takes the form 1, 1, 2, 3, 5, 8, 13, 21, . . . , un , un+1 , . . . where un = un−1 + un−2 then: un−1 = lim n→∞ un

√

5−1 . 2

Elliott gave some attention to recognizing that this limit is the ‘golden ratio’. Elliott traced the historical origins of the golden ratio back to the Egyptians and the dimensions of the Great Pyramid of Gizeh. Elliott claims both Pythagoras and Fibonacci learned of the golden ratio on visits to Egypt. Whether this particular historical interpretation is correct does not change the result that knowledge of the ratio first appeared in antiquity. Using the basic geometry of a line segment the result is easy enough. Divide a fixed line segment in two. The golden ratio appears when the ratio of the smaller segment to the larger segment equals the ratio of the larger segment to the whole line. Recognizing that the golden ratio is an irrational number approximately equal to 0.618, it follows that in the Elliott wave theory the length of time that the three primary waves of the bear market correction will last is about 61.8% of the time involved in the five primary waves of the subsequent bull market.

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Traditional Technical Analysis The Dow Theory

The Dow theory has a long pedigree stretching back to Charles Dow and the creation of the Dow-Jones rail and industrial averages circa 1897.11 Edwards and Magee (1992, p. 13) make the claim: “The Dow Theory is the granddaddy of all technical market studies”. The first key historical figure in the development of the theory is Charles Dow, founding editor of the Wall Street Journal. Dow originated the basic approach of using stock market averages to predict future movements in the market. The main source of information about Dow’s views is fifteen Journal editorials written between 1899 and 1902. (Dow did not publish any books on the subject or make reference to the ‘Dow’s theory’.) Reference to ‘Dow’s theory’ can be traced to a collection of these editorials that was published by Samuel. Nelson Armstrong, an author of practical books on finance and a personal friend of Dow, under the title The ABC of Stock Speculation. Despite having started the ball rolling, Dow did not contribute much detail to the theory that has come to bear his name. Shortly after Dow’s death in 1902, William P. Hamilton assumed the editorship of the Journal and developed the bulk of the theoretical structure for the Dow theory, mostly contained in Journal editorials published between 1908 and 1929.12 Though Hamilton did write a book outlining the theory (Hamilton 1922), the essential primary source of his views on the theory are these editorials that discussed and forecasted major trends in U.S. stock markets using the rudiments of the Dow theory. Brown et al. (1998) put the number of these editorials at 255. One of the oddities of the Dow theory is the untimely deaths of the major historical figures responsible for developing the theory. Just as Dow 11 A useful source on the history of the Dow theory is an article by Richard Russell that can be found on the website www.dowtheoryletters.com. The following discussion of Schaefer’s approach to the Dow theory is based on Russell’s discussion of Schaefer’s advisory newsletters that is contained in that article. Edwards and Magee (1966, Chaps. 3–5) has a useful overview of the main elements of the theory. This reference is to the fifth edition. There was not much change between this and the final seventh edition (1997) of this classic text. 12 There is some debate over the precise starting date for Hamilton’s contribution of the Dow theory. Brown et al. (1998) date the beginning in 1902, the year of Dow’s death. However, Clement (1997) observes that, while joining the newspaper in 1899, Hamilton did not have the job of editing the editorial page of the Journal — the source of early Dow theory prognostication — until 1908. Due to the presence of two brief tenures by others as Wall Street Journal editors following the death of Charles Dow, Hamilton was the fourth editor of the Journal. Hamilton held this position until his death in 1929.

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died shortly after bringing the theory on line, Hamilton died in December 1929 shortly after writing his last editorial on 25 October 1929 titled: ‘The Turn of the Tide’. The demise of Hamilton marks a turning point in the evolution of the Dow theory from the preserve of Journal editors into the domain of the investment advisory industry. This stage begins with Robert Rhea, a key figure in detailing, refining and popularizing the theory as it had been developed by Hamilton, e.g., Rhea (1932). Though Rhea closely followed Hamilton in his explanations of the theory, Rhea had the instinct to develop the ‘art’ of the Dow theory. This instinct permitted Rhea to call the bottom of the bear market almost exactly on 8 July 1932. Rhea developed techniques for using the averages for trading secondary, as well as primary, market trends. In November 1932, Rhea launched ‘Dow Theory Comment’, an investment advisory service that attracted considerable notoriety for being correctly bullish when the bears dominated market opinion. Rhea is also credited with correctly calling the bear market of 1937, a prognostication that added considerably to Rhea’s already significant standing on Wall Street. Throughout the 1930s, Rhea had been afflicted by tuberculosis, a disease that took his life in 1939. With the absence of its leading proponent in the investment advisory industry and without promotions on the editorial page of the Journal, it was not until after WWII that the Dow theory was rejuvenated by George Schaefer. This revival can be dated from 1948 when Schaefer started an investment advisory service, ‘Schaefer’s Dow Theory Trader’. Like Rhea, Schaefer had a keen instinct for the ‘art’ of using the Dow theory to predict stock market trends. In June 1949, shortly after starting the advisory service, Schaefer correctly called, almost to the day, the beginning of the major bull market that was to continue until 1966. In his advisory service newsletter, Schaefer used a ‘new version’ of the Dow theory to detail reasons for the start of a major bull market. Schaefer continued to be bullish throughout the seventeen year bull market, advising client’s to accumulate stocks on the numerous dips and drawbacks associated with the secondary movements of the market. In a remarkable prognostication, Schaefer turned bearish in early 1966 and held that position until his death, by suicide, in 1974. In another quirk in the murky history of the Dow theory, the year of Schaefer’s death marks the beginning of another primary bull market movement.13 13 Russell traces the bull market trend that ended in 1999 to a beginning in 1982 (Du Bois 2001). Much like Schaefer, the primary source of Russell’s views on the Dow theory are an

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As evidenced by continuing references to the Dow theory in the popular financial media, the theory continues to have a strong following of adherents in present day Wall Street, e.g., Du Bois (2000, 2001). The essence of the Dow theory is reflected in the words of Richard Russell, the modern version of the Dow theory investment advisor (see www.dowtheoryletters.com): “[The] Dow theory can’t be summed up in one or two sentences. It’s more of an art form than anything specific. It requires a lot of interpretation” (Du Bois 2001). This is consistent with the Graham and Dodd view that ‘intelligent technical analysts’ adopt the view that the forecasting methodology employed has to be viewed as an art form and not a science. Given that an art form cannot be precisely defined, it is still possible to sketch the basic conceptual elements. The first element in the Dow theory is that there are ‘three simultaneous movements in the market’ (Russell 1960, p. 4–5): The first [is] the great primary trend or tide. In a bull market, for example, this is a broad upward movement, interrupted by frequent reactions. The primary trend may last from one year to a great many years. The next movements are the so-called secondary reactions, which reverse and correct the tidal moves. They usually last from three weeks to three months, and then retrace one-third to two-thirds of the previous uncorrected primary moves. The final movements are the daily moves. These minor fluctuations admittedly can be manipulated by the news of the day. Although the least important, they are the ones to which the public pays the most attention. The single movement which every investor must be aware of at all times is the primary trend. Investors should always invest with this primary tide.

The Dow theory is a body of techniques that have been developed — partly based on empirical observation, partly based on intuition — to identify the primary trend in the stock market. As such, the Dow theory is concerned with timing the overall market and using the predictions to guide portfolio composition. Since the inception, Dow theorists have made an analogy between the three movements in the market and movement of the ocean. The primary trend is like the tide while the secondary reactions resemble the waves with the daily movements being ripples. As Russell observes (Du Bois 2001): investment advisory newsletter — ‘Dow Theory Letters’ — that Russell has produced continuously since 1958. Russell (1960) contains a collection of early newsletters. In addition to these sources, there a number of interviews and columns that have appeared in Barron’s.

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“It isn’t the waves that make or break you in this business, it’s the great ocean tide of the market”. Sail with the tide, not against it. While the analogy to movements of the tide is helpful, the analogy is also somewhat misleading. Unlike the gravitational pull of the moon that determines the tides and allows for accurate prediction, the primary trend in the stock market is considerably more difficult to determine. Dow theorists approach this problem by dividing the primary trend into phases. In the case of a primary bull market trend (Russell 1960, p. 5): Phase one is the rebound from the depressed conditions of the previous bear market. Here stocks return to known values. In the second and longest phase, shares advance in recognition of improving business and a rising economy. During the third phase they spurt skyward on the hopes and expectations of a continuing rosy future. This is the traditional period of great prosperity and unbounded optimism. It is here that the public enters the market wholeheartedly for the first time. The low-priced “cats-and-dogs” historically make great moves in this third phase, and market volume becomes excessive.

This distinction between the three types of market movement — primary trend, secondary reaction and daily fluctuation — and three phases of a primary trend — recovery, recognition and exuberance — can be a source of confusion. Another potential source of confusion about the Dow theory arises with the method used for determining whether and when the primary trend indicates a bull market or a bear market. The basic notion, derived from Hamilton and Rhea, is the concept of confirmation. Russell (1960, p. 5–6) describes the concept: Under the Dow theory, it is a bullish sign when successive rallies penetrate previous high points, and ensuing declines terminate above preceding lows. It is a bearish indication when rallies fail to penetrate earlier highs, and ensuing declines carry below their former lows. It is crucial to remember that the movements of both Rail and Industrial Averages always must be considered together. The action of one Average must be confirmed by the other before reliable inferences can be considered. A penetration of one Average unconfirmed by the other is meaningless for prediction purposes and frequently can be deceptive.

The concept of confirmation relates to predictions of future market movements based on analysis of changes in the Dow–Jones Industrial Average (DJIA) (see Table 2.1) having to be considered in conjunction with an analysis of changes in the Dow-Jones Transportation Average (DJTA) (see Table 6.1). The confirmation of these two signals is usually expected to be

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Table 6.1

Dow Jones Transportation Averages, 25 April 2003. Style

Primary Group

Mkt. Cap.

Wghtg.

US$ Close

Airborne Inc. Alexander & Baldwin Inc. AMR Corp. Burlington Northern Santa Fe Corp. CNF Inc. Continental Airlines Inc. Cl B CSX Corp. Delta Air Lines Inc. FedEx Corp. GATX Corp. J.B. Hunt Transport Services Inc. Norfolk Southern Corp. Northwest Airlines Corp. Roadway Corp. Ryder System Inc. Southwest Airlines Co. Union Pacific Corp. United Parcel Service Inc. Cl B USFreightways Corp. Yellow Corp.

New York SE NASDAQ NMS New York SE New York SE

ABF ALEX AMR BNI

VAL VAL VAL VAL

Air Freight Marine Transport Airlines Railroads

Sml. Cap. Sml. Cap. Sml. Cap. Lrg. Cap.

3.6311 4.794 0.8033 5.0916

19.89 26.26 4.4 27.89

New York SE New York SE

CNF CAL

VAL GRO

Trucking Airlines

Mid. Cap. Sml. Cap.

5.3983 1.5335

29.57 8.4

New York New York New York New York NASDAQ

CSX DAL FDX GMT JBHT

VAL N/A GRO VAL N/A

Railroads Airlines Air Freight Industrial Services Trucking

Mid. Cap. Mid. Cap. Lrg. Cap. Sml. Cap. Sml. Cap.

5.6703 2.1852 10.7326 3.224 6.2599

31.06 11.97 58.79 17.66 34.29

New York SE NASDAQ NMS NASDAQ NMS New York SE New York SE New York SE New York SE

NSC NWAC ROAD R LUV UNP UPS

VAL GRO N/A VAL GRO VAL GRO

Railroads Airlines Trucking Transportation Services Airlines Railroads Air Freight

Mid. Cap. Sml. Cap. Sml. Cap. Sml. Cap. Lrg. Cap. Lrg. Cap. Lrg. Cap.

3.7607 1.3071 6.6561 4.3412 2.7585 10.8367 11.0484

20.6 7.16 36.46 23.78 15.11 59.36 60.52

NASDAQ NMS NASDAQ NMS

USFC YELL

VAL VAL

Trucking Trucking

Sml. Cap. Sml. Cap.

5.1226 4.8451

28.06 26.54

SE SE SE SE NMS

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Fig. 6.1 Example of a Dow Theory Confirmation Signal. Source: Russell (1960).

accompanied by a high level of trading volume on the confirmation date (see Fig. 6.1 for an illustration). When asked to describe the Dow theory, it is this ‘confirmation of the industrial and transportation averages’ statement of the theory that will typically be identified. Supplementary interpretation concepts such as penetration, reversal, break-out and so on follow appropriately. As is evident from an inspection of the five year chart for the DJTA and DJIA index levels (Figs. 6.2 and 6.3) and 10-year chart for percentage changes in both index level series (Fig. 6.4), identification of confirming signals in the secondary movements in the DJIA and DJTA is often not an obvious exercise. For example, was a confirmation signal achieved on 11 March 2003 in Fig. 6.4. Though it came close, the low in the DJTA index level that occurred in March 2003 was not quite confirmed as the DJIA did not quite reach a new low on that date. The volume on that date was also not consistent with the ‘climax of volume’ signal for a change in primary movement. The picture is clearer on the primary trend. Comparing Figs. 6.2–6.4 with the stylized example in Fig. 6.1, it appears that the Dow theory has produced a strong signal for the end of the primary bear market trend that began in May 1999 and included the 2003 secondary bear market trend low.

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Dow Jones transportation index, 2004–2009 with 100 and 200 day MA.

Fig. 6.3

Dow Jones industrial index, 2004-2009 with 100 and 200 day MA.

The stock market trading environment has changed significantly since Dow, Hamilton and Rhea developed the corpus of the theory.14 For instance, 14 The

possibility of a substantive change in the Dow theory was recognized by Richard Russell in a interview published in Barron’s on 12 June 2000 (Du Bois 2000). Speaking of the first phase of the bear market that followed the change in primary market movement in May 1999, Russell observes: “In some ways, the current first phase is different from any other I’ve ever seen . . . Because it has lasted longer, because many more individuals and institutions are involved . . . and because a new phenomenon, the Internet, has emerged and is obviously changing the world. Then there’s volatility. I’ve never seen anything

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Fig. 6.4

Dow Jones industrial and transportation indexes, 1999–2009.

as illustrated in Table 6.1, the DJTA is no longer an index composed entirely of railway companies. This change has been effective since 1970. The implications of the significant change in the composition of the DJTA, when compared to the all-railway Dow (Railway) Transport index of Dow, Hamilton and Rhea, is difficult to formalize. The ability of leading Dow theorists to predict major primary market changes in 1929, 1932, 1974, 1982 and 1999 is strong evidence that the change in the DJTA did not substantively impact the predictive ability of the Dow theory. However, it is possible that the connection between the DJTA and DJIA may have been changed significantly by the impact of the 9/11 shock on the airline industry — if only because the impact on airline valuations reduced the share of this component in the DJTA. Perhaps this created an instance in 2003 where the theory failed to give an unambiguously clear signal. All indications are that the structural changes in the securities markets and the economy from 2003–2009 have given the Dow theory new life in the form of a primary bear market low in March 2009.

like what we have now. Among the reasons for it are day-traders moving in and out of stocks”. Structural changes such as the trading ‘circuit breakers’ introduced following the market collapse of October 1986 may have altered the underlying dynamics sufficiently to prevent a strong signal for the end of a bear market to emerge.

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Fortunately, there are other elements of the Dow theory that can be used to provide guidance about whether the traditional confirmatory signal has been altered by structural changes. Those with only a casual exposure to the Dow theory are usually surprised to discover that there is considerable divergence among Dow theorists about the central role of the confirmation feature of the theory. Old-style Dow theorists, followers of Hamilton and Rhea, base the art of interpreting the averages primarily on further properties of the charts. As Rhea observes (Russell 1960, p. 7): “Beginners frequently make the mistake of basing conclusions wholly on the matter of penetration. Familiarity with the co-related factors of duration, extent, activity, divergence, and secondary implications of primary bull markets is needed to make the correct diagnosis”. Yet, even old-style Dow theorists do not focus exclusively on the behavior of the averages, seeking also to identify elements that are expected to be present when there is a change in the primary movement. If these elements are not present, then confirmation of the averages alone is not sufficient. For old-style Dow theorists a change in primary movement of the market from bull to bear can only occur during the third phase of the bull market. Rhea describes the characteristics of the third phase of a bull market: This is the time when brokers and soothsayers prosper, and when an excited public, lured by the bait of advancing prices, buys stocks without regard to values, basing their action on nothing more than hopes and expectations . . . this is the phase where worthless stocks are bought for no other reason than because they look cheap, and because gamblers hope they will double in price. This condition has always prevailed in the third phase of bull markets.

If these types of activities are not witnessed in the marketplace, then confirmation signals are likely to be false, second phase indications of a change in the primary market movement. Unfortunately, the three phases are not symmetric across bull and bear markets. While the characteristics of the three phases of a bull market are readily specified, guidance from the Dow theory about the three phases of a bear market is less precise. It is recognized that the extent and duration of a primary bear market will be shorter than for a primary bull market, with the drop in the averages being much more rapid in a bear market than the rise in the averages during a bull market. Modern Dow theorists, such as Schaefer and Russell, put considerably less weight on the averages in determining the primary market movement. For example, Schaefer states: “A study of the Averages themselves

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can be highly rewarding. But in my opinion, a forecast based on past movements of the Averages cannot be conclusive. Predictions of events to come are more reliable if they can be reinforced by analysis of other technical and more conclusive factors”. These other factors include: the 200 day moving average of the Dow (see Fig. 6.3); the short interest ratio; the advancedecline line; market sentiment; market phases; and the bond yield cycle. Russell takes this approach even further (Du Bois 2001): “[confirmation of the averages helps] to identify the primary trend. However, value, dividend yield and other factors also play an important role. Without understanding all of them you’re lost”. Unlike Hamilton and Rhea who promoted active trading on secondary phase reactions in bull and bear markets, Schaefer advised: “Once stocks are purchased, both the minor and secondary movements in the market should be completely disregarded”. Second phase pullbacks in a bull market are buying (not rebalancing) opportunities, while second phase run-ups in bear markets are selling opportunities. Starting from the contributions of Schaefer, the modern form of the Dow theory makes ‘value’ the operative word. As Russell observes: “All other Dow theory considerations are secondary to the value thesis. Therefore, price action, support lines, resistance, confirmations, divergence — all are of much less importance than value considerations, although critics of the theory seem totally unaware of that fact”. The transformation of the old-style Dow theorist to the modern Dow theorist can be gleaned from statements made by Russell in April 2001 about the previous bull market and the state of the on-going bear market. The likelihood of nonconfirmation at market peaks is explicitly acknowledged (Du Bois 2001): the long bull market that began in 1982 ended on May 12, 1999 when the DJIA and the Transports both hit peaks. The Industrials eventually topped out at 11,722.98 in January 2000, but the Transports failed by a wide margin to confirm that record high. This bear market probably won’t end until there’s a final non-confirmation on the downside.

This statement suggests the possibility that the global low point for the DJIA in a primary bear market trend may not be confirmed by the DJTA. Rather the bottom could come when the DJTA hits a global low and the DJIA hits only a local low that is followed by an, unconfirmed, global low. This is something of a disconnect from the old-style Dow theory that, implicitly, assumes the DJTA and DJIA confirmation would be associated with global values, as subsequently happened with the global low in March 2009.

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Another element distinguishing old-style and modern Dow theorists is the emphasis on using measures of value to supplement conventional analysis of the averages. This emphasis on value measures is evident in Russell’s April 2001 analysis of the S&P 500 (Du Bois 2001): At its recent 1166, the S&P yielded about 1.2%. Were the yield to quadruple to 4.8% — and its been higher than that in the past — the S&P would drop to about 300. Interestingly, the S&P now trades at over three times revenues, six times book value and 75 times dividends. These figures are well above peaks seen at previous bear-market tops, and illustrate just how overvalued the S&P 500 is.

However, there are still key elements of the old-style Dow theory left in the analysis: Bear markets usually last about 25%–33% as long as the preceding bull market. Assuming the recent bull market ran from a low in 1982 to a peak in 1999, we’re talking 17–18 years. By this measure, I expect the decline to last four or five years, until 2005 or 2006. One possible difference this time is the speed at which the Nasdaq has plunged. If the Dow picks up momentum on the downside, the bottom could arrive sooner than 2003.

In considering the potential length of the current bear market, Russell still depends on the old-style notions of extent and duration. And what advice was Russell dispensing in April 2001? After acknowledging that he had already shifted his personal portfolio into U.S. Treasury bills, Russell observes: Take this bear market seriously. It’s never too late to do the right thing. In a primary bear market, the right thing is to play it safe. That means getting out of almost all common stocks and into US government paper. With cash in hand, you boost your buying power at the eventual bottom.

In retrospect, this advice was able to avoid the large drop in stock values but did not take advantage of the increase in bond prices associated with the downward shift in the Treasury yield curve that took place over the 2001–2002 period. This said, the quality of the market prediction is solid. To provide context to the predictions that Russell was making consider the following: resistance to believing we’re in a bear market is mind-boggling. People still seem to be hanging on for the “long haul”. This really is a tragedy. The losses in the average portfolio must be horrific. Foolish optimism and the speed of the Nasdaq decline literally have “locked in” millions of investors, the people who buy individual stocks and mutual

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funds . . . Way back at the turn of the 20th century, Charles Dow wrote that the most difficult concept to teach people is the inevitability of change. Sometimes the simplest ideas are the hardest to get across.

It is difficult to examine these notions and not be puzzled as to why so little attention has been given to the Dow theory in academic Finance. This is not to say that the Dow theory has been completely ignored in modern Finance.15 As Brown et al. (1998, p. 1311) recognize, empirical testing of the Dow theory was the impetus for Cowles (1934) “a landmark in the development of empirical evidence about the informational efficiency of the [stock] market”. However, unlike Cowles where it is found that “market timing based on the Dow theory results in returns that lag the market”, Brown et al. arrive at the opposite conclusion: we review Cowles evidence and find that it supports the contrary conclusion — the Dow theory, as applied by Hamilton over the period 1902 to 1929, yields positive risk-adjusted returns. The difference in the results is apparently due to the lack of adjustment for risk. Cowles compares the returns obtained from Hamilton’s market timing strategy to a benchmark of fully invested stock portfolio. In fact, the Hamilton portfolio, as Cowles interprets it, is frequently out of the market. Adjustment for systematic risk appears to vindicate Hamilton as a market timer.

Yet, all this speaks to old questions surrounding the Dow theory and has only indirect implications about the prospects of using the Dow theory in contemporary securities markets. Brown et al. begs a number of questions about whether the Dow theory is a viable method of market timing and about the feasibility of testing the Dow theory over a given sample. For example, there is the general question about whether it is possible to construct acceptable empirical tests of the Dow theory. Both Cowles and Brown et al. approach this problem by examining the prognostications of a specific, albeit important, early proponent of the Dow theory, W.P. Hamilton. However, at least since Stansbury (1960) and Bishop (1961) it has been recognized that the Dow theory has had to evolve through time, as market conditions and institutions change. As such, there is no ‘functional form’ that is applicable to the Dow theory and can 15 The Dow theory of technical analysis is not related to the ‘Dogs of the Dow’ theory that has been explored in some academic studies, e.g., Hirschey (2000), McQueen et al. (1997), and Visscher and Fillbeck (2003). Poitras (2005, pp. 561–564) provides more discussion of this stock selection strategy that recommends a portfolio composed of the 10 highest dividend yielding stocks in the Dow Jones Industrial Average.

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be estimated using, say, regression analysis. Rather, there are many Dow theorists, each with a distinct interpretation of what the theory says. While it is possible to estimate whether a basic feature of the Dow theory, such as the DJTA/DJIA confirmation signal, is capable of generating trading profits from market timing, the theory is more appropriately seen as a general qualitative guide to investment strategy as opposed to being a source of hard-and-fast trading signals.

6.2.2

Charting and Moving Average Systems

Types of Charts The modern Dow theory is something of an oddity in the realm of technical analysis. While it is predicated on the basic notion of all technical analysis that prices move in trends, the objective is to predict long-term movements in stock market averages. In contrast, most technical analysis is concerned with shorter trading horizons, usually focusing on the performance of individual stocks or commodities. As such, the primary objective for much of this type of technical analysis is speculation whereas the Dow theory is more relevant as a supplement to equity security investment strategy. Despite the rather chauvinistic attitude of fundamental purists and modern Finance believers, it is difficult to deny that some aspect of ‘charting’ does not enter into every practical equity security valuation or investment selection decision. Inspection of a three month, one year or three year price history is a typical first step in determining the value of a common stock. Technical analysis attempts to bring more structure to this process. In the absence of a unified theoretical foundation, the resulting vernacular procedures are derived inductively. By construction, technical analysis will be subject to the problems of using ex post analysis for making ex ante decisions. Even if an analyst has little belief in the efficacy of the various procedures used in technical analysis, it is difficult to deny that there are large numbers of traders that employ such techniques. At least in the short-run, the activity of these traders can impact the price of specific securities.16 16 The statement cannot be taken too literally. In general, it is not clear that technical analysts will move prices since technicians are not a homogeneous group. There are many different types of technical analysis and even analysts using the same approach may come up with conflicting buy and sell signals.

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As a consequence, even rigid nonbelievers in technical analysis can benefit from basic knowledge about certain elements of the approach. The starting point and, in many cases, the ending point for technical analysis is charts. As Edwards and Magee (1966, p. 7) observe: Charts are the working tools of the technical analyst. They have been developed in a multitude of forms and styles, to represent graphically almost anything and everything that takes place in the market or to plot an “index” derived therefrom. They may be monthly charts on which an entire month’s trading record is condensed into a single entry, or weekly, daily, hourly, transaction, “point-and-figure”, etc. They may be constructed on arithmetic, logarithmic or square-root scale, or projected as “oscillators”. They may delineate moving averages, proportion of trading volume to price movement, average price of “most active” issues, odd-lot transactions, the short interest, and an infinitude of other relations, ratios and indexes — all technical in the sense that they are derived, directly or indirectly, from what has actually been transacted on the exchange.

Though it is possible to use other ‘working tools’ than charts to accomplish the same result, e.g., Lo et al. (2000), the bulk of technical analysis is presented in terms of chart interpretations. As a consequence, in order to explain and assess technical analysis it is necessary to examine charting techniques. Outside the realm of technical analysis, the most commonly observed chart for common stocks is the ‘close-only’ chart. This type of chart is simply a time series of closing prices plotted using an arithmetic scale. The frequency of observation is typically daily, weekly or monthly depending on the length selected for the time period of interest. Observations for longer intervals, such as weekly or monthly, are usually for specific days, e.g., every Friday for weekly, though averages can also be used. Sometimes close-only charts are used because intra-day data is not available. In other cases, the close-only chart is selected because the technical analyst believes that the inclusion of high-low, open and other information on the chart tends to cloud the picture, i.e., the closing price is the appropriate summary of the key information. However, Schwager (1996, p. 21) reflects the typical view: “many important chart patterns depend on the availability of high/low data and one should think twice before ignoring this information”. While close-only charts can be used for various purposes, there are three other basic chart types that are more commonly used for doing basic technical analysis: bar charts (see Fig. 6.5); point-and-figure charts; and Japanese candlestick charts (see Fig. 6.6). Point-and-figure charts (not discussed

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S&P 500 (SPY) daily OHLC bar chart, 3/4/09 – 9/4/09.

S&P 500 (SPY) 3-month daily candlestick chart, 6/4/09 – 9/4/09.

here) are specialized charts more commonly used in futures markets, particularly by floor traders and day traders, than in stock markets.17 These 17 One service that does make extensive use of point and figure charts for stock analysis is Investor’s Intelligence. Examples of point and figure charting for stocks can be viewed at the service website: www.investorsintelligence.com. Standard drawing of trend lines applies to point and figure charts in the same fashion as bar charts and candlestick

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charts do not take account of time but, rather, view trading as a continuous process. For technical analysis of security prices, the bar chart comes in two formats with the high-low-close (HLC) chart being the most common type. For a daily HLC bar chart each day is represented by a vertical line connecting the high and low prices for the day with a small horizontal line indicating the close. As indicated in Fig. 6.5, the traditional bar chart can be augmented to an open-high-low-close (OHLC) bar chart that indicates the open with small horizontal lines on the right (left) side of the bar for the close (open). Bar charts for longer intervals, such as a weekly or monthly bar chart, are analogous. For, say, a weekly bar chart the vertical line represents the high and low for the week with the small horizontal line representing the final closing price for the week. Because of the different appearance of charts for different sampling intervals, it is common for daily, weekly and monthly bar charts to be examined when doing a technical analysis for a given security. Though the history of candlestick charts in Japan predates bar charts and point-and-figure charts, this method of charting was virtually unknown outside of East Asia prior to Nison (1991). Compared to bar charts, candlestick charts are more versatile and have more rules to generate signals than HLC bar charts. In effect, a candlestick chart contains all the information available in a close-only or HLC bar chart and more (see Fig. 6.6). Because a candlestick chart has more information it is also somewhat more complicated and requires more preparation effort. Such chart formats are available at publicly accessible internet futures charting services such as www.futuresource.com, and are increasing available at no-pay-for-use common stock charting services, e.g., www.bigcharts.com. The traditional HLC bar chart is still the standard format for stock charts. Casual inspection of a traditional bar chart reveals that while the high, low and close are indicated, there is no information about the open. While the OHLC charts does not reveal the relationship between open and close, the candlestick format aids signal identification. The information provided in the candlestick chart is a thin line for a given day that gives the high and low while the white/green and black/red boxes — called ‘real bodies’ — reflect the open and close. A black/red (white/green) real body indicates that the open was above (below) the close. The top of the real body indicates the open (close) with the bottom indicating the close (open). charts. Because technical analysis is not limited to spot (cash) market trading, a number of important technical analysis sites are concerned with futures prices.

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Candlestick charting has many aesthetically pleasing features. The nomenclature is one such feature. For example, the part of the thin line that lies above the real body is referred to as the ‘upper shadow’ with the part of the thin line below the real body being the ‘lower shadow’. If the open and close are equal or approximately equal then there will be no real body. This is a doji — literally translated as ‘indecision’. Dojis provide a signaling mechanism that is not available in bar charts. For example, the presence of a doji following a large white candle is a strong signal that a rally is stalling. Another key feature is the hammer which occurs where: the real body is at the upper end of the trading range (the color is not important); has a long lower shadow that is more than twice the height of the real body; and, little or no upper shadow. A hammer occurs when the market opened near the high, traded down during the day and rallied to close near the high. This is a bullish signal for near term trading. Of the three distinct hammers in Fig. 6.6 two were followed by a strong up move the next trading session with one followed by a down session. There are numerous other features of candlestick charts, e.g., dark cloud cover, hanging man, morning star. However, discussion of these aspects would require more attention than is warranted here.18 More detail on these issues can be found in Nison (1991, 1996) and at websites dedicated to technical analysis such as www.marketsource.com. 6.2.3

Chart Patterns

A key notion of technical analysis is that prices follow trends. Charts are used for identification of trends. As it turns out, trend identification is considerably more complicated than drawing a line on a chart. The process becomes subjective almost immediately. Consider the definition of a trend. Edwards and Magee (1966, p. 47) observe: Stock prices move in trends. Some of these trends are straight, some are curved; some are brief and some are long-continued; some are irregular and poorly defined and others are amazingly regular or “normal”, produced in a series of action and reaction waves of great uniformity. Sooner 18 In

addition to requiring considerable space for developing the requisite notions, there is also relatively little information available on the profitability of the various candlestick chart patterns. One study reported by Schwager (1996, pp. 296–305) provides results that “were not encouraging . . . The test . . . does not prove that candlestick charts have no value, but rather that a simplistic interpretation of candlestick patterns is not profitable”. It seems that, like other forms of technical analysis, candlestick charts are sensitive to whether there is a trend or a trading range in the underlying price series.

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or later these trends change direction; they may reverse (as from up to down) or they may be interrupted by some sort of sidewise movement and then after a time proceed in their former direction.

