Understanding Investments: Theories and Strategies [1 ed.] 0415891620, 9780415891622

Table of contents :
Dedication
Contents
List of Illustrations
Preface
Part I: INVESTMENT BASICS
1 The Investment Framework
2 The Investment Decision Process and Investment Strategies
3 Fundamentals of Risk and Return
Part II: FINANCIAL MARKETS, INTERMEDIARIES, AND INSTRUMENTS
4 The Global Financial Environment
5 Money and Capital Market Instruments and Strategies
6 Investment Bankers and Investment Companies
Part III: PORTFOLIO THEORY
7 Diversification and Asset Allocation
8 Efficient Diversification and Capital Market Theory
9 Market Efficiency and Behavioral Finance
Part IV: EQUITY PORTFOLIO MANAGEMENT
10 Equity and Fundamental Analysis
11 Equity Valuation and Investment Strategies
Part V: DEBT SECURITIES
12 Bond Fundamentals and Valuation
13 Bond Portfolio Management and Performance Evaluation
Part VI: DERIVATIVE MARKETS AND INSTRUMENTS
14 Options Markets and Valuation
15 Futures Markets and Strategies
16 Other Topics in Investments
Appendix
Index

Citation preview

Understanding Investments

The author’s main goal in writing Understanding Investments is to present the classic theories and strategies in the field of finance in a new, intuitive, and practical way. By approaching these concepts and applications from an economics point of view, this text offers students the story behind the concepts. This approach allows students to interpret the material, rather than memorize and regurgitate it. Incorporating real-life, currentevent examples, ‘international focus’ sections, and ‘economic analysis’ detours, the text offers context and grounding information to students truly looking, as the title indicates, to understand investments. Dr. Nikiforos T. Laopodis is a Finance and Economics Professor at Fairfield University, U.S. and at the Athens Laboratory of Business Administration at The American College of Greece, Greece. His areas of specialization are international finance and financial econometrics. He has taught at various universities in the U.S. and in Greece and has been invited to give lectures to universities and international organizations in Europe. He has published extensively in the fields of finance and financial economics focusing on interest rates, exchange rates, stock markets as well as monetary and fiscal policies. He is a regular member and contributor to professional organizations such as Financial Management Association and Eastern Finance Association.

Understanding Investments Theories and Strategies Nikiforos T. Laopodis

First published 2013 by Routledge 711 Third Avenue, New York, NY 10017 Simultaneously published in the UK by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business © 2013 Taylor & Francis The right of Nikiforos T. Laopodis to be identified as author of this work has been asserted by him/her in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging in Publication Data Laopodis, Nikiforos T., 1961Understanding investments : theories and strategies / Nikiforos T. Laopodis. p. cm. Includes bibliographical references and index. ISBN 978-0-415-89162-2 (hardback : alk. paper)—ISBN 978-0-415-89163-9 (pbk. : alk. paper)— ISBN 978-0-203-10577-1 (ebook : alk. paper) 1. Investments. 2. Risk management. 3. Portfolio management. 4. Securities. 5. Derivative securities. I. Title. HG4521.L3186 2012 332.601—dc23 2012003459 ISBN: 978-0-415-89162-2 (hbk) ISBN: 978-0-415-89163-9 (pbk) ISBN: 978-0-203-10577-1 (ebk) Typeset in Minion by Apex CoVantage, LLC

This textbook is dedicated to my special-needs son, Haralabos, who was patiently waiting for me to complete each section of each chapter before we started playing and learning.

v

CONTENTS

List of Illustrations

xxiii

Preface

xxix

Part I

INVESTMENT BASICS

Chapter 1

The Investment Framework Chapter Objectives Introduction The General Financial and Economic Environment Definition of Investments The General Investment Environment Securities Classification of Securities Equity Securities Debt Securities Derivative Securities Types of Investors Financial Markets and Intermediaries The Roles of Financial Markets The Roles of Financial Intermediaries The Objectives and Constraints of Investors Objectives of Investors Constraints of Investors The Investment Management Process The Role of Investment Information vii

3 3 3 3 3 4 5 5 5 6 6 6 7 7 8 9 9 10 11 12

viii s Contents

Chapter 2

Agency and Ethical Issues in Investing Asymmetric Information The Agent-Principal Problem Ethics in the Marketplace Social Responsibility So Why Study Investments? Chapter Summary The Plan of the Textbook Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems

13 14 15 16 17 18 20 21 21 22 23 23 25

The Investment Decision Process and Investment Strategies Chapter Objectives Introduction The Investment Process The Risk-Return Trade-Off The Asset Allocation Step in the Investment Process The Security Selection Step in the Investment Process General Investment Philosophies and Strategies Some Prominent Investment Philosophies Harry Markowitz Paul Samuelson John Bogle Warren Buffett What Is Your Investment Philosophy? Some Investment Strategies Top-Down and Bottom-Up Approaches to Investing Active and Passive Investment Strategies Other Investment Strategies Dollar-Cost Averaging Margin Purchases and Short Sales Margin Purchases Short Sales Types of Markets and Orders Types of Trading Markets Direct Market Brokered Market Dealer Market Auction Market

26 26 26 27 27 28 30 31 31 31 31 32 32 34 35 35 37 39 40 41 41 44 45 45 45 45 46 46

Contents s ix

Types of Trading Orders Market Orders Limit Order Finding the Equilibrium Price of a Share Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems

46 46 46 47 49 50 50 51 51 53

Chapter 3

Fundamentals of Risk and Return Chapter Objectives Introduction Measuring Return Holding Period Return Return over Multiple Periods Arithmetic Mean Geometric Mean The Effective Annual Rate Yield Definitions and Conventions Real Rate of Return Expected Rate of Return Measuring Risk Calculating the Risk of a Single Asset Required Returns and Risk Aversion Sources of Risk Risk and Investor Economic Decisions Utility and Risk Aversion Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems Appendix: A Brief Review of the Time Value of Money

56 56 56 56 57 58 59 59 60 61 61 63 64 64 68 69 71 71 73 74 75 75 76 77 78

Part II

FINANCIAL MARKETS, INTERMEDIARIES, AND INSTRUMENTS

Chapter 4

The Global Financial Environment Chapter Objectives Introduction The Functions of the Global Financial Market

85 85 85 86

x s Contents

Chapter 5

Economic Function Pricing Function Provision of Services Other Functions The Securities Exchanges US Organized Stock Exchanges US Over-the-Counter Securities Markets Some US Stock Market Indexes Some International Stock Exchanges The London Stock Exchange The Tokyo Stock Exchange The Prague Stock Exchange The Brazilian Stock Exchange The US Bond Market The International Bond Market Trading on the Exchanges Clearing Procedures Brokerage Services Trading Costs Automatic Trading Mechanisms Globalization and Regulatory Structure of International Stock Markets Globalization and Trends Investing Internationally and International Return Regulatory Structures in the US Exchanges Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems Appendix: Calculating a Stock Market Index

86 86 87 88 89 90 93 95 95 96 97 97 97 97 98 99 99 99 100 102 104 104 105 107 108 108 109 109 110 111 113

Money and Capital Market Instruments and Strategies Chapter Objectives Introduction The Money Market and Its Instruments The Money Market and Its Characteristics Money Market Instruments Nonmarketable Securities Marketable Securities Treasury Bill

115 115 115 116 116 117 117 117 117

Contents s xi

Chapter 6

Commercial Paper Bankers’ Acceptances Repurchase Agreements Federal Funds LIBOR Eurocurrency Yields and Spreads in Money Market Instruments The Capital Market and Its Instruments The Capital Market and Its Characteristics Fixed-Income Securities Government Bonds Municipal Securities Agency Bonds Corporate Bonds Yields and Spreads in Capital Market Instruments Equity Securities Derivative Securities Investment Risks in Financial Markets Some Investment Strategies Some Money Market Investment Strategies Deposit and Liability Management Strategy Market-Neutral Strategy Pairs-Trading Strategy Some Capital Market Investment Strategies Enhanced Cash Management Strategy Top-Down and/or Bottom-Up Strategies Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems

121 122 123 124 126 127 129 129 129 131 131 132 133 134 135 136 137 138 139 139 139 140 141 141 141 141 142 142 143 143 144 145

Investment Bankers and Investment Companies Chapter Objectives Introduction Investment Banking The Primary Market Shelf Registration The Investment Banker Initial Public Offering The Investment Companies Industry

148 148 148 148 148 150 150 152 155

xii s Contents

Functions of Investment Companies Types of Investment Companies Unit Investment Trust Closed-End Investment Companies Open-End Investment Companies Money Market Mutual Funds Equity Funds Bond Funds Index Funds International Funds Balanced Funds Asset Allocation Funds Fee Structure of Mutual Funds Performance of the Mutual Fund Industry Other Types of Investment Companies Real Estate Investment Funds Hedge Funds Exchange-Traded Funds Some Strategies in Mutual Fund Investments Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems Part III

PORTFOLIO THEORY

Chapter 7

Diversification and Asset Allocation Chapter Objectives Introduction The Diversification Principle Types of Diversification Naive or Random Diversification International Diversification Efficient Diversification Covariance and Correlation The Asset Allocation Decision The Process of Asset Allocation Some Approaches to Asset Allocation Implementing Asset Allocation Approaches Examples of Asset Allocation

157 158 158 159 161 161 162 162 163 163 163 163 163 168 169 169 170 170 173 175 175 176 177 177 179

185 185 185 186 186 186 188 189 190 192 193 195 197 197

Contents s xiii

Chapter 8

Risky Portfolios and Combined Portfolios Some Practical Problems for Asset Allocation The Capital Allocation Line Borrowing and Lending Opportunities on the CAL The Capital Market Line and Investment Strategies Asset Allocation and Risk Aversion Some Common Diversification Fallacies The Insurance Principle Time Diversification Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems Appendix A: Review of Regression Analysis Appendix B: How to Compute the Covariance and Correlation in Excel

197 201 202 204 206 207 209 209 209 211 211 212 213 213 214 216

Efficient Diversification and Capital Market Theory Chapter Objectives Introduction The Markowitz Diversification Approach The Markowitz Two-Asset Portfolio The Optimal Risky Portfolio and the Capital Allocation Line The Efficient Frontier Capital Market Theory The Capital Asset Pricing Model Assumptions of the CAPM Implications of the Assumptions Implication 1 Implication 2 Implication 3 The Capital and Security Market Lines Uses of CAPM Criticism of CAPM The Arbitrage Pricing Theory Comparing the CAPM and the APT Portfolio Performance Evaluation CAPM, APT, and Investment Decisions Chapter Summary Applying Economic Analysis

221 221 221 222 222 227 230 232 232 233 233 233 234 235 236 239 239 240 243 244 246 247 248

219

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Chapter 9

The 130/30 Strategy Lessons of Our Times Key Concepts Questions and Problems Appendix A: How to Find and Graph the Optimal Two-Asset Portfolio Using EXCEL Appendix B: The Single-Index Model

249 250 250 251

Market Efficiency and Behavioral Finance Chapter Objectives Introduction The Efficient Market Hypothesis The Notion of Market Efficiency The Forms of Market Efficiency Weak Form Semistrong Form Strong Form Implications for the Efficient Market Hypothesis Implications for Technical Analysis Implications for Fundamental Analysis Implications for Active and Passive Investment Strategies Implications for Investment Managers Implications for Asset Pricing Models Anomalies and Tests of Market Efficiency Market Anomalies Return Patterns Day-of-the-Week Effect January Effect Short- and Long-Horizon Returns Size and P/E Effects Announcement Effects Other Effects Summary of Market Efficiency Tests Weak Form of Market Efficiency Semi-strong Form of Market Efficiency Strong Form of Market Efficiency Is the Stock Market Efficient? Behavioral Finance Biases in Information Processing Biases in Behavior Models of Human Behavior Implications for Technical Analysis

261 261 261 262 262 263 264 264 264 264 265 266 269 271 271 272 273 273 273 274 274 276 276 278 278 278 279 279 279 280 283 283 285 286

254 256

Contents s xv

Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems Part IV

287 288 288 289 290 291

EQUITY PORTFOLIO MANAGEMENT

Chapter 10 Equity and Fundamental Analysis Chapter Objectives Introduction Equity Securities Common Stock Characteristics Shareholder Equity Shareholder Rights Voting Privileges Types of Common Stock Dividends and Splits Preferred Stock Characteristics Stock Market Quotations Management of an Equity Portfolio Passive Equity Portfolio Management Individual Investors Institutional Investors Active Equity Portfolio Management Individual Investors Institutional Investors International Equity Investing Fundamental Analysis Macroeconomic Analysis Macroeconomic Magnitudes Economic Policies The Business Cycle Industry Analysis Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems Appendix: Guidelines for Conducting Industry Analysis

297 297 297 298 298 298 298 299 300 300 302 303 304 304 304 305 308 308 309 310 311 312 313 314 318 322 325 325 326 328 328 330 331

xvi s Contents

Chapter 11 Equity Valuation and Investment Strategies Chapter Objectives Introduction Equity Prices and Returns Some General Valuation Measures Book Value Price/Book Value Price/Sales Value Liquidation Value Replacement Value The Dividend Discount Model and Its Variants The Dividend Discount Model The Constant Growth Model The Multistage Dividend Growth Model Using Earnings Instead of Dividends Other Equity Valuation Techniques Present Value of Free Cash Flows Options Valuation Approach Economic Profit Other Issues in Equity Valuation The Impact of Inflation on Stock Values Information Signals/Content of Dividends The P/E Ratio and the Stock Market Some Strategies on When to Buy/Sell Equities When to Buy/Sell a Stock Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems Part V

333 333 333 333 337 337 338 338 338 339 340 340 342 345 346 352 352 353 355 356 356 356 357 361 361 363 364 364 365 366 367

DEBT SECURITIES

Chapter 12 Bond Fundamentals and Valuation Chapter Objectives Introduction Overview of the Global Bond Market The International Bond Market The US Bond Market Overview of Bond Basics Features of a Bond

373 373 373 374 374 375 376 376

Contents s xvii

Bond Types and Characteristics By Type of Issuer Government Bonds Other Government and Government-related Bonds Corporate Bonds International Bonds and Eurobonds By Bond Feature By Other Characteristics Default Risk Bond Determinants and Covenants Junk Bonds Bond Pricing Basic Bond Valuation Formulas The Inverse Relationship between Prices and Yields Bond Yield Measures Current Yield Yield to Maturity Yield to Put Yield to Call Duration and Convexity Duration Convexity The Yield Curve Theories Explaining the Shape of the Yield Curve Market Expectations Theory Liquidity Preference Theory Market Segmentation Theory Preferred Habitat Theory Significance of the Yield Curve A Simple Strategy Using the Yield Curve Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems Chapter 13 Bond Portfolio Management and Performance Evaluation Chapter Objectives Introduction Overview of the Bond Invstment Management Process Identification of Investor Objectives and Constraints

376 376 376 378 382 382 383 384 384 385 385 386 386 388 393 393 393 394 395 395 395 399 400 401 402 403 404 404 404 406 407 408 409 409 410 411 415 415 415 416 416

xviii s Contents

Establishment of Investment Policy Selection of a Bond Portfolio Management Strategy Monitoring and Evaluating Portfolio Performance Passive Bond Investment Strategies Buy-and-Hold Portfolio Strategy Indexing Bond Strategies Pure Indexing Strategy Enhanced Indexing Strategy Immunization Strategy Rebalancing Dedication Strategy Active Bond Portfolio Strategies Interest Rate–Anticipation Strategy Credit Analysis Valuation Analysis Bond Swap Strategies Substitution Swap Yield Swap Yield Curve Strategies Horizon Analysis Other Active Management Strategies Horizon Matching Technique Contingent Immunization Bond Portfolio Performance Measurement and Evaluation Bond Portfolio Performance Measures The Arithmetic Average Rate of Return The Geometric Rate of Return The Dollar-Weighted Rate of Return Bond Portfolio Performance Evaluation Performance Attribution Analysis Bond Market Efficiency and Portfolio Management Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems Part VI

417 419 420 420 421 421 422 423 423 425 427 428 428 429 429 429 430 431 432 433 434 434 435 435 436 436 436 436 437 438 441 441 442 443 444 445 446

DERIVATIVE MARKETS AND INSTRUMENTS

Chapter 14 Options Markets and Valuation Chapter Objectives Introduction

451 451 451

Contents s xix

An Overview of the Options Market Basic Option Concepts Call and Put Option Concepts Profits and Losses on Options Options Payoffs at Expiration The Market for Options The Options Clearing Corporation Option Market Participants Options Products Securities with Options Some Option Trading Strategies Covered Call Protective Put Some Practical Issues Collar Straddle Married Put Spread Strategies Speculating with Options Option Valuation Fundamental Option Valuation Concepts Binomial Option Pricing The Black-Scholes-Merton Option Valuation Model Using the Black-Scholes-Merton Formula Put-Call Parity Formula Using Stock Index Options Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems Chapter 15 Futures Markets and Strategies Chapter Objectives Introduction The Futures Contract Elements of Futures Contracts The Clearinghouse Settlement and Margin Reversing Trades An Overview of the Futures Market Economic Functions of the Futures Market

451 452 452 453 455 456 458 459 459 460 460 461 462 462 464 465 466 467 468 469 470 472 474 479 480 481 483 483 484 485 486 488 491 491 491 492 493 493 495 497 497 498

xx s Contents

Price Discovery Risk Reduction Hedging Speculating Regulation of Futures Markets International Futures Exchanges The Commodity Futures Market Futures and Spot Prices Spot Futures Parity Basis Risk Financial Futures Contracts Some Financial Futures Contracts Stock Index Futures Interest Rate Futures Currency Futures Some Useful Information on Financial Futures S&P Futures versus Fair Value Leverage Futures Trading Strategies Hedging Speculating Program Trading and Index Arbitrage Using Currency Futures Arbitrage Trading Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems Chapter 16 Other Topics in Investments Chapter Objectives Introduction International Parities and Some Strategies Useful Concepts Interest Rate Parity Carry Trade International Arbitrage Credit Derivatives The Market for Credit Derivatives Credit Default Swap

498 499 499 499 500 502 503 505 505 507 508 508 508 509 510 512 512 513 514 514 515 515 517 517 517 518 519 519 520 521 524 524 524 524 525 525 526 527 528 529 529

Contents s xxi

Total Return Swap Asset Swap Collateralized Debt Obligation Alternative Investments What Are Alternative Investments? Real Estate Investment Trusts Hedge Funds Private Equity Infrastructure Funds Other Alternative Investments Putting It All Together Chapter Summary Applying Economic Analysis International Focus Lessons of Our Times Key Concepts Questions and Problems