Recognizing that there are numerous possible approaches to specifying trends, consider the commonly used definition: an uptrend is defined by a sequence where each ‘high’ is followed by a ‘high’ that is higher and each ‘low’ is followed by a ‘low’ that is higher. Similarly, a downtrend is defined by a sequence where each ‘high’ is followed by a ‘high’ that is lower and each ‘low’ is followed by a ‘low’ that is lower. The ‘highs’ and ‘lows’ — often referred to as ‘relative highs’ and ‘relative lows’ — occur because price charts appear as jagged lines. In drawing a trend line for a downtrend it is conventional to connect the sequence of lower relative highs. For an uptrend, the trend line will conventionally connect the sequence of relative lows. Where a trend line is drawn for both the relative lows and relative highs the resulting (hopefully) parallel lines form a trend channel. For a trend channel, the upper line is referred to as the ‘resistance line’ and the lower line as the ‘support line’ (Kaufman 1978, p. 139). The breaking of a trend line by a relative high or low is an indication that the trend may have ended. The practical difficulty that can arise with this exercise of defining a trend line is illustrated in Fig. 6.5 that provides 6 month bar chart for the S&P 500 (SPY). The trend line for this chart indicates that there is an identifiable uptrend over the period. Similarly, there clearly is an identifiable downtrend and uptrend on the five year DJIA chart in Fig. 6.3. Despite this, Schwager (1996, p. 25) captures the conservative conclusion that needs to be drawn from the breaking of a trend line: “It should be emphasized . . . that the disruption of the pattern of higher highs and higher lows (or lower highs and lower lows) should be viewed as a clue, not a conclusive indicator, of a possible long-term trend reversal”.19 19 Schwager

(1996) is concerned with doing technical analysis for commodity futures contracts, not stocks. Following Edwards and Magee (1966, ch.16), it is ‘true’, in general, that techniques used in technical analysis of stocks and commodities are the same, as long as “proper allowance is made for intrinsic differences between commodity futures contracts and stocks and bonds”. Included in these differences are: the limited life of individual futures contracts; the presence in futures markets of commercial traders involved in hedging which renders near-term support and resistance levels less effective for futures; the need to interpret volume differently and to account for open interest; and, the greater importance of certain news events such as droughts or flooding. Given these qualifications: “Under what might be called normal market conditions, those chart patterns which reflect trend changes in the most simple and logical fashion work just as well

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Proctor and Gamble, 2004–2009.

While technical analysis thrives on the presence of trends, in many situations there is no discernable trend. In these situations, prices move in a “horizontal corridor that contains price fluctuations for an extended period” (Schwager 1996, p. 57) referred to as a trading range also known as a rectangle (Edwards and Magee 1966, ch. 9).20 Following Poitras (2005, with commodities as with stocks”. However, Edwards and Magee make an important qualification to this statement: “successful speculation in commodities requires far more specialized knowledge, demands more constant daily and hourly attention. The ordinary individual can hope to attain a fair degree of success in investing in securities by devoting only his spare moments to charts, but he might better shun commodity speculation unless he is prepared to make a career of it”. 20 The distinction between a ‘trading range’, a ‘rectangle’ and a ‘consolidation’ is not always clear. Following Edwards and Magee, a consolidation is a period of sideways movement in a trending market. Flags, pennants and wedges are consolidation formations, as are head-and-shoulders, scallops and saucers. Edwards and Magee (1966, p. 168) describe the rationale for consolidations: “An army that has pushed forward too rapidly, penetrated too far into enemy territory, suffered casualties and out-run its supplies, must halt eventually, perhaps retreat a bit to a more easily defended position and dig in, bring up replacements and establish a strong base from which later to launch a new attack. In the military parlance which we have all become more or less familiar these past few years, that process is known as consolidating one’s gains”. In other words, a consolidation is a ‘sidewise’ chart pattern composed of minor fluctuations that continues until the market has ‘caught up to itself’ and ‘is ready to go on again’. In contrast to

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pp. 522, 523), Procter & Gamble (PG) is an example of a trading range stock (see Fig. 6.7). The 5-year price movement of PG is bounded above by $75 and below by about $50. Up-trends can stall out at the resistance level defined by the upper bound and down-trends can stall out at the support level, defined by the lower bound. A breakout occurs when prices penetrate either the resistance or support level. A breakout can be an important signal for securities with prices that have trading ranges. Once a breakout from a trading range has been established, the resistance level of the previous trading range becomes a support level for the next trading range. Determining whether a price chart represents a trading range or a trend is a key step in interpreting the chart. In the case of PG, the price did penetrate the support level during the market downdraft of February–March 2009 but soon rebounded back into the trading range. This illustrates the difficulty in identifying when a breakout has been confirmed. Most trading strategies used in technical analysis do not perform well in trading range markets. Those trading strategies that are designed to profit in trading range markets, such as oscillators, will tend to perform poorly in trending markets. Similarly, techniques for analyzing charts in trending markets, e.g., headand-shoulders, flags and gaps, have little meaning in trading range markets. There are practical difficulties in identifying and interpreting the support and resistance levels for a trading range. One difficulty involves the appropriate length of time to use in defining a trading range. As with the drawing of trend lines, changing the sampling interval will change the interpretation of the chart. Schwager observes that for a trading range to be established the horizontal corridor has to last at least a couple of months. Trading ranges can last for years. In such cases, it is often possible for the long-term trading range to be broken down into smaller trading ranges. In practice, breakouts from trading ranges are considered to be one of the most reliable technical indicators. Following Schwager (1996, p. 60), the reliability of a breakout signal depends on three factors: the duration of the trading range, the longer the duration of the trading range the stronger the signal; the narrowness of the trading range, the narrower the range the more reliable the signal; and, the ability of the breakout to meet criteria for confirmation, simply penetrating the support or resistance level is usually not sufficient to produce a trading signal. The use of breakout signals to trigger a consolidation, a ‘rectangle’ “defines a contest between two groups of approximately equal strength . . . Nobody . . . can tell who is going to win until one line or the other is decisively broken”. In effect, a rectangle more-or-less defines a trading range.

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trades has to be considered in the light of ‘the most important rule in chart analysis’. Schwager (1996, p. 180) describes this ‘failed signal’ rule: “A failed signal is among the most reliable of all chart signals. When a market fails to follow through in the direction of a chart signal, it very strongly suggests the possibility of a significant move in the opposite direction”. Was this the case with the February–March 2009 failed signal in Fig. 6.7? All this may seem confusing to the uninitiated. A breakout is a strong trading signal unless the breakout provides a failed signal in which case it provides a strong signal of a move in the opposite direction. This is compounded by the difficulty that arises with interpreting when a breakout has occurred. It is apparent that when a chart pattern has a breakout from a trading range through a resistance (support) level this is a buy (sell) signal. However, as Schwager (1996, pp. 67–69) observes: It should be emphasized that a prior high does not imply that subsequent rallies will fail at or below that point, but rather that resistance can be anticipated in the general vicinity of that point. Similarly, a prior low does not imply that subsequent declines will hold at or above that point, but rather that support can be anticipated in the general vicinity of that point. Some practitioners of technical analysis treat prior highs and lows as points endowed with sacrosanct significance. If a prior high was 1078, then they consider 1078 to be major resistance, and if, for example, the market rallies to 1085, they consider resistance to be broken. This is nonsense.

Schwager recommends that there be a stronger confirmation signal than simply trading above (below) the resistance (support) level, such as having some minimum number of closes above (below) the resistance (support) level or being above (below) the resistance (support) level by some percentage amount or both. Many technical analysts that evaluate stock charts emphasize the importance of high volume as a prerequisite confirmation signal for breakouts and reversals. There are no hard-and-fast rules on breakout confirmation. This is part of the art in technical analysis. The exercise reflected in Fig. 6.7 and the discussion of trends and trading ranges captures the significance of the following statement (Edwards and Magee 1966, p. 48): “the first and most important task of the technical chart analyst is to learn to know the important reversal formations and to judge what they may signify in terms of trading opportunities”. The number and variety of these chart formations is unsettling: the head-and-shoulders and the necktie breakout; flags, pennants and wedges; scallops and saucers; gaps, spikes and islands; triangle tops (bottoms) and

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rounded bottoms (tops); and, V tops and bottoms. Interpretation of the various chart formations depends on the initial determination of whether the price chart is in a trend or trading range. For example, flags and pennants represent continuation signals in a major trend. These patterns are sideways price formations that are associated with a pause in a major trend. Triangles are a more complicated version of a continuation signal. Head-and-shoulders, double tops and bottoms and islands surrounded by gaps are indicators of reversals. Combine this with the difficulties of determining whether the price chart reflects a trend or trading range and the conclusion of Schwager (1996, p. 147) is understandable: “chart analysis remains a highly individualistic approach, with success or failure critically dependent on the trader’s skill and experience”. Moving Average Techniques Breakouts, trading ranges, chart formations and the like are concepts that apply to the basic charts. Even the staunchest believer in technical analysis will acknowledge that the interpretation of chart patterns is complicated by the noisy character of prices. The drawing of lines on charts is a subjective process, at best. In order to remove some of the noisiness in prices, it is a natural development to consider further processing of the price data before plotting the information on a chart. Going back at least to Gartley (1930, 1934), technical analysts have explored the use of moving average techniques in order to smooth the time series of prices. Over time, more complicated processing of price data, such as oscillators and stochastics, have been introduced. Moving averages have the attractive property that the unit of measurement is the same as for prices, something that is not always true of more complicated processing procedures. As a consequence, moving averages can be plotted onto the price charts and used to aid in assessing the chart patterns. Because moving averages smooth the price data, conventional chart formations such as flags and pennants will not be apparent in the moving average. A moving average can take a variety of forms. The common element in the different forms is the use of a fixed sampling window. There is always a fixed number of observations used to calculate the moving average value for any given day. An T -day moving average uses the current price and the most recent T − 1 past prices to calculate the average at a given time t. As time moves forward, the most recent observation is added and the most distant observation is dropped, maintaining T observations in the average calculation. In particular the simple and weighted T day moving

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200-day vs. 100-day simple MA chart for SPY, 2004–2009.

averages at time t are calculated as T −1


Simple MA :

P¯ (t, T ) =

Weighted MA : P¯ (t, T )W =

i=0 T −1


P (t − i) T w(i) P (t − i)

i=0

where P¯ (t, T ) is the time t value of the simple moving average and P¯ (t, T )W is the time t value of the weighted moving average where the sum of the wi (≥ 0) weights is required to be equal to one. The simple moving average weights each of the observations equally (1/T ) (see Fig. 6.8). Variations of the weighted moving average approach, such as the exponential moving average, use different weighting schemes. A 1-day moving average is the original price chart. The simple T day moving average is a special case of a weighted moving average where wi = 1/T. Selecting the appropriate length for a moving average is a subject of considerable debate and study by technical analysts, e.g., Kaufman (1978, pp. 83–85). A number of different estimators are available in addition to the simple equally weighted moving average. A popular alternative is the exponentially weighted moving average (EMA) that has the form: EM A(t) = α P (t) + (1 − α) EM A(t − 1)

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where 0 < α < 1. Expressing in lag operator form, manipulating and solving for EMA(t), it follows that the EMA can be expressed as a infinite weighted moving average with weights wi = α(1 − α)i . More precisely: EM A(t) = α P (t) + α(1 − α) P (t − 1) + α(1 − α)2 P (t − 2) + α(1 − α)3 P (t − 3) + · · · In various sources, e.g., Schwager (1996, p. 602), it is stated that the EMA “corresponds roughly to a simple moving average” with length T where: α = 2/(T + 1) or T = (2 − α)/α. However, this condition only follows under certain conditions. Moving Average Patterns Depending on the objectives of the technical analyst, moving averages can be used to identify trends, generate trading signals or both. Conventional wisdom recognizes a moving average (MA) as a trend following procedure. In trading range markets, which are often the case, moving averages will not typically be a useful tool. Because a moving average takes into account both current and lagged values of prices, the relationship between the observed price series and the MA, or between moving averages of different lengths, can be used to identify the trend. Due to the lagging nature of an MA, in a rising market the moving average value for a given date will lie below the price, or a moving average with a shorter length, for that date. Conversely, in a declining market the MA will lie above the current price (see Figs. 6.8 and 6.9). Trend reversals, crossovers, occur when the sequence of current prices crosses the moving average, or a shorter MA crosses a longer MA. The transition from an uptrend to a downtrend occurs when the price series penetrates the moving average from above and vice versa for a downtrend to an uptrend. These crossovers are trading signals. In some cases, the moving average is compared with the original price series, in other cases a moving average of one length is compared with a moving average of another length. In Fig. 6.8, trading signals can be generated by comparing the 200-day moving average with 100-day moving average or comparing either with the raw price chart.21 One difficulty of using a moving average to identify a trend or generate a trading signal is that, by construction, the moving average will lag the 21 The

use of two moving averages of different lengths to generate trading signals is a basic type of oscillator system, e.g., Schwager (1996, p. 524). Such systems are usually referred to as ‘dual moving average’ or DMA systems.

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Fig. 6.9

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50-day vs. 13-day Exponential MA chart for SPY, 09/08-09/09.

actual price series. The longer the moving average, the longer is this lag, e.g., a T day moving average will have a shorter lag than a T + N day moving average. Examining the 200-day moving average in Fig. 6.8, it is apparent that the S&P peaked in October 2007 while the 100-day MA crosses the 200-day MA from above — a strong bearish signal — in Jan 2008. The bullish signal of the 100-day MA crossing the 200-day from below appears in July 2009. The use of the actual price series or short moving averages to determine crossovers raises the possibility of whipsaws where the price series crosses the moving average in one direction only to reverse course shortly thereafter and cross in the other direction. This is apparent in Fig. 6.10 in the period prior to October 2007 when the price series is used to identify crossovers. The failings of the moving average in a trading range market are apparent in Fig. 6.10 which provides results for 100- and 200-day moving averages for Procter and Gamble over a ten year sample period. Finally, while the preceding discussion focused on price charts, the scope of technical analysis does include a much broader set of variables. Charting, moving averages, momentum, oscillators and the like apply to this broader set of variables in much the same fashion as with prices. For example, some technicians actively monitor a breadth indicator to get a sense of underlying market demand and the general near-term or long-term direction of the market. Technical indicators for market breadth involve calculations

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Fig. 6.10

200-day vs 100-day sample MA chart for PG, 1999–2009.

with advancing and declining issues, sometimes supplemented by volume. Included in these indicators are: the advance–decline line; advance–decline ratio; absolute breadth index; breadth thrust; McClellan oscillator; and the summation index (see www.marketscreen.com). Perhaps the mostly widely followed technical indicator of breadth is the advance–decline line — the cumulative, ongoing sum of the difference between the number of stocks closing higher minus the number of stocks closing lower each trading day. Alternatively, there is the advance decline ratio — the ratio of advancing issues to declining issues.22 The daily difference between the number of advancing and declining issues (not cumulated) is typically evaluated as a momentum indicator. The typical intuition used to assess a breadth indicator is based on the presumption that the direction of the major market averages tends to persist at trend reversal points. Market averages such as the 30 stock DJIA or the value weighted S&P 500 give disproportionate emphasis to a narrow group of stocks. This leads to the following interpretation of, say, the advance–decline ratio: at market peaks (troughs), the narrowly based 22 The rise in the importance of breadth indicators is a relatively recent phenomenon. Edwards and Magee (1966), for example, do not examine breadth indicators. One example is the ‘breadth thrust’ indicator developed by Martin Zweig, a frequent guest on the once popular PBS program Wall Street Week with L. Rukeyser.

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DJIA will continue to increase (decrease) while market breadth declines (increases). In other words, a divergence in the advance–decline ratio and the DJIA is a signal of a change in market trend. Due to the day-to-day variation in the breadth indicator (and the DJIA), moving average methods can be used to smooth the series to give a better representation. Similarly, the market breadth indicator can be examined in isolation and used as a trend indicator. As with price charts, when the short-term, say 10-day, moving average of the breadth measure cuts the long-term, say 200 day, moving average from below (above) this is a signal for an upward (downward) movement in prices. In addition to changes in market trend, breadth indicators such as the McClellan oscillator can also be used to assess direction within trading range markets. 6.2.4

Contrarian and Contrary Opinion Strategies

Like ‘value’ and ‘growth’ stocks, the ‘contrarian approach’ to equity security analysis is a source of semantic confusion. The terminology ‘contrarian’, ‘contrarian strategy’ or ‘contrarian approach’ can apply to a wide range of strategies involving different measures, applicable in a variety of different situations. The basic motivation of the contrarian strategy is to trade in the opposite direction of the trend in prices or market sentiment. Differences in definition arise from the theoretical rationale used to motivate the contrarian strategy. In modern Finance, the ‘contrarian’ approach is often equated with ‘value investing’. For example, Levis and Liodakis (2001) claim: “The profitability of contrarian investment strategies is now one of the most well known empirical facts in the finance literature” where ‘contrarian’ refers “to various strategies based on buying/selling stocks that are low/high relative to three accounting measures of performance — earnings, cash flows, and book values — as well as strategies based on low/high EPS growth”. This claim of ‘most well known empirical fact’ is supported by references to a number of studies, including Fama and French (1998). Yet, Levis and Liodakis also proceed to observe that: “the outperformance of such strategies has declined and even reversed in the most recent years”. The process of presenting ‘strong empirical evidence’ that is later refuted is becoming a characteristic feature of modern Finance. This unsettling feature is compounded by another confusing feature: the tendency to redefine words that have an established but different meaning in either the vernacular or old finance usage. From the efficient markets hypothesis — where ‘technical analysis’ and ‘fundamental analysis’ are given interpretations that do not do justice to those approaches — to ‘contrarian’ investment

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strategies — where the emphasis is placed on the use of accounting measures to select stocks — modern Finance has taken an exclusionary attitude regarding previous approaches to the subject. Redefining words that already have established alternative meanings — such as ‘contrarian’ investment strategy — shows either ignorance of the internal workings for other approaches to Finance or a disappointing lack of respect for these approaches.23 It is not even clear that the use of ‘contrarian’ is grammatically correct. The connection between the use of accounting measures and a contrarian outcome depends on an empirical assumption that, say, high (low) P/E or P/BV stocks are past winners (losers), e.g., Lakonishok et al. (1994). Only if the strategy involves buying losers and selling winners can the approach be interpreted as contrarian, and even then the meaning is substantively different than used in other contexts. The confusion created by the definition of ‘the contrarian approach’ used in modern Finance is unfortunate because the long history of the contrarian approach contains many insights. The basis of this approach to equity security valuation is reflected, for example, by Keynes (1936, p. 155): “the professional investor is forced to concern himself with the anticipation of impending changes, in the news or in the atmosphere, of the kind by which experience shows that the mass psychology of the market is most influenced”. In effect, prices in equity security markets are the outcome of ‘crowd psychology’ or ‘mass psychology’. As Neill (1954, p. 5) observes: “What it comes down to in the final analysis is that a ‘crowd’ thinks with its heart (this is, is influenced by emotions) while an individual thinks with his brain”. Keynes (1936, p. 154) provides more substance for this observation: “A conventional valuation which is established as the outcome of the mass psychology of a large number of ignorant individuals is liable to change violently as the result of a sudden fluctuation of opinion due to factors which do not really make much difference to the prospective yield; since there will be no strong roots of conviction to hold it steady”. The

23 Siegel

(1998, ch. 5) is an exception. Siegel provides a brief discussion of Neill (1954) and overviews empirical evidence on a study of investor sentiment as captured in the indicator published by the investment advisory service Investor’s Intelligence. This indicator is based on sentiment scoring of a large sample of market newsletters. Over a 35-year sample, the indicator was found to have ‘strong predictive power’. However, Siegel (1998, p. 65) does contribute to the semantic confusion about ‘value investing’ as a contrarian strategy: “Value investors are contrarians who believe that swings of optimism and pessimism about the market and individual stocks are frequently unjustified, so buying out of favor stocks is a winning strategy”.

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contrarian attempts to be ahead of the crowd by identifying when mass psychology has driven prices too far in one direction. Though the basis of the contrarian approach can be traced back to early writings on security markets, e.g., de la Vega (1688), the development of an organized approach aimed at trading securities did not occur until the 1950s. A well developed association of contrary opinion with technical analysis can be traced to Drew (1951) where the views of Humphrey Neill were recognized. Neill (1954, p. 15) appraises the state of the subject in the mid-1950s: The Theory of Contrary Opinion is not something that one reads about in books or histories. There is no literature on the subject. Nothing has been written directly on the use of contrary opinion that I am aware of, except an excellent chapter pertaining to “contrary market opinion” in [Drew 1951].

Neill had been developing and writing about contrary opinion since the 1920’s, mostly in newspaper columns and an investment advisory newsletter, Neill Letters of Contrary Opinion. A driving concern for Neill’s inquiries was the question: why is the public so often wrong? Neill sought the explanation for this question in the role of ‘human nature in finance’, more specifically on the role of mass psychology and the actions of individuals in crowds. For Neill the ‘art of contrary thinking’ applies to a wide range of issues — political, social and economic: “The art of contrary thinking consists in training your mind to ruminate in directions opposite to general public opinions; but weigh your conclusions in light of current events and current manifestations of human behavior”. Though Neill has insights into various realms of human activity, it is the implications of contrary thinking for technical analysis that has received the greatest recognition (Neill 1954, p. 16): One can interpret charts almost any way he wishes. He can read into their ‘formations’ just about any probable result he hopes for. Which is to say, that if one is bullish at heart, his chart reading is likely to be interpreted optimistically; if bearishly inclined, charts accomodatingly will “say” that the market is going down. During one-way market trends (whether up or down) the trends are clearly enough defined on the charts; but when the market comes to an impasse and everybody is in a quandary as to the direction prices are likely to go, then the charts, too, are usually “silent”.

It is in these periods of indecision in the charts that “each person would interpret ‘technical action’ in accordance with his deep-seated personal

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opinions”. Wishful thinking takes over and the “inherent traits of hope, greed, pride-of-opinion, and similar human feelings” bias the analysis and contribute to making “successful speculation one of the most difficult arts to master”. For Neill (1954, pp. 44–46), the theory of contrary thinking is ‘intangible’, it is a habitual approach to examining the world. The public, the crowd is not wrong all the time. “The public is perhaps right more of the time than not. In stock market parlance, the public is right during the trends but wrong at both ends!” In other words, the public is ‘wrong when it pays the most to be right’. Neill recognizes that “when we adopt a contrary opinion, as a guide, we must recognize that we may be too far ahead of the crowd”. This is because events are often slow to change. Weeks or months may pass before a trend changes and the contrary opinion proves to be correct. However, as “there is no known method of timing events or trends . . . it is wiser to be early than to be late — in most economic decisions”. Neill makes the convincing point, based on years of heuristic inductive analysis, that consideration of contrary opinion improves forecasting ability: “Contrary thinking unquestionably helps one to avoid many common errors in forecasting — errors arising from miscalculating what the public will do”. If anything, the art of contrary thinking will alert the individual to the bombardment of self-serving information and news that is dispensed from brokerage houses, government departments and agencies, and the popular financial media. Making the theory of contrary thinking operational requires some method of measuring the sentiment of the ‘crowd’. Since Neill, considerable effort has been dedicated to this task. In the absence of well-developed or acceptable measures, Neill (1954, p. 22) observes: you will have to peruse a pile of news and comments. However, our radios, and magazines unload such a flood of economic news and propaganda these days, it is not difficult to get a fairly accurate cross section of what people probably are thinking about and what the composite opinion is likely to be. Also — and this is important — of what some groups want us to accept and believe.

Neill identified official economic releases as another possible source for market sentiment, because of the weight such opinions have on the public. At Neill’s time, the Council of Economic Advisors had an impact similar to what the Board of Governors would have at present. Neill also provides an important cue for later developments in the measurement of sentiment: “A consensus of businessmen — or brokers — is valuable in making an

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Fig. 6.11

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Investor’s intelligence investment advisory indicator.

analysis of opinions ‘to be opposite to’ because of their influence on general sentiment”. An example of how this notion has been made operational is provided by the Investor’s Intelligence investment advisory service (www.investorsintelligence.com) that calculates a number of contrary opinion indicators based on surveys of market sentiment expressed: in investment advisory newsletters, e.g., Siegel (1998, p. 87) and by NYSE members (see Fig. 6.11). In addition to surveys of investment advisory newsletters, opinions of floor traders and brokerage house recommendations, Siegel (1998, p. 89) makes reference to a “sentiment indicator based on the recommended portfolio allocations of market analysts and portfolio managers. Whenever their recommended allocation to stocks falls below 50%, indicating a high level of pessimism about the market’s prospects, subsequent returns have been high”. Siegel claims that the Director of Quantitative and Equity Research at Merrill Lynch “calls this his single most powerful quantitative markettiming barometer”. Like any mechanical investment strategy, there is the possibility that the feedback effect will undermine the effectiveness of such a contrarian strategy. However, measures based on surveys and analysis of newsletters have a number of features that would mitigate the

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feedback effect: the information is not widely disseminated and, in some cases, the measures are proprietary; being based on surveys and the like, the measures change slowly over time; and, the interpretation of the measure is subjective. It is arguable whether such contrarian measures are not more within the realm of fundamental analysis than technical analysis. In considering the performance of contrary opinion and other contrarian indicators, the forecasting horizon is a key variable. Based on the limited evidence that is available, it appears that contrary opinion indicators have been effective for determining turning points in long-term trends. However, the use of contrarian indicators for purposes of short-term speculation — the main battlefield of technical analysis — is likely to be less effective, if only because contrarian indicators tend to have a long-term focus. In order to be used for short-term trading, the contrarian measures need to be based on information sets that change on a regular basis. This runs the risk of altering the conceptual foundation upon which the contrarian approach is based. Some indicators that have been suggested in the past that could be used for short-term trading, such as the ratio of purchases to sales for odd-lot transactions (Kaish 1969) or mutual fund cash positions (Massey 1979), also seem to work best (if at all) for predicting long-term turning points. In an odd twist, the ‘buying losers and selling winners’ contrarian strategy suggested by modern Finance adherents seems to be the closest that a profitable ‘contrarian’ strategy comes to a short-term horizon. 6.3 6.3.1

Recent Developments in Technical Modeling Relative Strength

The epistemology of economic positivism requires, where possible, that theoretical valuation models be empirically tested on observed data. Knowledge is conceived to progress linearly as more precise empirical observations are obtained and theoretical hypotheses are developed that have better predictive power. In the process of empirical testing and observation, insights are gained inductively that permit the development of theoretical models with a better fit to reality.24 This intellectual process has produced 24 In practice, the process of producing theoretical models is guided by ‘stylized facts’ that have been identified in previous examinations of the data. This process of developing theoretical models from previously known empirical results and then testing those models as though there was no prior knowledge of the data has been explored by Leamer (1978). The progress of knowledge in economics and finance has been characterized by a variety of ‘specification searches’ that are explored by Leamer.

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enormous strides in the natural sciences, where an immutable physical reality is the object of analysis. The gains achieved have been more debatable in the human sciences where the exercise of free will by individuals undermines the assumption that the objective reality is immutable. In contrast to modern Finance, the bulk of technical analysis proceeds solely by empirical observation. As such, the ‘science of technical analysis’ (Edwards and Magee 1966, p. 6) is still subject to the general criticism aimed at modern Finance, i.e., that objective reality in the human sciences is not immutable. The assumption that chart patterns repeat over time requires a degree of predictability for human behavior that is difficult to reconcile with the exercise of free will and the evolution of the social and historical context. In any event, technical analysis is predicated on the assumption that ‘history repeats itself’. The subject is ‘forward looking’ in the sense that the reasons why history repeats are of relatively little interest compared to the identification of ‘repeatable patterns’ that permit prediction of future price movements. Induction drives the method of analysis. A range of these repeatable patterns includes the various types of chart patterns and associated moving average techniques. These methods of technical analysis can be characterized as traditional, in the sense that the information of interest can be presented on a single price chart. Over time, technical analysis has evolved methods of analysis that are more sophisticated, in the sense that the information of interest is mapped from the price chart to another chart, or from two price charts onto another chart. Included in these more sophisticated methods are indicators of relative strength, momentum and oscillation. These indicators involve evaluating functions of the original price series. In keeping with the conventional approach of technical analysis, the charts of these more sophisticated indicators are usually used as the method of evaluation, though this is not necessary. The indicators of relative strength, momentum and oscillation are closely related. In some presentations, relative strength and price momentum are used synonymously, e.g., Macedo (1995), though there are good reasons to make a distinction between the concepts. In an odd semantical twist, Wilder (1978) even introduced a form of oscillator referred to as the ‘Relative Strength Index’. In what follows, relative strength is interpreted in the traditional sense of Levy (1967, 1968) and others, e.g., Bohan (1981). To avoid potential semantic confusions, some sources refer to the traditional relative strength concept as comparative relative strength, e.g., www.marketscreen.com. Using the traditional definition,

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(comparative) relative strength is an extension of the basic notion in technical analysis that prices move in trends. The relative strength extension postulates that relative performance will also follow trends. Stocks or industries that are outperforming will continue to outperform until the trend is reversed. For stocks, this out-performance can be measured relative to the market average or to other stocks in the same industry or to some other stock or whatever. For industries, out-performance is measured relative to the market average or to other industries. Relative strength is a widely used concept that can be measured in various ways. The simplest measure — plotting of the relevant price series on a close-only chart — is widely available from most on-line charting sites. For example, Fig. 6.12 compares the relative strength of the S&P 500 and NASDAQ stock indexes using a one-year close-only chart of percentage price changes. For many applications, this assessment of relative strength is sufficient. Analysts requiring more precise information can calculate indicators from the price series. A simple example of such a relative strength indicator would be the ratio of a given stock’s price to, say, the S&P 500. If this ratio increases over time, then the stock has relative strength compared to the index. However, the scale of this measure would not be directly comparable to the ratio indicator value for another stock relative to the S&P. While it is possible to plot these individual ratio series and use chart analysis

Fig. 6.12 One-year comparative relative strength of S&P 500 and NASDAQ, 9/08-9/09.

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techniques to identify trends, trading ranges, breakouts and so on, direct comparison of indicators across stocks is not feasible due to the absence of scale comparability. This can be corrected by scaling the indicator relative to some base period and multiplying by 100 to create an index number. The base year could be selected to correspond to, say, the last major reversal in the sector or the market. Relative strength is somewhat different from most other technical indicators because it deals with the “co-movement” of prices. Even if successive price changes are serially uncorrelated, there may still be exploitable information in the co-movements. As Levy (1967) observes: “The intercorrelation or co-movement of stock prices could conceal existing dependencies in successive price changes”. For example, unlike momentum that measures directional change, relative strength can increase in both up markets and down markets. Consider the relative strength of a stock measured using the ratio of the stock’s price to the S&P 500. Both the price and the market average could be falling at the same time that the measure of relative strength is increasing. Typically, it is assumed that if, say, a given stock is outperforming the market, then this relative strength can also be expected to follow a trend. Using the tools of technical analysis, these trends can be identified. As long as the relative strength trend is unbroken, stocks that are strong in bear markets can be expected to outperform when the primary trend changes to a bull market. This co-movement of stocks with market averages, between stocks, between industries and so on can be examined using a range of tools from technical analysis. Levy (1967), for example, suggests the uses of ‘divergence ranks’ and ‘market ranks’. Despite holding considerable promise, there has been little interest in relative strength indicators in recent years. One possible reason for this is the emergence of the CAPM as an analytical tool. By construction, the market model representation of the CAPM provides two parameter estimates for a security: the alpha and the beta. The information provided by these parameter estimates is a statistically sophisticated form of relative strength analysis. When expressed in excess return form, the beta measures the comovement of the security return with the market return and the alpha measures the excess (deficit) return after adjusting the security return for equilibrium systematic risk compensation. In effect, the alpha of a security is a measure of relative strength, adjusted for systematic risk. As such, the use of alpha addresses concerns expressed in Levy (1967, pp. 609, 610) and other early studies of relative strength indicators about ‘the riskiness of the various technical indicators’. While useful, the temporal instability in the parameter estimates of the market model leaves room for improvement

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in the use of alpha as a relative strength indicator. Perhaps the use of charting techniques, moving averages and so on can be used to improve the usefulness of the market model? 6.3.2

Momentum and ‘Price Rate of Change’

It was observed that the development of technical analysis involved a gradual increase in the sophistication of techniques associated with the processing of price information. At least since Schabacker (1930), it has been recognized that, in order to deal with the noisiness of the raw price series, moving averages can be calculated. The values of a moving average are smoother than the price series and can be plotted directly on the price chart. The smoothing of the price information in this fashion alters basic chart patterns such as head-and-shoulders, flags and pennants that are the basic tools of chart analysis involving unprocessed prices. This leads to different trading rules for moving averages. Eventually, processing of price information had to achieve a level of sophistication where the resulting indicators could not be plotted directly on the price chart.25 Another chart or series of charts has to be prepared in addition to the basic price chart. (This use of additional charts in technical analysis was already the case with volume information that cannot be plotted directly on the price chart.) Much like a moving average, the objective is to calculate some function of the underlying price series and use that to identify trends, determine trading signals or both. Because of the large number of potential functions that could be applied, the scope for these types of extensions to technical analysis is almost limitless. Precisely when momentum entered the lexicon of technicians is unclear.26 It is only in the last three decades that considerable attention from both practitioners and academics has focused on the concept. As with so many concepts in Finance, there is divergence both between 25 Included in the more sophisticated group of technical indicators are techniques with appealing names such as Elliot waves, Bollinger bands, Moving Average ConvergenceDivergence (MACD), Lane Stochastics, and Double-Smoothed Stochastics, e.g., Blau (1995). 26 Bierovic (1996, ch. 15 in Schwager 1996) observes that: “As early as the 1920s, technical analysts were creating oscillators to measure a market’s momentum rather than limiting their efforts to determining the market’s trend”. However, no references are given. It is likely that Bierovic is referring to the introduction of ‘dual moving average’ techniques. Recognizing that the more general term ‘oscillator’ includes momentum as a special case, the logic of momentum analysis does have a long history.

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the vernacular and the academic definitions of ‘momentum’. For many practitioners, e.g., Schwager (1996), Blau (1995), and Kaufman (1978), momentum is defined as the rate of change of prices over a period of time. More precisely, the k day momentum indicator, M (t, k), is defined as M (t, k) = P (t)− P (t− k), where P is the closing price. The k day price rate of change, ROC(t,t−k), is defined as ROC(t, k) = P (t)/P (t − k) (or in percentage change terms ROC(t, k) = {(P (t) − P (t − k))/P (t − k)}100). Other practitioners, e.g., www.marketscreen.com, define momentum as the ratio of prices k days apart and the price rate of change as the first difference or percentage change in prices. It is also possible to define momentum using other variables than closing prices. For example, a moving average of prices can be used for a momentum indicator calculated by taking the difference of the moving average values k days apart. It is also possible to take a moving average of the momentum value. However, if only because of the differing interpretation of the momentum chart patterns, it is more appropriate to refer to these more involved momentum measures using different terminology. Whatever the definition, the basic intuition of momentum relates to the slope of the price chart. For purposes of illustration, consider a smooth nonlinear function that starts at zero and increases montonically to a maximum. (The cumulative normal distribution function is a practical example of such a function with the normal density function as the representation of the slope of that function.) Basic calculus provides the result that the slope of the function will initially increase and then start decreasing until the slope reaches zero when the function reaches a maximum. As such, the slope of the function signals a maximum prior to the maximum being reached; it follows that the momentum chart can theoretically provide a signal for a change from uptrend to downtrend. The momentum function will achieve a maximum prior to the price function, crossing zero when the price function maximum is achieved. A similar analysis applies for a minimum. This basic intuition of selling (buying) at the maximum (minimum) of the momentum function is complicated by the noisy fluctuations of market prices. Consider the simple case of the one-day momentum, {M (t, 1)}. Consistent with being a price difference, it is usually the case that the one-day momentum chart is not a smooth function, crossing the zero line numerous times over the time period, making the momentum signal difficult to evaluate. The difficulty interpreting the momentum function is usually approached by using larger differencing intervals to define momentum. For example, Poitras (2005, pp. 542, 543) uses momentum charts for {M (t, 3)}, {M (t, 9)} and {M (t, 20)} to demonstrate that, while still erratic, as the

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differencing interval is increased the momentum function becomes less erratic such that the ex post maximum and minimum values become easier to identify. The longer 20-day differencing interval does not have as many values in the extreme ranges. Recognizing that momentum can be interpreted as an oscillator, the maximum and minimum ranges can be used to define ‘overbought’ and ‘oversold’ levels that, in turn, can be used to specify trading signals. The use of specific differencing intervals is much like the choice of a sample length for a moving average, 100- and 200-day {M (t, 100)} and {M (t, 200))} momentum charts may have desirable properties. Selection of a specific differencing interval or comparison across a range of intervals are considerations that a technical analyst has to consider when constructing a trading system based on momentum indicators. Unfortunately, few on-line charting services provide the ability to change the default differencing interval. In considering momentum and moving average indicator, there are theoretical relationships among the indications that need to be recognized. In particular, observing that momentum and the simple T day moving average P¯ (t, T ) are defined as M (t, k) = P (t) − P (t − k) P¯ (t, T ) =

T −1
i=0

P (t − i) T

Setting k = T it is possible to specify the relationship between the momentum and moving average indicators. For example, consider the case where k = 5. In this case M (t, 5) = P (t) − P (t − 5). Similarly, P¯ (t, T ) = {P (t) + P (t − 1) + P (t − 2) + P (t − 3) + P (t − 4)}/5. But P¯ (t, T ) = P¯ (t − 1, T ) + {[P (t) − P (t − 5)]/5} and it follows that M (t, 5) = {P¯ (t, T ) − P¯ (t − 1, T )}5. More precisely, it is possible to show in general that for k = T : M (t, T ) = {P¯ (t, T ) − P¯ (t − 1, T )}k This result can be used to establish a relationship between a momentum oscillator and a dual moving average oscillator.27 On the interpretation of this connection between moving averages and momentum, Blau (1995, p. 13) makes the following statement: 27 It

is possible to use moving average techniques to smooth the momentum function. For this purposes, most technical analysts use exponential weighted moving averages (EMA), e.g., a 20-day EMA of M(t, 1). In some cases, e.g., Blau (1995), an EMA of different length is taken of the EMA resulting in, say, a 5-day EMA of the 20-day EMA of 1-day momentum. This process is called ‘double smoothing’.

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Moving averages performed on prices introduce a lag. The longer the duration of the moving average, the greater is the lag. A 300-day moving average, for example, produces a tremendous amount of lag. A single moving average performed on the momentum of price behaves in an altogether different manner. By contrast, the longer the duration of the moving average on momentum, the lower is the lag. A 300-day moving average, for example, approximates a zero-lag situation. With emphasis, again: A large moving average on momentum produces low lag price determination.

In the limit: “large moving averages of momentum . . . have, in the limit, the exact shape of price” (Blau 1995, p. 14). In contrast to the wide diversity of definitions and interpretations associated with momentum that are used by practitioners, academic studies of momentum use a relatively simple approach to definition and interpretation. Consider the ‘momentum’ strategy used by Jegadeesh and Titman (2001, p. 703) for a sample of all NYSE, Amex and Nasdaq stocks over a 1965–1998 sample: “at the end of each month we rank the stocks in our sample period based on their past six-month returns . . . then group the stocks into 10 equally weighted portfolios based on these ranks. Each portfolio is then held for six months following the ranking month”. While based on the notion of buying stocks using M(t,6 month), the connection to the concept of momentum used by technical analysts is decidedly underdeveloped. This lack of correspondence is not surprising when it is recognized that Jegadeesh and Titman (1993, 2001), Guiterrez and Kelley (2008) and other academic Finance studies that have examined ‘momentum strategies’, e.g., Chan et al. (1996) and Chan et al. (2000), are not concerned with testing the profitability of technical analysis. Rather, the concern is with testing the hypothesis of ‘buying winners and selling losers’ that is suggested by the behavioral finance challenge to the modern Finance orthodoxy.28 A number of academic studies have demonstrated the potential profitability of momentum strategies. The momentum differencing interval 28 The

general discussion of the rhetoric of Finance queried how much of the persuasion used in modern Finance is targeted at ‘conversations between academics’ that take place in selected academic journals. Jegadeesh and Titman (2001, p. 701) provides an interesting example of this discussion: “Because there are potentially large payoffs to any viable model that predicts stock returns (in terms of publications and/or money management revenues) many academics and practitioners have, no doubt, independently tested a wide variety of trading strategies”. Putting aside the questionable empirical validity of the statement, the connection between ‘large payoffs’ for academics and ‘publications’ (presumably in the appropriate journals) is difficult to avoid.

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varies across studies, e.g., Jegadeesh and Titman use a six-month interval while Chan et al. examine five differencing intervals varying between one week and six months. In contrast to the practice in technical analysis where an individual security is usually examined, the academic studies focus on classification of a universe of stocks into portfolios. Though these academic momentum studies have been subjected to the criticism of ‘datasnooping bias’ by other studies, it is difficult to ignore the sharpness of the statistically significant results for the profitability of the simple momentum strategies. For example, for the full sample of stocks over three different sampling periods (1965–1998, 1965–1989, 1990–1998), Jegadeesh and Titman (2001, p. 704) report monthly returns that decline monotonically from a high of (1.65, 1.63, and 1.69) for the highest decile of equally weighted momentum portfolios down to the lowest decile portfolios (0.42, 0.46, and 0.30). The strength of these results has led to the emergence of a ‘stylized fact’ that investors ‘under-react’ to short period returns. Whether this stylized fact will withstand closer scrutiny is, at present, unclear.

6.3.3

Oscillators and MACD

The reference to an ‘oscillator’ is inherited from physics where the term was originally used to describe the graphical representation of alternatingcurrent voltage flow. Recognizing that the fluctuations of the alternative voltage flow between a positive maximum and negative minimum display an oscillatory pattern, it follows that the name oscillator is associated with oscillation or frequent fluctuation. (The term now more generally refers to an electronic device used for the purpose of generating a signal.) In technical analysis, the term oscillator refers to a wide range of techniques that can be based on substantively different calculations and motivations. The unifying notion connecting the techniques is that the chart pattern calculated from the original price chart oscillates or fluctuates within a defined range. The defined range for an oscillator permits the specification of overbought and oversold levels for the oscillator that can be used to identify trading signals. Interpretation of overbought and oversold signals is aided by the concept of divergence. Because the oscillator is often constructed by taking the difference of two series, most oscillators are designed to be ‘counter-trend’ systems. This leads to the following result (Schwager 1996, p. 556): “Oscillators perform well when a market is in a trading range — that is, a sideways trend. They work poorly, however, when a market is in a strong uptrend or downtrend”.

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Fig. 6.13

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Twelve-day momentum for SPY, 2008–2009.

The oscillator covers so many techniques that some technical analysis websites do not make any reference to the concept, e.g., www.marketscreen.com, opting instead to list specific types of oscillators directly. Other sites use a narrow definition of oscillator that excludes many types of techniques that would be considered oscillators using a wider definition. An example of a narrow definition is found at www.futuresource.com which defines an oscillator as “the simple difference between two moving averages”. Adopting the wider definition, momentum can be viewed as a type of oscillator. As illustrated in the bottom chart from Fig. 6.13, the momentum chart oscillates above and below the zero slope line. M (t, 1) is, arguably, the simplest form of oscillator. A number of more sophisticated oscillators, such as the Relative Strength Index and the Lane Stochastic, are developments on the momentum oscillator. Though some forms of oscillator, such as the Lane Stochastic, have been in use since the 1950s, the fascination with the oscillator is a relatively recent development in technical analysis, gaining popularity starting in the early 1970s. For example, the concept is given only passing recognition in Edwards and Magee (1966). Kaufman (1976, p. 91) restricts “the use of the term oscillator to a specific form of momentum, that which is normalized or expressed in terms of values ranging between +1 and −1 or +1 and 0”. This definition would include the Relative Strength Index and the A/D oscillator.

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Fig. 6.14

MACD for SPY, 9/07–9/09.

In addition to oscillators based on momentum, a variety of alternative specifications are possible. In particular, another simple oscillator is the dual moving average (DMA) oscillator that is constructed by differencing two moving averages of different length: DM A(t, j, k) = P¯ (t, j) − P¯ (t, k) where j < k with the j period moving average being ‘fast’ and the k period moving average being ‘slow’. This oscillator is of interest because the moving average is a trend-following technique while an oscillator is a counter-trend technique. In effect, the DMA oscillator is designed to capture the momentum of the trend: “When the fast moving average is accelerating away from the slow one, prices are gaining momentum; when the fast moving average is decelerating toward the slow one, prices are losing momentum” (Schwager 1996, p. 524). The zero line is defined as the point where the two moving averages are equal. Unlike trend following systems that use the crossing of the zero line as a trade indicator, the DMA oscillator signals trades by specifying overbought and oversold regions on the DMA oscillator chart. It is also possible to examine divergence between the oscillator and the price chart. In the same fashion that using the zero line to signal trades will result in false signals and whipsaws in trading range markets, using the overbought and oversold regions will result in false signals in trending markets. The DMA oscillator is a graphical representation of the dual moving average trading system that can be implemented directly on the price

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chart. The analytical advantages that are gained by mapping particular price chart information into a different chart format are in this case, moreor-less, incidental. This suggests a natural extension of the DMA oscillator that does exploit the ability to map from the price chart to the oscillator chart: the Moving-Average Convergence-Divergence (MACD). Though in the form of an oscillator, the MACD is not usually referred to as an oscillator because the technique integrates both trend-following and counter-trend methods. Credited to Gerald Appel, the MACD constructs a MACD line by subtracting a 26-period EMA from a 12-period EMA (see Fig. 6.14).29 This step is a special case of a DMA oscillator that uses specific sample periods for exponential moving averages. To generate trading signals the MACD technique proceeds to calculate the signal line which is a 9-period EMA of the MACD line. As illustrated in Fig. 6.14 it is conventional for MACD charts to also contain a histogram of the difference between the MACD line and the signal line (in black in Fig. 6.14). The histogram provides an oscillator-like chart that can be used to identify trades. Because the signal line in the MACD involves taking a moving average of the price difference between two moving averages, the MACD can be classified as a ‘double-smoothed momentum indicator’ (Blau 1995). The process for determining trades using the MACD line and the signal line is described in Schwager (1996, p. 538): The basic method for trading with MACD is to buy when the MACD line crosses above the signal line and to sell when the MACD line crosses below the signal line. However, entering and exiting trades based solely on MACD line-signal line crossovers results in frequent whipsaw losses. To make the best use of MACD, it is advisable to wait for crossovers that are preceded by divergence and confirmed by the subsequent price action of the market.

The MACD is the featured technical indicator at a number of high traffic websites dedicated to technical trading, including the e-trade site. Though usually classified as an oscillator, the MACD does differ from other oscillators in having better theoretical properties in trend following situations. For example, the website www.trade10.com provides the following observation about MACD: “the signals generated by the MACD are trend following, occurring after the market has made movement in a new direction. For this 29 Appel

is a well-known technical analyst, publisher of the newsletter Systems and Forecasts, as well as a number of books on technical analysis, e.g., Appel and Zweig (1976) and Appel (1974).

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reason the MACD is used more as a conformational tool of the trend and can be used in trading decisions when combined with other indicators and platforms for decision and strategies”. As with the momentum oscillator, the MACD also requires interpretation of the scale. To partially adjust for this shortcoming, various technical analysis websites also report information on the stochastic. A limitation of the momentum chart is difficulty in interpreting the scale. In other words, when is the value of the oscillator ‘high enough’ to be overbought and ‘low enough’ to be oversold? A number of popular oscillators, such as the Relative Strength Index (RSI) and the Lane Stochastic are designed to produce a momentum indicator that has a scale varying between 0% and 100%. This scaling permits the overbought and oversold regions to be specified in a transparent fashion. Conventionally, overbought is >80% and oversold 70% and −5%) impact on stock returns. For example, for a sample of 663 successful tender offers, Jarrell et al. found bid premiums for the pre-announcement value of the target firm’s stock price of 19% during the 1960s, 35% during the 1970s and 30% during the first half of the 1980s. The empirical evidence on corporate acquisitions

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Compaq-HP merger in 2002 is just one recent example of these difficulties. Walter Hewlett, the son of a founding partner of Hewlett-Packard, was so seriously at odds with the HP management team led by Carla Fiorina over the valuation of Compaq that he initiated a proxy-fight to reject the merger and, when this was unsuccessful, filed suit in an attempt to prevent the merger on grounds that shareholders were misled by inaccurate financial statements concerning the merger. Though the suit was unsuccessful, it does serve as an extreme indicator of the difficulties in assessing the ‘private market value’ for a firm such as Compaq. Ultimately, the determination of acquisition value will depend on a range of factors such as: whether the acquisition is a hostile takeover, friendly takeover or merger; what the synergies would be for the acquiring firm; what the alternative cost of acquiring the assets of the target firm would be; and, whether the firm is a potential candidate for a leveraged buyout. While the liquidation value of a firm is determined by calculating the disposal value of the assets, the acquisition value of a going concern is based on the ‘reproduction cost’ of the assets. Unlike most liquidations where any ‘hidden assets’ have long since been dissipated or sold-off, going concerns often have a range of potentially valuable assets that are not recorded in the financial statements. For example, going concerns usually have well established customer relationships that will cost money for a new entrant to develop. Another example concerns R&D infrastructure that may be hard to replicate such as a drug company that has viable products that are in development but not yet generating cash flows. There may be licenses or franchises in place that permit the firm to carry on a business, such as a casino or a television station. Though it may be possible to obtain estimates for some of these hidden assets that were observed in related transactions, when the objective is to determine an estimated value for a going concern that is to be acquired there is a bundling of the hidden assets with tangible assets and management structure that makes the estimated value quite difficult to determine.

has led to the use of crude rules of thumb regarding acquisitions such as: a 20%–30% bid premium is required to obtain corporate control of a going concern in a friendly tender offer. Like most rules of thumb, such estimates of the bid premium will differ depending on the specifics of the acquisition involved.

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Following Hooke (1998, ch. 15) one method of determining an acquisition value is to assess the value of the company as a leveraged buyout (LBO) opportunity. Because an LBO does not place significant synergistic values on the target firm, the LBO acquisition value can be considered as a lower bound on the acquisition value. The relevance of the LBO estimate is supported by the approximately 150 investment firms that specialize in LBO’s. According to Hooke, there are another 50–100 investment banks, venture capital firms and general investment funds that also do some occasional LBO business. The estimated equity value of the top five firms in the industry is approximately $10–$15 billion dollars. Though there is considerable variation in the types of LBO deals, the conventional LBO transaction operates under four principles as much as possible: use other people’s money by leveraging the assets and cash flows of the target company; buy at relatively low multiples; search for targets in out-of-fashion industries; and, improve operating performance following acquisition. The actual valuations are done using ‘guideposts’ of 80%/20% (4×) target debt to equity post-acquisition leverage and 1.4 × interest coverage on cash flow. The final special situation valuation method is the cash-burn model. This valuation methodology is applicable to firms that have no substantial performing assets and are using the capital raised in an equity issue to achieve a positive earnings situation. Examples where this valuation model could be applied include start-up biotechnology firms, junior mining and oil exploration companies and dot.com’s. Because the operating structure of these type of companies is relatively simple, the period to period operating costs are usually quite predictable. After the initial costs of establishing the plant and equipment, the balance sheet will contain a sizeable amount of cash and near-cash assets that will be depleted as the project is in development. Because there is typically no revenues, the development/exploration costs represent a ‘cash burn’ rate that permits a length of time before additional financing, usually another equity issue, is required. For example, a small biotechnology firm could be undertaking to clear the FDA Phase I–III trials in order to produce a drug that can be marketed to the public. The length of time to complete the trials is estimated and used to determine whether the cash-burn will exhaust the available cash and near-cash assets. Combined with an estimate of the revenues generated by the drug if trials are successfully completed, it is possible to determine an approximate value for the company.

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Basics of Credit Risk and Default Risk

The Legal Aspects of Default Consideration of credit risk and default risk is relevant to equity security valuation for a number of resons. In particular, as a firm approaches brankruptcy, the value of equity securities approaches zero and the debt securities start to trade as an equity-like claim against the liquidation value of the firm. As such, bankruptcy laws and procedures assume a critical role in the valuation of firms in financial distress. Entry into, say, a chapter 11 bankruptcy results in de facto control of the firm being transferred to the court and the value of equity securities, in most cases, going to zero. For fixed income valuation purposes, there are considerable advantages to abstracting from embedded option features associated with credit risk. Yet, the bulk of fixed income securities do not conform to this abstraction. Even for bonds that would seem to conform to the abstraction of no credit risk, such as U.S. Treasuries, there is still an element of credit risk that has to be addressed. For example, on rare occasions the U.S. Congress has threatened to withhold legislation to increase the debt ceiling raising the possibility that the U.S. Treasury would be unable to make scheduled interest or principal payments on outstanding debt issues, e.g., Nippani et al. (2001). Following Fabozzi (2002, ch. 7), credit risk can be decomposed into three parts: default risk; credit spread risk; and downgrade risk. For bonds, default risk relates to the possibility that the issuer will not fulfill the obligations set out in the bond indenture. This could be due to the failure to make a coupon payment or to return the principal value at maturity or to meet some other provision in the indenture, such as a covenant on net asset value. Such events have a number of possible implications. Because the possibility of default varies across bond issuers, this will be reflected in the quoted prices and yields for different bond issues. The difference between yields for issues with different credit ratings is the credit spread. Due to a variety of factors, the credit spread changes over time. For example, in periods of contracting economic activity credit spreads will typically widen to reflect the pressure on firm cash flows needed to make debt payments. Credit spread risk relates to these changes in the difference between yields for issues with different credit ratings. To facilitate this assessment there are a number of services that provide ratings to the bond market. Related to credit spread risk is the concept of downgrade risk. While credit spread risk depends on general conditions such as aggregate economic activity, downgrade risk is more firm specific. For example, it is

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possible for, say, a telecom firm such as Worldcom to experience a credit downgrade from a rating agency at a time when the credit risk for telecom firms was narrowing relative to U.S. Treasuries. Another example would be a firm that experienced an unfavorable result in litigation, e.g., DowCorning with breast implants or Johns Mansville with asbestos. Given this, it is expected that the factors causing a widening of credit spreads will also contribute to an increase in downgrades for individual firms. Credit spread risk and downgrade risk are extensions of the issue of default risk. Credit spreads widen and narrow because of changes in the perception that default will occur. Downgrading of a firm’s debt by a credit rating agency occurs because there is the perception that default is more imminent. Yet, while driven by economic factors, default is a legal event. As such, it is necessary to detail the relevant laws and legal remedies associated with default on a debt obligation.35 A fixed income security is a debt instrument that is defined by a contract. For a corporate bond, this contract is the bond indenture. For publicly traded issues falling with the scope of the regulations of the SEC, such indentures must conform to the Trust Indenture Act (1939) that require appointment of a trustee to protect the interests of bondholders set out in the indenture. In addition, as publicly traded securities, the debt instruments must satisfy the relevant SEC rules regarding registration, resale of securities and the like. Debt instruments have a number of SEC Rules of specific relevance, such as Rule 415 on shelf registrations and Rule 144A on resale of privately placed securities. Though there is considerable variation in the specifics of indentures, the American Bar Association (ABA) does provide examples of model contracts for specific bond indentures. For example, there are 15 articles, plus preamble, for the model debenture indenture and 16 articles, plus preamble, for the model mortgage bond indenture. Given that there is variation between specific indentures and the model indenture outlined by the ABA, the indenture contents do have a common set of essential characteristics. The preamble will typically make reference to the basis under which the indenture was issued, e.g., “the articles of incorporation permit the board of directors to authorize up to $xxx million of senior subordinated debentures”. There will also be articles associated with the definition of terms, 35 Though

default on federal, state and local government debt is possible, the legal implications are more complicated. Though only the case of corporate default is examined in detail, the basic principles of the issuer seeking protection under the bankruptcy laws and the purchaser seeking remedies under the terms of the debt contract still apply to sovereign debt issues.

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methods of notifying trustees, the specific wording on the security certificate, the denominations, the record dates and so on. While such articles are important from a legal standpoint, it is the articles relating to remedies and covenants that are of greatest interest to the assessment of default risk. Articles relating to mergers and consequences of changes in the status of assets are also important, as are preambles and articles that describe the property securing a secured debt issue. The indenture sets out the conditions required to initiate a default proceeding. Conventionally, once a credit event sufficient to trigger a default has occurred, e.g., failure to make a scheduled coupon or principal payment, the trustee (or a holder of 25% or more of the outstanding debt) can demand payment in full of any outstanding obligations. Whether the trustee initiates such an action is not straight forward. Because the trustee has a fiduciary obligation to act in the best interest of the bondholders, the trustee may deem it more prudent to enter into negotiations with the issuer to attempt to get a resolution to the indenture violation. If the debtor is unable or unwilling to resolve the indenture violation, a U.S. corporate issuer would likely respond by filing for bankruptcy under the relevant chapter of the Bankruptcy Reform Act (1978). Similarly, if the trustee wants to proceed with a default action, a bankruptcy filing can be made by a creditor as well as a debtor. The Bankruptcy Reform Act has 15 chapters dealing with different types of bankruptcy. For filings resulting from a corporate debt issuer violating an indenture, the relevant chapter governing the bankruptcy filing would be either chapter 7, governing liquidation, or chapter 11, governing reorganization. The problems confronting a trustee having to decide the correct course in dealing with an issuer in default on an indenture provision are legally complex. Once the bankruptcy process is initiated for a corporation in default, a number of provisions of the bankruptcy code come into effect that create considerable uncertainty about the final disposition. In particular, a bankruptcy filing introduces the bankruptcy court into the decision making process. The law requires that there be an active role for judicial supervision and oversight. Decisions of the court are binding on the parties involved. Another provision of the bankruptcy code involves the imposition of a standstill agreement on all creditors. This is required to provide for an orderly process of liquidation or reorganization, preventing actions such as senior creditors seizing assets that are essential to the viability of the firm as a going concern or allowing the firm to make disbursements to certain creditors at the expense of others. One final provision of importance is

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the provision that the debtor retain control of firm operations during the period that the bankruptcy filing is being decided, unless a specific directive is ordered by the court such as the appointment of a receiver. In theory, a bankruptcy proceeds under the absolute priority rule. This rule dictates that senior creditors are to be paid in full before junior creditors receive any payments. For a number of reasons, the absolute priority rule may not be followed. One of these reasons has to do with the judicially supervised negotiation process between the debtor and the creditors that commences with the bankruptcy filing. Under chapter 7 filings, the negotiating process is usually not overly complicated and the division of assets conforms relatively closely to the absolute priority rule. However, under chapter 11 filings, the negotiating process can be onerous. The process is complicated by two provisions: during the reorganization the court may permit the firm to undertake new financing that is given a senior claim to existing claims; and, the reorganization plan does not require unanimous consent, only a majority of all creditors holding 2/3 of the outstanding value in each debt classification. This legal structure makes a bankruptcy filing under chapter 11 somewhat uncertain for debt holders. Not surprisingly, there is considerable evidence that the distributions in chapter 11 bankruptcies do not typically adhere to the absolute priority rule, e.g., Fabozzi et al. (1993) and Weiss (1990). Due to all the legal complexities and other uncertainties, there are real incentives for the trustee and large individual creditors to avoid formal bankruptcy proceedings and to attempt a resolution outside the court process. In addition to monitoring bankruptcy filings, the major credit rating agencies also issue credit event releases that recognize various types of financial distress and the associated resolution. All this makes the securities of distressed firms, whether in bankruptcy or working toward a resolution outside the court process, a potentially fruitful area for identifying abnormal returns using the techniques of security analysis, e.g., John (1993).

The Assessment of Credit Risk and Default Risk Information on credit risk and default risk comes from two sources: ratings agencies and market prices. Because of the large number of traded fixed income securities, firms have emerged that specialize in providing credit

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ratings for a wide range of different debt issues. In the United States, these firms are Standard and Poor’s Corporation, Moody’s Investors Services Inc. and Fitch Ratings (created by the merger of Fitch IBCA with Duff and Phelps Credit Rating Co.). It is often the case that firms pay the rating agencies to have their debt issues rated. In addition to ratings agency information, the larger investment banking firms and institutional investors will also have resources dedicated to doing credit analysis on specific firms and sectors that are of interest. There are also firms that specialize in ratings for specific industries such as Demotech, Inc. that assesses insurance companies and HMO’s. As illustrated in Table 7.17, there is a close correspondence in the symbolic method of specifying ratings used by the different ratings agencies. However, this does not mean that the same methodologies are used by different ratings agencies to arrive at a credit rating for a specific firm. Inspection of Table 7.17 reveals three general categories of debt ratings: investment grade, rated BBB− (Baa3) and above; speculative, below investment grade, rated BB+ (Ba1) to B− (B3); and, purely speculative, CCC+ (Caa) to D. The ratings category that a debt issue falls into can have an important impact on the pricing of the issue in the market. In particular, various institutional borrowers, such as pension funds and insurance companies, are restricted from holding issues that are classified as being below investment grade. When a debt issue is downgraded to a rating below investment grade this can have a significant impact on the price of the issue. Similarly, certain types of bond funds, e.g., high yield funds, invest only in issues that are below investment grade. The implication is that lower rated issues typically have to offer substantially higher yields in order to attract the types of investors that purchase debt with below investment grade ratings. Though there is a close correspondence between the credit rating issued by the rating services and, presumably, by the in-house credit analysts, the ratings do not translate precisely into pricing of debt issues. For example, it is possible for a bond with a lower credit rating to sell at a lower yield than a comparable bond with a higher credit rating. It is possible for this to happen because the relative credit ratings are not judged to be accurate by the market. However, it is more likely that this type of pricing occurs because the market price of an issue depends both on the credit rating and

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Table 7.17

Summary of Corporate Bonds Rating Systems and Symbols.

Fitch

Moody’s S&P

Summary description

Investment grade — high credit worthiness AAA Aaa AAA Gilt edge, prime, maximum safety AA+ Aa1 AA+ AA Aa2 AA High grade, high-credit quality AA− Aa3 AA− A+ A1 A+ A A2 A Upper-medium grade A− A3 A− BBB+ Baa1 BBB+ BBB Baa2 BBB Lower-medium grade BBB− Baa3 BBB− Speculative — Lower Credit Worthiness BB+ Ba1 BB+ BB Ba2 BB Low-grade, speculative BB− Ba3 BB− B+ B1 B B2 B Highly speculative B− B3 Predominately speculative, substantial risk, or in default CCC+ CCC+ CCC Caa CCC Substantial risk, in poor standing CC Ca CC May be in default, very speculative C C C Extremely speculative C1 Income bonds — no interest being paid DDD DD Default D D Source: Rating agency websites.

the potential recovery rate.36 The recovery rate is the payout on the debt issue that takes place when default occurs. For example, the recovery rate for a corporate mortgage bond will depend on the value of the collateral securing the issue. If the collateral is sufficient to repay the principal value of the borrowing, a default by the issuer will not have severe consequences. Similarly, it is possible that, though default may be less likely, the recovery 36 Other

important factors that can influence the yield spread between two different debt issues are: the liquidity; differences in covenants and special provisions such as callability; and, the tax status of the coupon and principal payments.