531 533 533 536 536 537 538 539 539 541 542 544 544 546 546 547 548

Appendix

551

Index

557

LIST OF ILLUSTRATIONS

Figure 2.1 The expected return-risk trade-off. Figure 2.2 Asset allocation and security selection. Figure 2.3 Asset allocation types. Figure 2.4 Top-down and bottom-up approaches to investing. Figure 2.5 Use of margin debt by the NYSE since 2000 (various months). Figure 2.6 Demand schedules. Figure 2.7 Supply schedules. Figure 2.8 Market price equilibrium. Figure 3.1 Annual historical returns of US stocks, Treasury bonds, and Treasury bills, 1960–2008. Figure 3.2 Compounded value of $100 invested in US stocks, Treasury bonds, and Treasury bills, 1960–2008 (values in logarithms). Figure 3.3 The relationship between nominal interest rates and inflation. Figure 3.4 The standard normal distribution. Figure 3.5 Histogram of Apple’s returns. Figure 3.6 Utility and wealth. Figure 4.1 The circular flow of funds in financial markets. Figure 4.2 Securities and securities exchanges. Figure 4.3 Prices of seats at the NYSE, 2005. Figure 4.4 NYSE membership prices, 1869–2005. Figure 4.5 The size of the US bond market, October 2011. Figure 4.6 Circuit breaker levels.

xxiii

28 30 34 36 42 48 48 49 58 58 62 66 67 72 86 89 91 91 98 103

xxiv s Illustrations

Figure 5.1 Figure 5.2 Figure 5.3 Figure 5.4 Figure 5.5 Figure 6.1 Figure 6.2 Figure 6.3 Figure 6.4 Figure 6.5 Figure 7.1 Figure 7.2 Figure 7.3 Figure 7.4 Figure 7.5 Figure 7.6 Figure 7.7 Figure 8.1 Figure 8.2 Figure 8.3 Figure 8.4 Figure 8.5 Figure 8.6 Figure 8.7 Figure 8.8 Figure 9.1 Figure 9.2 Figure 9.3 Figure 10.1 Figure 10.2 Figure 10.3 Figure 10.4 Figure 10.5 Figure 10.6 Figure 10.7 Figure 11.1 Figure 11.2

Direct and indirect investing in securities. The effective federal funds rate, 1954–2010 (monthly observations). Three-month LIBOR, January 1999–August 2010. Yield spreads between CD rates, federal funds rates, and the Treasury bill, 1964–2010. Yield spreads between AAA, BAA, and the 10-year T note, 1953–2010. Relationships between the firm, syndicate, and investors. Share of household financial assets held by investment companies, percent, year end, 1980–2009. Indirect investing. Worldwide classification of mutual funds by asset type, region, and fund type (for the second quarter of 2008). Performance of composite REITS relative to the S&P 500 Index. Portfolio risk and number of securities. The benefits of international diversification. The asset allocation process. A graphic illustration of the investor’s overall portfolio. The investor’s overall portfolio with borrowing opportunities. The investor’s overall portfolio with higher borrowing opportunities. The capital market line. Impact of correlation on portfolio risk. Impact of correlation on two-asset portfolio return and risk with varying weights. The investor’s opportunity set with the CAL. The investor’s optimal risk and overall portfolios. The Markowitz efficient frontier. The capital market line and the efficient frontier. The security market line. Security and portfolio characteristic lines. An example of market efficiency. The three forms of market efficiency. The S&P 500 Index, January 1968 to October 2009. Top-down equity fundamental analysis. Macroeconomic equilibrium. Macroeconomic equilibriums. Equilibrium interest rates. The business cycle and its phases. Leading Indicator Index for the United States, 2000−2011. The stages of the industry life cycle. Expected and required return from a stock. Market clearing stock price.

116 126 128 130 136 152 156 156 164 170 188 190 194 203 205 206 207 224 225 228 230 231 234 236 242 262 264 275 312 315 315 317 319 321 324 334 335

Illustrations s xxv

Figure 11.3 Figure 11.4

The S&P P/E multiple as a trading tool. Value Line Investment Survey Report: International Business Machines. Figure 11.5 The S&P 500 Index’s P/E ratio, from March 1960 to June 2007. Figure 12.1 The size of the global bond market, 2009. Figure 12.2 Bond prices and yields. Figure 12.3 Path of bond prices over time. Figure 12.4 Bond price-yield relationship and tangent line. Figure 12.5 Four actual shapes of the US yield curve. Figure 13.1 Some yield curve shifts and shapes. Figure 14.1 Payoff and profit/loss of a call option at expiration. Figure 14.2 Payoff and profit/loss of a call writer at expiration. Figure 14.3 Payoff and profit/loss of a put option at expiration. Figure 14.4 Payoff and profit/loss of a short put at expiration. Figure 14.5 A covered call strategy’s profit line. Figure 14.6 A protective put strategy’s profit line. Figure 14.7 A collar strategy’s profit line. Figure 14.8 A married put strategy’s profit line. Figure 14.9 Spread strategies. Figure 14.10 A multistate price tree. Figure 14.11 The Volatility (VIX) and S&P 500 indexes. Figure 15.1 The clearinghouse and its traders. Figure 16.1 A credit default swap. Figure 16.2 A total return swap. Figure 16.3 An asset swap. Figure 16.4 Alternative investment asset classes. Figure 16.5 Aggressive versus conservative investment portfolios. Table 1.1 Selected Balance Sheet Items of US Households and Nonprofit Organizations, 2010Q2 Table 1.2 Sources of Financial and Economic Information Table 1.3 Finance Payrolls and Average Pay, 2006 Table 2.1 Average Return of the S&P 500 Index by Decade, 1950–2007 Table 2.2 An Example of Dollar-Cost Averaging Table 3.1 Periodic Cash Flows of an Asset Table 3.2 Arithmetic and Geometric Means of US Stocks, Treasury Bonds, and Treasury Bills, 1928–2010 Table 3.3 Probability Distribution of HPR of Stock X Table 3.4 Calculation of the Variance of Stock X Table 3.5 Descriptive Statistics of US Stocks, Treasury Bonds, and Treasury Bills, 1928–2007 Table 4.1 Chronology of Selected Events at the NYSE

348 358 362 375 390 390 399 402 432 455 456 457 457 461 463 465 467 468 474 478 495 531 533 534 536 543

5 13 19 27 40 59 60 63 65 68 90

xxvi s Illustrations

Table 4.2 Table 5.1 Table 5.2 Table 5.3 Table 5.4 Table 5.5 Table 5.6 Table 6.1 Table 6.2 Table 6.3 Table 6.4 Table 6.5 Table 6.6 Table 7.1 Table 7.2 Table 7.3 Table 7.4 Table 8.1 Table 8.2 Table 8.3 Table 9.1 Table 10.1 Table 10.2 Table 10.3 Table 11.1 Table 11.2 Table 11.3 Table 11.4 Table 12.1 Table 12.2 Table 12.3 Table 12.4 Table 12.5 Table 13.1 Table 13.2 Table 13.3 Table 13.4 Table 13.5 Table 13.6 Table 14.1 Table 14.2

Dow Jones Industrial Average Components and Statistics Selected Money Market Instruments and Rates Recent Treasury Bill Auction Results Currency Assets and Liabilities of non-US Banks vis-à-vis all Sectors Equivalent Taxable Yields and Corresponding Tax-Exempt Yields Issuance of Bonds by Various US Entities, 2000−2010 Bond Ratings by S&P, Moody’s, and Fitch Companies Lead Underwriter Rankings: 10/12/2009−10/12/2010 Some IPO Pricings, Filings, and Withdrawals Some Initial Public Offerings Investment Company Assets (Billions of Dollars, 1995–2009) Comparison of Annual Returns between Two Funds Rates of Return of High-Yield Bond ETFs Portfolios and Expected Standard Deviations of Returns Economic Scenarios and Securities Returns Economic Scenarios and Securities Returns Summary of Portfolios’ Expected Returns and Risks Two-Asset Portfolio Expected Return and Risk for Three Correlation Coefficients Correlation Coefficients, Diversification Benefits, and Portfolio Risk Two-Asset Portfolio Expected Return and Risk with Short Sales The Prisoner’s Dilemma ALCOA’s Stock Quotations NBER Classification of Recessions and Contractions Components of Economic Indicators Stock Price and Returns Decisions to Buy or Sell a Stock Selected Balance Sheet Items for IBM, December 31, 2010 Selected Financial Information on IBM Selected Data on IBM The Evolving Size of the International Bond Market Treasury Bonds and Notes How TIPS Work Bond Prices and Yields Characteristics of a Hypothetical Bond Portfolio Example of a Laddered Bond Portfolio Example of a Bond Portfolio’s Immunization Example of a Bond Substitution Swap Example of a Bond Yield Swap Active Bond Portfolio Strategies and Their Risk Levels Performance Attribution Analysis Selected Call and Put Options on Hewlett-Packard Profit/Loss Outcomes of Unhedged and Hedged Options Portfolios

96 118 119 128 133 135 135 151 153 154 158 166 173 187 191 198 200 225 225 227 286 303 320 321 336 338 339 341 374 377 380 391 398 421 425 430 431 435 439 453 463

Illustrations s xxvii

Table 14.3 Table 14.4 Table 14.5 Table 14.6 Table 14.7 Table 14.8 Table 15.1 Table 15.2 Table 15.3 Table 15.4 Table 15.5 Table 15.6 Table 15.7 Table 15.8 Table 15.9 Table 16.1 Table 16.2 Box 1.1 Box 1.2 Box 2.1 Box 2.2 Box 3.1 Box 3.2 Box 4.1 Box 4.2 Box 4.3 Box 5.1 Box 5.2 Box 5.3 Box 6.1 Box 6.2 Box 6.3 Box 6.4 Box 6.5 Box 7.1 Box 7.2 Box 7.3 Box 7.4 Box 8.1 Box 9.1

Payoffs from a Collar Strategy Payoffs from a Straddle Strategy Profit/Loss from a Straddle Strategy Options Strategies and Investor Attitudes Factors Affecting the Values of Call and Put Options Investor’s Net Position from Put-Call Parity Examples of Futures Contracts Profit/Loss on a Futures Trade Changes in Margin Positions Reversing the Trade Useful Information and Insights before Trading in the Futures Market Some Commodity Futures and Their Characteristics 13-Week Treasury Bill Futures Some Tradable Financial Futures Products An Example of Speculation Amounts Outstanding of OTC Derivatives (in billions of US dollars) Example of an Asset Swap

Ponzi Scheme and Bernie Madoff CFA’s Code of Ethics and Conduct The Hedgehog Bests the Fox Example of a Risk Tolerance Questionnaire Returns and Risk Aversion The St. Petersburg Paradox A New World Monetary Authority? Some Broker Practices in the Trade of Securities The Impact of Margin Calls on the Equity Market during the 2008 Financial Crisis The Mechanics of Purchasing Treasury Bills Commercial Paper Situation during the Credit Crisis of 2008 Lehman Brothers and the Repo Market Primary Market Activity in Europe Google’s Road to Wall Street Investing in Oil and Gas UITs The Long-Term Capital Management Hedge Fund Creation and Redemption Mechanisms of ETFs and Implications How Diversified Are US Households? How to Hedge in Currency Markets Asset Allocation and Academics Problems of Insuring against Risks The 2000 Stock Market Crisis and the CAPM Fair Value Explained

464 466 466 468 472 481 494 495 496 497 501 504 509 511 515 530 534 17 20 32 33 69 73 88 101 104 120 122 125 150 155 160 171 172 189 193 195 210 240 267

xxviii s Illustrations

Box 9.2 Box 9.3 Box 9.4 Box 9.5 Box 9.6 Box 10.1 Box 10.2 Box 10.3 Box 11.1 Box 11.2 Box 11.3 Box 11.4 Box 12.1 Box 12.2 Box 12.3 Box 12.4 Box 12.5 Box 13.1 Box 13.2 Box 13.3 Box 13.4 Box 13.5 Box 14.1 Box 14.2 Box 14.3 Box 14.4 Box 15.1 Box 15.2 Box 15.3 Box 15.4 Box 15.4 Box 15.5 Box 16.1 Box 16.2 Box 16.3 Box 16.4 Box 16.5 Box 16.6

An Example of a Moving Average The Efficient Market Hypothesis and the Crisis of 2008 Some Instances of Return Effects Revisiting the Efficient Market Hypothesis Instances of Irrational Decisions Features of the S&P 500 Index as a Benchmark Index Risks and Benefits of Investing in International Equities The Consumer Confidence Index Intrinsic Value in Practice Actual Uses of the Dividend Discount Model by Firms Economic versus Accounting Profit Determining When to Buy and Sell Stocks Fannie and Freddie to the Rescue TIPS in Depth Duration Measures The Importance of Bond Convexity Factors that Affect the Shape of the Yield Curve and Their Implications Recent Developments in Marking-to-Market Rules Passive Investment Strategy and Pension Funds in the United Kingdom How PIMCO Uses Rebalancing in Its Global Bond Investment Strategies Benchmark Issues Bond and Fixed-Income Exchange-Traded Funds NYSE’s New Options Trading Floor Using the Collar Strategy to Mitigate Exchange Rate Exposure Time Value and Options Value Black-Scholes-Merton or Binomial Model? The First Futures Contract CME Group’s Financial Reform Efforts Organization of the Commodity Futures and Trading Commission The Financial Futures Association of Japan Interest Rate Futures in NYSE Program Trading Issues Episodes of Failed Carry Trades The European Union and the United States Begin Probes into the Use of Credit Default Swaps The Credit Derivatives’ Alphabet Soup Long-Short and Market-Neutral Alternative Funds Private Equity and Hedge Fund Deals in Brazil The Future of Alternative Investments

268 272 275 281 284 307 312 314 337 342 354 360 379 381 397 401 407 418 419 427 437 439 458 465 471 475 498 499 500 503 510 516 527 532 535 537 540 541

PREFACE

TO THE STUDENT Congratulations for studying finance and welcome to the exciting field of investments! You will be pleased to know that I decided to write this textbook in order to discuss and present the material in a different way than what current textbooks do. My main objective in this textbook is to write the material from an intuitive and practical way. This means that the concepts and applications will be presented from the economics point of view, that is, to tell the underlying story behind the investments notions. I have always taught investments in this way and students seem to appreciate it more than just learning and applying concepts in a dry, mechanical way. You will be shown to think of investments (as well as finance) as a special branch (application) of economics because many topics discussed in investments come from (micro and macro) economics but are simply termed differently. Let me present some illustrative examples: sWhen the interest rate (or the discount rate) is discussed in many investments textbooks, you may not realize that the interest rate is nothing but an opportunity cost (of money), as you have learned in your economics courses. sWhen decisions involving investor selection among investment alternatives are discussed, you may not see that what is really being applied is cost-benefit analysis or comparison between marginal costs and marginal benefits. sWhen discussing other investment topics, you may not be aware of the sound economic analysis that many market participants perform. For example, several financial organizations such as the Securities and Exchange Commission and the New York Stock Exchange routinely make economic decisions that you may not see in existing textbooks (because they are never explicitly exposed) but will see in this textbook. sWhen the role of financial markets is discussed, you may not infer (or read in other textbooks) that what is really meant concerns the efficiency with which

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xxx s Preface

resources are allocated in the economy for a mutually beneficial exchange among participants. sFinally, have you ever wondered how the equilibrium price of a share is determined? You guessed it, from the interactions of demand for and supply of shares in the market. Besides understanding the economics behind the actions of market participants, how else are you going to learn about investments from this textbook? There are several other ways: sEach chapter contains several boxes that enhance your understanding of the material and three specific sections labeled “Applying Economic Analysis,” “Lessons of Our Times,” and “International Focus,” all found at the end of each chapter. sIn addition, some chapters contain appendices that show you how to apply several investment techniques with real data, a financial calculator, and EXCEL. In some EXCEL cases, the equations are presented as cell information. sFinally, each chapter contains though-provoking questions and problems that require you to think critically of the answers and display good skills in solving the problems, thus avoiding tedious and useless memorization. So, let the challenge of learning the basics of investments begin and enjoy it!

TO THE INSTRUCTOR What led me to write this textbook is my continuous quest to find a textbook in investments that would present the concepts from the economics point of view so students can soundly interpret these concepts relying on economic theory. Therefore, the concepts herein are presented in a simple-to-understand way and with the minimum required rigor so students grasp them without too much effort. Thus, students will be able to put these investment concepts in perspective with the economic knowledge they have from lower level economics classes. I have found this to be invaluable to my students after teaching investments for more than a decade. The chapters are shorter than those in the conventional textbooks in the sense that unnecessary details on topics are not included. Only the important points on the subject will be presented and discussed so students remain focused on the essence of the topic. For example, when presenting topics such as stock exchanges, many textbooks present a lot of detail on how they operate but this can be done by simply directing the student to the appropriate website for more information or through a question/problem at the end of the chapter. Or, when discussing asset valuations, many undergraduate textbooks go into the details of empirical research which could either be redundant, if instructors omit it, or with no real value to the student, if instructors very briefly go over it. In this textbook, current research is presented in a concise fashion and abstracted from quantitative aspects so it can be useful to students. Furthermore, there are only sixteen chapters in the textbook for two reasons. First, the typical semester is about 14–15 weeks and thus instructors will be able to finish their syllabus fully. Because textbooks typically have many more than 20 chapters, instructors never get to all of them and thus may have to “cut corners”. This means that they either have to skip entire chapters, or sections of chapters, or select sections that they deem necessary. Thus, with the right number of chapters, instructors can avoid all of these forced decisions and simply concentrate on the delivery of material.

Preface s xxxi

Finally, the exercises at the end of each chapter are a mix of questions (for thought and discussion) and problems, and their number is be small. Questions are thoughtprovoking and problems often require knowledge of economics and statistics (which students typically have before taking the course), not mechanical applications of formulas. The idea of such questions/problems is to enable the student to continue learning the chapter material. As a result, the questions and problems come from real-life experiences in the financial markets. Some sources include the Wall Street Journal, Financial Times, and the Economist. And since the chapters are short, you can present a chapter per week, with some time left to go over some of the end-of-chapter problems in class for class discussion.

TARGET AUDIENCE This textbook is intended for undergraduate students majoring in finance who are taking an investments course at the 200 level in their field of study. The relevant course would be Introduction to Investments, Principles of Investments or Investments 101. In addition to the majors, students minoring in finance can use this textbook as well as students in economics who wish to take an elective course in investments. Majors and non-majors (other than in economics) can also take the course as a general business elective since it does not involve heavy quantitative analysis. In general, almost every major discipline requires some knowledge of mathematics and statistics and thus the textbook would be suitable for them.

AIMS OF THE TEXTBOOK The aim of this textbook is to introduce the students to the fundamentals of investments in a simple, intuitive, and practical manner. It will also enable the students to understand and intelligently debate current financial and economic events, and conduct basic yet rigorous financial evaluation of investment issues; and it will prepare them for further study in the field of finance and investments. To that end, the chapters are geared toward delivering an intuitive and a practical knowledge of investments, and the end-of-chapter questions and problems necessitate critical thinking to be answered or solved. Keep in mind that this textbook is not intended to make decisions for you or to assist you in making money, as the opening page of Part I emphasizes. It will provide you with essential information and sound guidance to make an intelligent investments decision.