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rate may also be lower in the event that default does occur, e.g., due to the asset structure of the company. For a portfolio of bonds, it is possible to calculate the “default loss rate” as the product of the default rate and the recovery rate, e.g., Fabozzi (2002, p. 202). For example, if 10% of the issues in a portfolio defaulted and a weighted average of 50% of the value of the investment was recovered then the default loss rate was 5%. Ignoring costs associated with the disruption of cash flow associated with having to wait until the defaulted issue is paid out to bondholders, if the portfolio was initially purchased with a promised yield of more than 5% above Treasuries then the investor would, ex post, have done better than investing in Treasuries. As such, analysis of fixed income securities subject to credit risk requires both the default rate and the recovery rate to be assessed to determine an appropriate valuation. Table 7.18 provides evidence from Altman and Karlin (2008) on both default rates and recovery rates for U.S. high yield corporate bonds for 1978–2007 Q3. Accurate interpretation of Table 7.18 requires understanding of how default rates are calculated. The numerous studies of default rates use a variety of calculation methods. For example, Asquith et al. (1989) report that about one in three high yield bond issues default. This is a cumulative default rate that is calculated by using the total outstanding amount of high yield debt issued in an initial year and dividing this value into the cumulative value of outstanding issues that defaulted for all issues for that year. In contrast, Table 7.18 reports the default rate by dividing the par value of outstanding bonds that default in a given year by the total par value outstanding issues for that year. This provides a year-by-year estimate. For example, Table 7.18 reports that the default rate on high yield bonds in 1997 was 1.25%. Until the wave of defaults in 2002, the highest level of default reported was for 1991 where a default rate of 10.27% is reported. Results in Altman and Karlin (2008) are not confined to this method of estimating default rates, a wealth of other information is provided including defaults by original rating, years to default from original issue date, and defaults by industry. Table 7.18 also provides information on recovery rates. This is calculated as the weighted average price after default, where the weights are the fraction of the par value of defaults in the year for that issue. Being all less than $30 per $100 par value, the recovery rates for 1999–2002 and 2004–2007 are at the bottom end of recovery rate values over the last two

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Table 7.18

Bond Default Rate and Losses, 1978–2007.

(Dollars in Millions)

Year

Par value outstanding($)a

2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 1986 1985 1984 1983 1982 1981 1980 1979 1978

1,075,400 993,600 1,073,000 933,100 825,000 757,000 649,000 597,200 567,400 465,500 335,400 271,000 240,000 235,000 206,907 163,000 183,600 181,000 189,258 148,187 129,557 90,243 58,088 40,939 27,492 18,109 17,115 14,935 10,356 8,946

Default weighted price Par value Weighted Default of default($) rate (%) after default($) coupon (%)loss (%)b 5,473 7,559 36,209 11,657 36,451 96,658 63,609 30,295 23,532 7,464 4,200 3,336 4,551 3,418 2,287 5,545 18,862 18,354 8,110 3,944 7,486 3,158 992 344 301 577 27 224 20 119

Arithmetic average 1978–2007 Weighted average 1978–2007

0.51 0.76 3.37 1.35 4.66 12.79 9.80 5.07 4.15 1.80 1.25 1.23 1.90 1.45 1.11 3.40 10.27 10.14 4.29 2.66 5.78 3.50 1.71 0.84 1.09 3.19 0.16 1.50 0.19 1.33

66.6 65.3 61.1 57.7 45.5 25.3 25.5 28.4 27.9 35.9 54.2 51.9 40.6 39.4 58.6 50.1 36.0 23.4 38.3 43.6 75.9 34.5 45.9 48.6 55.7 38.6 72.0 21.1 31.0 60.0

9.64 9.33 8.61 10.30 9.55 9.37 9.18 8.54 10.55 9.46 11.87 8.92 11.83 10.25 12.98 12.32 11.59 12.94 13.40 11.91 12.07 10.61 13.69 12.23 10.11 9.61 15.75 8.43 10.63 8.38

0.19 0.30 1.46b 0.59b 2.78b 10.15b 7.78 3.95 3.21 1.10 0.65 0.65 1.24 0.96 0.56 1.91 7.16 8.42 2.93 1.66 1.74 2.48 1.04 0.48 0.54 2.11 0.15 1.25 0.14 0.59

3.37 3.82

45.15

10.80

2.27 2.64

a

Excludes defaulted issues b Default loss rate adjusted for fallon angels is 9.3% in 2002 1.82% in 2003, 0.59% in 2004, 1.5% in 2005, 0.039% in 2006 and 0.20% in 2007.

Sources: Altman and Karlin (2008).

decades. The strong economic fundamentals of 1992–1997 permitted recovery rates that were usually in excess of $50 per $100. Table 7.19 provides further useful information on recovery rates by decomposing the results by type of issue. It is significant that senior secured debt does not provide full protection, with a low recovery rate of $26.90 in 1999, below that of the

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Weighted Average Recovery Rates on Defaulted Debt by Seniority per $100 Face Amount, 1978–2007. Senior secured

Default Year

No.

87.24 90.60 76.50 63.67 53.51 52.81 40.95 39.58 26.90 70.36 74.90 59.08 44.64 48.66 55.75 59.85 44.12 32.18 82.69 67.96 90.68 48.32

No.

%

10 26 44 33 108 254 187 47 60 21 12 4 9 8 7 8 69 31 16 19 17 11

36 52 36 48 53 75 67 29 47 62 48 17 27 36 22 12 44 27 21 31 55 20

$ 47.70 60.90 45.88 56.77 45.40 21.82 28.84 25.40 42.54 39.57 70.94 50.11 50.50 51.14 33.38 35.61 55.84 29.02 53.70 41.99 72.02 37.72

No.

%.

6 8 7 2 29 21 48 61 40 6 6 9 17 5 10 17 37 38 21 10 6 7

21 18 6 3 14 6 17 37 31 18 24 38 52 23 31 25 24 33 28 16 19 13

$ 63.98 50.24 32.67 37.44 35.98 32.79 18.37 25.96 23.56 17.54 31.89 48.99 39.01 19.81 51.50 58.20 31.91 25.01 19.60 30.70 56.24 35.20

Subordinated No.

%

2 1 0 0 1 0 0 26 2 0 1 4 1 3 9 22 36 24 30 20 4 30

7 2 0 0 0 0 0 16 2 0 4 17 3 14 28 33 24 21 39 32 13 54

$ 46.53 60.33 0.00 0.00 38.00 0.00 0.00 26.62 13.66 0.00 60.00 44.23 20.00 37.04 28.38 49.13 24.30 18.83 23.95 35.27 35.25 33.39

Discount and zero coupon No.

%

0 6 5 7 8 28 37 17 11 1 2 3 1 1 4 5 9 11

0 12 4 10 4 8 13 10 9 3 8 13 3 5 13 7 6 9

$ 0.00 76.31 74.21 43.06 32.27 26.47 15.05 23.61 17.30 17.00 19.00 11.99 17.50 5.00 31.75 19.82 27.89 15.63

All seniorities No. 28 50 123 69 203 340 281 164 127 34 25 24 33 22 32 67 157 116 76 62 31 56

$ 66.65 65.32 62.96 57.72 45.76 26.25 25.62 26.74 32.20 40.46 57.61 45.44 41.77 39.44 36.63 50.03 40.67 24.66 35.97 43.45 66.63 36.60

635

(Continued)

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35 18 64 39 28 11 3 8 11 18 16 17 15 23 6 22 3 10 11 21 13 14

$

Senior Sub ordinated

9in x 6in

10 9 67 27 57 37 9 13 14 6 4 4 5 5 2 15 4 12 9 13 4 8

%

Senior unsecured

Fundamental Analysis for Equity Securities

17:46:55.

2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 1986

November 3, 2010 10:47

Table 7.19

17:46:55.

Senior secured

1985 1984 1983 1982 1981 1980 1979 1978

2 4 1

7 29 13

74.25 53.42 71.00

1

100

72.00

342

$

16% $60.45 $17.69 $59.47

No.

%

$

3 1 3 16

11 7 38 80

34.81 50.50 67.72 39.31

2

50

26.71

1

100

60.00

1027

47% $36.95 $13.72

No.

%.

7 2

26 14

$ 36.18 65.88

Subordinated No.

%

15 7 4 4

56 50 50 20

41.45 44.68 41.79 32.91

2

50 100

16.63 31.00

1 420

$45.64

$34.00

251

11% $31.30 $17.78 31.96

No.

%

$

All seniorities No. 27 14 8 20 1 4 1 1

156

$ 41.76 50.62 55.17 38.03 72.00 21.67 31.00 60.00

7% $25.98 $20.70

2,196 $37.54 $14.28

$19.41

$41.77

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*Standard deviations are calculated based on the yearly averages. Source: See table 7.18.

19% $31.08 $14.47

$

Discount and zero coupon

9in x 6in

No.

Senior Sub ordinated

Valuation of Equity Securities

Year

Total/ Average Standard Dev* Median

%

Senior unsecured

(Continued)

November 3, 2010 10:47

636

Table 7.19

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Fundamental Analysis for Equity Securities

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637

recovery rate of senior unsecured debt in the same year. The implication is that the priority claim of security is less important than it would seem. Another interesting result is the absence of any defaults on subordinated debentures in 2001 and 2002. This is likely the result of less credit worthy companies being generally unable to issue this type of security.

17:46:55.

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CHAPTER 8

Resource Companies: Oil Sands Producers

8.1

8.2

8.3

The Oil Sands and the Syncrude Project 8.1.1 Investing in Resource Companies . . . . . . . . . . . 8.1.2 The Canadian Oil Sands . . . . . . . . . . . . . . . . 8.1.3 History of the Oil Sands . . . . . . . . . . . . . . . . 8.1.4 The Syncrude Project . . . . . . . . . . . . . . . . . Investment in Off-Shore Companies 8.2.1 Risk and Return for Foreign Equity Securities . . . . 8.2.2 Sources of Information and Trading . . . . . . . . . 8.2.3 Recent Developments in Canadian Unit Trusts . . . Fundamental Valuation 8.3.1 Canadian Oil Sands Trust (COS.UN) . . . . . . . . 8.3.2 Acquisition of the EnCana Share in 2003 . . . . . . 8.3.3 Current Valuation of the COS Trust Unit (COS.UN)

640 644 647 654 659 662 669 677 681 692

Mark Twain on Mining Companies Mark Twain is claimed to have said: “a mine is a hole in the ground owned by a liar”. A number of variations on this quote appear such as “a mine is a hole in the ground with a liar on top”. In an equity valuation context this becomes: “A mine is a hole in the ground owned by a liar selling common stock certificates in his limited liability company that owns the mine”. The basic quote was attributed to Mark Twain in The Autobiography of John Hays Hammond (Farrar and Rinehart, 1935, p. 97). Although Hammond knew Twain personally, there is no other record that Mark Twain made this statement (www.twainquotes.com/Miner.html).

639

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640

8.1 8.1.1

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Valuation of Equity Securities

The Oil Sands and the Syncrude Project Investing in Resource Companies

A Variety of Valuation Approaches In order to capture complexity, it is typically easier to start with the simplest case. Once that is explained, then a more complicated case can be tackled. As such, Canadian Oil Sands Trust represents a decidedly simple equity security valuation problem. The sole asset of the company is a known share in the Syncrude oil sands project that entitles the Trust to a pro rata share of the synthetic oil output generated by the Syncrude heavy oil upgrader plants together with the associated expenses required to generate the output. This oil is then sold, unhedged, into the cash market via the network of continental pipelines that connect with the Athabasca oil sands. Significantly, the process of extracting crude oil from the bitumen contained in the surface tar sands near Fort McMurray, Alberta involves mining, not drilling. Within the constraints involved using a complicated technology that upgrades the bitumen, upper and lower bounds on the amount of output from the Syncrude oil sands mines in a given period are reasonably predictable. Unlike oil and gas companies dependent on successful drilling programs to replenish depleting reserves, the vast size of the Athabasca oils sands resource base permits reasonable output estimates to be made for decades in the future. The equity security valuation problem would seem to be relatively straight forward, once the valuation methodology is determined. The correct method of valuing an equity security has eluded both vernacular and academic Finance practitioners since the beginning of trade in VOC shares. In the time since, considerable progress has been made in understanding how changes in the market value of equity occur. It is claimed the various valuation techniques based on fundamental analysis work well for some valuation problems and give little guidance in others. For example, value investors, such as Greenwald et al. (2001, p. 72), are averse to ‘commodity businesses’, a category which includes most resource companies: “It is a truth universally accepted that all sensible people abhor commodity businesses. The standard advice for avoiding this fate is to differentiate your product or service from all the others”. Graham and Dodd (1934) also viewed resource companies as primarily speculative. The logic of this position is that, because a commodity business involves the production of a relatively homogeneous product, if a firm is economically profitable then this

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will attract new entrants and economic profits will be soon driven to zero. In this theoretical approach, a commodity business is one where there is a combination of freedom of entry and an inability by firms in the industry to produce differentiated products, i.e., there is no potential for sustainable competitive advantage, e.g., Porter (1980, 1985) and Barney (1997). This interpretation illustrates the more-art-than-science aspect of fundamental analysis. The claim that the theoretical method of fundamental analysis for determining intrinsic value — DCF valuation — works only in particular cases raises a number of questions and concerns. The use of the ‘commodity business’ terminology is unfortunate because some conditions required for a ‘pure commodity business’ do not apply to the many companies operating in the natural resource sector, in general, and the oil sands producers, in particular. Even though the finished product, such as gold ingots or refined oil or finished lumber, may not differ significantly from firm to firm, the quality, location and accessibility of the raw material does serve to differentiate the firms. Technological progress is increasingly driving certain sectors. While the commodity model may apply to corn farmers or cattle feedlot operations, these cases are distinct from companies extracting natural resources such as the oil sands companies where the capital cost of projects imposes a significant barrier to entry. Natural resource companies also create difficulties for the Wall Street approach to equity security valuation. A variety of different valuation methods have also been identified. “Natural resource companies require a truly unique valuation approach. Replenishing the resource is a critical necessity to corporate survival ” (Hooke 1998, p. 299). For example, Hooke recommends an approach to valuing natural resource companies that focuses on four factors: the estimated reserve base; the physical assets in place used in extraction, processing and distribution; the liabilities used to finance the firm’s activities; and, the potential for the firm to replenish reserves. “This four-factor approach is quite unlike the discounted cash flow and relative value methods”. The reason for this is that the value of a natural resource company depends on the resources that are available for extraction. These resources will typically have a finite life. Following Hooke, the valuation problem can be further simplified by observing that the sum of the estimated reserves plus physical plant minus liabilities can be expressed as a single number, often referred to as ‘net tangible assets’ or ‘net asset value’. In turn, the estimated value of reserves depends ‘fundamentally’ on an assumption about the future path of resource prices.

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Valuation of Equity Securities

Dealing with Uncertainty of Natural Resource Companies Resource companies often require special accounting treatment for, among other items, the handling of depletion. Even though Graham et al. (1962) (GDC) does not dedicate much discussion to the valuation of natural resource companies, that which is provided focuses on the evaluation of depletion charges, ‘intangible drilling costs’, depletion allowances and the like. This is an appropriate emphasis because accounting variables that are usually of interest in equity security valuation, such as EBIT and net income, have less importance when considering resource companies than for, say, industrial companies. Much of this important accounting information is not found in the financial statements proper but, rather, in the notes to the statements. For example, EnCana Corp., the largest Canadian natural gas producer, provides fourteen detailed pages of “Supplementary Financial Information” and “Supplementary Oil and Gas Operating Statistics” in the 2008 Annual Report. Included in the latter are data on: exploration and development drilling; developed and undeveloped properties by geographical location and type of property ownership (lease, Crown or freehold); and producing and non-producing reserves by geographical area, both gross and net of royalties. These supplementary items are required to execute a sensible fundamental equity security valuation of EnCana. In the present context, EnCana is of interest because it was involved in the sale of a percentage share in the Syncrude operation to another entity involved in Syncrude, the Canadian Oil Sands Unit Trust (COS) in 2003. Poitras (2003) provides a fundamental ex ante assessment that the price COS paid EnCana for this property was well below fair value. This transaction is unusual because the sole income producing asset of COS before and after the transaction is a percentage ownership share in Syncrude. The transaction involved the sale of equity securities (trust units) and debt (notes) in order to raise the cash required to pay EnCana for the purchase of an additional amount of the same asset that secured the new issue of equity and debt. The pre-sale/pre-announcement market value of COS provided a practical tool for analyzing the transaction. If the price paid was overvalued, then the transaction would be diluting for pre-sale unit holders. If the price was undervalued, then for pre-sale unit holders the deal would be accretive. Based on subsequent market prices, it is now possible to determine ex post why the pre-sale market value of COS was under valued. The claim that fundamental analysis does not apply to natural resource companies lacks precision. In theory, DCF valuation can be applied to any

17:46:55.

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643

capital asset or financial security. In some respects, such companies present a straight forward valuation problem. In determining the future net cash flows and discount rates, the primary difficulty with natural resource companies quickly becomes apparent: total revenues depend critically on the uncertain future price of the commodity; and, production costs may be subjected to unexpected changes.1 Except in a few unusual circumstances, no single producer or group of producers is able to control the pricing process for a widely used commodity. Without even considering the difficulties associated with expense and output uncertainty, the volatility of commodity prices alone suggests that natural resource companies are inherently speculative. This applies whether discounted cash flows or the market value of net assets is used in the fundamental estimation of intrinsic value. Hence, the inapplicability of fundamental analysis for valuation of resource company equity securities is due to the predominance of the speculative commodity price element in such valuations, not to some inherent characteristic of resource companies that renders fundamental analysis inoperative. The aversion to resource stocks expressed by numerous value investors does not eliminate the possibility of using DCF techniques to structure the valuation exercise. Rather, the challenge is to incorporate uncertainty into the valuation problem. To do this requires an adjustment to the value investing method of estimating an intrinsic value. Following Shackle, making optimal decisions when confronted with true uncertainty, i.e., where the probabilities are non-additive, requires two basic steps: first, do the valuation one period at a time; and, second, determine a best and worst outcome. In contrast to the value investing approach that estimates an intrinsic value using a unimodal distribution, determining a best and worst outcome does not correspond to determining upper and lower bounds on the expected intrinsic value. Rather, both the best and worst ex ante outcomes have distributions and, as a consequence, upper and lower bounds 1 COS does not hedge output so issues surrounding the implications of a hedging program will not be examined in detail. While hedging does permit the future output price to be determined, if done using a fixed program this will result in smoothing of earnings. The overall level of prices at which output is sold over time will still be undetermined as derivative contract maturity dates, even in the oil market, are only available up to a certain date in the future. Contracts for deferred delivery have to be added as nearby contracts mature. The delivery price of these new contracts will depend on the current price of oil. As such, where hedges use contracts with deliveries going well into the future, this substitutes some price uncertainty for cost of input uncertainty. While the output price may be fixed, the cost of producing that output is not.

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644

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Valuation of Equity Securities

associated with each of the two modes. The dominance of one mode or the other is subjective and will change over time. Once the best and worst situations have been subjectively determined, the equity security valuation can be evaluated over the next period relative to those cases. As for the length of the valuation period, Shackle was profoundly concerned with the avoidance of mechanical time. To be consistent with Shackle, the length of the valuation period — the horizon over which valuation decisions are made and reevaluated — is determined by the fundamentals of the equity valuation problem. More precisely, selection of a valuation horizon depends on the characteristics of the company being valued and, perhaps more importantly, on the commodity being produced. In the case of North American oil producers, the seasonal fluctuations in market conditions suggest one year as the valuation period.2 However, oil prices also follow fundamental cycles that are longer than seasonal cycles, possibly extending over much longer periods. For example, the most recent oil price cycle began in Jan. 2007 with WTI oil prices near a monthly average bottom at U.S.$54 and achieved another bottom in February 2009 at $39, a price level not touched since June 2004. Similarly, it would be possible to extend the beginning of the cycle farther back to December 1998 when the monthly average price hit a global $11.31 bottom. These bottoms can be matched with a monthly peak of $134 in June 2008. A bifurcation occurred somewhere between June 2008 and February 2009. A bifurcation produces a reassessment of the ex ante distributions for best and worst outcomes and, as a consequence, marks the beginning of a new valuation period. 8.1.2

The Canadian Oil Sands3

What Are the Oil Sands? The Canadian oil sands are an immense resource located primarily in the province of Alberta, e.g., Chastko (2004). An oil sand is a naturally 2 It is often the case that oil prices are at seasonal lows in December to February and peak at the end of the shoulder season in late May and early June, just prior to the start of the summer driving period and just after the winter heating oil draw downs. However, such seasonal patterns are only indicative and can be overwhelmed by forces associated with longer price cycles. 3 Though often used interchangeably, oil sands are different than ‘tar sands’. Used in roofing and road construction, tar is a byproduct of the oil refining process. Tar is the sticky residual left after the gasoline, heating oil and light ends have been extracted from crude oil. In contrast, an oil sand is naturally occurring with the bitumen binding to sand or clay particles. Heating in combination with additional water and ‘slurrying’ separates the bitumen from the sand. The reference to tar sands is historic, as early uses of ‘tar’ were consistent with uses of oil sands. However, when used in road construction, oil sands are decidedly more brittle than tar asphalt.

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Resource Companies: Oil Sands Producers

Fig. 8.1

645

Physical composition of oil sand.

occurring mixture of bitumen, water and clay or sand (see Fig. 8.1). Following, Atkins and MacFayden (2008, p. 80), it is important to realize that Alberta’s oil sands and heavy oil deposits are not homogeneous . . . Among the important ways in which deposits differ are: specific gravity (some crudes are heavier than other oils), bitumen concentration (the proportion by weight or volume which is bitumen, ranging from 1% to 18%) and depth (where shallow deposits — usually up to 75 metres deep — are regarded as amenable to mining operations).

Bitumen is a sticky, viscous type of crude oil with low API gravity compared to other types of crude. A light sweet crude, such as the West Texas Intermediate (WTI) that is the deliverable commodity for the widely followed NYMEX crude oil futures contract, has an API gravity of not less than 37◦ and not more than 42◦ while a heavy crude, such as that produced in Saudi Arabia, has an API gravity of 10◦ –20◦.4 Even with the sand, clay 4 The

delivery specifications of the NYMEX (since late 2009, merged with the Chicago Mercantile Exchange) crude oil contract permit delivery of specific domestic crude oils with not more than 0.42% sulphur by weight and API gravity between 37◦ and 42◦ .

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Valuation of Equity Securities

and water removed, bitumen still has an API gravity well below 10◦ . The low sulphur, upgraded Syncrude sweet blend (SSB) produced by Syncrude prior to 2007 only obtained an API gravity of 30◦ with the Syncrude sweet premium blend produced since 2007 being slightly higher. Because oil from conventional drilled wells has to travel up the well bore in order to be recovered, the API gravity determines the potential recovery rate. Light sweet crude deposits have a recovery rate of about 30% while heavy crude deposits have recovery rates up to 20% using conventional recovery methods. The API gravity of bitumen depends on the depth of the deposit. Unlike conventional crude oil and heavy oil deposits that are accessible only by drilling, approximately 18% of the Alberta oil sands are at depths from the surface down to 245 ft. Even though this surface oil sand bitumen has an API gravity of from 0◦ to 10◦ , “the first two commercial oil sands mining plants built in Alberta . . . produce a little over 0.8 of a barrel of syncrude per barrel of bitumen” (Atkins and MacFayden, Ibid.) Allowance made for loss of bitumen in the slurrying process, which depends on the richness of the oil sands being mined, produces an additional loss of about 0.15. As a result, about 65% of the crude oil contained in the surface oil sand can be recovered because the resource at this depth range can be open pit mined. Oil sands at depths below 245 feet usually have an API gravity about the same as heavy crude and have to be recovered through drilling and in situ (in the formation) methods. While these deposits have a recovery rate of between 25%–75%, the costs of loosening up the solid oil sand for extraction makes for much higher recovery costs than for oil sands mining which, in turn, is considerably more expensive than conventional oil. Though a number of extraction techniques for bitumen deposits below 245 ft. are being explored, steam assisted gravity drainage (SAGD) has proven to the be most popular to date. This technology requires considerable energy to generate the steam. There are few alternatives to the use of steam, e.g., Toe-to-Heel Injection method used at the Whitesands project.

Though the contract is usually referred to as the WTI contract, a range of other crudes are deliverable including New Mexican Sweet, Oklahoma Sweet, North Texas Sweet, and South Texas Sweet. It is also possible to deliver a range of other crudes, such as UK Brent, at a discount. The common view that the NYMEX contract is for WTI is due to the contract delivery point being any pipeline or storage facility at Cushing, Oklahoma, a delivery site that tends to favor delivery of WTI. Gray (2002) discusses the calculation of API gravity.

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Resource Companies: Oil Sands Producers

8.1.3

647

History of the Oil Sands

The Alberta oil sands have fascinated people for centuries.5 The early European explorers and fur traders were impressed by the presence of large surface pools of bitumen in the Athabasca region of northern Alberta. For example, the famous explorer, Alexander Mackenzie, travelling through the region in 1788 recorded in his journal: At about 24 miles from the fork (of the Athabasca and Clearwater Rivers) are some bituminous fountains into which a pole of 20 feet long may be inserted without the least resistance. The bitumen is in a fluid state and when mixed with gum, the resinous substance collected from the spruce fir, it serves to gum the Indians’ canoes. In its heated state it emits a smell like that of sea coal.

The first geological survey of the area was conducted in 1875 with further exploratory efforts being made in 1882 and 1889. The first attempts to commercially develop the oil sands in the Athabasca region were initiated in 1906 by the entrepreneur Alfred von Hammerstein. This project was based on the assumption that the surface bitumen was originating from pools of oil deep beneath the surface. In an attempt to locate these pools, a series of well holes were drilled in the area north of Fort McMurray where the bulk of surface bitumen in the Alberta oil sands is located (see Fig. 8.2). This drilling activity continued from 1906 to 1917, with a total of 24 wells being drilled. Due to the faulty initial assumption, none of the drills holes was successful at finding oil. However, the drilling activity did discover salt deposits which became a major industry in the Fort McMurray area for 50 years, until it was eclipsed by the oil sands developments. Since the early attempts at locating conventional oil deposits by drilling, there have been ongoing attempts to identify a commercially viable method of extracting the surface oil in the region. The process that is used in Syncrude and other heavy oil mining projects involves the use of a hot water flotation method to separate the bitumen from the sand (see Fig. 8.3). The development of this method for processing oil sands has a long history. Early onsite research on this method began around 1913 when Sidney Ells, a federal Department of Mines engineer, began a series of experiments on the viability of applying this technique to the oil sands. Ells continued this work until 1945. One of these experiments involved shipping mined bitumen 5 The

following discussion is derived from information provided on the Syncrude website www.syncrude.com. Chastko (2004) is a helpful source on the history of the Alberta oil sands.

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Fig. 8.2

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Valuation of Equity Securities

Province of Alberta, Location of Oil Sands and Heavy Oil Deposits.

to Edmonton for use as road paving material. While it was demonstrated that paving material was a feasible use for the separated oil sand, the costs of application were not competitive with imported asphalt and the project was dropped. Another commercial attempt to develop the oil sands using the hot water floatation method began in the 1920s when an entrepreneur, R.C. Fitzsimmons, used the process to produce bitumen for roofing and road surfacing at a plant near Bitumount, 80 km north of Fort McMurray. Financial difficulties eventually forced Fitzsimmons to sell the operation in 1942. Much of the early history of oil sands development using the hot water flotation method involves research done by the federal and Alberta governments. In addition to the work of Sidney Ells, during the 1920’s

17:46:55.

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Fig. 8.3

b921-ch08

649

Bitumen recovery process.

Dr. Karl Clark, a scientist with the Alberta Research Council, also conducted experiments with a hot water flotation process which involved mixing oil sand with hot water and aerating the resulting slurry. This separates the oil sand into a floating bitumen froth and a layer of sand that settles to the bottom of the holding tank (see Fig. 8.3). In 1948, the Alberta government acquired the Fitzsimmons plant to investigate the application of extraction methods, such as those investigated by Clark, using large scale equipment. By 1949, the plant was processing 450 ton of oil sand daily. While an experimental success, the plant was closed because the Alberta government was not motivated to launch a commercial venture. Data from the experiments was used as the basis for a major study on the viability of commercial production. The resulting Alberta government report indicated that crude oil production from the oil sand could be a profitable venture. Though this created some commercial interest during the 1950s, it was not until the 1960s that major commercial ventures began to come on-stream. The research of the Alberta government about the possibility of commercially viable extraction of crude oil or oil byproducts from the oil sands

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Valuation of Equity Securities

was not without practical foundation. In 1936, an entrepreneur, Max Ball, founded Abasand Oils Ltd that used a plant west of Fort McMurray to produce diesel oil from the oil sands. Despite the relatively small scale and commercially unproven technology, there was a considerable interest in his project, especially during World War II when diesel oil was in short supply. During the War, the plant was sold to the federal government and soon thereafter the plant burned down and the project died. Commercial oil production from the oil sands did not come to fruition until the Alberta government launched an initiative in 1962 that resulted in the Great Canadian Oil Sands Project (GCOS). Though GCOS experienced a number of ownership changes after its incorporation and prior to the construction decision, by 1963 ownership of the project resided with the Sun Oil Company (later Suncor Energy). It was this Suncor project that came on stream in 1967 to become the world’s first commercial oil sands operation. The GCOS was soon followed by the Syncrude consortium that was formed in 1964. The Economics of Oil Definitions Various estimates have been proposed for the size of the oil reserves contained in the Alberta oil sands. Haines (2001, p. 32) quotes Alberta government estimates of 1.6 trillion to 2.5 trillion barrels of bitumen. In contrast, Reynolds (2005, p. 53) argues such figures are “poor and confusing information”. The total supply of bitumen resource available in the Alberta oil sands reserve base is larger than the world’s proven reserves of conventional oil deposits. However, due to the presence of clay, sand and other earth elements mixed with the bitumen, oil sands do not have the same production economics as for conventional oil reserves. For example, the separation of the clay or sand from the bitumen and obtaining sufficient viscosity in the bitumen for extraction requires heating which adds substantially to the extraction cost. The oil sands reserves are located in the Cold Lake, Athabasca and Peace River areas of Alberta (see Figs. 8.1 and Fig. 8.4). Recalling that only about 18% of these reserves are surface reserves that can be mined, the surface reserves are located primarily in the Athabasca region which is situated north of Fort McMurray. Even though the size of the surface reserves is small relative to the total oil sands base, the substantially higher recovery rate of bitumen from surface reserves and the high yield of SCO from the bitumen makes these reserves a larger exploitable portion of the oil sands reserve base. Casual inspection of Table 8.1 reveals that the widely respected estimates of world oil reserves produced annually by BP give only a small

17:46:55.

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Resource Companies: Oil Sands Producers

Fig. 8.4

b921-ch08

651

Alberta oil sands projects.

amount of credence to the reserve value of the oil sands. A significant amount of the increase for Canada between 1998 and 2007 in Table 8.1 is due to the addition of about 16 billion oil sands reserves to the Canadian total which is below that for Libya and the Sudan. This compares to reserve estimates of around 175 billion barrels of economically recoverable crude oil produced by the Alberta government, an estimate accepted by the U.S. Energy Information Administration. If accepted, this would place Canadian oil reserves behind only Saudi Arabia. This highlights the difficulties with straight forward assessment of the world oil market by examining supply and demand factors. The actual supply of economically recoverable oil varies with the assessment of market price and the costs of oil recovery. As this spread widens, previously uneconomic reserves become feasible. This tipping point toward profitability occurred with the early Alberta oil sands producers when WTI crude oil traded above $20 per barrel.

17:46:55.

BP Oil Reserves Estimates, 1988–2008.

17:46:55.

At end 2007 Thousand million barrels

At end 2008

At end 1988 Thousand million barrels

At end 1998 Thousand million barrels

35.1 11.9 53.0 100.0

28.6 15.1 21.6 71.3

30.5 28.6 12.2 71.3

3.7 4.4 1.6 9.7

30.5 28.6 11.9 70.9

2.4% 2.3% 0.9% 5.6%

12.4 24.1 10.3 14.8

Brazil Venezuela Total S. & Cent. America

2.8 58.5 95.6

7.4 76.1 95.6

12.6 99.4 123.5

1.7 14.3 17.6

12.6 99.4 123.2

1.0% 7.9% 9.8%

18.2 50.3

Kazakhstan Norway Russian Federation Total Europe & Eurasia

n/a 7.3 n/a 77.3

n/a 11.7 n/a 144.6

39.8 8.2 80.4 144.6

5.3 0.9 10.8 19.2

39.8 7.5 79.0 142.2

3.2% 0.6% 6.3% 11.3%

70.0 8.3 21.8 22.1

92.9 100.0 94.5 4.5 255.0 98.1 653.0 9.2 2.0

93.7 112.5 96.5 12.5 261.5 97.8 684.3 11.3 4.0

138.2 115.0 101.5 27.4 264.2 97.8 755.0 12.2 13.5

18.9 15.5 14.0 2.9 36.3 13.0 102.0 1.5 1.8

137.6 115.0 101.5 27.3 264.1 97.8 754.1 12.2 13.5

10.9% 9.1% 8.1% 2.2% 21.0% 7.8% 59.9% 1.0% 1.1%

86.9 — 99.6 54.1 66.5 89.7 78.6 16.7 19.7

Share of total

R/P ratio

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(Continued)

9in x 6in

Iran Iraq Kuwait Qatar Saudi Arabia United Arab Emirates Total Middle East Algeria Angola

Thousand million barrels

Valuation of Equity Securities

United States Canada Mexico Total North America

Thousand million tonnes

November 3, 2010 10:47

652

Table 8.1

November 3, 2010 10:47

Table 8.1

(Continued) At end 2008

At end 2007 Thousand million barrels

Thousand million tonnes

Thousand million barrels

Share of total

R/P ratio

Libya Nigeria Total Africa

22.8 16.0 59.0

29.5 22.5 77.2

43.7 36.2 125.3

5.7 4.9 16.6

43.7 36.2 125.6

3.5% 2.9% 10.0%

64.6 45.6 33.4

China Indonesia Total Asia–Pacific

17.3 9.0 39.9

17.4 5.1 41.3

16.1 4.0 41.3

2.1 0.5 5.6

15.5 3.7 42.0

1.2% 0.3% 3.3%

11.1 10.2 14.5

Total World

998.4

1261.0

1261.0

170.8

42.0

100.0%

42.0

of which: European Union OECD OPEC Non-OPEC Former Soviet Union Canadian oil sands Proved reserves and oil sands

8.3 118.3 764.0 173.5 60.9 n/a n/a

8.9 89.2 827.2 157.6 83.8 n/a n/a

6.7 90.3 957.1 174.7 129.2 150.7 1411.7

0.8 12.0 129.8 23.6 17.4 24.5 195.3

6.3 88.9 955.8 174.4 127.8 150.7 1408.7

0.5% 7.1% 76.0% 13.9% 10.2%

7.7 13.2 71.1 14.8 27.2

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Notes: Proved reserves of oil — Generally taken to be those quantities that geological and engineering information indicates with reasonable certainty can be recovered in the future from known reservoirs under existing economic and operating conditions. Reserves-to-production (R/P) ratio — If the reserves remaining at the end of any year are divided by the production in that year, the result is the length of time that those remaining reserves would last if production were to continue at that rate. Source of data — The estimates in this table have been compiled using a combination of primary official sources, third-party data from the OPEC Secretariat, World Oil, Oil & Gas Journal and an independent estimate of Russian reserves based on information in the public domain. Canadian proved reserves include an official estimate of 22.0 billion barrels for oil sands ’under active development’. Reserves include gas condensate and natural gas liquids (NGLs) as well as crude oil. Annual changes and shares of total are calculated using thousand million barrels figures.

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8.1.4

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The Syncrude Project

The initial objective of Syncrude was research on the technical and commercial feasibility of mining the surface bitumen from the oil sands in the Athabasca region north of Fort McMurray. Despite having grown into the largest single crude oil producing entity in Canada, the history of Syncrude to the present has involved a substantial R&D effort to lower the costs of production through technological innovation. After an initial startup phase, Syncrude’s proposal for a commercial production facility was eventually approved in 1969. Construction commenced on the Syncrude site in 1973. After five years of construction, the first barrel was shipped on 30 July 1978. This event was followed by the official opening of the Syncrude Project on 15 September 1978. Production has steadily increased since that time. On 16 April 1998, the billionth barrel was delivered to the consortium members, five years ahead of schedule. The production facilities have been progressively expanded in phases. In 2001, phase 3 expansion was approved by the consortium. Scheduled for completion in 2004–2005 and expected to add 100,000 barrels per day to Syncrude output, the initial estimated cost of this phase was C$4 billion. Consistent with previous experience in oil sands developments, this cost estimate gradually increased through the life of the expansion. Each consortium member is responsible for their pro rata share of the development costs. After a number of delays, the phase 3 expansion was finally brought on-line in August 2006 at a final cost of $8.55 billion. Syncrude’s production facilities now have the design capability to produce approximately 375,000 barrels per day “when operating at full capacity under optimal conditions and with no downtime for maintenance or turnarounds. Under normal operating conditions, scheduled downtime is required for maintenance and turnaround activities and unscheduled downtime will occur as a result of operational and mechanical problems, unanticipated repairs and other slowdowns” (COS 2008 Annual Report, pp. 5, 6). When allowances for downtime are included, the designed productive capacity of Syncrude’s facilities is approximately 350,000 barrels per day, on average. Syncrude is a joint venture partnership owned, circa September 2008, by Canadian Oil Sands (36.74%), Imperial Oil Ltd. (25%), Petro-Canada (12%), ConocoPhillips Oil Sands Partnership (9.03%), Nexen Oil Sands Partnership (7.23%) Mocal Energy Ltd. (5%), and Murphy Oil Company

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(5%).6 Syncrude is the world’s largest producer of crude oil from oil sands (at least until the Suncor PetroCanada merger is completed) and the largest single source oil producer in Canada. In 2008, Syncrude produced about 289,000 barrels per day or 105.8 million barrels for the year of SCO at an average cost of $35.26 per barrel. This was well below potential output for a number of reasons, including the need to conduct comprehensive scheduled turnaround in the newest coker (8–3) and circulation problems in the oldest coker (8–1). “For the second quarter of 2009, operating costs averaged $50.23 per barrel compared with $41.92 per barrel in 2008. For the six-month period, per barrel operating costs were $43.66 and $38.90 in 2009 and 2008, respectively” (COS, Q2-09 report). Lower production volumes are signficant because “Syncrude’s operating costs are largely fixed, so changes in production volumes significantly impact per barrel operating costs”. Syncrude is not the only operator working the oil sands, but it is the largest and, together with Suncor, one of the two oldest. The original oil sands project run by Suncor Energy Inc. produced about 228,000 barrels per day (bpd) in 2008 compared to 235,600 bpd in 2007. Recently, a number of other on-stream bitumen mining projects in the same area have come onstream including: the Athabasca Oil Sands Project — also called Shell Albian Sands — a joint venture by Shell Canada (60%), Chevron Canada (20%) and Marathon Oil Corp. (20%) with the Muskeg River Mine entering production in 2002 and full production achieved when the Scotford upgrader in Fort Saskatchewan, Alta. came onstream in 2003. With an original design capacity of about 155,000 barrels per day, there is currently a 100,000 bpd expansion underway that received regulatory approval in 2006. Other projects just completed include the Horizons Oil Sands project owned by Canadian Natural Resources (CNQ) that has an eventual project design capacity of about 255,000 bpd. The initial stage has a design capacity of 110,000, and came onstream in Feb. 2009 at a cost of just under $10 billion and was producing an above design capacity 120,000 bpd by July 2009.

6 With completion of the Suncor Petro-Canada merger, the 12% share is owned by Suncor. In April 2010, Conoco-Phillips announed the sale of the 9.03% share to the state owned China Pteroleum & Chemical Corp., often referred to as Sinopec. Once regulatory approval is given, the sale will take place in two stages, ending in 2011. Nexen was formerly called Canadian Occidental and Mocal was formerly called Mitsubishi Oil (fully owned by Nippon). In 2002, EnCana was formed from the merger of Pan-Canadian Energy Corp and Alberta Energy Company Ltd. Prior to this merger, the EnCana share was held by Alberta Energy Company Oil Sands Partnership.

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In addition to completed and currently producing projects, there are a number of projects at various stages of the development process (see Fig. 8.4). Escalating costs and other factors have contributed to a significant slowdown in development. Consider the Fort Hills Oil Sands Project where the original leases were owned by two junior oil and gas explorers: 78% by True North Energy, a full owned subsidiary of Koch Industries; and, 22% by UTS Energy. In April 2004, UTS agreed to acquire 100% control from True North. Not long after acquiring the company, UTS was able to get companies capable of bringing an oil sands project to completion involved by having PetroCanada purchase a 60% share and Teck Cominco a 20% share. The initial True North project plans were to have the Fort Hills project producing approximately 95,000 barrels per day starting in 2005, with plans to ship the bitumen to a Koch refinery near St. Paul, Minn. for processing. These plans have changed a number of times. Current initial stage plan is for only a bitumen mining operation, with design capacity of 160,000 bpd, and use of Suncor upgrading facilities. The ultimate objective was a 280,000 operation and upgrader in place for 2014. Due to increase in costs of 50% or more that took final costs to over $20 billion, the Fort Hills mining project was delayed indefinitely in September 2008. The mining operation at Syncrude is immense, easily one of the largest materials handling operations in the world, with an output equal to approximately 13 percent of Canada’s petroleum requirements. The bitumen is mined using open pit techniques. A site is prepared for mining by removing the ‘overburden’. This requires the use of ‘supersized’ trucks and shovels to expose the oil sands. There are currently three mines on the Syncrude properties. Due to the progressive development of mining and extraction technology, the original mine uses somewhat different and more costly mining and extraction techniques than the other two. The original Base Mine uses two draglines to mine the oil sand, which is piled in windrows along the sides of the mine pit. The oil sand is dug from the windrows by bucketwheels and placed on a conveyor system that transports the material to the extraction plant. This extraction method was scheduled to be phased out by 2007. The North Mine was the next to be developed. The extraction technology at this mine uses trucks and shovels in conjunction with two hydrotransport pipelines. The ore from the truck and shovel operation is crushed and then mixed with hot water. This produces an oil sand slurry that is screened to remove large materials and then pumped through the hydrotransport pipeline to the extraction plant. The most recently developed mine, the Aurora Mine, was completed in 2000. This mine employs a slightly more cost effective technology than

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that used at the North Mine. Though the basic technology is the same, the cost savings come from the use of a new generation of larger trucks and shovels and an expanded use of the hydrotransport technology. Consistent with the history of Syncrude, the third of four (possibly five) planned expansion phases begun in 2001 was scheduled for completion in 2005 and finally went in process by 2006. Operating at full design capacity, this phase is expected to double Syncrude’s output of synthetic crude oil (SCO). This phase includes the development of a new mine, Aurora 2, followed by an expansion of the upgrader facilities. Of the total cost for phase 3 of C$8.55 billion, the mining development costs were significantly less than the cost of the bitumen upgrader and fluid coker plants. Phase 3 is estimated to add 130–135 million barrels per year to Syncrude’s design capacity. Following completion of phase 3, the fourth expansion phase that was initially scheduled for completion in 2010 has been moved back. This includes a further expansion of the Aurora mine and followed by another upgrader expansion. This phase is estimated to add 150–160 million barrels to capacity when it does occur. Due to the different mining technology used at the Base Mine, the extraction phase differs from that used at the Aurora mine. The bitumen from the Base Mine is extracted from the oil sand at the Base Plant where the oil sand from the Base Mine is fed into tumblers — large horizontal rotating drums — and mixed with steam, hot water and caustic soda in preparation for bitumen separation. The slurry from the tumbling phase is screened to remove large rocks and other such material before being pumped into four primary separation vessels (PSV’s). At this stage, feedstock from the slurry coming from the North Mine hydrotransport system can be added to the process. A distributor directs the North mine slurry to any or all of the four PSV’s, where it supplements feed from the tumblers. In addition to the Base Mine extractor, there is also an extraction plant at Aurora North. This extraction plant uses a low energy extraction process developed by Syncrude that is designed to operate at 25◦ C. Included in the Syncrude technological innovations used at this plant are the hydrotransport of high-density slurry, froth underwash, lean froth recycle, and air injection to enhance flotation. The resultant froth from Aurora North is transported to the Base Plant via a pipeline for further processing at the froth treatment plant. At this stage, the frothy bitumen from the extraction plant is diluted with naphtha and cleaned using a combination of centrifuges and inclined plate separators. Following the bitumen extraction phase, the naptha treated bitumen froth enters the upgrading phase that eventually results in the output of

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SCO. The first step in upgrading is naphtha recovery for recycling back to the froth treatment plant. The naptha reduced bitumen is then fed into two fluid cokers and one LC-Finer hydroprocessor for upgrading. The LC-Finer breaks down bitumen by adding hydrogen with the aid of a catalyst to produce gas oil. Gray (2002, p. 53) describes the relevance of this step: “Hydroconversion processes, such as LC-Fining . . . , use catalyst and hydrogen to control coke formation and maximize yields”. Residuum from the LC-Finer are sent to the fluid cokers where it is mixed with bitumen. Each of the cokers can process up to 105,000 barrels of bitumen per day. High temperatures in the coker reactors cause the cracking or decomposing of the bitumen molecules into various products. The lighter products, primarily naphtha and gas oils, become the main ingredients of crude oil. Carbon is rejected in the fluid coking process as coke, some of which is burned to generate heat for the bitumen cracking process, while the remaining coke is stored in coke cells. Over time Syncrude has made improvements in the design and efficiency of the cokers and the LC-Finer to permit the processing of a heavier feed derived from the vacuum distillation unit (VDU). Following start-up of this unit in 1999, the gas oil extracted now is directed to the hydrotreaters. The products from the cokers, the LC-Finer, and the gas oil from the VDU are processed in hydrotreating units that adds hydrogen using fixed bed catalytic reactors. This stabilizes the products, removes the nitrogen and sulphur and reduces product density, making SCO a highly desired feedstock for oil refineries. This is a crucial step as Gray (2002, p. 53) observes: “The contributions of various reactions show that sulphur and nitrogen removed in the coke have the biggest impact on product density. Higher sulphur and nitrogen removal and lower hydrogen losses increase volumetric yield and product gravity”. Though all this discussion of extraction and upgrading may seem more appropriate to a chemical engineer than a security analyst, the relevance lies in the potential for: improvements in SCO quality; and reducing the cost of the extraction and upgrading process. The Syncrude project requires substantial amounts of energy to produce steam and hydrogen for the catalytic reactors. Internally generated fuel gas is used as the primary source of energy to generate electricity and steam, while natural gas is used mainly to produce hydrogen. Potential energy savings or reduction in hydrogen loss and the like by technological improvements will ultimately translate into gains for unitholders. What are the physical limits to technological improvements in the upgrading process? Efforts to answer the question are an active area of research in chemical engineering. Because a number of different chemical

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reactions are occurring at once in the different stages of the upgrading process, it is difficult to predict precise outcomes. The bitumen entering the Syncrude upgrading process is typically around 7◦ API with 4.75% sulpur and 0.42% nitrogen. The LC-Fining hydroconverson process removes about 65% of the sulphur and 15% of the nitrogen but produces about 5.3% light ends. The delayed coking process removes only 37% of the sulphur, little or no nitrogen and produces about 2.0% light ends. Following Gray (2002, p. 53): “any change in the coking process that increases sulphur and nitrogen concentration in the coke will enhance volumetric yield and product quality . . . if hydrogen lost to light ends and to coke were halved, the volumetric yield of liquids would increase 1.8% and product gravity would increase by 2◦ API . . . More effective catalysts for nitrogen removal would give significant benefit in product yield”. On balance, despite the potential for some improvement in API gravity and product yield, there is an underlying problem that adding more hydrogen to improve sulphur removal also tends to increase the amount of coke produced. Though some future gains are possible, physical limitations dictate that sizable increases in API gravity or product yield in the future do not seem too likely. 8.2 8.2.1

Investment in Off-Shore Companies Risk and Return for Foreign Equity Securities

For a U.S. investor, COS.UN is a foreign security because it is traded in Canadian dollars on the TSX. This requires an adjustment in the domestic currency return. The calculation of the domestic currency return on foreign assets is complicated because the equity security price is denominated in foreign currency terms. Showing the distinction requires some notation. Let: the domestic currency denominated return on a foreign security position be R$ ; the foreign currency denominated return on a foreign asset be R£ ; let e be the growth rate of the currency, (S(1) − S(0))/S(0) = (∆S/S(0)), where S(t) is the spot exchange rate measured as units of domestic currency for one unit of foreign currency at time t. In order to distinguish from the domestic values, let Div* be the single dividend which is known to be paid in units foreign currency at t = 1 and P ∗ be the security price in foreign currency terms. Given this notation: 1 + R$ = 1 + =

[P ∗ (1) + Div ∗ (1)] S(1) − P ∗ (0) S(0) P ∗ (0) S(0)

P ∗ (1) + Div ∗ (1) S(1) = [1 + R£ ][1 + e] P ∗ (0) S(0)

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In effect, the security return can be decomposed into the returns associated with local factors, R£ , and currency changes, e. Fig. 8.5 has the five year history for the Canadian dollar. The presence of foreign securities in the portfolio selection problem raises substantive difficulties, if only because the relevant return, R$ , is a function of two random variables: R£ ; and e. This complicates the calculation of the variance: var[1 + R$ ] = var[1 + R£ + e + R£ e] = var[R£ ] + var[e] + var[R£ e] + 2{cov[R£ , e] + cov[R£ e, R£ ] + cov[R£ e, e]} It is conventional to simplify this calculation by using the approximation, ln[1 + R$ ]
R$
ln[1 + R£ ] + ln[1 + e]
R£ + e (where
means ‘approximately equal to’). This permits all the terms in var[R$ ] involving (R£ e) to be ignored. However, this approximation is only valid if R£ and e are sufficiently small. In this case the variance simplifies to: var[R$ ]
var[R£ + e] = var[R£ ] + var[e] + 2cov[R£ , e]

Fig. 8.5

Canadian dollar, 2004–2009, with MA(50) and MA(10).

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A number of sources provide information on the relative contributions to var[R$ ] of the local return (R£ ) and the exchange rate (e). For example, Table 8.2 reports empirical results for the decomposition of var[R$ ] into these components. Evidence is presented for the U.S.$ denominated monthly returns of securities from seven different countries. Returns for both intermediate term bonds and the major stock index for each country are provided. Returns are measured monthly. The fifth and last column gives the contribution due to (R£ e) and indicates that this component is not significant. Hence, for these returns measured at a monthly frequency, the log approximation is valid. The results also indicate that, with the exception of Canada, the component of the variance of bond returns due to local price changes is significantly less than that due to exchange rate changes. This result is changed for the variance of stock returns where the component associated with changes in the local stock prices is significantly larger than that due to exchange rate changes.

Table 8.2 Decomposition of the Variance of the U.S.$ Currency Return for Six Foreign Equity and Bond Indices, 1978–1989∗ . Components of var(R$ ) var[R$ ]

var[Ri ]

var[ei ]

2 cov[Ri , ei ]

∆var

Canada France Germany Japan Switzerland United Kingdom United States

15.29 16.48 21.53 24.70 21.16 27.67 10.24

10.82 2.82 2.59 3.03 1.14 8.88 10.24

1.72 12.74 13.84 15.13 17.64 12.39 0.00

2.67 0.60 4.91 6.09 2.34 6.08 0.00

0.08 0.32 0.19 0.45 0.04 0.32 0.00

Stocks Canada France Germany Japan Switzerland United Kingdom United States

37.70 59.75 43.82 41.47 34.81 40.96 21.16

30.58 43.03 29.27 19.45 20.07 29.27 21.16

1.72 12.74 13.84 15.13 17.64 12.39 0.00

5.37 3.75 0.00 5.83 −3.76 −1.52 0.00

0.03 0.23 0.71 1.06 0.86 0.82 0.00

Bonds

∗ The

variances are computed using monthly percentage returns. Source: Poitras (2002), p. 338.

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Sources of Information and Trading

General Format for Fundamental Analysis Depending on the source, a number of somewhat different formats can be used to present a valuation analysis for the common stock of a particular company. A ‘model analytical structure’ suggested for an academic fundamental analysis report is described by Penman (2001, p. 11). A five step process is proposed. The general outline of this process can be described as: How to Prepare a Fundamental Analysis Step 1: Economic and Market Analysis Structure of the industry: competition and market dynamics Products being produced: what the products do, technology, substitute products Firm cost structure and revenue composition Firm Strategy: what are the firm’s stated objectives for the future Regulatory Environment Step 2: Analysis of Financial Statements Balance sheet: Price to book value of equity; net market value of assets Income statement: free cash flow, revenues, EVA Cash flow statement: Operating, financing and investing Other factors not included in the financial statements: industry and government publications Step 3: Forecasting Relevant Payoffs What are the ‘value drivers’ ? What are ‘best guess’ forecasts of the value drivers? What factors could act to undermine the forecasts? Step 4: Formulating a Security Value Specifying the approach to valuation Applying the valuation model to the available data from steps 1–4 Step 5: Making a Recommendation For an outside investor, recommend buy, sell or hold. Stating qualifications to the forecast While this general model is useful for the analytical purposes of academics, it differs from the form that is common in ‘Professional’ security analysis

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reports. On the issue of form, English (2001, p. 393) recommends: “Financial analytic reports need five sections: recommendation and summary, earnings forecast, valuation, elaboration, and detail. This is the law of nature. The order is important. You can reverse the earnings and valuation, but the recommendation always comes first, and the detail last”. English reiterates the point: “Financial writing, has far more in common with journalism than with scientific writing. Conclusions always come first”. The aim of the professional security analysis report is to persuade, to convince the reader that the investment argument being made is sound. The Wall Street Approach Penman is approaching the problem of preparing a security analysis from the perspective of an academic researcher. Careful and systematic analysis of the information at hand is required, proceeding systematically to determine whether specific points are relevant. Discussion of the basis for accepting a given interpretation or rejecting the importance of a particular aspect of the available information is relevant. Once all the available data has been analyzed and processed, the final conclusion is reached and a recommendation is made. This is in contrast to the ‘Wall Street’ approach to preparing a security analysis where the report is also an exercise in persuasion. Details are only important insofar as the argument supporting the recommendation is aided. Keep the logical development as straightforward as possible. “Logical traps can sink an otherwise strong investment argument. Avoid chained logic, in which a number of conditions must be met for the argument to succeed. If one condition is successfully challenged, the entire argument is lost”. In general, the analytical style needs to contain “mostly positive, concrete statements; and, most importantly, be brief” English (2001, p. 393). English honed his skill in writing security analysis reports through 25 years of experience, most of which were spent at JP Morgan. The recommended approach to preparing a ‘professional’ security report is also reflected in various other sources. For example, Hooke (1998, p. 70) provides the following model for a security analysis research report: Table of Contents Section 1. 2.

Topic Introduction Macroeconomic Review

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3. 4.

5.

6.

7. 8.

Relevant Stock Market Prospects Review of the Company and Its Business Industry analysis Company specific analysis Future prospects Financial summary Financial Analysis Historical evaluation Current earnings power estimate Review of accounting methods Adjustments to historical financial data Financial Projections Listing of principal assumptions Projected data Application of Valuation Methodologies Recommendation Comparison of analyst’s valuation to market price of the stock Recommended investment decision

Similar to English, Hooke (1998, p. 69) states explicitly: “The model research report begins with a short description of the company that has issued the common stock under evaluation, and a summary recommendation for investment action”. Hooke goes beyond English to recommend: “Included in the introductory paragraph are the company’s product lines, its areas of operation, and its annual sales and profits”. The first paragraph in the introductory section is followed by three additional paragraphs, the second dealing with the company characteristics in more depth, including longer term trends in key variables such as sales and earnings. The third paragraph deals with significant developments in the company’s business with the final paragraph detailing the general rationale for the recommendation. The need for ‘sell side’ analysts to prepare a hard hitting, easy-tounderstand, persuasive and informative research report is not difficult to see.7 Brokerage house reports receive a wide circulation to an audience that 7 Hooke

(1998, p. 19) estimates that only about 30% of full time professional security analysts work for the sell side, composed of the investment banks and brokerage houses involved in the business of bringing to market, trading and marketing common stocks,

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varies considerably in the degree of expertise. The reports play a key role in the marketing efforts of all brokerage firms. Many buy side firms award brokerage and other business based on the quality of the research reports received from sell side firms. Though less obvious, most buy side analysts also need a writing style similar to sell-side analysts. Instead of targeting reports at client accounts, buy side analysts are writing for in-house consumption. Depending on the type of buy side firm, this will usually include portfolio managers, other analysts and traders. Though the report can take on a more sophisticated level of discussion because the audience is other investment professionals, this does not reduce the need to have a report that is concise, interesting to read and informative. Unfortunately, the appropriate format and style of the Wall Street sell side equity security research report does not apply when the analysis is primarily academic. The securities being examined are selected to illustrate certain principals not to decide whether the security is a ‘strong buy’, ‘buy’, ‘hold’, ‘sell’, or ‘strong sell’. The format and substance of the brokerage house reports is designed to facilitate the purchase of common stocks and other securities. The relative absence of sell and strong sell recommendations in brokerage house reports is well known. The unethical aspect of this practice was apparent in the sizable fines associated with the legal settlement that New York Attorney General Eliot Spitzer was able to obtain from the largest Wall Street sell side securities firms in 2003. This settlement also required these firms to supply clients with stock reports from three independent research firms to supplement the research reports that the securities firms prepare in-house for distribution to clients. It is not known, at present, whether this settlement has achieved the goal of mitigating the conflict-of-interest that the sell side firms have between investment banking activities and the marketing of equity securities to clients. Sources of Information on the Internet The information revolution that has emerged since the early 1980s has had a profound impact on equity security analysis and valuation. The tedious process of assembling and, to some extent, analyzing various types of fundamental information needed to determine the value of an equity security bonds and other securities. About 60% work for the ‘buy side’ of the market, composed of the institutional money managers such as pension funds, insurance companies, and the closed and open ended mutual fund companies. The remaining 10% work for a range of other organizations such as the regulators, the exchanges, the credit rating agencies and independent research firms.

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has been dramatically simplified. While the emergence of the internet has played a central in this information revolution, there has also been a dramatic increase in the number of media outlets dedicated either largely or exclusive to security analysis. The success of international cable television stations such as CNBC, which is available 24 hours a day in major centers around the world, as well as national outlets such as BNN in Canada, has been another factor increasing access and exposure to various types of information about securities. These developments have been accompanied by an increase in the number and sophistication of the traditional hard copy print media. The impact of the information revolution has been felt at both the individual and institutional level. Computerized and on-line trading systems, video conferencing with companies and other analysts, the emergence of sophisticated information platforms such as Bloomberg screens, together with an increase in the breadth and depth of information have all contributed to the information revolution at the institutional level. For the individual investor the problem of assembling and analyzing information has been transformed from a problem of access and cost to one of near-information-overload. There are now so many sources of information that it is difficult to filter and process what is available. The links page on the author’s website www.sfu.ca/∼poitras/links.htm collects and organizes information sites that are available on the internet into various categories, such as: ‘general websites’ for stock prices and other general market news and information, e.g., www.globeinvestor.com; security analysis websites for more detailed information e.g., www.thestreet.com and www.berkshirehathaway.com; academic websites, for universities, departments and invididual professors, e.g., www.fisher.osu.edu; futures, options, and stock exchange websites, e.g., www.cme.com; websites specializing in derivative sercurities and risk management, e.g., www.garp.com; and, websites for government agencies and departments, e.g., www.sec.gov. The links page is aimed primarily at being an aid to students doing securities research, ease of navigation has been a guide. In most cases, the first place to start an investigation of an equity security from the links page is the general websites. Being a collection of sites that are of general interest, the general websites only provide a first cut for the information required to effectively execute an insightful security analysis. Each individual stock will require a range of additional sites to be examined that provide information about the specific industry and company of interest. For example, consider some companies that have been examined in this book: Boeing; Canadian Oil

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Sands Trust; and, American Airlines. Once the basic information from general websites such as www.bloomberg.com has been examined, it is usually advisable to proceed to the website for the company of interest. In the case the Boeing, the website is www.boeing.com which contains links to both the annual report and the important SEC filings, such as the 10-K (audited) and 10-Q (unaudited) reports. Virtually all publicly traded US companies today have the annual report and SEC filing information easily accessible on the company website, usually accessible from the main web page under an ‘investor relations’ link. In addition, there is usually other types of useful information to examine about, say, the products and ‘links to other sites’. Having obtained the information from the company website, the equity security analysis will also benefit from examining information from websites dedicated to the particular industry. For an equity security valuation of, say, Molson-Coors (TAP), a number of possible industry sites that could be searched are: www.nbwa.org (National Beer Wholesalers Association) that provides institutional information about the wholesaling step in the U.S. beer distribution system. There are also industry related sites such as http://www.beerinstitute.org, the Beer Institute, and a range of more general beverage related websites, e.g., http://www.beveragenet.net/ which is mostly concerned with wines and http://www.bevindustry.com. Recognizing that beer has a significant taxation component, http://www.itds.treas.gov/Food Beverage.htm is a links site maintained by U.S. Customs and Revenue. Finally, an assessment of the competition for TAP can be obtained from the sites of competitors such as http://www.sab.co.za/, the website for SABMiller. A similar information search process applies to searching for information that can be used in an equity security analysis and valuation of Canadian Oil Sands Trust. The Globe Investor website, www.globeinvestor.com, associated with the Toronto Globe and Mail newspaper, is an excellent site for quotes and basic information on Canadian securities. The company website can be accessed at www.cos-trust.com. In addition to the annual report (no SEC filings as this security is traded in Canada), this site also has a considerable information about the Syncrude project. Even more information about the Syncrude project can be obtained from the Syncrude website at www.syncrude.com. There are other related sites such as the oil sands website at Ft. McMurray, http://oilsandsdiscovery.com; the Government of Alberta sponsored www.oilsands.alberta.ca; and, the Oil Sands Review, www.oilsandsreview.com. The Alberta government Energy Resource Conservation Board, www.ercb.ca is an excellent government site.

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The valuation of a crude oil producer requires information about the oil industry and markets for petroleum products. There are a range of industry sites concerned with these issues such as http://api-ec.api.org/ for the American Petroleum Institute and www.ipaa.org for the Independent Petroleum Association of America which have a considerable amount of production, refining and demand data on U.S. markets. In Canada, the Canadian Association of Petroleum Producers (www.capp.ca) has useful information on Canadian production, detailed monthly price series going back to the 1980s and a ‘related links’ that connects to a range of hard to identify sites, e.g., the Alberta Oil and Gas Abandonment and Reclamation Association, also known as the Orphan Well Association (http://www.orphanwell.ca/). The numerous media sites include www.oilandgasinvestor.com, Oil and Gas Investor, and www.oil.com, part of the WorldNews network. If information about international petroleum markets is desired there are sites such as www.iea.org for the International Energy Agency. Finally, the various major oil companies often have oil markets analysis and information on the company websites. An example of one such website is the British Petroleum site that has an excellent report on oil markets that can be accessed at: http://www.bp.com/. These sources of information can be contrasted with the internet information available for American Airlines. The annual reports and SEC filings can be accessed at the company website for American, www.aa.com. Usually there is an investor relations link apparent on the website home page. However, airlines are one instance where the website has an alternative use, in this case as an access point for online ticketing. The ‘investor relations’ link is hidden in the ‘About Us’ category on the home page. Given the national and global importance of the airline industry, there are a significant number of government and industry websites that provide an overwhelming amount of relevant information. A number of such sites include: www.airlines.org, the Air Transport Association; www.iata.org, the International Air Transport Association; www.nata-online.org, the National Air Transport Association (an industry group); and, www.icao.int, the International Civil Aviation Organization. In addition to these industry focused groups, there are US government agency websites such as the U.S. Department of Transportation site, www.dot.gov, the related site www.bts.gov, for the Bureau of Transportation Statistics, and www.faa.gov, the Federal Aviation Administration website (information on regulations). Similar to the useful information provided by BP on the oil industry, the Boeing website has a report on developments in the airline industry that has a wealth of material that is useful for doing a equity security valuation for an airline.