PEDAGOGY The innovative features of the text are its pedagogy and the additional boxes, where students can read how professionals deal with real problems. Moreover, each chapter has a section on some strategies that investors can apply in specific situations, as well as the pros and cons of each strategy. The overall, innovative features of this textbook are the following: 1. Presentation of material from the economics point of view stressing the interpretation of concepts not the mere memorization and mechanical application of them.

xxxii s Preface

2. Shorter chapters so instructors and students can focus on the main points of subjects rather than wrestle with unnecessary details distracting them from the main issues. 3. Fewer chapters than in current textbooks so instructors can comfortably finish their syllabus (or the entire textbook) within a semester. 4. Illustrations of current events through boxes which can be used to further the students’ knowledge on the subject without having to follow the text’s flow. 5. Three types of special boxes appear in each chapter: boxes with “International Focus,” boxes with “Applying Economic Analysis,” and boxes with ideas from well-known economists and professionals on a given issue, labeled “Lessons of Our Times.” 6. Inclusion of a section on strategies in each chapter that investors can use and explanations of their pros and cons. 7. A short list of thought-provoking questions addressing real-life issues and problems gleaned from current headlines are located at the end of each chapter.

Part I INVESTMENT BASICS

What is an investment and why do people invest? Investment is the sacrifice of your resources (time, money, and effort) today for the expectation of earning more resources tomorrow. What can you do with your money? Spend it, save some of it, or invest it? If you choose the latter, where are you going to invest it? There are many investment alternatives (like stocks and bonds), and the amount of information on each of them is staggering. What is your goal in investing? What are your constraints and risks? Once you have defined these, what is the next step? Are you going to do the investing on your own, or are you going to hire a professional money manager? These are some of the questions that you need to address as a (novice) investor, and we will deal with them in this part of this textbook. In the remaining chapters, we will have more to say about the field of investments in general, the strategies that you can apply to achieve your goals, and the risks involved in investing. Chapter 1 examines the general investment framework by defining investments and the various investment alternatives available in the market. It also presents the objectives and constraints of individual and institutional investors and the roles of the various financial intermediaries that assist you in investing. Chapter 2 lays out the investment process (that is, the two main steps that you need to take before investing) and presents some very basic and simple investment strategies. Finally, Chapter 3 discusses in detail the basic elements of investments: risk and return. This chapter also addresses the objective of investing, which is the maximization of your expected return, and its constraint, which is (subject to) risk. We end with a cautionary word. This textbook cannot make investment decisions for you! It can only assist you in making informed decisions by providing you with valuable information so that you can apply it to your particular investment situation.

1

1 THE INVESTMENT FRAMEWORK

CHAPTER OBJECTIVES After studying this chapter, you should be able to sSee what investment is and distinguish between real and financial assets sKnow the various classes of securities sUnderstand the roles of the financial markets and financial intermediaries sKnow your investment objectives and constraints sEvaluate the role of financial information on investment alternatives sUnderstand some of the issues that arise in financial markets, such as agency theory, asymmetric information, and ethical investment behavior

INTRODUCTION This chapter deals with the general economic and financial environment in which market participants make investment decisions. Specifically, it discusses the securities an investor can invest in as well as the financial markets that facilitate the trading of securities among investors. In this respect, the functions of financial markets and financial intermediaries are explored. The chapter also discusses the objectives and constraints of investors, individual and institutional alike, and concludes with some issues that arise within financial markets. These include problems encountered by market participants while engaging in mutual trades of securities and the occurrences of unethical investment behavior in the marketplace. We end the chapter with the significance of learning and practicing investments.

THE GENERAL FINANCIAL AND ECONOMIC ENVIRONMENT Definition of Investments To understand investments in general terms, let us start with a basic question. Why did you come to college? Surely you could do other things with your money and time, 3

4 s Investment Basics

such as work, travel, and so on. But because you chose to go to college means that you have some expectations for the future (after you graduate). Perhaps you expect to earn a higher salary or to achieve a higher standard of living, or both. Therefore you sacrifice money and other resources today for (hopefully) more money (or wealth) tomorrow. In a broad sense, this sacrifice you currently make for future returns is called investment. Stated differently, you are investing in your future tomorrow by going to college today. This definition of investment involves several elements worthy of special mention. First, you are spending time and money (or resources in general). Your resources are scarce and thus valuable. Investments deal with the efficient management of your money (or financial wealth) today in hopes of receiving more money (or returns) in the future. This brings us to the next element of investment: uncertainty of the future. In other words, the fact that you can have only an expectation for higher returns in the future means that you are faced with risk. But why do people invest? Can’t they just keep their money in the form of cash and stash it under their mattresses or bury it in their backyards? Well, you recall from economics that cash has an opportunity cost. Opportunity cost is defined as the value of an activity that must be given up in order to engage in another activity. Another insight from economics is that income is either consumed, saved, or both. Saving means sacrificing consumption today for (the expectation of) greater consumption in the future. Investing also involves a similar sacrifice, as already discussed. However, there is a fundamental difference between saving and investment. Saving does not entail risk (or at most very little), but investment does. For example, if you put your money in a bank account like a certificate of deposit, you incur no risk of losing your money because your savings up to $250,000 (at the time of writing) is insured by the federal government (the Federal Deposit Insurance Corporation, or FDIC). But if you invest in the stock market, you are faced with significant risk that you may lose all your invested capital. In general, investment assets carry various amounts of risk ranging from no risk to very high risk. The General Investment Environment In general terms, the investment environment refers to the various investment assets (or instruments) that individuals and institutions can buy and sell as well as the markets in which these assets are traded. The assets can be grouped into two major categories: real assets and financial assets. Real assets are tangible and can be used to produce a good or a service. Examples of real assets are machinery, factories, and land. Financial assets are intangible (or electronic entries) and represent claims on the revenues generated from real assets or claims created by the government. Unlike real assets, financial assets do not produce a good or a service but indirectly help the production of real assets. Examples of financial assets are the stocks or bonds that you own or a security offered by the government. Table 1.1 shows the latest data (second quarter of 2010) on the balance sheets of households and nonprofit organizations in the United States. As you see, the financial assets of households and nonprofit organizations include not only stocks and bonds but also items like bank accounts, pension funds, and life insurance funds. How do financial assets help with the production of real assets? Well, if we buy shares of a car company (in the primary market where securities are issued by the company and not from another investor), the company uses the money to expand its productive capacity and sell more cars so it can pay us back from the revenues generated from

The Investment Framework s 5 Table 1.1 Selected Balance Sheet Items of US Households and Nonprofit Organizations, 2010Q2 Assets Real Assets Real estate Equipment owned by nonprofits Consumer durables Financial Assets Deposits Money market shares Credit market instruments Treasury sec’s Agency and GSE sec’s Municipal sec’s Corporate and foreign bonds Mortgages Corporate equities Mutual fund shares Life insurance reserves Pension fund reserves Other Total Assets

Billions of $

Liabilities and Net Worth

Billions of $

28,543.5

Credit market instruments

13,418.5

23,675.2 282.8 4,585.5

Home mortgages Consumer credit Bank and other loans

10,150.4 2,403.7 351.2

43,737.6 7,559.1 1,109.5 4,329.6 10,63.6 23.6 1,033.3 2,033.1 96.4 6,767.6 4,056.2 1,266.6 11,653.8 2,745.2 53,504.1

Net Worth

53,504.1

Source: Federal Reserve System, Board of Governors, Flow of Funds Accounts of the United States. Amounts outstanding end of period, not seasonally adjusted. Assets and liabilities sides do not add up because of omitted items.

selling its cars. Similarly, if we buy a government instrument, the government then uses that money to finance its expenditures, as in laying a highway or building a bridge. It is investments in financial assets that we will discuss in this textbook. Securities A generic term for a financial asset is security. A security is a legal claim on the revenue streams of financial assets or real assets. Examples of securities with claims on a financial asset are bonds and stocks. Although many securities have a specific collateral (or pledge) to back up the claim to a revenue stream, others do not; rather, they simply represent a promise to pay. An example of a security with a claim on a real asset with collateral is a mortgage bond (where the collateral is the actual house). A share of stock is an example of a security without collateral and represents a promise to pay whenever the corporation’s directors deems appropriate. Classification of Securities Financial securities are classified in three major categories: equity, debt, and derivative securities. We briefly explain each below but explore them in greater detail in Chapter 5. Equity Securities Equity securities, or common stocks, represent ownership interest in a corporation. A common stockholder is an investor who owns a share in a company, and each share

6 s Investment Basics

entitles the owner to one vote in the corporation’s important financial matters. Common stockholders are the residual claimants in the sense that if the corporation is liquidated, they are the last in line among other claimants (like creditors, the government, and so on) to receive what is left. Many common stocks pay dividends, which are cash payments made by many corporations to their common stockholders. Preferred stock, although an equity security, also has the characteristics of a debt security. It resembles an equity instrument (because it pays dividends) and a bond (because those dividend payments are fixed in amount and known in advance). Thus, preferred stock is sometimes known as a hybrid security. Debt Securities Debt securities are claims on some known, periodic stream of payments until the end of their lives (the maturity dates). Debt securities are also known as fixed-income securities because they promise a fixed stream of payments or pay a stream of payments on the basis of some formula. The most important category of debt securities is a bond. A bond is a contractual obligation of the issuer (or seller) of the bond to repay the holder (or buyer) of the bond a certain amount of interest on the loan in fixed dates throughout its life plus the loan’s principal (or initial amount lent) at the maturity date. There are other categories of bonds (or debt instruments) that do not pay interest periodically and sell at discount and return their face value to the investor. These are known as (pure) discount bonds; an example is the Treasury bill. In general, there are several categories of debt and other fixed-income securities, such as corporate bonds, government bonds, agency bonds, municipal bonds, and international bonds (they are all discussed in detail in Chapter 5). Derivative Securities Derivative securities, also known as contingent claims, are securities whose values are derived from (or are contingent upon) the underlying asset(s). The two most important types of such securities are options and futures. In general, an option entitles (or gives the right but not the obligation to) its owner to buy (a call option) or sell (a put option) something. Options and futures have exploded in growth since the 1990s and have received wide use since then as a means of hedging (or insuring against) risk. A futures contract obliges the trader to buy or sell an asset at a prespecified price within a specified time frame. For example, a buyer might be committed to purchase the commodity in exchange for cash given to the seller upon delivery of the commodity on the delivery date. The distinction between the right to do something and the obligation to do something makes options more flexible instruments. However, this flexibility comes at a price, called the premium, which is the compensation to the option purchaser upon exercising the option when there is a profitable opportunity. Types of Investors Within an economy there are four types of security investors (or players, or market participants): households, businesses, the government, and the rest of the world. A further classification of investor types is retail and institutional. In general, a retail or individual investor is one that has a “small” amount of money to invest, whereas an institutional one invests millions of dollars (or more). Examples of individual investors are you and me (or households), and examples of institutional investors are mutual funds, banks,

The Investment Framework s 7

insurance companies, and other financial institutions. What are the differences and characteristics of each of these players? Let us start with households. Households comprise consumers and individual (or retail) investors; they invest in securities in order to earn higher returns (and accumulate wealth) to meet their future needs. Typically, they are savers, and they are the ones supplying the funds to other market participants. Households invest in a wide variety of securities, just like institutional investors, but they differ in many ways. Specifically, retail investors cannot always enjoy all the benefits of investing due to their unique financial circumstances limited budgets, and tax liabilities, which may not be relevant for institutional investors. For example, households may be responsible for paying taxes on receiving income from an investment, but institutional investors may have the (lawful) ability to pass their tax liabilities on to you, the investor (as we will see in Chapter 6). Hence institutional investors are much larger (in terms of portfolio size) than retail investors and have a unique position within the financial system. The government, in its three levels—namely, federal, state, and local—is another type of market player. The government is also the regulator of many investment activities and sets the rules of the game in the market. The government, at any point in time, can either be a net borrower of funds or a net supplier of funds. By net borrower we mean that it runs a budget deficit—that is, when its expenditures exceed its revenues—and by budget surplus, the opposite is true. Most of the time (except for a few years in the late 1990s) the US government ran (and still runs) budget deficits; thus it continuously needs to borrow funds from the public. Finally, it is important to realize that all of the above players can also be foreign entities, that is, a foreign individual (investor), a foreign corporation, or a foreign (sovereign) government. For example, the multinational corporation is a foreign investor because it borrows funds from the global financial markets to run its worldwide operations. It is through trade and investment (financial and real) that foreign investors play an important role in any economy. Financial Markets and Intermediaries Financial markets exist to facilitate the flow of funds from one group of people, the savers or lenders, to another group of people, the investors or borrowers. The economic function of the financial markets is to increase the efficiency of a mutually beneficial exchange among people or institutions. Financial intermediaries are institutions that bring together lenders and borrowers of funds. In other words, they issue claims against themselves (by selling financial assets) in order to receive funds to purchase other financial securities. Examples of financial intermediaries are banks, mutual funds, and investment banks. The economic function of financial intermediaries is to provide financial services to customers in an efficient manner. The Roles of Financial Markets Let us begin with a simple question: Which assets contribute to the wealth of an economy, real or financial? The answer is real assets, such as land and plant and equipment, because they produce goods and services. So would it be possible for an economy to produce goods and services if there were no financial markets to facilitate the flow of funds from those who have excess funds (the savers) to those in need (the investors)? No, because it would not be possible to trade financial assets! Therefore the role of financial markets

8 s Investment Basics

is to efficiently allocate financial resources among competing uses and ultimately contribute to the production of real assets in the economy. Real assets define the wealth of an economy, whereas financial assets define the allocation of wealth among individuals. By efficiency in financial markets we mean that it should not be possible for an investor to find bargains in security markets. In other words, security markets (or assets) should incorporate all relevant information quickly and efficiently regarding the value (price) of those securities, so that no investor has an advantage over them. This notion, referred to as the efficient market hypothesis, is discussed in detail in Chapter 9. It is important to note, at this point, that financial markets are not always efficient.1 There can always be factors (exceptions) that will permit an astute investor to exploit the market (or an asset) and earn a higher (abnormal) return, but this occurs only temporarily and not on a consistent basis. We refer to such factors as anomalies. One can ask, then: How efficient are financial markets?’ We will learn that there are three types of market efficiency. But even if the markets are mostly efficient, there will always be people who will not believe that asset prices are fair (correct), will employ different investment strategies, or have a need of a professional to manage their portfolios. In an efficient market, asset prices would be fair, only one investment strategy would be the best, and investors would invest on their own. Again, we will discuss these situations and more in Chapter 9. Another role of financial markets is to enable individuals to shift their consumption patterns over their lifetimes. When individuals do not wish to consume all of their income in the present, they can save a portion of it for consumption or investment in later periods. Furthermore, they can select among the vast diversity of financial instruments with varying degrees of risk in making their investments. If an investor wishes to purchase stock in a company, she or he is taking on more risk than simply “parking’ ” the money in a safe bank account. So financial markets permit investors to spread or allocate risk in their investment holdings depending upon their tolerance for risk. This issue is further taken up in Chapter 3. The box titled International Focus discusses the causes that created the global financial market crisis of 2008. The box titled Lessons of Our Times highlights the issues that financial institutions faced and which contributed to the global financial crisis; it discusses the lessons learned from that experience. In sum, financial markets allow individuals to achieve a higher level of utility in the future than would be possible in their absence. More discussion on these and other functions of the global financial markets is offered in Chapter 4. Please see the box Applying Economic Analysis for an example of how financial markets maximize the utility of individuals. The Roles of Financial Intermediaries As stated above, financial intermediaries bring together surplus funds units (savers) and deficit funds units (investors). Thus financial intermediaries accept funds from savers and lend funds to investors. In addition, some financial intermediaries issue their own securities to finance purchases of other institutions’ securities. In general, financial intermediaries differ from other companies in the sense that their business is in financial assets. For instance, if we compare General Motors (GM) with a commercial bank, we will see that GM has more real assets (like plant and equipment) and fewer financial assets, whereas the opposite is true for the bank. This is so because a commercial bank simply channels funds from households to the business sector. That is the social function of such intermediaries. Another example of a financial intermediary is an investment

The Investment Framework s 9

company, commonly known as mutual fund. A mutual fund simply pools the funds of small investors and invests the resulting big sum in a variety of financial assets on their behalf. The ability to invest in such a great variety of instruments and the efficiency with which this is done while also achieving a low cost (per unit) of investing is referred to as economies of scale. The latter also generate huge advantages for small investors who obtain timely information on their current and prospective investment choices.

THE OBJECTIVES AND CONSTRAINTS OF INVESTORS Recall the general definition of economics: the study of how a society manages and allocates its scarce resources to satisfy human wants. Society achieves this when it employs its resources efficiently. Let us adapt this definition to the study of investments. Investors also have scarce resources, such as time and money, as we discussed earlier. In addition, given their appetite for risk (recall risky versus safe investment instruments), investors would like to maximize their reward to the highest extent possible. So investors need to prioritize their investment alternatives, just as consumers prioritize their wants and select those that would give them greater utility (or satisfaction) sequentially. Therefore investors must know their objectives, such as the maximization of reward, and their constraints—their budgets, for instance—before they begin investing. To better understand the objectives of investors, individual and institutional, we need to explain the term risk and the three attitudes (or appetites) they possess toward risk. Risk has a lot of definitions. For example, it can be defined as the probability that there might be an unfavorable fluctuation in the rate of return of a security. This means that the actual rate of return may be different from the expected one due to the uncertainty of expected cash flows of the asset. Even in the case of a safe investment, such as the Treasury bill, there is still the risk of receiving less in real terms (due to inflation). The point is that there are several risks in investing, but we will discuss them in more detail in Chapter 3. The three attitudes toward risk are risk-loving, risk-averse, and risk-neutral. A risk-loving investor is one who would take a fair game (a fair game is one where an equal chance of winning / losing is present or where the expected payoff is zero). In other words, the utility (or satisfaction) investors derive (from a bigger game) from winning exceeds the disutility (or dissatisfaction) from losing. A risk-averse investor is one who is reluctant to accept risk. However, the investor would take more risk if she or he expected to earn a higher return. Relative to a risk lover, the risk-averse investor would not take the fair gamble. Finally, a risk-neutral (or risk-indifferent) investor is one who does not care much about risk. These attitudes toward risk are also known as the investor’s risk tolerance (or degree of risk aversion). Let us now specify the investors’ objectives with the two elements of investing—namely, risk tolerance and return—in mind. Objectives of Investors Individual investor objectives (such as education, family, large purchases, retirement) can vary among each group and can arise from various factors. One factor is the investor’s age. Age can define an investor’s objective by making him more aggressive or conservative in his investment choices. Simply put, when individual investors are young, or at the early years of their productive and earning years, they can tolerate taking some risks. The reason is that they have ample time ahead of them not only to recoup any losses that would occur during their working lives but also to increase their expected rates of return.

10 s Investment Basics

So we can say that such investors have a high level of risk tolerance and can be aggressive in their investment choices. At the other extreme, it is possible for a conservative investor to outlive her investment income because she was overly conservative! By contrast, older individuals such as retired people cannot afford to assume much risk because they not only have a smaller number of years left to live but also because they live on fixed incomes. So for these investors, risk tolerance diminishes and they usually (tend to) invest in more conservative securities. Another factor is individual investor preferences. These include investments in human capital or major purchases during the lifetime of the investor. The former pertains to education and/or building up their earning power. A great concern of individual investors during their prime working years is also protection against risk (due to sickness or loss of employment). In this sense, individuals purchase insurance as a hedge (or protection) against disability or death. Major purchases involve real assets, such as a house, and financial assets, such as stocks and bonds. These investments are made possible by the increase in the investor’s earning power over time and have become an essential element in an investor’s portfolio. No wonder then that an entire financial industry (i.e., professional investors) has emerged to assist these individuals with their investment choices by giving them advice and/or managing investment accounts for them. Institutional investors such as mutual funds, pension funds, endowment funds, insurance companies, and banks, which provide investment services for a fee, also have objectives. For example, mutual funds, which pool together individual investors’ funds and invest them on their behalf, have specific objectives (called investment policies) for their businesses, which are outlined in their prospectuses. For example, an equity fund’s objective is to invest primarily in stocks and to provide its customers with either high current income (or high dividend yields) and /or capital gains. A bank’s objective is to maximize its earnings by earning a positive spread between lending and borrowing rates. Finally, a life insurance company’s objective would be to earn sufficient funds to meet future obligations for its policyholders. Constraints of Investors Individual and institutional investor constraints are either internally defined, that is, arising from investors’ specific circumstances and needs, or externally imposed. For instance, age, taxes, and regulation are obligatory, whereas liquidity and other special needs are investor-specific. In general, constraints limit investment choices and, along with the objectives, determine the investor’s appropriate investment mix. Let us briefly explain each of these constraints. Taxes on investment returns usually have to be paid (unless the investment instrument is a tax-exempt one, like a municipal security), and the correct rate of return on an investment should be defined as the after-tax return. Both investor groups are concerned with tax-sheltering policies or tax-deferred investments in the effort to meet their respective objectives. The regulatory environment also limits investor actions. For example, institutional investors are bound by federal, state, and local rules and regulations regarding their conduct of business. The prudent man law, for example, refers to the fiduciary responsibility that professional investors have to serve the best interests of their clients (or investors). Several agencies—such as the Securities and Exchange Commission (SEC) and the Federal Reserve (Fed)—regulate the business of investing. Liquidity constraints pertain to both investor groups and refer to the ability and the cost with which an asset can be converted into cash. For example, if an investor has a

The Investment Framework s 11

specific need to set aside an amount of money for a major purchase, this amount is considered a (liquidity) constraint. An asset that can be exchanged for cash quickly and with little cost is a liquid asset. Money market instruments, such as Treasury bills, are highly liquid, whereas capital market instruments, such as bonds, are less liquid. Cash is the most liquid asset and real estate is the least liquid asset. These (and more) market instruments are discussed in Chapter 5. Age can also be a constraint because it defines the investor’s investment horizon. As explained above, although the stage in the investor’s life shapes the investment objectives, it can also affect the choice among assets. For example, if an investor knows that she will need a specific amount of money at some future period, then investing in a bond whose maturity coincides with that period could be the rational choice. Finally, investors differ among themselves in their specific circumstances at different stages of life if they are individual investors or in their unique investment policies if they are institutional. For example, a married couple with children will naturally have to think about their children’s education, while for a single individual, this may not be a concern. An institutional investor, say an endowment fund (which entails the management of portfolios for the benefit of a nonprofit institution such as a university), usually applies a conservative investment policy, but such an objective can change given a substantial change in the university’s circumstances. A written description of an investor’s return objectives and constraints along with her or his investment horizon and risk tolerance is known as the investor’s investment policy statement (IPS). Such a statement serves as the foundation before the professional portfolio manager takes any investment action on behalf of the investor (the client). The next step is to create the investor’s portfolio, execute it, and then monitor and evaluate it. Let us now explain briefly the (portfolio) investment management process.

THE INVESTMENT MANAGEMENT PROCESS Investment management refers to the professional management (investment) of a person’s money (funds). Investment management is part of the financial services industry, which provides services to individuals and companies in achieving their goals. We said above that once the client’s IPS is prepared, the next step is the construction of the actual portfolio (comprising of the asset allocation and security selection steps) and finally an evaluation of the portfolio’s performance. It is important to stress that the process does not stop there. Once the portfolio is built, the manager (and the client) can’t just sit back and relax! Since investing is an ongoing process, the portfolio must be continually monitored and adjusted, aligning it with the investor’s objectives and constraints. This is a dynamic and systematic process that can be both simple and complex. We will treat the investment (management) process in greater detail in Chapter 2. What is the objective of the investment management process? First of all, recognize that professional portfolio managers get paid for managing other people’s money and that their pay is fee-based. This means that the more money a manager is handling, the greater the resulting fees and the larger the manager’s salary. The objective of the portfolio manager is to use the inputs (i.e., funds, technology) as efficiently as possible in order to generate the greatest expected return possible for the client, given the constraints. The inputs are spelled out in the investor’s policy statement and the constraints are the investor’s risk tolerance and preferences. Thus the objective of investment management is to maximize a client’s expected return given her risk constraints.

12 s Investment Basics

What could the future for investment management hold? Gary Brinson, a 35-year veteran investment manager, argues that investment analysis and management will become more rigorous in the future.2 In addition, the process of constructing global portfolios will change dramatically, becoming much more focused and specific. For example, country equity asset allocation will be replaced by global sector or industry asset allocation. Furthermore, due to the fragmentation and lumpiness of investment management, investment advisers (and their clients) need to be more careful in recognizing the characteristics of the markets. He hopes that “investors will spend more time on an organization’s investment philosophy, process and people than on past results and, when analyzing past performance data, will apply statistically rigorous performance evaluation.”3

THE ROLE OF INVESTMENT INFORMATION In order for an investor to achieve his objectives (given the constraints), it must be possible to obtain adequate information on the available investment choices. Some of the desirable properties of information are accuracy, timeliness, and relevance. Therefore, before making a final investment selection, the investor needs to ask questions such as, What type of information do I need? How and when can I use it? Financial markets, as well as market participants such as brokerage firms provide ample information on financial and real assets and the economy in general. Investors use this information to make rational choices among investment alternatives and meet their investment objectives. For example, an individual who plans to buy a house will need to know the specifics of obtaining a mortgage as well as the prevailing interest (or mortgage) rates. Similarly, another investor who wishes to save part of her income will need to know the savings rates and other comparable interest rates that banks in her neighborhood currently offer. Finally, asset prices and market interest rates guide a firm’s management to appropriately select among investment projects and arrange for their financing. There are numerous sources of information for investors on practically all sorts of investment alternatives. Investors can read newspapers, navigate the Internet, watch television, listen to the radio, go to the library, or simply consult a company. When investors wish to obtain comprehensive and structured information, they may visit a brokerage firm (such as Charles Schwab, Goldman Sachs, or J. P. Morgan-Chase) and pay a service fee. The brokerages who offer such information are known as full-service firms, whereas those who do not provide information to their clients but only transact on their behalf are known as discount brokers. We will discuss these brokers and their sources of information in detail in Chapter 6. Table 1.2 contains some sources of financial and economic information an investor typically uses. Despite the abundance of information (even public information), information is not free but comes at a cost. Economic intuition will help us understand why information is costly. Theoretically, an investor can collect enormous amounts of information about a specific security before making a decision. But the gathering of information is costly in terms of time, money, effort, and so on. In addition, the amount of information will surely contain conflicting notions about the security of interest, and the investor may not be able (or knowledgeable enough) to ignore this “noisy” information. Here, we assume that all available information may not be embedded in the current asset’s price, which

The Investment Framework s 13 Table 1.2 Sources of Financial and Economic Information Newspapers Wall Street Journal Barron’s Investor’s Business Daily

Web Address www.online.wsj.com www.online.barrons.com www.investors.com

Periodicals The Economist Financial Times BusinessWeek Forbes

www.economist.com www.ft.com www.businessweek.com www.forbes.com

Web-Based Yahoo! Finance Bloomberg Standard & Poor’s Morningstar

www.finance.yahoo.com www.bloomberg.com www2.standardandpoors.com www.morningstar.com

Government Securities and Exchange Commission Federal Reserve System Securities Investor Protection Corp.

www.sec.gov www.frb.org www.sipc.org

is why the investor searches for additional information (this is an important topic on informational efficiency and financial markets and is discussed at length in Chapter 8). So the investor needs to balance the extra (marginal) cost of obtaining information with the marginal benefit of using the information before making a decision on the asset (to purchase, buy, or hold it), among other things. Here is an example. On average and on a consistent basis, money (mutual) funds managers have been unable to beat the stock market—that is, to earn a higher return than the aggregate market. Any informational advantage they (thought they) possessed was quickly dissipated through the (global) investment community and thus eliminated any excess gains to be made. This is true given the widespread availability of information and the speed with which such information is transmitted. So, any additional information that you might have collected or uncovered as an individual investor might not work to your benefit. We will explore this situation in greater detail in Chapter 9.

AGENCY AND ETHICAL ISSUES IN INVESTING We stated in the beginning of this chapter that the investment environment is composed of the various securities and security markets as well as the various players in the economy. The players in any economy are households, businesses, the government, and the rest of the world. These players interact with one another on a daily basis and, because of this interaction, several problems (issues) emerge. In this subsection, we discuss three conflicts that arise when financial markets are not functioning efficiently. Conflicts arise among the firm’s stakeholders (a stakeholder is anyone who has an interest, a stake,

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in the business such as owners, creditors, customers, the government, and so on). These conflicts are asymmetry of information, the agency problem, and the crisis in corporate governance. In addition, we will take up the subject of ethics in investing, which is always a current topic when people manage other people’s money. Asymmetric Information The problem of asymmetric information arises when one party has more (or better) information than the other party in a transaction. If the party with the additional information cannot reveal it to the other party, we have an inefficient allocation of resources. Consider a similar example of the market for used cars, which highlighted George Akerlof ’s award of the Nobel Prize in Economics in 2001 and his famous paper titled “The Market for Lemons: Quality, Uncertainty, and the Market Mechanisms.” The potential buyer of a used car cannot know how the car’s previous owner drove it or its exact condition. In this case, the seller of the used car has more information that the potential buyer. The alternative would be to buy a similar used car from a dealer. The price of the dealer’s used car would be higher than the price of the private person’s used car. Only if you knew with certainty that these two used cars were nearly identical might you be indifferent between the two cars. In some cases, asymmetry of information is powerful enough to distort a market or shut it down completely. Why should asymmetric information concern investors? First, because it poses significant problems to a firm’s shareholders. For example, managers usually have better information than investors about the (uncertain) prospects of a proposed project. If the firm does not have sufficient funds internally to finance this project, it may be forced to raise those funds from new investors (new shareholders). A conflict may arise in this case because existing shareholders will be unwilling to share their portion of ownership with new investors, since they will suffer a dilution (or spread) of earnings as a result. In addition, managers may have to give up an investment project that would potentially raise the wealth of both current and new shareholders. Foregoing a potentially profitable project because of such conflicts is economically wasteful and results in an inefficient allocation of resources. Second, asymmetric information generates two equally important (and related) problems for firms and their stakeholders. One is adverse selection, which emerges when one person is more informed about the qualities of a commodity than another person and, as a result, the other less informed person runs the risk of purchasing the lower-quality commodity. For example, people who purchase health insurance know more about their personal health than their insurance companies do. Furthermore, if these people have serious health problems, they will tend to buy more insurance than other people who are relatively healthy. So if insurance companies are to stay in business, they must price the provision of health care higher than average to reflect the costs of the sicker people, on average. This pricing policy, in turn, may discourage average healthy individuals from purchasing health insurance, which implies market failure. The second problem of asymmetric information is moral hazard. Moral hazard is closely related to the agent-principal problem we discuss next. It arises when one party cannot effectively monitor the actions of another party who is hired to do a job (say, a manager in a corporation). As a result, the hired person has an incentive to shirk and/or work to benefit himself much more than his employer.

The Investment Framework s 15

Can you exploit asymmetric information to your advantage, as an individual investor? Perhaps. Consider this example. You are researching to find companies that you wish to invest in and thus you spend time, money, and effort to select among the thousands of possibilities. In order to have a chance at success, you should be able to uncover something that other investors have not found or simply do not know about. For example, if you look at the companies near where you live, it is possible to know a bit more about them (for instance, how they conduct business with the public, whether they give to the community, what their relationships with employees and suppliers are, and the like) than investors who live far way. Thus you have an upper hand on the publicly available information because you know a bit more about the company that is not published anywhere, especially if you are dealing with the company as a customer. Thus, by looking at such companies, you lower the cost of your search (for information) but increase your marginal benefit from the extra information you have. Thus you might profitably exploit such informational asymmetry to your benefit, meaning that if you invest in the company, you might be rewarded. The Agent-Principal Problem Within a corporation, which is a legal entity separate from its owners (i.e., the stockholders) or principals, an agent (manager) is hired by the principals to manage the business. A conflict arises when the agent does not pursue actions in the best interests of the principals, as should be the ideal case. In fact, if stockholders are unable to monitor the performance of the manager, the manager may very well act in her own interest to the detriment of the stockholders. For instance, the manager may engage in actions that promote her own well-being and display extravagance in public, knowing that the cost will be borne by stockholders. How do stockholders mitigate this problem? There are mechanisms in place that tie the manager’s compensation to the realization of the objective of the corporation, which is the maximization of shareholder wealth. One such mechanism is stock options, which increase in value when the company’s stock increases (which, naturally, is a result of prudent manager actions). Another, more drastic mechanism to ensure the best performance from the manager is the threat of takeover by another company. When another firm acquires a firm that is underperforming, the latter firm’s manager(s) are usually fired and replaced by officers from the takeover firm. Another conflict arises when the interests of shareholders and creditors are different. For example, consider the situation where the manager wants the corporation to engage in a risky project without selling more shares (to raise the funds to finance the project) but instead decides to borrow money from creditors. The conflict arises because the stockholders know that if the project goes sour, they will lose, but the creditors will still be paid. If the project is successful, both creditors and shareholders will share the potential reward. Also, the creditors have another incentive to push for this investment, because they know that in the event of liquidation of the company, they will be first in line to be compensated. Consider another example of this conflict. Assume that stockholders persuade management to take on a venture that creditors find to be riskier than expected. The higher risk causes the value of existing debt to go down and thus put creditors (who have supplied additional capital to the firm) at risk. However, if the project goes well, all the rewards will accrue exclusively to the stockholders, because creditors get only a fixed return. On the other hand, if the project fails, bondholders may also have to share the loss. From the shareholders’ point of view, this situation is a “heads I win, tails you lose” game, which may not be viewed well by creditors.

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Ethics in the Marketplace In addition to the problems discussed above, other kinds of behavior by some professional managers are typically found in the marketplace and particularly in investments. This behavior might be motivated by the lax regulatory environment and the trust that unsophisticated, uninformed investors place in the professional managers who are handling their money. Unethical or questionable behavior may also come from various market participants, such as investment advisers, accountants, or investment banks, and in various forms like misrepresentation of a company’s financial strength, manipulation of financial / accounting information, publishing misleading research, and so on. Specifically, within the institutional investor body, there are state laws and “prudent man” laws (or prudent investor rules) that govern the professional manager’s behavior and /or limit the allowable types of investments. In other words, such professionals have the fiduciary responsibility to serve the interests of their clients as best as they can. Unfortunately, some of them do not take that responsibility very seriously. Fortunately, however, these people amount to just a small fraction of the profession. Let us present some recent examples of such unethical behavior. In the early 2000s, Enron corporation (a company dealing in energy) misrepresented its financial statements and used questionable accounting practices to convince investors that the company was healthy. The company hid its huge debt and artificially inflated its earnings. The company went bankrupt in 2001, and its chief financial officers and other managers were indicted and/or paid significant fines. WorldCom corporation, the number 2 long-distance telecommunications company in the United States, declared bankruptcy in 2002, when it was revealed that shady and fraudulent accounting methods were used to cover the company’s declining financial condition and to increase its share price. The company’s chief executive officer (CEO) and chief financial officer (CFO) were found guilty in 2005 and sentenced to prison. Parmalat, an Italian-based multinational corporation dealing in dairy products, claimed that it had accounts in US banks; these, however, were nonexistent. The company’s actual debt was hidden and huge amounts of money were transferred to the founder’s family business. The company’s CEO went to prison in Italy and the company collapsed in 2004. In 2008, a wave of financial companies like Bear Stearns, Lehman Brothers, and others filed for bankruptcy or were liquidated because they were involved in risky securities in the housing industry and withheld word of those risks from their investors. These companies’ CEOs either were under federal investigation or indicted. Finally, another example of unethical behavior by one of Wall Street’s top brokers came to light in 2008/2009 which, as expected, burned many investors from a so-called Ponzi scheme. See Box 1.1 for details. Other scandals involving a different kind of behavior rocked Wall Street in the 1990s. Accounting scandals involving the once-major accounting firm Arthur Andersen (in association with Enron and other corporations), or investment banking scandals such as Credit Suisse First Boston and Citigroup/Solomon Smith Barney. In Arthur Andersen’s case, the company was barred from auditing companies’ books and was ultimately dissolved. Investment bankers help a firm to go public and launch a first-time stock offering called an initial public offering (more on that in Chapter 6). The firms allocated shares to preferred clients as a quid pro quo for their investment banking services. Several CEOs from these banks were indicted and sentenced to jail and /or required to pay huge fines. So what is being currently done to suppress future episodes of unethical behavior? Despite the mechanisms already in place to deter such wrongdoings, unscrupulous people

The Investment Framework s 17

BOX 1.1 Ponzi Scheme and Bernie Madoff One of the most severe financial frauds in the history of the United States came to the fore in 2008, when Bernard Madoff, a former NASDAQ chairman, was arrested by federal agents. The charge was that he ran, for years, a $50 billion “Ponzi scheme” and deceived investors by operating a securities business that only lost money. Essentially, he was paying off some investors with the funds put up by other (new) investors in the business—which is the basis of a Ponzi scheme. The Securities and Exchange Commission (SEC) defines a Ponzi scheme as follows: “A Ponzi scheme is an investment fraud that involves the payment of purported returns to existing investors from funds contributed by new investors.” Typically, such schemes tend to collapse when inflows of new money dry up or when existing investors want to cash out. See the SEC’s website: http://www.sec.gov/answers/ponzi.htm.