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8.2.3

669

Recent Developments in Canadian Unit Trusts

Canadian Unit Trust Structure Canadian Oil Sands Trust (COS) is an open-ended investment trust formed under the laws of the Province of Alberta. COS is referred to as a ‘unit trust’ because the ownership claims in COS are issued as ‘trust units’ with terms and conditions governing the units being specified in a ‘trust indenture’ contract.8 Each unit has the characteristic of a common stock in being marketable and transferable with a variable cash flow dependent on the return provided by a real asset. The units for COS are traded on the Toronto Stock Exchange under the ticker COS.UN. Trust units also have features of an incorporated mutual fund insofar as the trust holds assets — in this case a 36.74% interest in the Syncrude project — and passes income received from the underlying asset through to the individual unit holders.9 Prior to the tax changes imposed by the Halloween 2006 massacre, these cash flows are not usually taxable at the trust level, but are fully taxable when received by the unit holder. Though each unit is entitled to one vote in decisions of the trust, e.g., in the election of the board of directors, this right does not carry over to the assets that the trust holds. COS is only represented in Syncrude as a partner in the consortium. In both Canada and the United States, equity securities for a ‘publicly traded flow through entity’ were historically associated with the holding of real estate assets — in the form of real estate investment trusts (REIT’s). In a REIT, trust units are issued to raise capital that is invested in real estate assets, such as mortgages, construction loans and real properties. In the United States, the investment trust is also closely related to the master limited partnership used in natural resource industries, especially the oil and gas sector. In contrast to Canada, the U.S. imposes considerable legal 8 The trust indenture defines the relationship between the parties to the contract: the grantor that creates the trust; the beneficiaries that receive the benefits of the trust; the assets that are properties transferred to the trust; and, the trustee(s) that manages the trust assets and distributes the income from those assets according to the term specified in the indenture. In addition to the trust indenture, other relevant legal documents typically include, where applicable, the ‘articles of incorporation’ and a ‘management and administration agreement’. The latter is required because many trusts are not large enough to support an administrative structure to efficiently conduct trust activities such as collection and distribution of trust income, the purchase of relevant insurance, negotiations for acquisitions and dispositions, and so on. 9 Before passing the income along as distributions to unit holders, administrative expenses and any other advisory and management fees are deducted. For COS, 99% of the revenue received from the Canadian Oil Sands Limited is distributed to unit holders.

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restrictions on the use of ‘flow through entity’ security structures such as master limited partnerships.10 In theory, unit holders in a unit trust are not entitled to the limited liability protection afforded common stock. However, given “the integrity of the trust sponsors and inherent safeguards built into the [Trust Indenture], the potential of future liabilities for unit holders is considered remote” (Canadian Securities Institute 1992). In 2004, the provinces of Ontario — where units trade on the TSX — and Alberta — where COS is formed as a trust — legislatively eliminated any residual legal liability of unit trust holders. BC passed a similar act, the “BC Income Trust Liability Act”, in 2006. The open-ended unit trust is a novel development in the history of managed funds, e.g., Botz (1994). Following Aggarwal and Mintz (2004, p. 797): An income trust is a mutual fund trust for the purposes of the Income Tax Act. The income trust must meet four criteria: (1) it must have Canadian-resident trustees; (2) it must limit its activities to passive investing (although it can hold both Canadian and foreign property); (3) it must act in accordance with specified conditions (its units must be qualified for distribution, and it must have a minimum of 150 holders holding 100 units, each having a value of at least $500) relating to the distribution and ownership of its units; and (4) it must not be established or maintained primarily (more than 50 percent) for the benefit of nonresident persons. Once the mutual fund trust is established, the trust units are sold to investors, who are the beneficiaries. The income trust is a flowthrough vehicle for tax purposes. Income earned by the trust flows through to investors, who will pay tax on dividends, interest, or capital gains earned by the trust. The unitholders must also pay capital gains taxes on changes to gains realized from the sale of the units.

The concept of double taxation of corporate income, first at the corporate level and subsequently at the shareholder level, has been the subject of debate for decades. A number of tax code initiatives have been implemented over the years to dampen the possibly inequitable impact of double taxation. Dividend tax credits are one method used to reduce the personal 10 Prior

to the Halloween massacre, the large Canadian investment banks attempted to build on the ‘success’ of unit trusts in Canada and expended efforts to introduce trust units into U.S. markets. However, Canadian and U.S. tax laws differ significantly. The tax advantages associated with flowing tax implications through to unit holders is not as readily accomplished in the United States. However, there are other motivations for the trust structure, such as the requirement that the trust pay out the bulk of cash flow in distributions.

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671

tax burden. Similarly, various forms of tax deferred retirement accounts offered in Canada, the United States, and other countries shift the personal income tax burden to a future period, reducing the near term personal tax burden. Capital gains taxes further shield both personal and corporate income from double taxation. Theoretically, the unit trust seeks to rectify the double taxation situation by capitalizing the purchase price of the operating entity using high yielding debt. The corporate cash flow is then being flowed through to unit holders without incurring tax at the corporate level. To accomplish this result, restrictions inherent in the trust structure have to be followed. The legal structure associated with the conventional Canadian unit trust structure is described by Aggarwal and Mintz (2004, p. 798): The basic structure of an income trust is consistent across all industries. A Canadian resident trust indirectly purchases either a business or income-producing assets using the proceeds garnered from the public offering of trust units. The trust, however, also acts as a lender to the operating company and capitalizes the firm with a serviceable debt load that reduces or eliminates the amount of equity capital required. This is in essence what private equity funds do when an LBO is structured, although they often rely on external lending and supply only the equity capital.

Instead of using debt to generate the interest shield, some trusts purchase the operating assets and then lease the assets back to the operating entity. In this case, the lease payments serve much the same purpose as the interest payment in the conventional trust structure. In effect, unit trusts are not directly granted tax exempt status. Rather, the method of structuring an income trust using the tax shield associated with interest payments has similarities to the traditional leveraged buyout structure. As such, if income generated by the operating unit in any taxation period exceeded the amount that could be shielded by interest payments, there would be a corporate tax liability on the unshielded income. This income would flow to the trust in the form of dividend income. Traditionally, an income trust is terminology used when the holdings of the trust are primarily fixed income securities. However, reference to an income trust gradually came to be applied to trusts holding a wide range of ‘stable’ cash flow assets. Though the legal process by which the trust is created provides considerable protection to unitholders, it was when the size and number of business trust issuance assumed ominous characteristics that limited liability characteristics of ‘income trusts’ were clarified starting

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in 2004. For various business trusts, the assumption of ‘stable’ cash flow assets is seemingly fictional. Consider examples of the types of real assets that backed issues of ‘income trusts’ and ‘income funds’ that were listed on the Toronto Stock Exchange in 2002–2003: Connors Bros. Income Fund (CBF.UN), a sardine canner in New Brunswick; Menu Foods Income Fund, a Toronto pet-food maker with the trading symbol (MEW.UN); and, Big Rock Brewery Income Trust (BR.UN), a small Western Canadian brewer that recently converted to a trust from a company. Another example of a company that converted to a unit trust structure around that time is the Fording Coal operation, known as Fording Canadian Coal Trust (FDG.UN), subsequently purchased by Teck Cominco in 2008.11

The 2006 ‘Halloween Massacre’ Prior to 31 October 2006, the business trust component of the unit trust sector was threatening to take over the Canadian equity securities market. Unit trusts are referred to using a number of interchangeable names — income trust, income fund, unit trust, investment trust, mutual fund trust, royalty trust — with the usage often depending on the sector involved, e.g., royalty trusts in the oil and gas industry. The unit trust concept is a rough extension of the real estate investment trust (REIT) that emerged in the 1980s and early 1990s. A business trust is a unit trust where the primary asset is an operating business. Though there were only a small number of unit trust offerings in the early 1990s, income trust market capitalization grew from $15 billion in May 1999 to approximately $79 billion as of April 2004. The number of issuers more than doubled from 65 in May 1999 to over 160 by 2002 (Heizl 2003). As of 30 September 2006 there were some 255 income trusts listed on the TSX composing about 11% of total market capitalization, up from 7 percent in 2003 (see Fig. 8.6). Of total Canadian equity issuance, income trusts accounted for 41 percent in 2002, 37 percent in 2001, and 12 percent in 2000. The trend toward income trust

11 In addition to business trusts, there are also a long list of ‘trusts’ that hold a diversified portfolio of equities or fixed income securities, such as First Premium Income Trust (FPI.UN), that holds mostly Canadian equities. When issued in closed-end form, such securities are not substantively different from closed end funds traded on U.S. exchanges. There are also a number of income trusts, such as Enervest Diversified Income Trust (EIT.UN), that hold a diversified portfolio of other income trusts, REIT’s and shares in limited partnerships. Together with REITs, such equity securities are substantively different than business trusts.

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Fig. 8.6

673

Canadian Flow Through Entities, 1995–2006 (oct.).

Market Capitalization ($billions)

280 Limited partnerships

Real estate trusts

Energy trusts

Business trusts

240

∗

200

160

120

80

40

0 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

Year

∗ Conversions to trusts announced in 2006, not yet implemented.

Source: Government of Canada, Department of Finance (2006).

arrangements is evident as early as 1997, when income trusts accounted for 29 percent of equity financing (Aggarwal and Mintz 2004). The situation become dire in late 2005 and early 2006 when major Canadian telecommunications companies, Telus and BCE, announced plans to convert to unit trust status. Major Canadian banks, such as the Royal Bank, were also publicly musing the possibility of trust conversion. In early 2006, the newly elected Conservative federal government addressed this issue by lowering the dividend tax rate but to no avail. The federal government described the situation as (Department of Finance 2006): A major reason for the proliferation of these entities — and a major reason for the concern they have generated — is the unbalanced income tax treatment that applies to them and their investors. In short, tax rules that were designed essentially for non-commercial and portfolio investment trusts (and for owner operated partnership businesses) are being used by large-scale business entities that are widely held and publiclytraded, and the results are not appropriate.

In a closely held announcement that improved on a leaky announcement by the Liberal government on unit trusts in the previous year, on 31 October

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2006 the Minister of Finance, Jim Flaherty, made the following unexpected announcement: A more appropriate tax regime will be introduced for [flow through entities]. Under this regime their tax treatment will be more like that of corporations, and their investors will be treated more like shareholders. Specifically, certain distributions of FTEs’ income will be subject to tax at corporate income tax rates. Those distributions will — like the dividends that corporations pay — not be deductible by an FTE that is a trust, and will be taxed in the hands of an FTE that is a partnership. The investors in the FTE will be taxed as though the distributions were dividends.

This announcement was particularly irritating to some investors because, prior to the election, the Conservative government had promised to leave the tax status of unit trusts alone. Though certain types of trusts, such as the traditional, mostly closed end ‘non-commercial and portfolio’ trusts, were exempted from the new tax changes, the new business trusts did not escape.12 The impact on the prices of unit trusts was immediate (see Fig. 8.7). An average income trust impacted by the tax change lost about 17% of value on the first day of trade. Some business trusts, especially those with weak business models that had been created primarily to take advantage of the favourable taxation of trusts, fell much more. Though all affected trusts experienced unit price pullbacks, the blow was softened for trusts that began trading prior to 2006. Instead of being subject to corporate taxes starting in the 2007 tax year, these older trusts were granted an exemption from the new rules until the 2011 tax year. These older trusts, such as COS, can carry on business as usual until the tax change in 2011. Though the primary reason given for the tax changes was loss of tax revenue, this rationale has been challenged, e.g., Jog and Wang (2004), because the taxes would eventually be paid by investors. Because a significant portion of unit trusts 12 In order to differentiate income trusts subject to the new tax regime from those not subject, the Department of Finance defined the “specified investment flow through” entity — referred to as a SIFT — that would be subject to the new tax regime: “As a practical matter it can be assumed that all of the entities conventionally known as ‘income trusts’ are SIFTs, as are any publicly traded partnerships that hold significant investments in Canadian properties” (Department of Finance 2006, p. 8). In Canada, REIT’s already had a different tax structure than conventional corporations due, for example, to treatment of some trust income as return of capital. Allowing REIT’s to continue with tax treatment that had been worked out prior to the emergence of the business trust was sensible.

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675

Fig. 8.7 Impact of Halloween 2006 income trust tax changes (7 Nov. 2005 to 7 Nov. 2006).

were held in tax deferred retirement accounts, this meant a delay in the offsetting tax payment. In addition, there were severe provincial inequities because provinces with the bulk of corporate tax losses, such as Alberta with the oil and gas trusts, were not in a position to recapture the personal income taxes which most accrue to provinces in which the investors reside, primarily Ontario and Quebec. The unit trust provides a useful contrast between disparate viewpoints on the appropriate legal structure for equity securities. Some academics “argue that income trusts may represent a new method of market discipline whereby managers are obliged to distribute free cash flow and are required to go to capital markets for the financing of new opportunities, thus reducing potential agency costs associated with the monitoring of managerial decisions” (Jog and Wang, p. 856). In addition, income trusts provide a resolution to long standing issues associated with double taxation of dividend income. In contrast, government officials are concerned with the loss of corporate tax revenue and the inequitable regional distribution of tax recapture through personal income taxes. In addition, loss of tax revenue to foreigner investors — previously subject to only a 15% withholding tax — was a concern as 20% or more of some trusts were held offshore. Finally,

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there are sceptics that see the unit trust as another venture by investment bankers to extract fees and generate unwarranted returns for investors.

‘Our Fair Share’ Alberta Royalty Review The Halloween 2006 massacre of unit trusts illustrates the difficulties of valuing equity securities under the assumption that the government will not change the rules of the game. This general situation is even more complicated for oil sands producers due to the dramatic evolution of the industry which grown from a few players in the early 1990s, struggling to cover costs, to represent the largest producing sector of the Canadian crude oil industry. While the Halloween 2006 massacre dealt with the federal income tax implications of unit trusts, there were still outstanding issues associated with provincial royalty taxes in the oil and gas industry, e.g., Plourde (2009). These tax issues impacted all firms in the industry, not just the unit trusts. Royalty taxes on natural resource producers are especially important in Canada as, under the Canadian constitution, the provinces have ownership rights for natural resources located within the province. Conventionally, lease transactions are used to facilitate resource exploitation, with the province retaining ownership rights to the land. Lease auctions and royalties on production are the two main methods for provinces to extract revenues from the oil and gas industry. The tax and royalty regime in the oil sands sector can be divided into three phases: pre-1997; 1997–2007; and post-2007. Prior to 1997, taxes and royalties varied by firm. In contrast to the boom phase that appeared with significantly higher oil prices, activity in the oil sands was limited. The long established oil sands miners, Suncor and Syncrude, negotiated individual Crown Agreements with the province of Alberta for royalties. Other firms, such as Imperial Oil, were expected to negotiate individually with the province to determine royalties for specific projects. The costs and scale involved in oil sands production are such that both the federal and provincial governments provided a variety of corporate tax incentives, such as accelerated capital cost allowances, and a favourable method of determining royalty payments to attract firms to the industry. In this process, significant advantages were conferred on the oil sands miners, versus the in situ producers. Due to changes starting in 1997 and completed in the ‘Our Fair Share’ for Alberta royalty review of 2007, these advantages for Suncor and Syncrude have been negotiated away and, on a declining scale, are due to expire in 2015 (see Table 8.3).

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Table 8.3

677

COS 2008 Annual Report, Note 20.

Note 20. CROWN ROYALTIES In 2008, Canadian Oil Sands and the other Syncrude joint venture owners exercised their pre-existing option to convert to a bitumen-based Crown royalty. Effective 1 January 2009. Syncrude will calculate Crown royalties based on deemed bitumen revenues less allowed bitumen operating, non-production and capital cost rather than paying Crown royalties based on the production of synthetic crude oil (‘SCO’). As part of the conversion to a bitumen-based royalty, only costs related to producing bitumen rather than the fully upgraded SCO can be deducted. In addition, deductible costs in calculating Crown royalties will be reduced in future years by approximately $5 billions ($1.8 billion net to the Trust) resulting in future Crown royalties of approximately $1.25 billion plus interest ($459 million plus interest net to the Trust) over a 25-year period. The cost reductions relate to capital expenditures that were deducted in computing Crown royalties on SCO in prior years and that are no longer associated with the royalty base. Also in 2008, Canadian Oil Sands and the other Syncrude owners reached an agreement with the Alberta government on terms to transition the Syncrude Project to Alberta’s New Royalty Framework. Under the agreement the Syncrude owners will pay the greater of 25 percent of net deemed bitumen revenues or one percent of gross deemed bitumen-based revenues, plus an additional royalty of up to $975 million ($358 million net to the Trust) for the period 1 January 2010 to 31 December 2015. The additional royalty of $975 million is reduced proportionally on bitumen producion of less than 345,000 barrels per day over the period and is payable in six annual installments in respect of the following periods:

Syncrude Canadian Oil Sands Share

8.3 8.3.1

2010

2011

2012

2013

2014

2015

Total

$75 $27

$75 $27

$100 $37

$150 $55

$225 $83

$350 $129

$975 $358

Fundamental Valuation Canadian Oil Sands Trust (COS.UN)

Trust Company Description Though the Syncrude consortium was formed in 1964, the history of COS is more recent. The trust began operation on 30 November 1995 when an operating subsidiary, Athabasca Oil Sands Investment Inc., acquired an 11.74% interest in the Syncrude project. On 26 June 1996 the trust’s other operating subsidiary, Canadian Oil Sands Investments Inc., acquired a 10% interest in Syncrude from Pan-Canadian Petroleum Limited. In a one-forone exchange of units, on 5 July 2001 these two subsidiaries were merged into the single entity Canadian Oil Sands Limited (COS) which then held

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21.74% of Syncrude.13 Shortly thereafter, the current President and CEO of COS, Marcel Coutu, was appointed by the board of directors. Prior to this, Coutu had accumulated over 20+ years of oil industry experience, though little of this experience had been at the senior executive level. Coutu came to COS after a two year stint as CFO at Gulf Canada which was taken over by Conoco just prior to his departure. Prior to being at Gulf Coutu worked at Trans-Canada Pipelines (TRP) where he attained a position at the head of the international unit. In February 2003, COS successfully completed the purchase of an additional 10% of the Syncrude project from EnCana with an option to buy EnCana’s remaining 5% share which was subsequently exercised. Coutu is still the CEO and public face of COS. One shortcoming of unit trusts often identified by critics is the weak management and governance structures of such entities. This is the case at COS. In addition to Coutu, the management team at COSL is relatively small. Assuming that the activities of COS are not directly involved with the production of oil at Syncrude, this is not surprising. However, the management of COS does have significant activities that relate primarily to the running of the trust and in the marketing of SCO. There is a Chief Operations Officer on staff with extensive knowledge of bitumen mining and heavy oil upgrading operations. The implementation of administrative and general management activities for the trust within COS began in 2002. Prior to this time, this aspect of COS operations was conducted under an Administrative Services Agreement with EnCana (and its predecessors). While moving these activities within COSL did result in some cost savings to unitholders, the demand on management was such that: “In 2006 Syncrude Canada Ltd. entered a Management Services Agreement with Imperial Oil Resources. It provides Syncrude with operational, technical and business management services” (COS Annual Report 2008). The responsibility for the marketing of SCO by COSL stems from the Syncrude joint venture partnership agreement where Syncrude is responsible for delivering SCO to each consortium member ‘at the plant gate’. Being a unit trust, the impact that the management of COS has on the income that is generated for unitholders comes largely through participation in shaping the development of the Syncrude project. The passive

13 Though COSL is not directly responsible for the operations of Syncrude, Coutu does serve as Chairman of the Syncrude CEO and Management committees, the key decision making groups within Syncrude. The president and CEO of Syncrude since 2007 is Tom Katinas, previously with Exxon/Mobil the parent of Imperial Oil.

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character of the classical unit trust makes it difficult for trust management to expand the underlying business. While there is some scope for oil and gas royalty trusts to issue units or use cash flow to purchase additional properties to offset depletion in current properties, the legal intention is that trusts would be passive investors. As the trust sector expanded, especially into business trusts, the notion of passive management was increasingly ignored. Corporate tax and other advantages associated with unit trust issues meant such securities sold at a premium relative to common stock of comparable non-trust corporations. As such, business trusts were able to use this advantage to takeover other corporations and capture the premium associated with moving the real assets to trust tax status. This contributed to an increasing trend toward unit trusts absorbing non-trusts, contributing to the further erosion of the corporate tax base. Ultimately, valuation of COS depends on the value of the Syncrude project. Understanding this valuation depends on a detailed understanding of the mining and oil extraction technology that is being used at the Syncrude leaseholds. The eight leases involved cover 102,160 hectares making Syncrude the largest leaseholder of Alberta’s surface oil sands deposits and, together with Suncor, holder of the leases with the highest concentrations of bitumen (see Fig. 8.8). Because Syncrude is a bitumen mining project, the actual size of the bitumen reserve on these leaseholds cannot be subjected to conventional methods of reserve estimation. In addition, the recovery of SCO from the bitumen is much higher than for conventional well bore production. Because the resource is being mined, substantially more of the sweet crude oil contained in the bitumen is recovered. Due to the high quality of oil sand deposits in the Syncrude leases, as much as 85% of the bitumen recovered from the slurrying process is used to produce SCO which is a low sulphur, high quality light crude that trades at a premium to WTI due to the higher potential refinery yield of more expensive byproducts, especially gasoline. Being a light crude, SCO is easier to ship by pipeline than heavy crude and the lower sulphur content makes SCO attractive to refineries concerned about sulphur dioxide emissions.14

14 SCO has a sulphur content approximately one third of the maximum 0.42% sulphur content for WTI light sweet crude that is deliverable on a NYMEX contract. The API gravity of SCO tests about 32◦ compared to the minimum 37◦ to maximum 42◦ range for NYMEX deliverable WTI.

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Valuation of Equity Securities

Fig. 8.8

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COS oil sands lease map.

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8.3.2

681

Acquisition of the EnCana Share in 2003

The following press release was distributed by COS on Monday 3 February 2003: Canadian Oil Sands Trust said on Monday it will buy EnCana Corp.’s 10-percent stake in the Syncrude Canada Ltd. oil sands project for C$1.07 billion (U.S.$705 million), making it the biggest interest holder in the sprawling mining and synthetic crude operation. Canadian Oil Sands said the acquisition from EnCana, North America’s top oil explorer and producer, will be funded by two-thirds equity and one-third debt, and boost its interest in Syncrude to 31.74 percent. The company also said it had an option to buy EnCana’s remaining 3.75 percent interest until the end of the year.

A press release on 4 February 2003, indicated that the offering price on ‘$375 million’ of the equity issue was to be $35. A subsequent press release on 27 February 2003 revealed: Canadian Oil Sands financed the [C$1.07 billion] acquisition with 68 per cent equity and 32 per cent debt, which is slightly more conservative than the Trust’s capital structure prior to the transaction . . . Approximately C$431 million of the equity financing was raised through the issuance of approximately 12.3 million trust units by way of a public offering of subscription receipts . . . The remainder of the equity was financed through a private placement of trust units with a large institutional investor for approximately C$325 million. The balance of the purchase price was financed with senior bank debt of approximately C$350 million.

The press release further stated that the number of trust units had increased to ‘approximately 80 million’. Rough calculations indicate that this represents an increase of ‘approximately 22.3 million’ units from the preacquisition level of 57.7 million units. Netting the 12.3 million from the 22.3 million increase reveals that the ‘large institutional investor’ paid a price of ‘approximately’ C$32.50 per unit, though this is not stated directly in the press release, nor is the name of the large U.S. institutional investor identified. The 2002 Annual Report for COS claims: “Most importantly, the [early 2003] acquisition created value for our unitholders. The purchase price of $1.07 billion was approximately 14% less than the value implied by Canadian Oil Sands’ enterprise value as at 31 January 2003”. Is management’s claim that the purchase created value for shareholders valid? Valuing the COS purchase of the EnCana share permits the size of

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Canadian Oil Sands Ltd., Statistical Summary, 2004–2008.

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2006

2005

2004

Financial Revenues, after crude oil purchases and transportation expense Operating costs Non-production costs Crown royalties Administration Insurance Interest, net Depreciation, depletion and accretion Foreign exchange loss (gain) Future income tax expense (recovery) and other Income (loss) from discontinued operations Net income Per Trust Unit1 ($) Cash from operating activities Per Trust Unit1 ($) Unitholder distributions Per Trust Unit1 ($) Capital expenditures

4,169 1,368 78 599 17 6 68 444 159 (93) — 1,523 3.17 2,241 4.66 1,804 3.75 281

3,250 1,034 63 485 20 8 85 351 (117) 579 1 743 1.55 1,377 2.87 791 1.65 183

2,432 907 70 232 17 6 98 255 (5) 17 (1) 834 1.79 1,142 2.45 512 1.10 300

1,967 731 85 19 12 8 104 198 (29) 8 — 831 1.81 949 2.07 184 0.40 800

1,352 601 48 18 9 9 95 172 (80) (29) — 509 1.14 594 1.33 180 0.40 942

(Continued)

b921-ch08

2007

9in x 6in

2008

Valuation of Equity Securities

($ millions, except as indicated)

November 3, 2010 10:47

682

Table 8.4

November 3, 2010 10:47

Table 8.4

(Continued) 2007

2006

2005

2004

1.0 1.8 2.0 0.8 105,986

1.0 1.8 2.1 0.8 112,298

1.0 1.8 1.4 N/A 91,844

1.0 1.8 1.4 N/A 75,994

1.0 1.8 1.4 N/A 84,575

107.473 35.26 15.44 56.77

79.29 25.23 11.83 42.23

72.56 27.07 6.93 38.56

70.91 26.34 0.71 43.86

43.68 19.40 0.58 23.70

0.4 20.0 33.9 37.7

0.7 18.6 24.7 18.3

1.1 24.6 24.4 22.7

1.7 32.8 37.1 27.6

2.8 39.0 21.5 21.4

b921-ch08

(Continued)

9in x 6in

Reserves (billions of SCO bbls, net to Canadian Oil Sands) Proved reserves Proved plus probable reserves Contingent resources Prospective resources Average daily sales (bbls)2 Operating netback ($/bbl) Revenues, after crude oil purchases and transportation expense Operating costs Crown royalties Netback Financial ratios Net debt to cash from operating activities (times) Net debt to total capitalization (%) Return on average productive capital employed (%) Return on average Unitholders’ equity (%)

2008

Resource Companies: Oil Sands Producers

17:46:55.

($ millions, except as indicated)

683

(Continued) 2007

2006

2005

2004

$/Trust unit prices1 High Low Close Trading volume (millions of Trust Units) Number of Trust Units outstanding (millions)

55.25 18.15 21.10 463.6 481.6

38.88 25.09 38.71 373.8 479.4

38.75 24.32 32.61 406.6 470.9

28.60 12.42 25.20 356.9 462.6

13.64 8.05 13.52 389.2 457.2

Unit information has been adjusted to reflect the 5:1 Unit split that occurred on 3 May 2006. Trust’s sales volumes differ from its production volumes due to changes in inventory, which are primarily in-transit pipeline volumes, and are net of purchased crude oil volumes. 3 Revenue includes sulphur sales. Average net realized SCO selling price after transportation and hedging was $106.91 per barrel. 2 The

9in x 6in

2008

Valuation of Equity Securities

($ millions, except as indicated)

1 Trust

November 3, 2010 10:47

684

17:46:55.

Table 8.4

b921-ch08

November 3, 2010 10:47

9in x 6in

b921-ch08

Resource Companies: Oil Sands Producers

685

the bid premium (discount) paid to be calculated. What makes this particular transaction pedagogically interesting is that the bid premium calculation is relatively transparent. The capital structure, book value and market value of COS equity before the transaction are known (see Tables 8.5 and 8.6), as are the capital structure and book values after the transaction. The

Table 8.5

Consolidated Statements of Income and Unitholders’ Equity.

For the years ended 31 December ($ thousands, except per trust unit amounts) Net revenues Syncrude Sweet Blend revenues Transportation and marketing expense

2003

2002

$967,884 (35,821)

$722,076 (6,774)

932,063

715,302

Expenses Operating Non-production Crown royalties (Note 18) Administration Insurance Interest, net (Note 15) Depreciation and depletion Foreign exchange gain Income and Large Corporations Tax (Note 12) Future income tax recovery (Note 12) Dividends on preferred shares of subsidiaries

514,912 38,235 11,936 9,047 7,418 67,832 94,750 (135,165) 17,422 (2,246) —

308,877 19,392 7,378 7,355 5,812 38,737 55,091 (2,956) 5,413 — 275

624,141

445,374

Net income

$307,922

$269,928

$956,501 (244) 956,257 307,922 999,282 (169,885) 835 $2,094,411

$804,951 (36,886) 768,065 269,928 33,163 (114,655) — $956,501

Unitholders’ equity, beginning of year As previously reported Prior period adjustment (Note 3) As restated Net income Issue of Trust units (Note 13) Unitholder distributions (Note 16) Contributed surplus (Note 14(a)) Unitholders’ equity, end of year Weighted-average trust units Trust units, end of year Net income per trust unit Basic and diluted

79,656 87,195

57,182 57,684

$3.87

$4.72

Note: See Notes to Consolidated Financial Statements COSL 2003 annual report.

17:46:55.

November 3, 2010 10:47

9in x 6in

686

b921-ch08

Valuation of Equity Securities

Table 8.6

Consolidated Balance Sheets.

As at December 31 ($ thousands) Assets Current assets Cash and short-term investments Accounts receivable Inventories (Note 5) Prepaid expenses Capital assets, net (Note 6) Other assets Reclamation trust (Note 19) Deferred financing charges, net

Liabilities and Unitholders’ Equity Current liabilities Accounts payable and accrued liabilities Unit distribution payable Current portion of other liabilities (Note 7) Other liabilities (Note 7) Long-term debt (Note 9) Future reclamation and site restoration costs (Note 19) Deferred currency hedging gains (Note 10) Future income taxes (Note 12) Unitholders’ equity (Note 13)

2003

2002

$16,702 116,162 57,351 4,643 194,858 4,022,927

$229,970 93,444 26,132 4,547 354,093 1,470,671

16,553 25,520 42,073 $4,259,858

12,878 12,759 25,637 $1,850,401

$245,926 43,598 665 290,189 93,636 1,437,413 57,565

$169,279 28,843 2,740 200,862 22,013 622,283 32,237

21,886 264,758 2,165,447 2,094,411 $4,259,858

16,505 — 893,900 956,501 $1,850,401

Note: See Notes to Consolidated Financial Statements, COS 2003 annual report.

$1.07 billion paid resulted in COS issuing more units and debt in order to increase the share of Syncrude from 21.74% to 31.74%. If, for example, the amount of debt and number of trust units outstanding both doubled from the pre-purchase level, then the residual claim of a single unit against the Syncrude project would be significantly reduced. Conversely, if there were only, say, a 20% increase in debt outstanding and number of units, then the unit holder would have an increased claim. Examining just the percentage change in number of units, the purchase increased the COS Syncrude share by 46% and the number of units by 39.1%. The 7% differential would tend to support management’s claim that

17:46:55.

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9in x 6in

b921-ch08

Resource Companies: Oil Sands Producers

Table 8.7

687

Consolidated Statements of Cash Flows.