have always found (and naturally will continue to find) ways around the laws to pursue their own self-interest. New laws have been enacted in recent years in response to these waves of unethical practices (now called crises in corporate governance) that have resulted in severe financial crises, such as the Sarbanes-Oxley Act of 2002 and the Securities and Exchange Commission’s Fair Disclosure regulation put forth in 2000. The Sarbanes-Oxley Act created the Public Company Accounting Oversight Board to oversee the auditing of companies, and it made CEOs personally responsible for certifying their firms’ financial reports. The SEC’s regulation prohibits the dissemination of relevant information to outsiders, such as analysts, before it is made public. The rationale for this is to quell biased analysts’ research in exchange for other services by the company. A securities investor has some extra protection coming from the Securities Investor Protection Corporation (SIPC). This is a nonprofit corporation that insures customer accounts with brokerage member firms (for up to $500,000) against failure. An investor can seek damages from a brokerage firm (that is, a firm that buys and/or sells securities on his behalf) if he is not happy with its advice and services. This is done via arbitration before a major stock exchange body (the National Association of Securities Dealers, or NASD, as we will see in later chapters). Finally, another way to deter such practices by professional managers and advisers is for the investor to shun such organizations. In other words, investors should reward institutions that apply ethical behavior or social investing and “punish” those that do not. As an example, investors might want to avoid investing in firms that pollute the environment irresponsibly. An actual example can be drawn from the 1980s, when US multinational corporations and other investors avoided investing (or doing business) in South Africa (because of apartheid). Social Responsibility Another issue worthy of treatment is social responsibility, which refers to the efforts that businesses make to enhance society’s welfare. Some relevant questions must be addressed regarding social responsibility. For example, should businesses act in the best interest of their shareholders (owners) or be responsible for the welfare of all other stakeholders in

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general? Surely businesses have an ethical responsibility to provide a safe product, safe environments for their workers, and so on. However, socially responsible actions have costs, and if one firm acts in that manner and another does not, the former will be at a disadvantage in many respects. This, in turn, may make the firm less competitive, incur higher borrowing costs, and cause its stock price to decline. Let us consider the following scenario to trace out the impact on investors. An investor is considering investing in two firms, one that behaves in a socially responsible manner and another that does not. In all likelihood, most investors will ignore the former firm for the following reason: why should the investor of one corporation subsidize society to a greater extent than another corporation? But does all this mean that firms should not engage in socially responsible manner? No. Firms realize that socially responsible behavior is not only good for the society but also a benefit for them in the long run. Hence social responsibility is desirable and investors are very much cognizant of that. A related issue is socially responsible investing (SRI), which encompasses additional socially conscious investment activities such as those that do not harm the environment, that protect human rights, and that generally promote (and maximize) the social good. Investors concerned with SRI are urged to shun companies that pollute the environment, apply unfair labor practices, or engage in unethical business practices. In general, socially conscious investors use three investment strategies to maximize both their return and the social good: they remove their investment portfolios from abuser firms (called screening), they take an active role in discussing general societal or business-governance concerns (called shareholder activism), and they direct their investment activities toward less advantaged communities (known as community investing). According to the 2010 Report on Socially Responsible Investing Trends, more than 12% of all assets under management in the United States involved some type of SRI activity, with community activism being the largest and fastest growing.4

SO WHY STUDY INVESTMENTS? We end this chapter with an important question: Why did you enter the field of finance (and its subcategory, investments) as a college student? Well, in order to answer this question—and of course answers will vary among students (but not much!)—let us recall why people invest. People invest for reasons such as earning a higher income on top of their normal income, enjoying potential capital appreciation from their investments, securing (to the extent possible) a better retirement, or even for the thrill of the act itself. Investing is practical and is a means to an end. Therefore, for all the above reasons you have decided to enter this exciting field, or perhaps because you have heard that employment opportunities in the areas of finance and investments are growing and are highly rewarding, or because you simply wished to follow a parent’s career. In general, finance is divided into three related areas of study: investments, financial markets and institutions, and corporate finance. Obviously, the area of investments involves the decisions made by individuals, companies, and institutions in forming investment portfolios. As mentioned earlier, the greater investments area also includes investment management or the services provided by professional retail and institutional agents to individual investors and companies. The area of financial markets and institutions (or money and capital markets or money and banking) deals with the various financial markets, institutions, and instruments that interact with the four players in the economy. Specifically,

The Investment Framework s 19 Table 1.3 Finance Payrolls and Average Pay, 2006

Kind of Business Commercial Banking Savings Institutions Credit Unions Real Estate Credit Investment Banking and Securities Dealing Securities Brokerage Securities and Commodity Exchanges Other Financial Investment Activities

Employees (1,000) (1)

Payroll (Billions of $) (2)

Avg. Pay (Thousands of $) (3) = (2)/(1)

1,634 263 250 402

91.5 13.0 9.5 26.5

55.99 49.43 38.00 65.92

156 339

38.2 49.2

244.87 145.13

9

1.0

111.11

417

57.8

138.61

Source: Statistical Abstract of the United States, US Census Bureau, 2010, Table 1128. Note: Average pay computed by author.

financial markets supply the means by which households, businesses, and governments obtain financing. Financial institutions are the intermediaries in the financial markets because they create the financial instruments that enable the players to achieve their functions (and goals). Global financial markets (or the global financial environment) are explored in detail in Chapter 4. Finally, corporate finance deals with the operation (running or management) of a firm itself. This includes managerial functions like investment and financing decisions, planning and forecasting, and dealing with the financial markets. So, you have ample choices in starting a professional career in the fields of finance and investments. The Statistical Abstract of the United States (published by the US Census Bureau) shows the kinds of businesses in the investment field along with their average rates of pay (see Table 1.3). As you see, the average pay for each of the investment category ranges from a low salary for credit union employees to a high salary for employees in investment banking and dealing (investment banking is discussed in Chapter 6). Finally, the national mean wage for financial analysts in 2009 (according to the US Bureau of Labor Statistics) was $85,240. In conjunction with Table 1.3, the industries with the highest levels of employment in the “financial analyst’” occupation were the “Other Financial Investment Activities’” and “Securities and Commodity Contracts Intermediation and Brokerage’” categories. The three top-paying industries in the same occupation were “Other Financial Investment Activities,’” “Securities and Commodity Exchanges,’” and “Insurance and Employee Benefit Plans.’” But even if you entered the field of (finance and) investments without necessarily seeking a job there (perhaps you want, instead, to be a lawyer or an academic economist), you would still need to understand finance in general and investments in particular in order to make simple everyday decisions. For example, you should know how to compare the investment alternatives offered by your bank or to determine which is a better deal in obtaining a mortgage or refinancing an existing one. Therefore the study of investments is a highly rewarding one for all practical purposes, at the very least enabling you personally to feel good about making wise lifetime decisions.

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CHAPTER SUMMARY In this chapter, the investment environment and the way an investor should begin making investment choices were addressed. The idea is to carefully define the specific objectives and balance them against the constraints in order to make the best decision. This is a daunting task not only for individual investors but also for professional (or institutional) investors. The investment environment is vast and complex; unless the investor is cognizant of its way of functioning and caveats, he might not be able to effectively realize or achieve his goals. Although individual investors always have the option of seeking professional advice on investment alternatives, they can also seek investment education from a nonprofit institution called the Chartered Financial Analyst (CFA) Institute. Its mission includes the establishment of a code of ethics and professional conduct, in which the guidelines for appropriate professional investment behavior are outlined. Box 1.2 describes this organization’s mission.

BOX 1.2 CFA’s Code of Ethics and Conduct The CFA’s Institute Code of Ethics and Standards of Professional Conduct (Code and Standards) are fundamental to the values of the CFA Institute and essential to achieving its mission to lead the investment profession globally by setting high standards of education, integrity, and professional excellence. High ethical standards are critical to maintaining the public’s trust in financial markets and in the investment profession.

THE CODE OF ETHICS sAct with integrity, competence, diligence, respect, and in an ethical manner with the public, clients, prospective clients, employers, employees, colleagues in the investment profession, and other participants in the global capital markets. sPlace the integrity of the investment profession and the interests of clients above their own personal interests. sUse reasonable care and exercise independent professional judgment when conducting investment analysis, making investment recommendations, taking investment actions, and engaging in other professional activities. sPractice and encourage others to practice in a professional and ethical manner that will reflect credit on themselves and the profession. sPromote the integrity of capital markets and uphold the rules governing them. sMaintain and improve their professional competence and strive to maintain and improve the competence of other investment professionals.

STANDARDS OF PROFESSIONAL CONDUCT sProfessionalism sIntegrity of capital markets sDuties to clients sDuties to employers sInvestment analysis, recommendations, and action sConflicts of interest sResponsibilities as a CFA institute member or CFA candidate Source: CFA Institute

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The various sources of obtaining information on various investment instruments (vehicles) as well as on the various financial institutions so as to compare among instruments and select the ones that would (or should) offer you the best risk-return combination were discussed. Some issues that arise because of the nature of a corporation— such as asymmetric information, adverse selection, and agency conflicts—were also presented. The sources of asymmetry and its consequences (and benefits) were explored. The discussion also involved the reasons why conflicts might arise between managers and shareholders and between shareholders and creditors. The chapter concluded with the question “Why should you study finance and investments?” We arrived at the conclusion that such knowledge is not only useful for practitioners in the areas of investments, capital markets, and corporate finance—the three interrelated areas of finance—but also for making decisions in everyday life.

THE PLAN OF THE TEXTBOOK The textbook consists of six parts, comprising the following chapters: Part I (“Investment Basics”) contains Chapter 1, on the investment framework; Chapter 2, on the investment process and strategies, and Chapter 3, on risk and return. Part II (“Financial Markets, Intermediaries, and Instruments”) consists of Chapter 4, on the global financial environment; Chapter 5, on the money and capital markets; and Chapter 6, which details the functions of investment bankers and investment companies. Part III (“Portfolio Theory”) includes three chapters: Chapter 7, on diversification and asset allocation; Chapter 8, on efficient diversification and capital market theory; and Chapter 9, on stock market efficiency and behavioral finance. Part IV (“Equity Portfolio Management”) contains two chapters: Chapter 10, on equity and fundamental analysis, and Chapter 11, on equity valuation and relevant investment strategies. Part V (“Debt Securities”) includes Chapter 12, on bond fundamentals and valuation, and Chapter 13, on bond portfolio management and performance evaluation. Part VI (“Derivative Markets and Instruments”) has two chapters: Chapter 14, on option markets and valuation, and Chapter 15, on futures markets and strategies. Finally, Chapter 16 (“Other Topics in Investments”) briefly discusses some current issues in investments, including credit derivatives and alternative investments.

APPLYING ECONOMIC ANALYSIS One of the central propositions in economics is that people obtain a higher utility (satisfaction) by engaging in a mutually beneficial exchange. This utility, however, is made possible by the presence and the efficient functioning of financial markets. Let us illustrate with a simple example. Assume that there are two people in an economy, Mr. Nick and Mr. Haris. Assume also that Mr. Nick wishes to spend less than his current income and Mr. Haris more than his current income (assume for simplicity the rates are the same for both individuals). Hence, Mr. Nick would be a lender (saver) and Mr. Haris a borrower (an investor). This also means that if Mr. Nick agreed to finance Mr. Haris’s excess spending (consumption) then both parties would

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engage in a mutually beneficial exchange. They would be able to do that by having an intermediary create a contract (financial claim). Therefore, one of the functions of the financial markets would be to facilitate such exchanges and allocate the resources efficiently. A variation of the above would be for the economy to allocate the saved resources (money here) into other uses such as capital goods (or real assets) like plant and equipment instead of consumer goods. In this way, both individuals would have the ability to enjoy more goods and services in the future thanks to the accumulation and use of (more) factors of production. Again, financial markets are at the heart of transferring funds from Mr. Nick to Mr. Haris, who could own such factors of production. In sum, the role of financial markets would be to enhance the utilities of both individuals and reduce, at the same time, the cost of providing the opportunity to enjoy goods and services. In other words, if one person’s utility is increased without reducing another person’s utility, then economic efficiency is achieved.

INTERNATIONAL FOCUS CAUSES AND CONSEQUENCES OF THE FINANCIAL CRISIS OF 2008 The financial (credit) crisis of 2007−2008 began in the US housing market; experts say that it started as a bubble. This was because the real estate market in the United States peaked in 2006, ending up with a sharp decline in the values of the underlying securities. Therefore the owners of such securities—the mortgage-backed securities and collateralized debt obligations— who are scattered throughout the world, suffered severe losses. In addition, the financial institutions that originated the mortgage loans and those who owned such securities were equally damaged. Major US and European financial giants—like Lehman Brothers, American International Group, Merrill Lynch, and Freddie Mac—who owned such securities ended up collapsing or being “taken over’ ” by the government. The impact was immediately felt in the stock markets worldwide, which collapsed. Investor trust in the global financial system was shattered. Naturally the declines in equity markets impacted the real economy, as it hampered the ability of financial institutions to extend further lending (financing) to economic agents (like households, businesses, and the government); this slowed down economic activity and raised unemployment. Defaults by homeowners and foreclosures on their properties rose to unprecedented heights in the United States and spread throughout Europe and Asia. The International Monetary Fund (IMF) estimated that banks in the United States and Europe lost more than $1 billion on such assets (termed “toxic assets”) from 2007 to mid-2009. According to IMF estimates, US bank losses amounted to 60% and Eurozone (and British) to about 40%. Finally, many world political leaders started massive efforts to shore up their financial markets in an effort to moderate the crisis’s impact and save their nations from default. However, some nations (like Greece) were forced to seek IMF assistance in order to survive this truly global financial crisis. In general the financial crisis has brought into question national financial architectures as regards systemic financial institutions and the evaluation of risks and vulnerabilities. The global nature of the financial crisis has made it clear that integrated financial markets have benefits and risks, with potentially huge global economic consequences.

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LESSONS OF OUR TIMES LESSONS OF THE GLOBAL FINANCIAL CRISIS The crisis has forced anew the debate on whether macroeconomic policy should be concerned with high asset price increases and leverage. It has also underscored the deficiencies in national financial regulation and supervision. Several voices in both academia and world organizations have expressed their concern about the way the global financial system functions and proposed various ways to fix the system and avoid future financial crises of such magnitude. Specifically, they propose the following reforms:

1. Macroeconomic Policy Lessons These lessons involve the objectives and implementation of monetary and fiscal policies as well as the regulatory environment.

2. Redesigning Prudential Regulation and Supervision It is accepted that one cause of the global financial crisis was the deficiencies or shortcomings in the countries’ financial regulatory environment. Suggestions include better and more prudent supervision of financial institutions, capital regulation, and liquidity issues. The consequences of financial activities need to be better understood so that improved information disclosure, corporate governance practices, and greater coordination within and across countries can be implemented.

3. Reform of the International Financial Architecture Better surveillance of financial risks and vulnerabilities is needed; this can be achieved by closer cooperation among international agencies. Better information is essential to the understanding of risk assessment. Source: Adapted from S. Claessens, G. Dell’Ariccia, D. Igan, and L. Laeven, “Lessons and Policy Implications from the Global Financial Crisis.” IMF Working Paper, February 2010.

KEY CONCEPTS Investment is the sacrifice you currently make for the expectation of higher future returns. Opportunity cost is defined as the value of an activity that must be given up in order to engage in another activity. Saving means sacrificing consumption today for greater consumption in the future. Real assets are tangible and can be used to produce a good or a service. Financial assets are intangible (or electronic entries) and represent claims on the revenues generated from real assets or claims created by the government. A security is a legal claim on the revenue streams of financial assets or real assets. A common stockholder is an investor who owns a share in a company; each share entitles the owner to one vote in the corporation’s important financial matters.

24 s Investment Basics

Preferred stock, although an equity security, also has the characteristics of a debt security. Debt securities, or fixed-income securities, promise a known, fixed stream of payments periodically until the end of their lives (or maturity dates). Derivative securities, also known as contingent claims, are securities whose value is derived from (or contingent upon) the underlying asset(s). In general, an option entitles (or gives the right but not the obligation to) its owner to buy (a call option) or sell (a put option) something. A futures contract obliges the traders to buy or sell an asset at a prespecified price within a specified time frame. A retail or individual investor is one who has a “small’ ” amount of money to invest, whereas an institutional is one who invests millions of dollars (or more). Financial intermediaries are institutions that bring together lenders and borrowers of funds. Risk is defined as the probability that an adverse event is going to take place, or in the case of investors, that there could be an unexpected fluctuation in the rate of return of a security. A risk-loving investor is one who would take on a fair game (a fair game is one whose expected payoff is zero). A risk-averse investor is one who would be reluctant to accept risk. A risk-neutral (or indifferent) investor is one who would not care much about risk. Individual and institutional investor constraints are either internally defined, that is, arising from investors’ specific circumstances and needs, or externally imposed. Taxes, the regulatory environment, liquidity, age, and the investor’s investment horizon are examples of constraints. In order for an investor to achieve his or her objectives (given the constraints), it must be possible to obtain adequate information on the available investment choices. The problem of asymmetric information arises when one party has more (or better) information than the other party in a transaction. A principal-agent conflict arises when the agent does not pursue actions in the best interests of the owners, as in the ideal case he would be expected to do. Adverse selection emerges when one person is more informed about the qualities of a commodity than another person; as a result, therefore, the other, less informed person runs the risk of purchasing the lower-quality commodity. Moral hazard is another problem of the principal-agent problem. Unethical kinds of behavior by professional managers are typically found in the marketplace and particularly in investments. Social responsibility refers to the efforts that businesses make in enhancing the society’s welfare.

The Investment Framework s 25

QUESTIONS AND PROBLEMS 1. As a potential investor, what would be your objective(s) and constraints? What major trade-offs do you face? 2. Why is it inappropriate to say “I want to make as much money on my investments as possible”? What are you ignoring? 3. Take a look at the cafeteria in your college campus. You and most of the other students go there on a daily basis for food and drinks. If the man working there to serve you is always shirking his work responsibilities, how would you advise him to help him keep his job? 4. We discussed the conflicts that arise between a company’s manager and its stakeholders. Can you suggest some other ways to align a manager’s goals to those of the firm’s owners? You might want to scour the Wall Street Journal to find some relevant articles. 5. Consider the following scenario: Suppose your parents asked their neighbor (who consistently pays attention to the stock market because he is an active investor) for advice on a particular stock. Your parents want to decide whether it makes sense to buy the stock. If the neighbor’s opinion on the stock is favorable and he says that the company will do fine in the future, is it unethical to make such a statement? Answer the question assuming that your parents believed that the neighbor’s opinion was based on a good knowledge of the company. 6. We discussed the conflicts that arise between existing and new stockholders when management wishes to undertake new projects financed by equity. Now consider the following scenario: The management of the firm has no other means of financing a new risky project but to sell bonds. If bondholders knew of the project’s riskiness (which might be greater that they would be willing to bear), they would outright refuse to provide the funds. Explain the outcome of such behavior by the bondholders. Do we have an instance of market failure? What if the bondholders did not know of the project’s risk? What impact would that have on the bondholders’ wealth (relative to that of the stockholders)? 7. We discussed social responsibility in the text. Can you advance an argument for the mandatory and for the nonvoluntary requirement of such behavior for firms by government law? 8. Would you be willing to accept more risk if you expected to earn higher return? If so, which attitude toward risk would you have? 9. How do you understand the term efficiency as applied to the financial markets? 10. Classify the following assets as real or financial: factory, stock, option, pencil, knowledge, education. 11. Which business has more or less financial and/or real assets, a bank or IBM? What is each business’s social function?

NOTES 1. 2. 3. 4.

See Justin Fox, The Myth of Rational Markets (New York: HarperCollins Publishers, 2009). Gary P. Brinson, The Future of Investment Management, Financial Analysts Journal, 61(4), 2005, pp. 24–28. Ibid., p. 28. See www.socialinvest.org and 2010 Report on Socially Responsible Investing Trends, p. 7.

2 THE INVESTMENT DECISION PROCESS AND INVESTMENT STRATEGIES

CHAPTER OBJECTIVES After studying this chapter, you should be able to sUnderstand the two steps of the investment process sGrasp the risk-return trade-off all investors face sSee how investors apply the investment process sSee the difference between a passive and an active approach to investing sLearn some other investment strategies including the dollar-cost averaging technique sKnow how to engage in margin purchases and short sales as well as their pros and cons sLearn the various types or orders for securities purchases or sales

INTRODUCTION To make an investment decision, the investor must follow a few steps. These steps constitute the investment process, which broadly describes how investors choose among the various securities, how much money to allocate to each security, and when to make the investment. In the previous chapter we discussed the three broad categories of financial assets that the investor has at his or her disposal in addition to other marketable securities like money market instruments, government securities, real estate, and commodities. The marketable securities are discussed in detail in Chapter 5. Broadly defined, the investment process starts with the establishment of the investment policy, continues with the construction of a portfolio, and ends with an evaluation of the resulting portfolio’s performance. Traditionally, however, investors have applied the process using a two-step approach consisting of asset allocation and security selection. Although it is well understood that an investor must first carefully define his objectives and constraints before doing anything, that is, to set his investment policy, in

The Investment Decision Process and Investment Strategies s 27

actuality that step has received the least attention from investors. Nonetheless, it is this process that is explained and used here.

THE INVESTMENT PROCESS At the outset, we must define the term portfolio. A portfolio is simply a basket of various securities. Just as a college student has a portfolio of courses to take (such as major, collegewide, and electives), investors collect various securities that they want to invest in. Given the investor’s objective, which is the achievement of the highest return possible given the risks involved, one must first understand the basis for making an investment decision. This commonly refers to the risk-return trade-off. The first step in the investment process, asset allocation, is considered first, followed by the second step, security selection. The Risk-Return Trade-Off Let us begin with a simple question Why would an investor want to invest in a risky asset, say a stock, and not in a safer asset, like a savings account in his local bank? The answer is equally simple: because the investor would like (or try) to earn higher return and to come out on top when inflation eats part of his money. In fact, because he expects to earn a higher return by investing in a risky asset, what matters for him is the expected return. This example highlights the risk-return trade-off. Higher return can come only with higher risk. Let us take a more detailed look at this trade-off, however. We said that it is the expected return that the investor anticipates earning at the end of his investment horizon which is relevant. What is hidden or implied in this statement are the (sharp) fluctuations in the market during the investment period, during which the investor may or may not end up realizing the anticipated return. This is the familiar “ceteris paribus” (or other things being equal) assumption in economics, which says that all other things remain equal. For example, during the crash of 1929, which led into the Great Depression, the stock market lost more than 40% of its value in 1 year (1931). More recently, in October 2008, the stock market witnessed its worst performance since 1929 and lost more than 40% of its value in just a couple of weeks. Of course, you also have the market’s normal best performances, as in the 1980s and 1990s, when it gained 17% and 18% total return, respectively. See Table 2.1 below with the S&P 500 returns, nominal and real, by decade from 1950 to 2009. Table 2.1 Average Return of the S&P 500 Index by Decade, 1950–2007 Decade

Total Nominal Return

Total Real Return

1950s 1960s 1970s 1980s 1990s 2000s

19.3% 7.8% 5.8% 17.3% 18.1% –3.5%

16.7% 5.2% –1.4% 11.6% 14.7% –6.4%

28 s Investment Basics

So the ceteris paribus assumption does not really hold; if it did, investors would be expected to prefer to invest in those instruments that would give them the highest return possible. But too many events take place in between that might not allow the return to grow as expected. In addition, there would be no urgency to acquiring these high-yielding assets without bearing the extra risk. Therefore we conclude that there is a positive riskreturn trade-off, which implies that the expected return must be large enough to compensate the investor for taking the additional risk. Figure 2.1 depicts this relationship for various securities. As seen from the graph, lowyielding securities like government bills and bonds carry low(er) risk than high-yielding assets such as stocks and derivatives. The intercept of the line at rf refers to the lowest return, or the risk-free return, and is available to all investors. This asset is called the risk-free asset and is represented by the Treasury bill (a short-term government security). It is important to realize from the graph that the trade-off refers to an ex ante (or before the fact) situation, which means that before an investment selection from these assets is made, the investor expects higher returns from the higher-yielding assets. This is the logical expectation of risk-averse investors and represents the marginal investor. Of course, the actual or realized return, or the ex post (or after the fact) return, may be different, and the investor must understand that. Moreover, given this trade-off, how would an investor select among the various combinations of risk and return? Is the risk increasing linearly with the riskier asset (as the Figure 2.1 suggests), and how should we measure risk? We address these questions in the Chapter 3, where we learn how to quantify both risk and return and guide you as you select among various asset classes to construct a portfolio. The box titled Applying Economic Analysis describes a situation for an investor who has to choose between two investment alternatives. He does so by applying a maximization rule regardless of his risk tolerance. The Asset Allocation Step in the Investment Process We now start with the first step in the investment process, asset allocation. Asset allocation refers to the allocation (or the fractional disposition) of your investment budget Futures Expected Return Stocks

Options Risk-Free (rf)

Bills and Bonds

Risk

Figure 2.1 The expected risk-return trade-off.

The Investment Decision Process and Investment Strategies s 29

among the various available asset classes (such as equities, debt, derivatives, and other assets). This step in the investment decision process is relatively straightforward. Asset allocation is the major determinant of the expected risk-return trade-off of a well-diversified portfolio much more than the (selection of the) individual securities comprised by this portfolio (the second step in the process). A well-diversified portfolio means including various assets and not just one security in the portfolio in order to minimize its risk exposure (the concept of diversification is discussed in detail later and in Chapter 7). Prominent professional managers, like John Bogle of the Vanguard Group of Investment Companies, advocate asset allocation as the most important step in the investment process: “The most fundamental decision of investing is the allocation of your assets: how much should you own in stock? How much should you own in bonds? And how much should you own in cash reserves?”1 The box titled Lessons of Our Times discusses Warren Buffett’s asset allocation, designed to navigate profitably during economic crises. Buffett is another guru of investing and has made a fortune following basic investment principles (as we will see later). For more information, you may visit the website of the Securities and Exchange Commission (SEC) and look for the article “Beginner’s Guide to Asset Allocation, Diversification, and Rebalancing.”2 Let us use a very simple example to show such an allocation. Say you have $10,000 to invest and you consider purchasing equities, bonds, and real estate as well as opening up a savings account. Of that amount, you wish to place $8,000 into the risky asset classes (equities, bonds, and real estate) and the rest, $2,000, into the safe asset, the savings account (or a money market account). So 80% ($8,000/$10,000) is invested in the risky assets and 20% ($2,000/$10,000) in the safe asset. This is an example of asset allocation. Let us say that the risky assets basket comprises only stocks and bonds. So if you allocate your $8,000 into these two asset classes equally (that is, using 50–50 weights or $4,000 in each asset class), then this is also an asset allocation decision. Specifically, you have the following fractions in your total investments: sfs = fraction invested in stocks (s) = $4,000/$10,000 = 0.40 or 40% sfb = fraction invested in bonds (b) = $4,000/$10,000 = 0.40 or 40% sfa = fraction invested in bank account (a) = $2,000/$10,000 = 0.20 or 20% for a total of 100% invested Let us take this example further to where we change the amounts invested (that is, the weights) in the risky assets but leave the fractions of each asset the same (that is, 40% in each risky asset). Why would the investor want to reallocate these assets and buy more of the safe asset? The reason is that she wants to decrease the risk exposure to her portfolio. So if she plans to reduce the amount invested in the risky assets from $8,000 to $7,000, the risky portfolio’s portion of the total budget would be 0.70 ($7,000/$10,000). The $1,000 difference (from the initial risky asset allocation) is allocated to the purchase of more of the safe instrument, so that total holdings of the safe asset increase to $3,000. In order to keep the weights of each risky asset (the stock and the bond) the same (50–50), the investor needs to sell $500 (0.50 × $1,000) from each asset: ws = ($4,000 – $500)/($8,000 – $1,000) = 0.50 wb = ($4,000 – $500)/($8,000 – $1,000) = 0.50

30 s Investment Basics

In this exercise, the investor simply shifted funds from her portfolio’s risky holdings proportionately (when considered as one class, the risky assets) to the money market account. This too is an asset allocation example and will be useful in our further discussion of the risk and return (Chapter 3). The Security Selection Step in the Investment Process The second step in the investment process is security selection and analysis. Security selection refers to the analysis of individual securities (or portfolios of securities) considered for inclusion in the investor’s portfolio. Security analysis, which involves estimating the value of a security for inclusion or not in the portfolio, can be done by professional managers and by individual investors such as yourself. There are several differences between the two types of security analysts. First, professional (institutional) managers have the time, money, and information to analyze these securities, but individual investors usually do not. Second, professional analysts have the knowledge and tools to value these securities because it is their job to do that. Individual investors are amateurs and do not always understand the complexities of the security valuation process. Figure 2.2 illustrates a simple example of the asset allocation and the security selection processes. At first, the investor has his investment budget, which he allocates between two asset classes, equities and debt securities, thus completing the asset allocation step. Next, he chooses among the various equities, such as IBM, McDonald’s (MCD), and other potential stocks and among the various debt instruments such as government bonds, corporate bonds, and the like. This completes the security selection step. There are many ways to conduct a security analysis, but two stand out: technical and fundamental analysis. Technical analysis refers to the identification of recurring patterns in the prices of individual stocks. Fundamental analysis deals with the economics of the firm in the sense that the company’s financial health or weakness is examined to determine its fair stock price. Both approaches seek to identify “good bargains” or mispriced securities for inclusion in the investor’s portfolio. We will see them again later in this chapter. The application of either approach to securities is difficult and challenging. As Chapter 4 explains, the analysts must deal with several pieces of information emanating from the company itself, the industry in which the company operates, and the economy, and they extend Investment Budget

Equities

IBM?

Figure 2.2 Asset allocation and security selection.

Debt

MCD?

Corporate Bonds, Government Bonds,?

The Investment Decision Process and Investment Strategies s 31

their analysis to the global economy. In addition, analysts analyzing equity securities must grapple with the notion of efficient markets, because if they are present in the markets for these securities, the security analyses are fruitless (as we will also see in Chapter 8).

GENERAL INVESTMENT PHILOSOPHIES AND STRATEGIES At the outset, every investor, whether individual or institutional, must adhere to the following steps: define his objectives and constraints, determine asset allocation, proceed with security analysis, and continue with portfolio evaluation and monitoring. Within this general framework the investor must answer some basic questions: How do I decide which asset classes to consider and which securities within each asset class to invest in? What is my investment state of mind? What strategy should I apply to my investment portfolio? How and how often do I assess the performance of my portfolio? This section discusses the various investor philosophies or investment styles and presents, in a very simple and brief manner, (some of) the investment strategies. Some Prominent Investment Philosophies This subsection contains the advice of a few prominent investment advisers, academic and professional, for the purpose of helping you understand various investment philosophies. Naturally, one question in particular might be in the minds of many investors: Can I beat the market? We will see that many (but not all) of the well-known professional managers, including those presented below, confess that they cannot beat the market. The market is efficient, they admit, and thus is it impossible to consistently find bargains. Let us now present two academics, Harry Markowitz and Paul Samuelson, both Nobel Laureate in Economics, and two professional managers, John Bogle and Warren Buffett, both legendary professional investment managers. Harry Markowitz Markowitz is considered the father of portfolio theory (which is discussed in Part III). He argued for a well-diversified portfolio (that is, selection of securities across a wide spectrum of investment instruments) in order to reduce risk. In building your portfolio, Markowitz said, you should take care not to include assets that move in tandem, that is, all going up or all going down at the same time. In that way, you minimize the risk of a “crash” of your portfolio when the market trends downward. Therefore he advocated not to “put all your eggs in one basket” but to diversify as much as possible. Paul Samuelson Samuelson said that it is not always true that you cannot lose money if you hold equities for the long run. Although he concedes that this may be a rational strategy for many investors, risk is not completely eliminated over the long run (whatever the definition of the long run is, 30 or 50 years). So his advice was not to spend too much time on checking and adjusting your investments. Investing should not excite you, he said, because you might be tempted to do something that you might regret later. Samuelson noted that the true value of a security is determined in the market from the wisdom of the masses and not by the intelligence of one (like your broker) or a few traders. Thus, if your broker gives you a “hot tip” on a stock, you should run for the hills, because he is simply speculating. He should not have any information that the market does not already have.

32 s Investment Basics

BOX 2.1 The Hedgehog Bests the Fox The Greek philosopher Archilochus tells us that the fox knows many things but the hedgehog knows one great thing. The fox—artful, sly, and astute—represents the financial institution that knows many things about complex markets and sophisticated marketing. The hedgehog— whose sharp spines give it almost impregnable armor when it curls into a ball—is the financial institution that knows only one great thing: long-term investment success is based on simplicity. The wily foxes of the financial world justify their existence by propagating the notion that an investor can survive only with the benefit of their artful knowledge and expertise. Such assistance, alas, does not come cheap, and the costs it entails tend to consume more value-added performance that even the most cunning of the foxes can provide. Result: the annual returns earned by investors who depend on financial intermediaries such as mutual funds have averaged less than 80% of the stock market’s annual return. The hedgehog, on the other hand, knows that the truly great investment strategy succeeds not because of its complexity or cleverness but because of its simplicity and low cost. The hedgehog diversifies broadly, buys and holds, and keeps expenses to the bare-bone minimum. The ultimate hedgehog, the all-market index fund, operated at minimal cost and with minimal portfolio turnover, virtually guarantees 100% of the market’s return to the investor. In the field of investment management, foxes come and go but hedgehogs are forever. Source: P. Jenks and S. Eckett, Investing Rules from the Masters (Englewood Cliffs, NJ: Prentice-Hall, 2002).

John Bogle The founder of the Vanguard Group of Mutual Fund Investments is an adamant advocate of a specific investment approach: passive. He advocates strategies such as buyand-hold and investing in an index fund. Thus you should invest in those assets that have the lowest expenses (trading costs) and be happy that you will earn what the average market earns. He believes that professional managers cannot beat the market (by actively trading in the market) and that it makes no sense for the investor to pay for such underperformance. In short, Bogle advises: Invest your well-diversified portfolio for the long run, paying attention to costs and taxes, and do not worry about your investments. See Box 2.1 for an additional insight from Bogle who uses the parable of the fox and the hedgehog to describe two types of financial institutions in their investing quests. Warren Buffett Owner and CEO of Berkshire Hathaway Inc., Buffett made his fortune by applying valueinvesting philosophies and strict discipline in his investment moves. He was a student of Benjamin Graham, the father of modern investing and value investing, and followed this conservative rule for stock picking: Buy a company’s shares that are much cheaper than the company’s overall net worth would imply. Also, invest in well-known companies whose names are deeply entrenched in the minds of all investors—in companies whose businesses you can appreciate and understand, and do your homework before investing (that is, study the fundamentals of the companies you are interested in). One of his famous sayings is “Try to be fearful when others are greedy and greedy when others are fearful.”3 The common message from these great minds is that you must be an intelligent, patient, and disciplined investor. You would be better off investing for the long run and not

The Investment Decision Process and Investment Strategies s 33

BOX 2.2 Example of a Risk Tolerance Questionnaire What is your age? 50 years (15 points)

Do you expect your annual income to grow or decline moderately or strongly over the next 5 years? Yes, grow moderately (5 points)

Yes, grow strongly (10 points)

When would be your expected (estimated) need for money over the next 5 years? 10 years (15 points)

How much more risk are you willing to bear in order to (potentially) earn higher returns in the future? Data Analysis > Descriptives.15 The output is shown below.

Diversification and Asset Allocation s 217 Descriptive Statistics on the Stocks Stock X Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count

Stock Y 0.12 0.003477 0.12 0.12 0.013009 0.000169 −0.84974 −4.2E−15 0.04 0.1 0.14 1.68 14

Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count

0.031429 0.00312 0.03 0.03 0.011673 0.000136 −0.43903 0.020726 0.04 0.01 0.05 0.44 14

You should be able to see that the mean of stock X is 0.12 or 12% and the mean of stock Y 0.031 or 3.1%. Their standard deviations are 0.013 and 0.011, respectively. From your statistics course, you should know what the other summary statistics imply. We next present the outputs for the two stocks’ correlations and covariance(s), using again the same menu (do the following: Tools > Data Analysis> Covariance or Correlation). The outputs are: Correlation Stock X Stock Y

Stock X 1 0.202622108

Covariance Stock Y 1

Stock X 0.000157143 2.85714E-05

Stock Y 0.000126531

The correlation between stocks X and Y, XY = 0.202, implies a weak positive correlation between the two stocks. The other two correlation numbers are not used but simply show the correlation of each stock with itself. The covariance between the two stocks, covXY = 2.857 − 05 (which means that there are five zeros before the number 2) implies a positive covariation between the two stocks. In sum, there is very little positive comovement (covariation) between the two stocks. Finally, the regression output was created by going again to Tools > Data Analysis > Regression and inputting into the required slots in the menu window the column (or row) for Y and then for X and clicking OK. In essence, you run the following regression equation: Yt = a + b Xt + et where Yt is the dependent variable, Xt is the independent variable, et is the error term, and a and b are parameters to be estimated. This regression simply states that we assume some stochastic relationship between X and Y over time and that we assume that X affects Y. We are mostly interested in the estimated equation and the values of the coefficients, the constant, a, and the slope, b. An excerpt of the regression output is as follows:

218 s Portfolio Theory

Regression Statistics 0.202622108 0.041055718 −0.038856305 0.011897833 14 Coefficients 0.00961039 0.18181818

Intercept X variable

Standard Error 0.030605157 0.253662662

T Stat 0.314012095 0.716771559

P Value 0.75890368 0.48723197

The numbers of interest are the coefficients for the constant (intercept) and the X variable. We can now rewrite the above equation as the estimated regression equation, as follows: Y t = 0.0096 + 0.1818 X t

where the “hat” above the dependent variable denotes the estimated variable. The regression line’s intercept is 0.0096 and the slope is 0.1818. The intercept implies an average rate of return for stock Y when there is no influence by stock X. The slope means that if X changes by say 10%, stock Y’s return would change by 10% · 0.1818 = 1.81%. The slope is a very important number when we run regressions between a stock (or a portfolio) as Y or against a market index as X (as we will see in the next chapter). Finally, the R-square value, 0.0410, indicates that only 4.10% in the variation of Y is explained by changes in X. The rest (95.9%) is due to factors we have omitted. The graph below shows the estimated regression line or by checking the “line fit plot” square in the regression dialog (the red diamonds are the values between X and Y) and the red upward-sloping line is the estimated regression line (in fact, if you extend the solid line all the way to the vertical axis, you will see that it intersects it at 0.0096). 0.06 0.05

Y

0.04 0.03 0.02 0.01 0 0

0.05

0.1

0.15

X

We will see the significance and interpretation of this line and the difference between the dots (the red diamonds) and the line itself in the next chapter. But now it is sufficient for you to refresh your memory on how regression is run in EXCEL and how to interpret some basic outputs.