For the years ended December 31 ($ thousands) Cash provided by (used in) Operating activities Net income Items not requiring outlay of cash Depreciation and depletion Site restoration provision Amortization Foreign exchange on long-term debt Future income tax recovery Stock-based compensation Site restoration costs Net change in deferred items Funds from operations Change in non-cash working capital Financing activities Issuance of medium term and senior notes (Note 9) Net drawdown of bank credit facilities (Note 9) Unitholder distributions (Note 16) Issuance of Trust units (Note 13) Redemption of preferred shares (Note 11) Net change in deferred items Change in non-cash working capital Investing activities Acquisition of Syncrude working interests (Note 4) Capital expenditures Reclamation trust Change in non-cash working capital Decrease in cash Cash, beginning of year Cash, end of year Supplemental Information Income and Large Corporations Tax paid Interest charges paid

2003

2002

$307,922

$269,928

90,494 4,256 3,061 (147,162) (2,246) 591 (1,065) 17,000 272,851 (51,033) 221,818

51,994 3,097 874 (4,065) — — (1,150) 5,766 326,444 29,321 355,765

571,740

—

390,552

—

(169,885) 999,282 — (16,040) 14,755 1,790,404 (1,475,260) (785,587) (3,675) 39,032 (2,225,490) (213,268) 229,970 $16,702 $17,765 $60,858

(114,655) 33,163 (4,400) — 453 (85,439) — (403,203) (2,559) 8,093 (397,669) (127,343) 357,313 $229,970 $1,507 $50,519

Note: See Notes to Consolidated Financial Statements, COSL 2003 annual report.

17:46:55.

November 3, 2010 10:47

9in x 6in

688

b921-ch08

Valuation of Equity Securities

the purchase did enhance shareholder value. However, there are a number of pitfalls associated with using simple calculations for assessing the value of the transaction. One pitfall concerns adjustments for any change in the debt to equity ratio (see Table 8.6). One of the rationales for the merger of the two trusts to form COS was that the combined entity would have better access to capital markets, especially debt markets. Changes in firm leveraging will affect the valuation. The 2002–2003 balance sheet indicates the transaction did not substantively alter the long-term debt to book value of equity ratio. Another, more important pitfall concerns the future cash flows represented by the 10% interest. Syncrude is an expanding project. The Aurora 2 mine is coming on stream with Phase 3 scheduled for ex ante completion in 2005, eventually replacing the more expensive material originating from the old Base Mine. For a firm in an expansion mode, generating a sequence of negative near-term free cash flows and lower net income levels in order to significantly enhance long-term free cash flow and net income, it may be misleading to only consider numbers from the accounting statements. Examining the purchase using market values may give a different assessment of the purchase. The market price of COS just prior to the announcement of the Encana purchase was around C$39 and the unit price had been as high as C$43 in April 2002. Yet, new units were sold at $35 per unit to an underwriting syndicate and $32.50 per unit to a large institutional investor. These prices represent discounts of about 12% and 20% to the pre-announcement date unit price. The price on 10 April 2003 had fallen to C$34.75, approaching the 52 week low around C$34 reached in October 2002 (see Fig. 8.8). Ceteris parabus, the post-settlement market value does not appear to support the view that the transaction was value enhancing for unitholders on the completion date. Why did the trust unit market price fall if the transaction was value enhancing for unitholders? COS paid C$1.07 billion cash for a 10% share in Syncrude. This translates to an all-equity market value of C$2.326 billion for a 21.7% share. Based on a price of C$39 (C$35), the market value of the 57 million pre-purchase units is C$2.223 (C$2.014) billion. Adding to this value the C$622 million book value of the long term debt produces an estimated market value that is well in excessive of the implied value associated with the purchase price of the 10% share. These calculations again support the claims of management about the transaction (see Table 8.4 and Figure 8.9).

17:46:55.

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Resource Companies: Oil Sands Producers

Fig. 8.9

b921-ch08

689

COS unit price, 2004–2009.

Based on the subsequent performance of the units, eventually splitting 5:1 in May 2006, examining the behavior of unit prices around the transaction date for the purchase of the Encana share provided little substantive information about intrinsic value. Given the size of the transaction, considerations of market liquidity likely played a much larger role in the pricing around the transaction settlement date. Management was more or less correct in assessing and structuring the transaction as being marginally beneficial to unit holders, using prices and valuations applicable to the transaction date. The ex ante difficulties of assessing the immense and uncertain capital expenditures associated with the future production increase associated with the stage 3 expansion are apparent in Tables 8.4. The timing of the expansion phase fortuitously combined with structural changes in the global crude oil market to produce a pricing bifurcation. The factors which fueled the expansion reflected in Table 8.4 have been fundamentally altered from those confronting Poitras (2003). One valuation

17:46:55.

November 3, 2010 10:47

9in x 6in

690

b921-ch08

Valuation of Equity Securities

Table 8.8

Consolidated Balance Sheets.

As at December 31 ($ millions) Assets Current assets Cash and cash equivalents Accounts receivable Inventories (Note 6) Prepaid expenses

2008

2007

$279 184 93 6

$268 379 102 6

561

755

6,277

6,427

52 43

52 37

$6,933

$7,271

Liabilities and unitholders’ equity Current liabilities Accounts payable and accrued liabilities (Note 8) Current portion of employee future benefits (Note 9)

$284 17

$289 16

Employee future benefits and other liabilities (Note 9) Long-term debt (Note 11) Asset retirement obligation (Note 12) Future income taxes (Note 13)

301 99 1,258 235 1,130

305 128 1,218 226 1,222

3,023

3,099

3,910

4,172

$6,933

$7,271

Property, plant and equipment, net (Note 7) Other assets Goodwill Reclamation trust (Note 12)

Unitholders’ equity (Note 14)

Commitments, Contingencies, and Guarantees (Notes 21, 22 and 23, respectively) Note: See Notes to Consolidated Financial Statements, COS 2008 annual report.

period has ended and another is underway. Following Shackle, a reassessment of the ex ante best and worst outcomes for COS.UN is needed to provide an appropriate equity security valuation faced with the commodity price uncertainty associated with crude oil and the production uncertainties of oil sands production.

17:46:55.

November 3, 2010 10:47

9in x 6in

b921-ch08

Resource Companies: Oil Sands Producers

691

Table 8.9 Consolidated Statements of Income and Comprehensive Income. For the years ended 31 December ($ millions, except per Trust Unit amounts) Revenues Expenses Operating Non-production Crude oil purchases and transportation expense Crown royalties (Note 20) Administration Insurance Interest, net (Note 16) Depreciation, depletion and accretion (Note 7) Foreign exchange loss (gain) Earnings before taxes from continuing operations Future income tax expense (recovery) (Note 13) Net income from continuing operations Income from discontinued operations Net income Other comprehensive loss, net of income taxes Reclassification of derivative gains to net income Comprehensive income Weighted-average trust units (millions) Trust units, end of year (millions) Net income per trust unit1 Basic (Note 14) Diluted (Note 14)

2008

2007

$4,543

$3,633

1,358 78 374

1,034 63 383

599 17 6 68 444

485 20 8 85 351

159 3,113 1,430 (93) 1,523 — 1,523

(3)

(117) 2,312 1,321 579 742 1 743

(6)

$1,520 481

$737 479

482

479

$3.17 $3.16

$1.55 $1.54

1 Discontinued operations did not have a material impact on basic or diluted net income per Trust Unit. Note: See Notes to Consolidated Financial Statements, COS 2008 annual report.

17:46:55.

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692

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Valuation of Equity Securities

8.3.3

Current Valuation of the COS Trust Unit (COS.UN)

The fundamental valuation of a classical Canadian oil and gas unit trust is somewhat easier than for common stock due to the flow through share feature of the trust units combined with the restriction to one line of business and, in the case of COS.UN, one operating asset. However, even with a fairly immediate connection between revenues and global crude oil pricing, there is considerable production uncertainty in the valuation of COS.UN, as evidenced in the 2009-Q2 Report: reduced production volumes resulted in higher per barrel operating costs in 2009 compared with 2008. For the second quarter of 2009, operating costs averaged $50.23 per barrel compared with $41.92 per barrel in 2008 [Q2]. For the six-month period, per barrel operating costs were $43.66 and $38.90 in 2009 and 2008, respectively. Syncrude’s operating costs are largely fixed, so changes in production volumes significantly impact per barrel operating costs.

For full year 2008, Syncrude produced 289,000 barrels per day at a cost of $35.26 per barrel. Daily productive design capacity was increased to 350,000 barrels of synthetic, sweet crude oil in 2006 and the target is to bring production to this design capacity by the end of 2010. However, the 2009-Q2 Report has production at mid-2009 well below 2008 levels: For the first half of 2009, sales volumes averaged about 89,000 barrels per day versus 98,000 barrels per day during the 2008 period. In 2009, Syncrude conducted a scheduled, comprehensive turnaround of Coker 8– 3 and related units, the primary upgrading unit brought into operation in August 2006 as part of the Stage 3 expansion.

In the 2009-Q2 Report, management explains the alarming escalation in costs with the following: Reducing per barrel operating costs is primarily a function of increasing production volumes. Most of our operating costs are fixed so the higher the volume we can process, the lower our operating cost per barrel should be. Over the past few years, we have experienced significant cost inflation as a result of the increase in crude oil prices and the rapid escalation of activity in the oil sands sector. We believe costs will begin to moderate with the decline in commodity prices and the resulting slowdown in development. The cost of energy-sensitive consumables, such as natural gas, has already declined, concurrent with the decrease in crude oil prices. Our largest cost component, however, is labour and we expect these costs to moderate more slowly.

17:46:55.

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9in x 6in

Resource Companies: Oil Sands Producers

b921-ch08

693

Comparison with the ex ante valuation problem confronting a unit holder around the time of the 2003 Encana purchase reveals substantive differences with both the best (focus gain) and worst (focus loss) likely outcomes. Poitras (2003) identifies COS.UN as having ‘home run’ (4 bagger) potential, an ambitious target that was exceeded within three years. As reflected in a comparison of the capital expenditure lines in the cash flow statements of Tables 8.10 and 8.7, in 2003 Syncrude was embarking on a sustained program of capital construction associated with the phase 3 expansion. A number of years of heavy capital requirements for COS fortuitously coincided with an upward movement in oil prices from the $35 dollar level in February 2003 to the $60 level at the end of 2005. This permitted capital costs to be met without substantial unit holder dilution. A favorable royalty regime and unit trust status meant that much of the COS cash flow was largely exempt from taxation. It was inevitable that the curse of commodity businesses would appear together an amazing public interest increase in the oil sands expansion. From a niche player in the oil markets in the mid-1990s, the oil sands emerged as a significant continental player in the crude oil market by the 2006. An ex ante valuation of COS.UN at year end 2008 finds phase 3 has been completed and the capital programs for phase 4 are on hold. Instead of an impending and eventually realized design increase of 100,000 barrels relevant to the 2003 valuation, near term production growth prospects from 2008 can only come from getting production closer to design capacity. Based on the first two quarters of 2009, production is going slightly in the opposite direction. The dramatic escalation of costs associated with firms ‘piling into’ proposed and in construction oil sands mining projects, raises significant questions about capital costs of future significant expansions. It seems the potential for substantial growth from production increases available in 2003 is gone. The increasing congestion of projects in the oil sands has negative implications for labour costs, an important component of operating costs. The two pronged ex ante benefit of higher potential future output and increased oil prices that loomed in 2003 is no longer available. The friendly tax environment is ending, both provincially — scaled out to 2015 — and federally, starting in 2011. This places considerable pressure on crude oil price movements to sustain a best case outcome (Fig. 8.10). In the spirit of McCloskey (1985), the economics of oil sands mining is a story about mega-projects. Capital costs are immense and oil prices have to be sufficient to warrant the long time horizon construction projects required to get an oil sands mine into operation. More importantly, because

17:46:55.

November 3, 2010 10:47

9in x 6in

694

b921-ch08

Valuation of Equity Securities

Table 8.10

Consolidated Statements of Cash Flows.

For the years ended 31 December $millions) Cash from (used in) operating activities Net income Items not requiring an outlay of cash Depreciation, depletion and accretion Unrealized foreign exchange loss (gain) on long-term debt Future income tax expense (recovery) Other Net change in deferred items Funds from operations Change in non-cash working capital (Note 24) Cash from operating activities Cash from (used in) financing activities Repayment of medium term and Senior Notes (Note 11) Net drawdown (repayment) of bank credit facilities (Note 10) Unitholder distributions (Note 17) Issuance of Trust Units (Note 14) Cash used in financing activities Cash from (used in) investing activities Capital expenditures Acquisition of additional Syncrude working interest (Note 5) Disposition of properties Reclamation trust funding Change in non-cash working capital (Note 24) Cash used in investing activities Increase (decrease) in cash and cash equivalents Cash and cash equivalents, beginning of year Cash and cash equivalents, end of year Cash and cash equivalents consist of Cash Short-term investments

2008

2007

$1,523

$743

444 204

351 (153)

(93) 2 (41) 2,039 202 2,241

578 (3) 26 1,542 (165) 1,377

(150) (16)

(272) 16

(1,804) 21 (1,949)

(791) 3 (1,044)

(281) —

(183) (231)

— (6) 6 (281) 11 268 $279

4 (7) (1) (418) (85) 353 $268

$18 261 $279

$4 264 $268

Supplementary Information (Note 24). Note: See Notes to Consolidated Financial Statements, COSL 2008 annual report.

the surface oil sands are of varying quality and depth, there is a first mover advantage to miners able to obtain leases on the deepest and richest concentrations of bitumen. The global oil market is vast compared to the 350,000 bpd maximum produced by Syncrude. Circa 2005, Saudi Arabia alone produced about 9 million bpd. In a year where oil prices averaged almost $100, COS.UN was able to return $3.17 in cash. Ceteris paribus,

17:46:55.

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9in x 6in

b921-ch08

Resource Companies: Oil Sands Producers

695

160.00

140.00

120.00

US$/bbl

100.00

Crude Oil

80.00

60.00

40.00

0.00

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May

20.00

2006

Fig. 8.10

2007

2008

2009

Monthly average WTI crude oil price, 2006–2009.

this amount would be reduced if the post-2010 trust-to-corporation income tax rules applied, recognizing that the cash flow would only be subject to taxation at dividend income rates, instead of the personal income tax rates applicable to unit trust distributions. Based on results to 2009-Q2, it appears oil prices will average well below $100 in 2009. Combined with lower production volumes and higher costs from increased royalties, it is difficult to find a growth story for COS.UN that does not rely heavily on significant improvement in the global oil market. If the first half of 2009 is indicative of full year results, oil prices will average slightly below 2007 when the COS.UN returned $1.61 in cash distributions to unit holders. At a mid-September 2009 price of $28, an annual cash payout of, say, $1.00 would barely be a 3% return. Further reductions in future payouts will arise from increased corporate and royalty taxes. With WTI oil prices above $140, the unit price was only able to attain a maximum price of just over $55 (see Fig. 8.9). However, it is not the maximum value of the commodity price that matters for unit price valuation. Rather, actual and sustained increases in cash payouts would be needed to justify considerably higher unit prices. For example, if a commodity price in the C $150 range was maintained for a sustained period of time, cash payouts could rise to, say, $5.50 if taxes are assumed to hold steady. At a 6% dividend yield, this could sustain a price above $90. As such, this best

17:46:55.

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9in x 6in

696

b921-ch08

Valuation of Equity Securities

case outcome for COS.UN falls from the ‘home run’ category into the ‘extra base hit’ category. This outcome depends on a reasonable expectation that production volumes will stay within, say, 80,000 bpd of design capacity and needs a more-than-cooperative global oil market. As with the best case, it is not the result associated with the worst possible outcome that is of interest. Rather, it is the outcome that appears if the most plausible adverse events materialize. For example, oil prices could fall to the low teens level that appeared in 1999. However, this is not a credible worst case scenario. Oil markets have come too far to realistically expect a collapse in prices to levels of 10 years ago. This might happen in some future decision period, but not in the present. Given the current tax and cost scenarios, it is more possible that a sustained period of WTI oil prices below C$50 could see a return to the conventional ‘Mark Twain’ mining stock model of value reduction through dilution to sustain on-going losses. While further expansion into less productive resource deposits seems unlikely, regulatory and taxation attacks, such as environmental pollution restrictions and imposition of carbon offset taxes on production volumes could appear in future decision periods. The possibility of a technological innovation that impacts the use of gasoline as the transportation fuel of choice is another scenario that is too remote to be other than a tail point in the worst case scenario distribution. More likely is an innovation that permits additional recovery from depleted wells or improves the recovery rate for current and future producing wells.

Recommendation and Epilog This book employs two, somewhat disparate, philosophical approahces to the dealing with the problem of determining an accurate ex ante valuation for an equity security. In opposition to the economic positivism that underpins the academic theories of modern Finance, a version of skeptical empiricism is proposed that questions both the empirical validity of the logical relationships and the empirical methodologies used to generate and test the received theories. The search for immutable laws of nature in the equity security pricing process is futile. Logical arguments alone are insufficient; empirical guidance is required. Yet, no improvement in measurement can overcome the fallibility of knowledge obtained by empirical observation. It is this fallibility that also undermines the naive empiricist philosophy underpinning the technical analysis methodologies popular among vernacular Finance practitioners. being based exclusively on inductive reasoning,

17:46:55.

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Resource Companies: Oil Sands Producers

b921-ch08

697

technical analysis is unable to avoid the ‘measurement without theory’ criticism that Koopmans (1947) and others, similarly, aimed at the insitutional school of economics. At least since David Hume (1711–1776), it has been recognized that sceptical empiricism is a slippery philosophical slope. The world goes on. Daily decisions have to be made. Some process of sorting and managing information has to be emplyed. In the limit, sceptics can have difficulty determining whether the sun will come up each day. For a true sceptic, valuing an equity security is an insurmountable problem. Absent the possibility of immutable laws that can be identified using ‘rigorous mathematical theories and carefully documented empirical studies’, the valuation decision falls back on ‘rational intuition’ which is guided by ‘accounting practices, rules of thumb and anecdotes’ to determine the ‘Keynesian convention’ guiding equity market pricing. At any point in time, the ‘conventional’ market valuation can differ from the ‘long term prospective yeild’. Yet, even for a relatively simple equity security valuation such as COS.UN, determining the appropriate ‘long term prospective yield’ is difficult. The tools of fundamental analysis can give the false appearance of accuracy, further exacerbating the difficulty of determining whether the current market prie is ex ante fairly valued. The relevant value drivers in the fundamental valuation of the ‘long term prospective yield’ for COS.UN are changes in variables such as oil prices, technology, taxes and regulations. Such changes are not resolvable ex ante with more than a vague, intuitive precision that can colloquially be called ‘the story’. In contrast to the vagueness of the story, the relevant probabilities required to calculate distributional parameters such as the mathematical expectation, beta or variance cannot be accurately determined from the amount of empirical information available. Similar issues arise with vernacular predictions about target prices over fixed horizons, e.g., the targt price is X for stock Y over the next Z months. Is this any more informed than saying the target number is X heads in game Y in Z tosses? As Graham and Dodd (1934) observed, there are only certain situations — those promising safety of principal and satisfactory return — where the ‘rules of thumb’ that comprise equity security analysis can be applied. There has to be some method of rational calculation and speculative situations do not qualify. Is this the case with COS.UN? The oil sands are a vast resource capable of delivering a relatively predictable volume of crude oil from a given plant using a proven, if dirty, technology. The security of supply and predictability of output has seen

17:46:55.

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698

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an increasingly larger fraction of US crude oil imports originating from the mine-able Athabasca oil sands. Increasingly, the oil sands miners are assuming the role of marginal producer and, as such, have a key role in oil market pricing. Crude oil prices north of US$100 per bbl, generated significant incentives for expansion of oil sands plant and capacity, providing a crude upper bound on the profitability of oil sands mining over the decision horizon. Alternative cost-effective production technologies, such as the deep-sea, deep bore hole drilling recently introduced in the Gulf of Mexico to tap deeper conventional oil deposits, pose severe enviornmental risks. Less cost effective technologies, such as SAGD, are not producing sufficient volumes to have the impact at the margin of the oil sands miners. With no feasible alternative on the horizon to the use of gasoline for transportation fuel, the underlying business fundamentals suggest that COS.UN is a viable candidate for a fundamental equity security valuation. However, COS is in a commodity industry and, as such, is subject to the vagaries of crude oil pricing. Regarding the conversion to a corporate tax regime in 2011, COS has declared no intention of changing from a flow-through-entity model. Conversion will only impact the size and tax implications of the investor cash flow; the corporation has no intention of expanding into other ventures. Given this, the likelihood of cash flows achieving the C$3.17 level of 2008 over the valuation horizon seems remote. While high global oil prices may have short term benefits, the negative macroeconomic shock has a severe dampening impact on economic activity, leading to a subsequent downturn in oil prices. In addition, sufficiently attractive returns to oil sands mining tempts in new entrants. There are currently billions in planned oil sands projects that have been shelved, awaiting an improvement in oil prices. First mover advantages have dissipated as the industry has matured and there are no significant enhancements to production on-going. With gradually escalating costs and uncooperative oil prices, the ex ante cash payouts on COS.UN will be thin and dividend yields comparable with, say, Canadian REITs, but with more volatility in the payout amount. Recognizing ex ante that safer comparable yields are obtainable elsewhere, the intrinsic value of the position is primarily associated with the long term play on the mine-able oil sands resource. This is the basic ‘story’ for COS.UN. Following Shackle, making rational decisions under uncertainty requires decisions to be made one period at a time. In an equity valuation context, this period is determined by ‘the story’, which allows a best (focus gain) and worst (focus loss) case scenario to be heuristically determined. For COS.UN,

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a return to, say, C$3.17 annual payout or higher could signal that the best case was at hand; a cut in the distribution to zero in the face of costs exceeding revenures could signal a worst case. All this is set against the long-term play on the oil sands resource. Substantive changes in the story that alter the long-term view, e.g., a prohibitive tax on carbon emissions or a technological change altering the primary transportation fuel, would definitely be an end to the decision horizon. When to sell? how long to hold? and so on are determined by the story which, by construction, is based on intuition about the fundamentals of the company. Because the basic story is long-term and positive, the ex ante valuation that is as close to ‘vaguely right’ as possible has COS.UN trading between the mid-twenties to midthirties, with cash payout of 4% to 8% in an oil price environment between US$50 and US$100.

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b921-Index

Index

Amsterdam, 103–109, 112, 113, 116, 120, 122, 124, 127, 128, 132, 143, 146–148, 189, 190, 229 Amsterdam Exchange, 104–107, 113, 122, 128, 146 anomalies, 57, 67, 70, 76, 77, 89, 119, 323, 461, 467, 476, 478 anticipation approach, 473, 537–539, 541 Antwerp/Antwerp Exchange, 104 arithmetic average, 46–49, 361, 403, 422–424, 427 arithmetic average return, 47 Arthur Anderson, 169, 612 asset pricing models, 66, 478 asset valuation models, 621 auction rate preferred stock, 24 Ayer, A.J., 79

abnormal earnings model, 347, 349, 350, 356 see also residual income model absolute priority rule, 630 academic Finance, 88, 89, 176, 200, 235, 261, 267, 270, 271, 455, 494, 521, 534, 640 accounting profession history, 1, 22, 32, 33, 43, 50, 54, 58, 60, 61, 64, 65, 82, 84, 87, 89, 97, 98, 102, 104, 111, 113, 117, 120, 124, 128, 136, 140, 144, 149, 156, 161, 165, 177, 187, 199, 203, 206, 215, 216, 225, 227, 232, 234, 235, 242, 249, 260–262, 264, 270, 274, 280, 294, 306, 320, 323, 325, 330, 337, 369, 378, 416, 417, 430, 465, 470–472, 483, 484, 495, 498, 510, 515, 518, 538, 540, 548, 554, 577, 597, 618, 620, 647, 648, 654, 657, 660, 670, 677 adjustable rate preferred stock, 24, 25 Alberta/Alberta oil sands, 646, 647, 650, 651, 668 alpha, 408, 414, 476, 517, 518 Amaranth Advisors LLC, 244 American Airlines (AMR), 592, 596, 667, 668 American Bar Association, 629 American depository receipts, 10, 563 American Express, 162, 163, 264 American Institute of Certified Public Accountants, 255

Babson, Roger, 90, 158, 171–175, 177, 266, 533, 538, 547 balance sheet, 4, 10, 16, 28, 35, 168, 227, 259, 275, 300, 307, 308, 334, 337, 562, 567–570, 579, 583, 594, 612, 614, 616, 619, 624, 627, 688 Bank of England, 109, 110, 134, 135, 137, 145, 146 bankruptcy, 4, 5, 7, 23, 30, 31, 99, 143, 144, 150, 169, 230, 248, 324, 395, 590, 591, 594, 614, 618–621, 624, 625, 627–631 Bankruptcy Reform Act, 30, 629 bar charts, 496, 498 Barnard’s Act, 113–115, 117–119, 189, 190 741

November 3, 2010 10:47

742

9in x 6in

b921-Index

Valuation of Equity Securities

barometer, 172–174, 513 barometric index, 171, 172, 533 Basel I and Basel II accords, 380 behavioral finance, 76, 89, 461, 477, 521 Berkshire Hathaway, 6, 292–301 Bernstein, Peter, 50, 262–264, 268, 280, 306, 311, 345, 535, 563, 576 best efforts marketing, 36 beta, 91, 285, 309, 317, 327, 362, 365, 366, 407, 408, 413–415, 438, 449, 517, 603, 610, 697 bifurcating process, 455, 479 bifurcation, 428, 435, 451, 453–455, 480, 644, 689 Birkhoff, G., 416, 417, 431, 432, 434, 439, 440, 458 blue sky laws, 30 Boeing Corporation, 10, 18 Boltzmann, L., 416–419, 431, 434 bond indenture, 231, 628, 629 see also bond income bonds, 4, 5, 20–22, 24, 26, 27, 35, 45, 46, 102, 108, 136, 143, 150, 153, 155, 164–167, 173, 175, 181, 182, 185, 212, 213, 215, 230, 231, 234, 236, 269, 270, 273, 274, 277, 311, 312, 316, 318, 319, 329, 335, 336, 367, 375–377, 381–386, 421, 481, 500, 535, 542, 549, 553, 593, 627, 632, 633, 661, 665 book-to-market effect, 70 breadth indicators, 507–509 breakouts, 502, 503, 517 British East India Company, 126 brokers, 90, 111, 114–116, 118, 124, 140, 143, 144, 146, 147, 149–151, 188, 190, 191, 196, 197, 222, 491, 512 Bubble Act, 114, 140, 190 Buffett, Warren, 66, 85, 290, 292, 302, 327, 356, 542, 554, 556, 562, 568, 600, 603, 616, 620, 625 business cycle, 260, 430, 479, 548, 553–556 Buttonwood Agreement, 149, 150

buy-and-hold, 68, 76, 278, 290, 315, 355, 475, 553, 560, 561 Canada, 9, 28, 46, 217, 231, 240, 242, 261, 262, 317, 352, 355, 360, 385, 563, 566, 651, 652, 654–656, 661, 666–671, 673, 674, 676, 678, 681 Canadian Oil Sands/Canadian Oil Sands unit trust (COS), 368, 640, 642, 644, 650, 654, 667, 669, 677, 681–683 Canadian Securities course, 576, 583 candlestick charts, 496–499 capital allocation line, 398, 400, 404 capital asset pricing model (CAPM), 75, 308, 401, 406, 477 capital market line, 317, 400, 404 cash burn model, 627 cash flow, 3, 5, 16, 22, 121, 142, 144, 178, 194, 201, 226, 235, 259, 276, 282, 283, 289, 291, 299, 301, 307, 308, 313, 314, 329, 333–339, 342, 346, 347, 351, 353, 355–359, 361, 362, 364, 365, 369, 370, 374–376, 378, 380, 382, 383, 509, 527, 536, 537, 540–542, 545, 546, 562, 566, 568–570, 572, 573, 575–581, 583–585, 591, 594, 597, 600–603, 605–607, 610–612, 620–622, 624–626, 633, 643, 662, 669–672, 675, 679, 688, 693, 695, 698 cash flow statement, 16, 562, 569, 570, 572, 575, 578, 579, 581, 594, 605, 693 cash management, 312–314, 316 caution coefficient, 304 central limit theorem, 423, 424, 427 Chapter 11 filing, 590, 591, 596, 621, 625, 630 Chapter 7 filing, 621, 630 Chebyshev’s inequality, 423, 424 Chicago Board Options Exchange (CBOE), 196 Chicago Mercantile Exchange (CME), 645 Choquet capacities, 428

November 3, 2010 10:47

9in x 6in

Index

Cicero, 100, 101 Claviere, E., 142–145, 529 clean surplus equation, 342, 345, 346, 569 Clews, Henry, 149, 152 closed end fund, 36, 182, 228, 229, 233, 238, 563, 672 Coca-Cola, 162, 163, 301, 546, 586, 598, 599, 602–609, 611, 612 combat finance, 371, 542 Commercial and Financial Chronicle, 149, 161 commodity business, 640, 641 common stock, 4–9, 16, 18, 21–24, 26, 28, 35, 36, 46, 53, 58, 77, 78, 126, 154, 155, 161, 178, 181–183, 185, 186, 195, 229, 233–237, 252, 254, 255, 262, 265, 273–275, 277–281, 284, 285, 288, 289, 291, 292, 297, 298, 304, 307, 308, 329, 334, 335, 337–339, 342, 344–346, 355, 356, 362, 369, 375, 409, 475, 493, 495, 496, 498, 531, 535, 537, 541–543, 547, 549, 550, 552, 553, 560, 567–569, 579, 587, 589, 591–593, 596, 598–600, 603, 607, 610, 612, 619, 621–623, 625, 639, 662, 664, 669, 670, 679, 692 common stock theory, 181, 183 company analysis, 548 Compaq, 7, 625 Comte, Auguste, 79, 164 confirmation signal, 488, 491, 503 Constantinides, G., 316, 420 contrarian strategy, 509, 510, 514 contrary opinion, 509, 511–514 corporate bond, 4, 27, 166, 182, 234, 316, 336, 382, 633 corporate charter, 8 corporate tax, 6, 28, 231, 395, 674–676, 679, 698 corporation law, 7–9, 29, 30, 154 Cottle, S., see also Graham and Dodd/Graham, Dodd and Cottle (GDC), 235, 259, 271, 279, 337, 537, 556

b921-Index

743

covariance stationarity, 425, 431 Cowles Commission/Cowles Foundation, 264, 265, 267, 268 Cowles, A., 90, 264, 267, 268 credit risk, 27, 627, 628, 631, 633 credit spread, 627, 628 critical realism, 77 crown royalties, 373, 374, 677, 682, 683, 685, 691 cumulative voting rights, 7 curb trading, 112, 150 current yield, 24, 375, 377, 378 Damodaran, A., 338, 359–362, 365–367, 398, 409, 581, 603 Davidson, P., 50, 418, 420, 430, 431, 433, 455 day-of-the-week effect, 70 de la Vega, J., 57, 113, 116, 119–123, 511 de Witt, Jan, 106 debentures, 5, 136, 629, 637 default, 4, 31, 115, 146, 164, 166, 186, 232, 312, 376, 377, 380, 383–385, 398, 520, 539, 627–634, 637 default loss rate, 633 default risk, 146, 380, 384, 385, 398, 627–629, 631 defensive stocks, 548 Defoe, D., 113, 187, 189 Delta Airlines (DAL), 590 depreciation, 17, 165, 168, 289, 301, 302, 355, 373, 566, 567, 569, 574, 575, 578–582, 591–593, 595, 599, 605, 608, 616, 618, 620, 682, 685, 687, 691, 694 derivative security, 105, 113, 116, 117, 122, 186, 187, 192–195, 199–201, 207, 209, 594, 597, 619 Dice, Charles Amos, 177 diffusion, 435, 436, 442, 445, 447, 450, 452, 453, 455 Direct Order Turnaround (DOT), 207, 221