Diversification and Asset Allocation s 219

You should try to do regression with a stock of your own choosing and the market, for example. Convert both the stock and the market index into returns and do the regression. The intercept is the stock’s alpha coefficient and the slope its beta coefficient. We will see this regression in the next chapter in some detail. But for now, just try to estimate the regression equation.

APPENDIX B How to Compute the Covariance and Correlation in EXCEL xcel The menu in EXCEL to compute these magnitudes, as well as each stock’s rate of return and standard deviation, is found in the menu Data by selecting the submenu Data Analysis. If you cannot find this submenu in the Data menu, do the following (see also note 9 at the end of the chapter): sClick on the Microsoft icon on the top left of the EXCEL page. sAt the bottom of that window, click on Excel Options. sOn the left column of the new window, select (and double-click) Add-ins. sAt the bottom of the new window, select Excel Add-ins and click Go. sFinally, check the first two squares for Analysis ToolPak and Analysis Toolpak—VBA and click OK. sThen go to the original, main EXCEL menu and select Data. sYou should see, at the far right of the horizontal row of submenus, Data Analysis. sThat is the tool you will need to do the above computations and more. Using the data for the two stocks, X and Y, from Appendix A, we computed the covariance and correlations between the two stocks. Note that these calculations are based on Eqs. 13 and 14 because we use historical data and not expected data. The EXCEL output is shown below. X

Y

Covariance output

0.1

0.03

0.12

0.05

Column 1

0.000157143

0.11

0.04

Column 2

2.85714E-05

0.13

0.03

0.12

0.04

0.14

0.05

0.1

0.03

0.11

0.02

Column 1

1

0.13

0.04

Column 2

0.202622108

0.13

0.03

0.12

0.01

0.14

0.02

0.12

0.03

0.11

0.02

Column 1

Column 2

0.000127

Correlation output Column 1

Column 2

1

220 s Portfolio Theory

What is the covariance between stocks X and Y? It is 0.0000285714 (highlighted in red). Thus, we conclude that the two stocks positively covary or comove. The correlation coefficient between the stocks is 0.2026, which is positive but small. Thus we infer that the two stocks correlate positively but weakly.

NOTES 1. 2. 3.

4. 5. 6. 7. 8.

9. 10. 11. 12. 13.

14. 15.

Meir Statman, How many stocks make a diversified portfolio? Journal of Financial and Quantitative Analysis, 22, September 1987, p. 355. Bruno Solnik, Why not diversify internationally rather than domestically? Financial Analysts Journal, July 1974, pp. 48–54. The graph was generated in EXCEL using hypothetical data on a 60-asset portfolio with a standard deviation of 30% and a correlation coefficient of 40%; then the same number of securities were used assuming that they had a standard deviation of 25% and a correlation coefficient of 20% (to simulate the international portfolio). Nikiforos T. Laopodis, Portfolio diversification benefits within Europe: implications for a US investor, International Review of Financial Analysis, 14, 2005, pp. 455–476. See http://www.vanguard.com/pdf/icrieid.pdf Harry M. Markowitz, Portfolio selection, Journal of Finance, 7(1), 1952, pp. 77–91. Appendix A to this chapter offers a review of regression analysis, which differs from correlation analysis, and will be useful in later chapters. Gary P. Brinson, L. Randolph Hood, and Gilbert L. Beebower, Determinants of portfolio performance, Financial Analysts Journal, 42(4), July/August 1986, pp. 39–48, and Determinants of portfolio performance II: an update. Financial Analysts Journal, 47(3), May/June 1991, pp. 40–48. Roger G. Ibbotson and Paul D. Kaplan, Does asset allocation policy explain 40, 90, or 100 percent of performance? Financial Analysts Journal, 56(1), January/February 2000, pp. 26–33. William Jahnke, The importance of asset allocation, Journal of Investing, 9(1), Spring 2000, pp. 61–64. Roger G. Ibbotson, The importance of asset allocation, Financial Analysts Journal, 66(2), 2010, pp. 1–3. See Zvi Bodie, Alex Kane, and Allan J. Marcus, Essentials of Investments (New York: McGraw-Hill, 2007), p. 134, for this analysis of A. The variance of this portfolio, and its square root or standard deviation, is found by substituting z and (1-z) in lieu of the w’s (wH and wN weights) in equation (3) in Chapter 8, and recalling that the standard deviation of the risk-free rate is zero, noting that its covariance with the risky asset (or portfolio) is also zero. Paul A. Samuelson, Risk and uncertainty: a fallacy of large numbers, in Joseph E. Stiglitz, ed, The Collected Scientific Papers of Paul A. Samuelson (Cambridge, MA: MIT Press, 1966), pp. 153–158. If your version of EXCEL does not have Data Analysis in the Tools main menu, do the following: from Tools, click Add-ins, and select the Analysis Toolpaks-VBA. Then return to Tools and you will see Data Analysis toward the end of the drop-down menu.

8 EFFICIENT DIVERSIFICATION AND CAPITAL MARKET THEORY

CHAPTER OBJECTIVES When you finish studying this chapter, you should be able to sUnderstand how covariance and/or correlation affect portfolio risk sFind the optimal risky portfolio sOptimally allocate funds between a riskless asset and the optimal risky portfolio sUnderstand the capital market theory and its implications for pricing assets sDerive and apply the capital asset pricing model (CAPM) and the arbitrage pricing theory (APT) sUse the CAPM and APT to make investment decisions sCompare the performance of risky portfolios

INTRODUCTION The previous chapter showed how to compute and interpret the portfolio’s expected return and risk as well as the covariance and correlation between two risky assets. Then it was shown how simple diversification strategies work between two risky assets and between two risky assets with the risk-free rate in a portfolio. In this chapter, we extend (generalize) the analysis to many risky assets, illustrating the Markowitz principles of efficient diversification. This analysis is known as mean-variance analysis and is based on the construction of an efficient portfolio of risky assets. Next, we examine two very important market equilibrium theorems in finance and investments that involve specifying and estimating the expected return/risk trade-off. One is the capital asset pricing model (CAPM) and the other is the arbitrage pricing theory. Finally, we compare them to see which one is “better.” We then conclude with some investment strategies that these two models suggest.

221

222 s Portfolio Theory

THE MARKOWITZ DIVERSIFICATION APPROACH Before we begin showing this approach, it will be useful to reproduce some formulas learned thus far. We will also provide an alternative way to compute the risk of a risky portfolio. 1. The rate of return and the expected rate of return on a portfolio of two risky assets, N and H, are: rp = wN rN + wH rH and

E(rp) = wN E(rN) + wH E(rH)

(1)

2. The sum of the weights, w, of n risk assets is: n

∑ wi i =1

=1

so in our case, wN + wH = 1

(2)

3. The variance of a two-asset risky portfolio, with variances  2N and  2H, is:  2p = (wN  N)2 +(wH  H)2 + 2 (wN  N)(wH  H)ρNH or  2p = (wN  N)2 +(wH  H)2 + 2 wN wH CovNH

(3) (3a)

The variance of the two-asset portfolio is the sum of the weighted contributions of each risky security’s variance plus a term with the correlation (or the covariance) between these two assets. This rule highlights the impact of covariance (or correlation) on portfolio risk. A positive/ negative covariance increases/decreases portfolio variance. Viewed another way, a positive/ negative correlation enhances/reduces the volatility of the portfolio and, in the case of a hedge, a negative correlation enhances its riskreduction feature. Recall that in Chapter 7 we computed the variance of the two risky assets, N and H, and called it the hedged portfolio, using Eq. 3, and found the variance to be 4.00 (the standard deviation is 2.00%). The weights for each security, N and H, were 50:50, and their respective standard deviations 8.28% and 4.59%. The correlation coefficient was −0.9653, and their covariance was −36.68. Now let us apply Eq. 3a to see if we obtain the same result:  2p = (0.5 × 8.28)2 + (0.5 × 4.59)2 + 2 × 0.5 × 0.5 × (-36.68) = 4.00 and  p = 2% A standard deviation of 2% is exactly what we found previously. Needless to say that we would have found the same result if we had applied Eq. 3. You can try it as an exercise. Now let us continue with an illustration of the Markowitz diversification strategy. The Markowitz Two-Asset Portfolio Markowitz’s diversification strategy is more effective in reducing portfolio risk than the simple diversification strategy suggested. That is what we showed, in part, in the previous

Efficient Diversification and Capital Market Theory s 223

chapter, when we calculated the risk/return characteristics of the hedged portfolio. What we ignored then was the relationship between the two assets as measured by the covariance or correlation, and that is why we did not use Eqs. 3 or 3a. To further understand the significance of the correlation between the two assets (or more, as we will show later) let us work with the previous example again. The assets’ standard deviations were 8.28% and 4.59% for N and H, respectively. To compute the risky-asset portfolio’s standard deviation, one could simply say: Let us sum up the two assets’ standard deviations (assuming equal weights) and divide by 2. The result would then be 6.43% [or (8.28 + 4.59)/2], which would have incorrectly increased the portfolio’s risk by 4.43%! In reality, the addition of the second stock to the original stock reduced the portfolio’s risk substantially, to 2%. This gain in diversification is like a “free lunch,” because it allows for the full contribution of a risky asset’s expected return while keeping the overall portfolio’s standard deviation below the average of each of the risky asset’s standard deviations. What is the impact of the values of the correlation coefficient on the portfolio’s risk? The correlation coefficient is bounded between −1 and 1 and has the following interpretations (to refresh your memory from Chapter 7):

NH = +1

This means that there is a perfectly positive correlation between N and H. For example, if one asset’s return changed by 10%, the other asset’s return would change by exactly 10%:  2p = (wN  N)2 +(wH  H)2 + 2 (wN  N)(wH  H)ρNH or  2p = (wN  N + wH  H)2 That is, NH = −1. This means that there is a perfectly negative correlation between N and H. For example, if one asset’s return changes by 10%, the other asset’s return will change by exactly 10% in the opposite direction:  2p = (wN  N)2 +(wH  H)2−2 (wN  N)(wH  H)ρNH or  2p = (wN  N−wH  H)2 That is, NH = 0. This means that there is no correlation between N and H. For example, if one asset’s return changes by 10%, the other asset’s return will not change at all:  2p = (wN  N)2 +(wH  H)2 because the third term is zero. Note that a negative correlation coefficient reduces the portfolio’s standard deviation, but a positive one increases it to the fullest extent. To gain further insight on the above, assume that you have two risky securities, N and H, whose rates of return are 10% and their standard deviations 25%. To form various two-asset portfolios, you need to know the percentages invested in each asset and their return correlation. If you apply a 50:50 weighing scheme and vary the return correlation coefficients only, you would have the following results: for every different correlation value, the portfolio’s rate of return would not change, it would always be 10%. The portfolio’s risk, however, would change as follows:

224 s Portfolio Theory

If NH = +1:  2p = (0.5 × 25)2 +(0.5 × 25)2 + 2 (0.5 × 0.5 × 25 × 25 × 1) = 625 and p = 25.00% If NH = 0:  2p = (0.5 × 25)2 +(0.5 × 25)2 + 2 (0.5 × 0.5 × 25 × 25 × 0) = 312.5 and  p = 17.67% If NH = -1:  2p = (0.5 × 25)2 +(0.5 × 25)2 + 2 (0.5 × 0.5 × 25 × 25 ×−1) = 0 and  p = 0.00% Figure 8.1 below shows these three outcomes. As you see, portfolio risk can be completely eliminated when one is holding only two assets whose return correlation is −1. In reality, however, this does not happen since (S&P 500) equity securities, for instance, have a positive correlation coefficient that is about 0.45.1 By holding two securities whose return correlation is a perfect 1, there is no risk reduction whatsoever. A more illuminating example is to vary the weights invested in each of these assets and changing their return correlation. Assume that the two securities have the following data: E(rN) = 10%; E(rH) = 15%;  N = 20%;  H = 30%. Table 8.1 shows the data and the results from various weight-correlation combinations. As you observe, the levels of portfolio risk change as correlation changes (the portfolio’s expected returns remain the same). In fact, if you do this exercise with greater precision (i.e., by changing the weights by 0.01), you could see the impact on the portfolio risk much better. This effect is also exhibited in Figure 8.2 (where expected return is on the vertical axis and risk on the horizontal axis). When the correlation coefficient is 1, you simply increase risk, as shown by the straight upward-sloping line starting at 20% risk and ending at 30%. When the correlation coefficient is zero, you get some reduction in risk, as seen by the curved line. But the more profound evidence of full and costless risk elimination takes place when the correlation coefficient is −1. Risk goes to zero, as evidenced by the bent straight line intersecting the vertical axis. A summary of the above important results is contained in Table 8.2.

expected return 20% ρNH = −1

ρNH = 0

ρNH = +1

10%

0

10%

20%

30%

40%

portfolio risk (σ)

Figure 8.1 Impact of correlation on portfolio risk.

Efficient Diversification and Capital Market Theory s 225 Table 8.1 Two-Asset Portfolio Expected Return and Risk for Three Correlation Coefficients Weights in

Portfolio ( = +1)

Portfolio ( = −1)

Portfolio ( = 0)

N

H

E(rp)

p

p

p

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00

15.0% 14.5 14.0 13.5 13.0 12.5 12.0 11.5 11.0 10.5 10.0

30.0% 29.0 28.0 27.0 26.0 25.0 24.0 23.0 22.0 21.0 20.0

30.0% 25.0 20.0 15.0 10.0 5.0 0.0 5.0 10.0 15.0 20.0

30.00% 27.07 24.33 21.84 19.69 18.02 16.97 16.64 17.08 18.24 20.00

20.0%

Expected Return-Risk

15.0% 10.0% 5.0% 0.0% 0.0%

10.0%

20.0%

30.0%

40.0%

Figure 8.2 Impact of correlation on two-asset portfolio return and risk with varying weights.

Table 8.2 Correlation Coefficients, Diversification Benefits, and Portfolio Risk Correlation

Diversification Benefits

Portfolio Risk

= +1

= −1

=0

No diversification benefits Full benefits to diversification Substantial benefits to diversification

Increases Goes to zero Decreases

An interesting question arises at this point. If investors are shown all this, what would be the optimal investment proportions that would reduce portfolio risk? First, let us observe the results in Table 8.1 and Figure 8.2. The minimum-variance portfolio for = 0 is 16.97% and for = −1, 0.00%. Now, let us find the optimal weights for N and H so as to achieve this minimum-variance portfolio. We will show this for = 0 and = −1.

226 s Portfolio Theory

Recall Eq. 3 above for the portfolio’s risk. Setting = 0, we obtain  2p = (wN  N + wH  H)2. Expanding the equation and setting wN = 1—wH, we get:  2p = (wN  N)2 + (wH  H)2 = (1- wH)2  2N + w2H  2H Setting the above equation equal to zero and taking its first derivative with respect to wN, we obtain (after dropping the 2s): 0 = 2(1−wH)  2N + 2wH  2H   2N − wH  2N + wH  2H = 0   2N = wH  2N + wH  2H and finally, solving for wH, we arrive at the final equation: wH =  N2 / ( N2 +  H2)

(4)

Applying Eq.4 to the data above, we obtain: wH = (20)2 / [(20)2 + (30)2] = 0.30. Thus, 30% should be allocated to security H and 1−0.30 = 70% to security N. In a similar fashion, we derive the optimal weights when the correlation coefficient is −1. In this case, Eq. 3 is a complete square; thus we can easily drop the two squares from both sides of the equation. We are then left with

p = wN  N−wH H

And since there is a possibility that the final result might be negative, we conventionally express it as an absolute value, as follows: p = |wN  N−wH H| Setting again wN = 1−wH, we have:

p = (1−wH)  N − wH  H  N−wH N − wH H

Then, by setting the equation equal to zero and solving for wH, we get: wH = N / (N + H)

(5)

Applying it to the data above, wH = 20 / (20 + 30) = 0.40, or 40% allocated to H and 60% to N, which are exactly those weights (from Table 8.1) that bring the portfolio’s standard deviation to zero. A related question is whether the investor should prefer the minimum-variance portfolio to another portfolio. The answer depends upon the investor’s preferences and risk tolerance. One simple way of understanding this is to realize that the minimum-variance portfolio also has the lowest expected return. Perhaps there is another portfolio of securities available (in the asset universe) that offers the same risk but a higher return. Although we will not give the full answer here, the investor’s portfolio adviser needs to provide his client with the full set of possible portfolios. In other words, the investor must choose from the investment opportunity set, which is composed of all the available portfolio risk/ return combinations. We need to examine this case carefully, and we will do that below.