November 3, 2010 10:47

744

9in x 6in

b921-Index

Valuation of Equity Securities

discount rate, 300, 337–339, 361, 362, 371, 545, 552, 600, 603, 604, 607, 610, 643 discounted cash flow (DCF), 276 discounted dividend model (DDM), 342 see also dividend discount model diversifiable risk, 309, 393, 394 diversification, 20, 57, 77, 143, 144, 165, 166, 181, 182, 204, 234, 237, 245, 273, 277, 278, 290, 303–305, 322, 392, 393, 404, 405, 414, 415, 420, 561 see also portfolio diversification dividend, 4–9, 13–15, 23–25, 27, 28, 42, 44, 48, 61, 62, 78, 104, 110, 120, 121, 126, 132, 138, 169, 178, 182, 185, 212–214, 229, 231, 232, 235–237, 254, 258, 273, 274, 276, 277, 280, 281, 286, 287, 289, 293, 294, 299, 303, 307, 308, 333–347, 349–359, 361–363, 365–368, 377, 492–494, 534, 539, 540, 542, 543, 545–547, 549, 550, 556–559, 565, 566, 573, 576, 581, 583, 598, 599, 601–604, 607, 608, 610, 611, 622, 659, 670, 671, 673–675, 695 discount model, 337, 346, 362, 367, 368, 545, 601, 610 puzzle, 33, 86, 310, 354, 360, 456, 465, 494 yield, 6, 24, 214, 229, 274, 299, 333, 335, 338, 363, 377, 492, 494, 542, 549, 556–559, 695 Dodd, David, see also Graham and Dodd/Graham, Dodd and Cottle (GDC), 21, 22, 26, 126, 145, 148, 156, 159, 167, 168, 234, 252, 254–259, 265, 271, 273–276, 278–283, 285, 289, 291, 292, 298, 300, 322–324, 337, 471–476, 485, 539–541, 548, 556, 559–561, 640, 697 doji, 499 dollar cost averaging, 313 double smoothing, 520

double tops and double bottoms, 504 Dow Jones index, 489 Industrial Average (DJIA), 161–163, 224, 286, 494 Dow Jones Transportation Averages (DJTA), 487 Dow Jones & Co., 160, 161 Dow theory, 172, 265, 476, 481, 483–485, 488 Dow, Charles, 159, 160, 471, 483, 494 downgrade risk, 627, 628 Drew, D., 152, 153 dual class share, 9 dual moving average, see also oscillator, 506, 518, 520, 524 Duer, W., 150 Durand, D., 91, 268, 269 Dutch East India Company (VOC), 32, 104, 106, 120 dynamic trading strategy, 211, 213, 214, 219 see also portfolio insurance earnings, 8, 11–19, 24, 42, 75, 78, 138, 154, 168, 172, 178–183, 229, 233, 254, 258, 273–277, 279–281, 288, 289, 291, 292, 294, 297, 299–301, 307, 308, 324, 326, 334–337, 342, 345–351, 353–356, 358, 362, 363, 365, 366, 368, 474, 509, 533–535, 575, 577, 592, 612–618, 691 management, 612, 616–618 manipulation, 613–615 per share, 18, 19, 178, 294, 299, 362, 365, 366 economic profit model, 357, 577, 583, 584, 589, 611, 612 Economic Value Added (EVA), 357, 577, 582 efficient frontier, 57, 310, 317, 318, 396–401, 404, 406, 407, 411 efficient markets hypothesis (EMH), 3, 56, 58, 60, 61, 63, 75, 324, 420, 461, 462, 464, 476, 478, 509, 534 Elliott, R.N., 448, 465, 467, 479–482

November 3, 2010 10:47

9in x 6in

b921-Index

Index

Elton, E., 49, 67, 78, 79, 249, 312, 316–318, 394, 396, 412, 413 empiricism, 79, 81, 696, 697 EnCana, 642, 655, 678, 681 Enron, 8, 169, 612, 618, 619 epistemology, 67, 76, 78–82, 93, 514 equity risk premium, 46, 91, 360, 361, 367, 610 equity Security Classification, 20, 30 Definition, 4, 5, 33, 34, 59, 61, 62, 64, 86, 90, 146, 154, 167, 193, 227–229, 244, 246, 257, 258, 280, 310, 311, 313, 314, 346, 349, 354, 356, 375, 376, 382, 383, 387, 390, 392, 416, 425, 432–435, 454, 460, 499, 500, 509, 510, 515, 519, 521, 523, 534, 540, 556, 576, 578, 586, 605, 613, 629 ergodic process/ergodic stochastic process, 92, 389, 428, 430, 433, 434, 454, 455 ergodicity, 50, 59, 60, 92, 420–422, 425, 427, 430–434, 454 Erie Railway, 152 ex ante, 3, 20, 52, 53, 78, 91, 92, 94, 96, 224, 367, 376, 389, 402–406, 412, 428, 454–456, 474, 478, 479, 495, 544, 546, 591, 598, 604, 610, 642, 644, 697–699 Exchange Alley, 110–112, 187 exchange traded fund (ETF), 141, 237, 240, 241, 310 executive stock options, 615, 616 expected return, 44–47, 49, 61, 63, 64, 91, 166, 228, 303, 305, 309, 314, 319, 322, 324, 338, 345, 346, 360, 375, 387, 390–397, 399, 402, 403, 405–408, 410, 411, 603, 610 expected utility, 20, 49, 88, 304, 310, 400, 401, 404, 406, 409, 418 exponential moving average, 505, 525 ex post, 52, 53, 88, 89, 92, 94, 96, 219, 224, 302, 318, 335, 389, 402–405,

745

420, 454–456, 466, 478–480, 495, 520, 553, 597, 598, 633 Exxon-Mobil, 362 failed signal, 503 fair game model, 60, 61 Fama, E., 58, 63, 67–69, 72, 76, 85, 87, 92, 279, 305, 309, 351–354, 396, 409, 410, 477, 478, 509, 534, 552 feedback problem/feedback effect, 474 Feller, W., 59–61, 422–424, 435–437, 445 Fellowship of Merchant Adventurers, 103 Fibonacci numbers/Fibonacci sequence, 465 filter trading rule, 68 Financial Accounting Standard (FAS), 193 Financial Accounting Standards Board (FASB), 563 Financial Industry Regulatory Authority (FINRA), 210 financial statement analysis, 273, 535, 562, 566 Fiorina, Carla, 625 Fisher effect, 550 Fisher, Irving, 57, 84, 90, 158, 176, 177, 233, 235, 252, 264, 303, 360 Fisher, Philip, 90, 277, 278, 280–283, 285, 286, 291, 298, 531, 536, 543, 560, 561 Fitch rating, 24 fixed rate preferred stock, 26 flags/flags and pennants, 244, 502–504, 518 floating rate perpetuity, 379 Ford Motor Company, 564, 565, 570, 573 foreign securities, 105, 305, 405, 563, 660 Fort McMurray, 640, 647, 648, 650, 654 forward equation, 436–438, 444–447, 452, 453, 456, 457 frame dependence, 89

November 3, 2010 10:47

746

9in x 6in

b921-Index

Valuation of Equity Securities

France, 109, 130–132, 137, 140, 164, 197, 217, 242, 295, 352, 360, 661 franchise, 301, 626 free cash flow (FCF), 5, 346, 347, 356–358, 572, 576, 580, 581, 583, 584, 594, 601–603, 605–607, 611, 662, 675, 688 free cash flow to the firm (FCFF), 356 Friedman, M., 77, 79–82, 359 fundamental analysis, 3, 70, 126, 258, 273, 274, 298, 305, 368, 462, 463, 469, 470, 474, 509, 514, 534–537, 548, 556, 561, 640–643, 662, 697 Gadamer, H., 77, 83, 84, 87, 257 Gann, W., 471 Gaussian distribution, 455 see also normal distribution, normal density function General Electric, 6, 154, 161–163, 586 General Motors, 163, 337, 543, 545 generalized Pearson distribution, 448 generally accepted accounting principles (GAAP), 10, 562 Geneva, 144 geometric average, 47, 48, 361, 386 geometric average return, 47 geometric Brownian motion, 442, 443, 445 Gibbs, J., 417–419, 432 golden ratio, 479, 482 goodwill, 11, 299–301, 565, 568, 570, 571, 582, 609, 618, 690 Gordon dividend growth model/Gordon model, 604 Gordon, M., 148, 150–152, 255, 337, 338, 342, 344–347, 349, 354, 355, 358, 359, 361–367, 375, 547, 590, 601–604, 607 Gould, J., 152–154, 156 government securities, 108, 188, 230, 237 Graham and Dodd/Graham, Dodd and Cottle (GDC), 21, 22, 26, 126, 145, 148, 156, 159, 167, 168, 234, 252, 254–259, 265, 271, 273–276,

278–283, 285, 289, 291, 292, 298, 300, 322–324, 337, 471, 473–476, 485, 539–541, 548, 556, 559–561, 640, 697 Graham, Benjamin, 1, 85, 90, 121, 159, 556 growth optimal/growth optimal portfolio, 48 growth stock, 270, 273–277, 279–283, 287, 289–291, 477, 556, 559, 561 Hagstrom, R., 292 Hamilton, W.P., 150, 172, 174, 259, 265, 341, 471, 476, 481, 483, 484, 486, 489–492, 494 hammer, 499 Haugen, R., 323–327, 367 Hayck, F. von, 77 head and shoulders, 466, 501–503, 518 Hecksher, E., 103, 330 hedge fund, 31, 33–35, 202, 203, 209, 217, 226, 239, 240, 242, 244–249, 529 Heidegger, M., 83 heuristic/heuristic bias, 66, 89, 215, 257, 274, 276, 283, 512, 544, 560 Hewlett-Packard, 7, 162, 163, 286, 545, 586, 588, 625 Hicks, J., 418 Houghton, J., 108, 112, 115–117, 191, 198 human sciences, 77, 82–84, 257, 323, 474, 515 implied zero coupon interest rate, 383–385 income statement, 168, 259, 275, 562, 564, 566, 568–570, 572, 612, 624 incorporation, 5, 7, 8, 629, 650, 669 indenture, 4, 5, 231, 628–630, 669 see also bond indexes stock market, 24, 43, 69, 71, 72, 76, 94, 108, 124, 129, 140, 148, 158, 160, 161, 164, 174, 176–179, 183, 187, 194, 195,

November 3, 2010 10:47

9in x 6in

Index

216, 219, 220, 222, 226, 235, 252, 265–268, 275, 279, 281, 292, 296, 297, 309, 327, 353, 367, 462, 468, 470, 473, 475, 479, 481–486, 489, 495, 512, 527–529, 531, 548, 553, 554, 598, 622, 623 inductive method, 310, 323, 326 industry analysis, 664 inflation, 46, 50, 312, 313, 347, 371, 372, 548–553, 692 initial public offering (IPO), 35, 190, 622 institutional economics/institutionalism, 172, 259 interest rate, 25, 29, 44, 99, 126, 127, 141, 212, 221, 223, 263, 269, 313, 330, 359, 375–378, 380, 383–388, 394, 398, 404, 450, 473, 477, 536, 548, 549, 551–553 internal rate of return, 375, 383 Internal Revenue Code (IRC), 27 International Accounting Standards Board (IASB), 563 intrinsic value, 3, 18, 20, 43, 128, 155, 206, 235, 257–259, 276, 277, 288, 291, 292, 294, 296, 302, 315, 337, 342, 368, 371, 375, 472, 473, 475, 537, 539, 540, 561, 569, 600, 621, 622, 641, 643, 689, 698 intrinsic value approach, 473, 475, 537, 539, 540, 561 intuitionism, 95 invested capital, 62, 65, 114, 165, 317, 347, 358, 406, 582–584, 589, 611 Investment Advisors Act (1940) (IAA), 236, 244 investment bank, 36 Investment Company Act (1940) (ICA), 30, 236 Investment Company Institute, 239, 241 investment horizon, 212, 312–314, 398, 403, 409, 553, 559

b921-Index

747

investment strategy, 47–49, 77, 282, 283, 303, 317, 320, 387, 406, 495, 510, 513, 537, 539, 548, 559, 561 investment trusts see also unit trust, 4, 36, 141, 165, 166, 172, 177, 182, 184, 230–236, 305, 405, 617, 669, 673 Investor’s Intelligence, 510, 513 Italy, 9, 100, 102, 352 January effect, 70, 75, 76, 477 Japan, 217, 352, 498, 661 joint stock company, 5, 103, 140, 168 Kahneman, D., 326, 327, 461 Keynes, J.M., 50, 52, 84, 169, 184, 226, 252 Knight, Frank, 1, 52, 53, 55, 93, 95, 577 Lane Stochastic, 518, 523, 526 law of large numbers, 59, 61, 423, 428, 432 Law, John, 130–133, 137, 139 Le Maire, I., 107, 127–129 Lehman Bros., 237 leveraged buyout (LBO), 621, 625, 626, 671 limited liability, 5, 20, 34, 103, 104, 230, 231, 639, 670, 671 liquidation, 7, 23, 181, 620, 621, 624–627, 630 Little, J., 150 Loeb, G., 159, 264, 290 logical positivism, 77, 79, 80 London, 43, 104, 108, 110–119, 132, 140, 145–149, 157, 159, 164, 167, 172, 189, 190, 223, 228, 231, 232 London Stock Exchange, 115, 119, 147 loss aversion, 91, 326 lump sum investing, 314, 315 Macaulay, F., 90, 174, 259–264, 268, 269, 329, 342, 344, 554

November 3, 2010 10:47

748

9in x 6in

b921-Index

Valuation of Equity Securities

Magee, J., 327, 464, 472, 483, 496, 499–501, 503, 508, 515, 523, 528 Malkiel, B., 57, 58, 344, 462 managed fund, 165, 227–238, 240, 245–247, 249 management expense ratio (MER), 242 management fees, 239, 240, 669 margin of safety/margin of safety principle, 277, 278, 288, 294, 474, 556, 561, 600 MARhedge, 248 market capitalization, 273, 274, 364, 569, 672 market model, 64, 308, 408, 412–414, 517, 518, 535 market portfolio, 310–312, 316, 317, 319, 394, 401, 406–410, 412–415, 477, 558 market value added, 585 Markowitz, H., 44, 57, 78, 85, 144, 176, 264, 271, 302, 303, 305–310, 324, 396, 409, 420, 477 martingale, 59–63, 65, 66 martingale difference sequence, 62, 63 martingale process, 59, 63 Maxwell distribution, 418, 419, 431 McCloskey, D., 45, 85–89, 159, 462, 693 McKinsey and Company, 357, 577, 582, 583 mean reversion, 368 mean square ergodicity, 427 mean-variance expected utility, 304 mean-variance portfolio analysis, 78 mergers, 24, 30, 154, 538, 568, 621, 629 Merrill Lynch, 192, 513 Merton, R., 85, 94, 302, 309, 315 Microsoft, 162, 163, 528, 586, 617 Miller, M., 94, 260, 269, 289, 305, 306, 324, 436, 445, 557 minimum variance portfolio, 392, 405 Mirowski, P., 325, 417 Mississippi scheme, 130–133, 140, 191, 228, 258

Mitchell, W., 158, 259–261, 263, 268, 554 modern Finance, 20, 44, 52, 62, 67, 69, 76–79, 81, 82, 84, 85, 87, 90–94, 96, 156, 161, 166, 176, 181, 183, 245, 269–271, 273, 277, 278, 287, 289, 302, 303, 305–313, 318–327, 360, 389, 394, 412, 420, 425, 428, 461, 462, 467, 470, 472, 476–478, 494, 495, 510, 514, 515, 521, 534, 536, 548, 557–560, 622, 696 modern portfolio theory, 45, 144, 182, 304, 307, 308, 318, 468 Modigliani, F., 94, 269, 289, 305, 306, 324, 552, 557 momentum, 476, 478, 493, 507, 508, 515, 517–527 Moody’s Investor Services, 4, 631 Mortimer, T., 112–114, 119, 123–127, 167, 187–189 moving average, 47, 71, 464, 467, 471, 477, 492, 496, 504–507, 509, 515, 518–521, 524, 525 moving average system, 47, 477 multimodal density, 435 mutual fund, 36, 144, 177, 182, 228, 232, 236–240, 242, 245, 247, 249, 279, 313, 316, 463, 494, 514, 665, 669, 670, 672 mystical finance, 467, 476, 480 National Association of Security Dealers Automated Quotation system (NASDAQ), 33 National Bureau of Economic Research (NBER), 172 National Investors Corporation, 279 Neill, H., 510–512 neoclassical economics, 52 net current asset rule, 623 net present value (NPV), 577 New Era theory, 254, 255 New Finance, 270 New York, 6, 30, 36, 147–150, 152, 153, 159, 160, 162, 177, 179, 192,

November 3, 2010 10:47

9in x 6in

Index

196, 221, 223, 239, 255, 263, 268, 283, 361, 472, 487, 528, 623, 665 New York Stock Exchange (NYSE), 6, 149 normal distribution/normal density function, 213, 424, 435, 444, 446, 447 NYSE Euronext, 36, 43, 209–211 oil sands, 372, 640, 641, 644–651, 653–656, 667, 669, 676, 677, 679–683, 690, 692–694, 697–699 old finance, 274, 282, 302 open end fund, 238 Ornstein-Uhlenbeck Process (OU process), 444 oscillator, 464, 496, 502, 504, 506–509, 515, 518, 520, 522–527 over the counter (OTC), 36 par value, 8, 11, 24, 26, 43, 126, 138, 166, 229, 376, 380, 382, 570, 571, 595, 609, 624, 633, 634 Paris bourse, 97, 140, 141, 144, 145, 147, 191, 229 partial differential equation (PDE), 435 participating preferred stock, 24 path dependent/path independent, 214, 315, 428 Pearson system of distribution, 437 Penman, S., 346, 347, 535, 562–564, 572, 578, 596, 598, 601, 611, 662, 663 pennants see also flags and pennants, 501, 503, 504, 518 perfect capital markets, 307, 308, 395, 557 perpetuity, 24, 334, 354, 375, 378–381, 547, 611 phenomenological approach, 435, 455 Philadelphia, 148, 197, 255 Philosophy of investment, 57 pitchfork bifurcation, 428, 453 point and figure chart, 497

b921-Index

749

Polybius, 100–102 portfolio diversification, 143, 144, 392 portfolio insurance, 207, 211, 212, 215, 216, 219, 220, 222–224, 227, 310 portfolio management, 165, 184, 219, 224 portfolio theory, 144, 182, 273, 304, 307, 308, 312, 318, 323, 394, 468 Portus Alternative Asset Management, 244 positivism, 69, 77, 79–82, 94, 251, 308, 322, 326, 476, 514, 696 Post Keynesian/Post Keynesianism, 50, 417, 431, 434, 435 preferred stock, 4–8, 21–28, 178, 234, 274, 377, 378, 567, 568, 579–581, 622 present value of growth opportunities (PEG ratio), 354 price to book value (P/BV) ratio, 346 price-earnings (P/E) ration, 179, 345, 560 primary issue, 35, 36, 277 priority of claim, 4, 5, 22 Procter and Gamble, 507 program trading, 207, 211, 222, 224 prospect theory, 326 proxy fight/proxy vote, 7 Public Utility Holding Company Act (1935), 30 public utility preferred stock, 27 publicani, 100–102, 227 quadratic utility, 316 quartic exponential density/quartic exponential distribution, 449, 450 random walk, 58, 65, 66, 121, 161 random walk hypothesis, 58 rational bubble, 339–341 rebalancing, 47, 48, 214, 278, 313–315, 317, 319–321, 359, 398, 492 recovery rate, 633, 634, 637, 646, 650, 696

November 3, 2010 10:47

750

9in x 6in

b921-Index

Valuation of Equity Securities

rectangles, 481 reflecting barriers, 435, 436, 440–442 relative strength, 476, 515–518 relative value approach, 371, 537, 539, 544, 545 remarketed rate preferred stock, 25 Remington Rand, 176 rescontre, 114, 122–124 residual income model, 346, 347, 349, 355, 587, 601–605, 610–612 see also abnormal earnings model resistance level, 466, 500, 502 resource companies, 285, 590, 621, 622, 640–643 retained earnings, 11, 16, 294, 307, 308, 334, 335, 345, 351, 583, 585 return on equity (ROE), 294, 346, 587 return on invested capital (ROIC), 582 Rhea, R., 471, 481, 482, 484, 486, 489–492 rhetoric, 85–87, 90, 521, 548 rights issue, 5, 6, 36 risk, 20, 25, 26, 36, 44–46, 50, 52, 53, 55, 56, 64–67, 75, 77, 91, 95, 122, 141, 144, 164, 178, 181, 193, 211, 213, 216, 217, 219, 222, 228, 232, 247–249, 262, 271, 273, 283, 302–305, 311, 312, 314, 315, 317, 318, 322, 326, 340, 360–363, 367, 377, 391–394, 396, 399–401, 405–407, 413–416, 420, 470, 471, 477, 494, 514, 552, 553, 558, 560, 562, 603, 610, 619, 628, 666 risk premium, 46, 91, 360–362, 367, 407, 413, 414, 553, 603, 610 riskfree rate/riskless rate, 314, 398, 400, 406, 407, 409, 411 Royal Exchange, 104, 110–112, 140, 228 see also London Exchange Rubinstein, M., 176, 214, 216, 220, 271, 303, 305, 306, 308 Rue Quincampoix, 133 runs test, 68, 69

Russell, R., 295, 474, 483–486, 488, 489, 491–493 Saint Peterburg paradox, 337 see St. Petersburg paradox Salomon Bros./Salomon Smith Barneyt, 220 Samuelson, P., 46, 58, 92, 269, 316, 320–322, 418, 420 Sarbanes–Oxley Act (2002), 8, 30, 32, 613 Schaefer, G., 483, 484, 491, 492 science of investments, 166 secondary issue, 35 Securities Act (1933), 30, 32, 155, 179, 195–197, 199, 236, 245, 333 Securities and Exchange Act (1934), 30, 32, 333 Securities and Exchange Commission (SEC), 30, 196, 236 security analysis, 26, 30, 77, 119, 124, 126, 149, 156, 158, 160, 167, 168, 176, 179, 254–258, 271–277, 280, 282, 285, 292, 298, 303, 309, 310, 321, 323, 358, 371, 471, 474, 509, 535, 537, 539, 541, 542, 560, 562, 569, 575, 576, 584–586, 589, 590, 600, 602, 631, 662, 663, 665–667 security market line, 408 security/securities, 3, 4, 8, 18, 20–22, 24–27, 29–32, 35, 43, 44, 46–48, 50, 52–55, 57–59, 61, 62, 64–69, 75, 77, 84, 85, 88–90, 92–95, 101, 105, 110, 113, 114, 116, 117, 119, 121, 122, 124, 126–129, 140, 141, 144, 145, 148, 149, 152, 156–160, 164, 167, 168, 170, 171, 174, 176, 179, 183, 184, 186, 187, 190–195, 199–201, 205–207, 209, 210, 212, 222, 224–230, 232–234, 236–240, 242, 244, 246, 248, 251, 252, 254–259, 262, 270–285, 291, 292, 294, 298, 302–304, 307–313, 315–317, 319, 321–323, 327, 333, 334, 337, 342, 345, 358, 359, 368, 369, 371, 375, 379, 380, 391–398, 406, 408, 410,

November 3, 2010 10:47

9in x 6in

Index

411, 414–416, 421, 424, 454, 461–463, 465, 467–474, 477, 478, 495, 498, 509–511, 517, 522, 528, 529, 534–539, 541, 542, 545–550, 553, 556, 560–564, 569, 572, 575, 576, 584–586, 589–591, 594, 596, 597, 600–602, 611, 616, 618, 619, 621, 627–629, 631, 637, 640–644, 658–660, 662–668, 670, 690, 696–698 See’s Candies, 295, 300 self-regulation, 31, 32, 151, 152, 156, 197, 205, 255 Shackle, G., 91, 95–97, 428–430, 454–456, 479, 480, 643, 644, 690, 698 share repurchases, 10, 342, 346, 350–352, 354, 355 shares, 5–9, 11–16, 18, 21–28, 32, 34, 44, 56, 99–110, 112, 114, 115, 119–122, 124, 126–130, 132–134, 140, 143, 145–147, 153–157, 164–167, 171, 180, 184–187, 196, 197, 204, 207, 208, 221, 223, 228–232, 234–238, 240, 244, 274, 277, 278, 287, 288, 308, 315, 330–332, 351, 354, 373, 375, 391, 474, 486, 535, 563, 565, 568–571, 576, 583, 595, 599, 606, 607, 609, 612, 619, 623, 640, 653, 672, 685, 687 Sharpe ratio, 322, 403, 476 Sharpe, W., 305, 308, 314, 316, 322, 396, 403, 404, 409, 476, 550–552 Sherman Anti-Trust Act (1890), 30, 154 short sale/short selling, 35, 107, 119, 123, 129, 130, 196, 201–203, 222, 225–227, 248, 312, 317, 318, 396, 463 short squeeze, 117, 151 Siegel, J., 44, 161, 176, 177, 462, 463, 510, 513, 549, 550, 553, 554, 559 signal line, 525 single index model, 409, 413 see also market model

b921-Index

751

small firm effect, 70, 76, 477 Smith, E., 80, 158, 159, 178, 181–183, 187, 192, 233, 327, 333, 335, 360, 548, 549 South Sea Bubble, 114, 118, 130, 131, 134, 136–138, 190, 254 Southwest Airlines, 487, 588, 590 speculation, 21, 26, 52, 55, 90, 102, 107, 115, 116, 118, 122, 124, 129, 130, 133, 140, 150, 151, 155, 156, 160, 169, 182, 185, 186, 190, 200, 221, 235, 255–257, 272, 275, 303, 465, 469, 470, 473, 495, 501, 512, 514 St. Petersburg paradox, 270 Standard and Pool’s 500 (S&P 500), 179 standard deviation, 46, 47, 369, 391–393, 399, 408, 424 standard deviation of return, 46 standard normal density, 444, 446 see also normal distribution Standard Oil, 154, 155, 163 standby underwriting, 36 statement of stockholders’ equity, 572 see also statement of stockholders’ equity stationary distribution, 92, 418, 419, 430, 432, 433, 435, 437, 438, 442, 444–446, 448–452, 454–456 stationary process, 425–427, 434, 441 statutory voting, 7 steam assisted gravity drainage (SAGD), 646 Stern Stewart & Co., 577 stochastic differential equation (SDE), 431 stochastic process, 59, 60, 62, 389, 420–422, 424–428, 430, 431, 433, 434, 445, 455, 479, 480 stock/stocks, 4–9, 16, 18, 20–28, 30, 31, 35, 36, 45, 46, 49, 53, 58, 75–78, 89, 108, 110, 112, 118, 120, 121, 123, 124, 126, 127, 130, 140, 145–151, 154–158, 160, 161, 165–167, 170, 171, 174, 177–183,

November 3, 2010 10:47

752

9in x 6in

b921-Index

Valuation of Equity Securities

185–188, 191, 192, 194, 195, 197, 202, 204, 207, 208, 211–213, 215, 216, 220–223, 228, 229, 233–237, 239, 248, 252, 254, 255, 257, 262, 265–267, 270, 273–292, 297, 298, 304, 305, 307, 308, 312, 316, 318, 319, 321, 322, 326, 327, 329, 333–335, 337–339, 342, 344–346, 350, 352, 354–356, 362, 367, 369, 375, 377, 378, 397, 409, 413, 414, 421, 464, 473, 475, 477, 479, 484, 486, 490–498, 500, 501, 508–510, 513, 516, 517, 521, 522, 528, 529, 531, 535–543, 546–554, 556–561, 567–569, 579–581, 587, 589, 591–593, 596, 598–600, 603, 607, 610, 612, 619, 621–623, 625, 639, 643, 662, 664, 665, 669, 670, 679, 692 stockholders’ equity statement, 562, 568, 570, 571 see also statement of stockholders’ equity stockjobbing/stockjobber, 110, 113, 114, 117, 118, 124, 133, 186–190, 192, 199, 203, 205, 209 strategic asset allocation, 311, 312, 315, 318–320 strict stationarity, 425, 433 strong law of large numbers, 416, 432 Sturm-Liouville theory (S-L), 435, 436, 444 submartingale, 61, 62 Sunbeam, 614 Suncor, 567, 650, 655, 656, 676, 679 Swift, Jonathan, 1, 113 Syncrude, 368, 646, 647, 667 syndicates, 141, 167 systematic risk, 65, 75, 213, 394, 407, 408, 414, 471, 494, 517 see also nondiversifiable risk

tangency portfolio, 312, 317, 401, 403–411 Tax Reform Act (1986), 27, 28 taxation, 28, 29, 32, 185, 298, 354, 667, 670, 671, 674, 675, 693, 695, 696 Taylor, H., 59, 60, 69, 97, 124, 141–144, 229, 420, 425–427, 435, 438, 441, 457 technical analysis, 47, 68–70, 75, 89, 389, 406, 428, 462–466, 470–481, 494–504, 507, 509, 511, 514–518, 521–523, 525–529, 534, 537, 696, 697 technological growth factor, 280 tilt, 319–321 time bargain, 108, 110, 113, 116–118, 133, 190 time series, 44, 46, 47, 63–65, 92, 266, 403, 413, 420, 421, 428, 433, 451, 464, 477, 496, 504 Toronto Stock Exchange, 240, 669, 672 tracking error, 320, 321 trading range, 499, 501–504, 506, 507, 509, 517, 522 transaction costs, 64, 212 transition density/transition probability density, 432, 437, 443, 448, 452, 454 Treasury security, 248 triangles, 481, 504 Trust Indenture Act (1939), 236 trusts, 4, 23, 36, 141, 154, 165, 166, 172, 177, 182, 184, 230–237, 255, 304, 305, 368, 405, 617, 669–676, 678, 679, 688 turn-of-the-year effect, 75, 76 Tversky, A., 326, 327, 461 Twain, M., 639, 696 two fund separation, 308, 310–313, 316, 317, 406, 412

tactical asset allocation, 278, 319–322 takeover, 7, 23, 24, 154, 248, 297, 621, 625, 679

uncertainty, 43, 50, 52–56, 88, 90, 91, 94–96, 170, 171, 206, 210, 211, 235, 252, 303, 323, 418, 419, 428, 429,

November 3, 2010 10:47

9in x 6in

Index

434, 455, 456, 467–469, 478, 624, 630, 642, 643, 690, 692, 698 underwriting, 35, 36, 278, 688 unit trusts, 236, 670, 671, 673, 674, 676, 678, 679 United Airlines (UAL), 590, 624 unseasoned issue, 35 unsystematic risk, 394 see also diversifiable risk value driver, 585–590, 596–598, 600, 601, 662, 697 value investing, 167, 226, 274, 292, 300, 301, 315, 368, 510, 540, 556, 560, 561, 607, 622, 643 value stock, 120, 477, 556, 559, 591 Vanderbilt, C., 152–154 variance, 46, 47, 49, 50, 60, 66, 78, 91, 92, 212, 303, 304, 309, 310, 319, 341, 389–397, 399–407, 409–412, 414, 415, 420, 421, 423–427, 431, 435, 444, 447, 449, 450, 455, 456, 477, 604, 660, 661, 697 Veblen, T., 259, 260 vernacular finance/vernacular analysis, 85, 88–90, 183–185, 225, 226, 302, 311, 408, 412, 478, 618, 696 von Neumann, J., 81, 96, 416, 418, 431, 432, 434 voting rights, 7–9, 23, 24, 154 Wall Street, 33, 149–152, 155, 156, 158–161, 174, 192, 265, 361, 471, 476, 478, 483–485, 508, 539, 540, 641, 663, 665

b921-Index

753

Wall Street approach, 156 Wall Street Journal, 149, 158, 160, 161, 174, 483 warrant bond, 21 warrants, 4, 5, 42, 133, 139, 153, 193, 195, 619, 621 weak law of large numbers, 423 weekend effect, 70 weighted average cost of capital (WACC), 358, 580, 582, 601 Weiner process, 450, 453 Weiner, N., 418, 419, 450, 453 whipsaw, 507, 524, 525 Williams, J.B., 158, 233, 235, 277, 278, 291, 303, 305, 306, 329, 337, 342, 367, 526 Withers, H., 149, 158, 167–171, 256, 271, 600 Wittgenstein, L., 534 Worldcom, 8, 30, 612, 616, 618, 619, 628 Wyckoff, R., 470, 471 yield curve, 25, 212, 382, 383, 385, 386, 388 yield to maturity, 376, 377, 382–384, 386 zero coupon bond, 376, 377, 383, 384, 387, 388 Zweig, M., 508, 525 ZZZZ Best, 614