Efficient Diversification and Capital Market Theory s 227 Table 8.3 Two-Asset Portfolio Expected Return and Risk with Short Sales Weights in

Portfolio (ρ = +1)

Portfolio (ρ = −1)

Portfolio (ρ = 0)

σp

σp

σp

N

H

E(rp)

−0.2 −0.1

1.2 1.1

16.0 15.5

32.0 31.0

40.0 35.0

36.2 33.0

1.00 0.00

15.0% 10.0

30.0% 20.0

30.0% 20.0

30.00% 20.00

9.50 9.00

19.0 18.0

25.0 30.0

22.2 24.7

0.00 1.00 1.1 1.2

−0.1 −0.2

Let us now extend the above analysis to consider situations where the investor borrows some money to invest in addition to his own money. In that way, investors create leveraged or borrowing portfolios. The investor borrows money (from his broker) to invest in more securities, and by doing so he attaches negative weights to these securities. Negative weights can be thought of as representing a short sale of securities. Alternatively, negative weights mean that the investor has constructed (or built on margin) a borrowing portfolio by purchasing securities using borrowed money (which must be returned in the future, of course) but gets to keep the proceeds (if the investor is an institutional investor). In the preceding analysis, the weights were all positive, but they still need to sum up to 1 (or 100%). The result with negative weights would be a continuation of the values in Table 8.1. We show some of these negative weights and values (in boldface) in Table 8.3, with selected weights so you can get the idea. First, what is the economics behind this analysis? As you might recall, leveraged positions magnify expected returns, and as you see from Table 8.3, the expected returns are higher than 15% because of borrowing. What is more important from the above analysis is that if you sell short the low-yielding asset, here H, to obtain funds to finance a higher position in the high-yielding asset, here N, you earn a higher return. The opposite is true when you sell short the higher-yielding asset to finance a greater position in the loweryielding asset. In this case, your expected rate of return on your portfolio declines (to 9% if you sell H short). The other insight from this analysis is that the investor’s opportunity set is expanded when it allows for short sales. Although short selling is prohibited by some institutional investors, such as mutual funds; other funds, such as hedge funds, are heavily leveraged. But as you already know, leverage can hurt you badly during bad economic times, such as the financial crisis of 2008. Hedge funds took a beating as investors withdrew their funds and hedge funds had to continue deleveraging to meet these demands. The box titled International Focus discusses three European pension fund managers’ perceptions of long-short strategies. The Optimal Risky Portfolio and the Capital Allocation Line Now let us expand our analysis to find the optimal risky portfolio to be paired with the risk-free rate in an effort to find the investor’s optimal overall portfolio. Including

228 s Portfolio Theory CAL1

expected return

CAL2

CAL3 O

A

B

opportunity set

3.0%

0.0%

5.0

10.0

16.6 17.0 17.6 20.0 25.0 portfolio standard deviation

30.0%

Figure 8.3 The investor’s opportunity set with the CAL.

the risk-free rate involves the capital allocation line (CAL). We start the analysis with the same two risky assets, N and H, and then expand it to all the risky assets. Assume that the risk-free rate yields 3%. Figure 8.3 shows the investor’s opportunity set (the curved line) with three possible CALs. Which one (i.e., CAL) offers the best possible risk-return combination between the risky and the risk-free assets? We learned in the previous chapter that the CAL shows the return per unit of risk; thus the better that ratio, the better off the investor. The opportunity set in the graph was derived with NH = 0. Which is the best CAL? To answer that, we need to compute each CAL’s slope. Let us use the data from Table 8.1. Consider CAL3 first. The expected return on the portfolio is 11% and its standard deviation 17.08%. The slope of that CAL, S3, at point B is as follows: S3 = (E(rp)−rf ) / p  S3 = (11−3) / 17.08 = 0.4684 This means that the investor obtains 0.4684 extra expected return per unit of risk. Is that the best the investor can do? Let us examine CAL2, which is drawn (on purpose) through the minimum-variance point on the opportunity set at point A. The expected return on the risky portfolio was 11.5% and its standard deviation 16.64%. What is the slope of that CAL, S2? S2 = (11.5 − 3) / 16.64 = 0.5108

Efficient Diversification and Capital Market Theory s 229

Since the slope is higher, CAL2 is a steeper line than CAL3. This means that this combination of risky assets with the risk-free asset gives a higher expected return per unit of risk by 0.5108 − 0.4684 = 0.04. Hence, risk-averse investors would want to have overall portfolio A, on the graph, and not portfolio B. Hence in this sense portfolio A dominates portfolio B. But why stop at portfolio B? Can the investor go beyond it to achieve an even better risk/return mix? Yes, and we can examine an even steeper CAL, CAL1. This CAL is shown to be tangent to the opportunity set at point O. At that point, the investor achieves the best possible mix of risky and the risk-free assets because it attains the highest return per unit of risk. Let us show this using the data from Table 8.1. The optimal weights for N and H are found using the formula below (for NH = 0):

wN =

[E(rN ) − (rf )] σ2H [E(rN ) − (rf )] σ2H + [E(rN ) − (rf )] σ2 N

=

(10 − 3) 302 = 0.5678 (10 − 3) 302 + (15 − 3) 202

w H = 1 − 0.5678 = 0.4324 Also, given the above weights, the portfolio’s expected return is now 12.16% and its standard deviation 17.24%. Now we are ready to find the slope of CAL1: S1 = (12.16 − 3) / 17.24 = 0.5313 which is the highest number for any slope using the data in our example. Thus CAL1 is the steepest one, and it is just tangent to the opportunity set at point O, the optimal point. Why is point O the optimal one? Can’t the investor improve his mix by being on an even steeper CAL? The answer in this case is no. Think for a moment why, from your economics course, a demand curve (for a product) exists. If you recall, a demand (for a product) exists when both the willingness and the ability to buy exist. Therefore in this case the willingness to achieve a better risk/return combination exists (you would like that—and, of course, more is preferred to less, as you also know from microeconomics), but the ability to achieve that higher level of return/risk mix does not exist! This means, that there is no opportunity set (or assets) beyond point O that would give you a higher risk/return mix. Therefore, we have reestablished that point O is the optimal point for the investor and that point is found by the point of tangency between the highest-sloping CAL and the opportunity set. The tangency portfolio is also known as the optimal risky portfolio, which then can be combined with the T bill to form the investor’s overall portfolio. Finally, what about the investor’s overall portfolio’s expected return and risk? Given the optimal weights for the two risky assets computed above and recalling (from Chapter 7) that the investor had selected 52% of her funds to be invested in the risky portfolio (specifically, 0.5678 × 52% = 0.2953 in N and 0.4324 × 52% = 0.2248 in H for a total of 52%) and the rest (48%) in T bills, we obtain:

E(ro) = 3 + 0.52(12.16 − 3) = 7.76% o = 0.52 × 17.24 = 8.97%

230 s Portfolio Theory Expected return optimal

12.16%

CAL

overall 7.76% 3%

0.0%

8.97% Portfolio standard deviation

17.24%

Figure 8.4 The investor’s optimal risky and overall portfolios.

Figure 8.4 shows the investor’s overall portfolio with a expected return of 7.76% and standard deviation of 8.97% and the optimal portfolio with expected return of 12.16% and standard deviation of 17.24%. The Efficient Frontier Let us begin with a simple question. How can additional risky assets improve the investor’s investment opportunity set? The easiest way to answer this is to look at Figure 8.5. In that figure, the dots represent various risky assets and are plotted by their expected returns and their standard deviations. We have labeled some of them as A, B, C, and D. Now let us explain some of these points. Start with asset B. The question is this: Would you prefer asset B to asset A (which is directly above asset B)? The answer is no. You would prefer asset A to B because A offers higher expected return with the same level of risk as B. Thus you would move north from point B. A similar question is whether you prefer B to C (which is horizontally to the left of B). Again, you should answer no because C gives you the same expected return but with lower risk. Thus you would move left(ward) in the risky-asset plane. Finally, would you prefer asset D to B? Yes, because D offers a better risk/return mix than asset B. Therefore you would move northwest. In sum, by moving west, north, and northwest we would find those assets that would be closer to the drawn curved line and specifically those that would lie on that line. This curve is called the efficient frontier (EF) and represents the set of assets (or portfolios) that offer the highest possible risk/expected return combinations. All other assets that lie within the curve are inefficient or are dominated by other portfolios. In other words, they are not efficiently diversified and thus do not offer the best possible risk/return mix. Only those on the efficient frontier have those characteristics. Another way to interpret this is to notice that the investment opportunities to an investor are represented by a convex curve. Finally, point M shows the minimum variance portfolio, which implies that all efficient portfolios should lie above that point on the EF. What are the two conditions that must be satisfied, or the mean variance criteria, for deriving the efficient frontier? E(rA)  E(rB) and A  B

Efficient Diversification and Capital Market Theory s 231 Expected return Efficient frontier A D C

B

M

0.0%

Portfolio standard deviation

Figure 8.5 The Markowitz efficient frontier.

where A and B are the same assets above. In general, portfolio A is said to dominate portfolio B if all investors prefer A over B. This would be the case only if A has higher expected return and lower variance than B. Now we are in the position to generalize the investor’s optimization problem, which is to find the optimal risky portfolio and combine it with the risk-free asset. The steps are as follows: sFind the optimal mix of risky assets (point O) sCombine it with the risk-free rate (by finding the steepest CAL) sChoose the appropriate mix between optimal risky assets and the risk-free rate Appendix A at the end of this chapter shows how to find the optimal point with two assets and the risk-free rate. The investor’s problem is facilitated by the investment adviser’s ability to offer him (and to any investor, for that matter) the optimal risky portfolio irrespective of his (or the other investors’) degree of risk aversion. This is the technical component of the determination of the investor’s overall portfolio. The investor’s task, however, entails selecting the fractions of funds invested in the risky portfolio and the risk-free rate. That depends upon his specific level of risk tolerance. The investor’s input is the second component of this process. These two parts imply that the investor’s portfolio choice can be separated into the technical and the personal part is known as the separation theorem (or property), first put forth by Tobin (1958),2 the 1983 Nobel laureate in economics. Another implication of this theorem is that if the optimal risky portfolio is the same for all investors, then professional management can deliver that with maximum efficiency and at the least cost. In fact, the wide applicability of this theorem gave rise to the explosive growth of the mutual fund industry. That is why the theorem is sometimes also called the mutual fund theorem. Some caveats are in order. First, some investors may be constrained from having the optimal risky portfolio because of tax considerations, dividend yield requirements, short sales, or other specific preferences. But the point is that the optimal risky portfolio will be sufficient to meet the investment needs of the average investor. Second, a major problem

232 s Portfolio Theory

in the creation of the efficient frontier is the plausibility of input assumptions. In other words, although some inputs are known (from historical data), others either need to be estimated or may be uncertain. Finally, an equally important difficulty is selecting the appropriate portfolio on the efficient frontier. Although based on economic theory, the answer is easy: just select the one that maximizes the investor’s expected utility; in reality, no investor can specify a “utility function.” Instead, the investor makes subjective judgments, and these may not always be the optimal ones. At this point, read the box titled Applying Economic Analysis, which discusses how a utility function can be specified and how it helps an investor with decisions that involve risk. You would probably recognize that the above analysis is an example of normative economics, which deals with what the investor should do. In the next section, we discuss the appropriate way to price an asset—that is, we will apply positive economic analysis.

CAPITAL MARKET THEORY In this section, we present and discuss economic equilibriums, where the supply of and demand for an asset meet so that the price of the asset does not change. Two market equilibriums are the capital asset pricing model (CAPM) and the arbitrage pricing theory (APT). Both provide an economic framework for pricing assets by relating a security’s expected return to a measure of risk for that security that emanates from the market. Thus expected return is positively related to the level of risk involved. But what is the mathematical relationship between expected return and risk? We begin with the CAPM. The Capital Asset Pricing Model Let us begin with an important question: If all investors select the optimal risky portfolio, what would be the impact on security expected returns and prices? The answer involves knowledge of how equilibrium prices and expected returns are achieved. We start by recalling the concept of the capital market line (CML) and its relevant equation: E(rp) = rf + [(E(rm) − rf ) / m] p

(6)

This equation suggests that the expected return on an efficient portfolio is composed of the minimum compensation required by the investor, offered by the Treasury bill, plus a risk premium for bearing risk inherent in the portfolio. The magnitude of the risk premium—the market risk premium—is adjusted by the portfolio’s standard deviation and the current market risk premium per unit of market risk. This relationship depicts market equilibrium, where the quantity of shares demanded by investors just equals the quantity of shares supplied in the market. A related and broader relationship is the security market line (SML), which relates an individual security’s (or a portfolio’s) expected return to the risk-free rate and the relative risk of the security (or portfolio). The SML’s equation is as follows: E(ri) = rf +i [(E(rm) − rf )]

(7)

Efficient Diversification and Capital Market Theory s 233

As before, the difference between the expected return on the market and the risk-free rate is the market risk premium. In this case, however, the risk premium is adjusted in relative terms through a coefficient known as the beta coefficient. What are some other differences between CML and SML? The CML uses standard deviation as a measure of risk, whereas the SML uses the security’s beta coefficient (which reflects the security’s risk contribution to portfolio risk). Also, CML delineates efficient portfolios, while SML defines (or graphs) all portfolios (efficient and inefficient). Finally, SML is a tool to determine whether a security is undervalued or overvalued for inclusion or not in the portfolio, respectively. We discuss this further below. Let us now begin deriving the CAPM by stating its assumptions first.3 Then we will trace the implications and elaborate on them. Assumptions of the CAPM To derive the basic version of the model, we need to make several simplistic assumptions. The main idea behind these assumptions is that investors are very much alike and that they face the same objectives and constraints. The only thing that differs is their relative degree of risk aversion. Although the assumptions do not really represent actual security market conditions or investor behavior, they are nonetheless useful in deriving a simple model of market equilibrium. The following assumptions state that all investors: sPossess homogeneous expectations. This means that all investors have access to all available information, process it the same way, and derive the same risk/return characteristics (that is, expected returns, standard deviations, correlations, etc.) for all assets. sFunction in a frictionless market. In this simplistic economy, there are no transaction costs, no taxes, and each investor has no impact on a security’s price. This, in turn, implies that investors operate in a perfectly competitive environment. Only aggregate trades cause asset prices to move to equilibrium. sHave an identical investment planning (holding) horizon. This means that there is only one holding-period horizon for all investors and that horizon is the long run. sAre mean-variance optimizers. This means that all investors construct efficient frontier portfolios and attempt to maximize their utility. The latter implies that investors are never satiated and if given the opportunity to choose among portfolios, they would select the one with the highest expected return. sHave access to the same available universe of publicly traded assets. This further implies that assets are assumed to be infinitely divisible and that investors are free to borrow and/or lend at the same risk-free rate. Implications of the Assumptions Given the above assumptions, what are their implications for market equilibrium? Let us list these implications and discuss them further. Implication 1 All investors will select the market portfolio. What is the market portfolio (M)? A market portfolio is one that includes all publicly available traded assets. Each asset is held as proportion to its market value. We had called it the market portfolio (in Chapter 7), replacing the risky portfolio (P). In the previous section, we generalized it and called

234 s Portfolio Theory Expected return

CML EF M

E(rm)

σm

Standard deviation

Figure 8.6 The capital market line and the efficient frontier.

it the optimal risky portfolio. Therefore the market portfolio is also the optimal risky portfolio (O) and it will lie on the efficient frontier (EF). This is one of the most important implications of the standard version of the CAPM (which we will derive later). Consequently the investor will attempt to construct his optimal overall portfolio by combining the risk-free rate and the market portfolio, which is found at the tangency point between the CML and the efficient frontier. Graphically, that tangency point is M (see Figure 8.6). Why would all investors want to hold the market portfolio? In view of the above assumptions, holding the market portfolio would be rational because it is the optimal one. Furthermore, the market portfolio is the most widely diversified portfolio, which essentially means that there is no way to further diversify risk. Let us do some economic analysis to see why all securities should be included in the market portfolio. Assume that a particular stock, N, is not part of this portfolio. If no one wants to hold security N, its demand will be zero and its price will tumble. As its price falls continuously, beyond a certain price it will begin to look attractive to investors relative to other securities. The low price will make investors purchase it and ultimately include it in their portfolios. Such continuous price adjustments (either downward or upward) will guarantee that all securities will be included in the market portfolio. Now what about the investment strategy that investors should apply if the CML is the optimal one? The model suggests that a passive approach to investment is the optimal one. In equilibrium (point M on Figure 8.6), there is no more profit to be made by investors. Investors who simply invest in a market index derive the full benefits from this market (or the efficient) portfolio. At the same time, they economize on costly and time-consuming security analysis, which would be part of the alternative active investment strategy. Implication 2 The market risk premium will be a function of both the investor’s degree of risk aversion and the variance of the market portfolio itself. Algebraically, E(rm) − rf = A 2m

(8)

Efficient Diversification and Capital Market Theory s 235

as you might recall from Chapter 7 (the equation here is without the scalar factor, but this does not alter the result or the interpretation). Let us explain this implication. The forces of demand for and supply of assets drive up and down their prices and down and up their expected returns, respectively. Therefore, as risk premiums change, investors would reallocate funds between risky and the risk-free assets. For example, if the risk premium falls, more risk-averse investors would allocate more funds to the risk-free rate and less to the risky market portfolio. If the risk premium is high relative to the average level of investor risk aversion, there would be an excess demand for securities and their prices would rise, thus lowering their expected returns. In equilibrium, the market portfolio’s risk premium will be proportional to the average investor’s degree of risk aversion and the risk of the market. Implication 3 The security risk premium will be a function of the market risk premium adjusted by the security’s beta coefficient. This coefficient simply means that the security’s rate of return is a function of the market portfolio and measures the extent to which the return on the security changes following changes in the market portfolio. Mathematically, E(ri) = i [(E(rm) − rf )]

(9)

where i is the security’s beta coefficient. We know that investors demand a premium for bearing risk, but they are primarily concerned with portfolio risk rather than the risk of an individual security. Therefore how should the riskiness of individual security be measured? The answer is this: The theoretically relevant riskiness of an individual security is its contribution to the riskiness of the market portfolio. The security may be quite risky if held in isolation, but if most of its risk can be diversified away, it is the relevant risk or its contribution to the portfolio risk that matters, which may be rather small. Are all securities equally risky in the sense that when added to a well-diversified portfolio they would have the same impact on the portfolio’s risk? No. Securities differ in risk levels and thus have different degrees of relevant risk. A security’s relevant risk is measured by the extent to which a particular security (stock) moves with the market—that is, by its beta coefficient. Specifically, there are three types of beta values. The market beta, by definition, is 1. An average-risk stock is one that has a beta coefficient of 1. This means that it moves exactly with the market. For example, if the market (risk premium) advances/falls by 5%, the stock’s return will also advance/fall by 5%. A stock with higher-than-average risk would have a beta coefficient of more than 1. Such a stock would be riskier than the market, because if the market risk premium advances/declines by 5%, the stock’s return would advance/decline by more than 5%. For example, if the beta coefficient is 1.5, then the stock’s return would change by 1.5 × ±5% = ±7.5%. Finally, if a stock’s beta is less than 1, it would be a stock with lower-than-average risk and its risk would be less than the market. For instance, if its beta coefficient was 0.5, a 5% increase/decrease in market risk premium return would increase/decrease the stock’s return by 0.5 × ±5% = ±2.5%. Therefore a stock’s risk premium should be proportional to its beta coefficient. Growth stocks (like those of tech industries) have betas greater than 1, and defensive stocks (like those of utilities) have betas less than 1.

236 s Portfolio Theory

The Capital and Security Market Lines Now we are ready to derive the CAPM. If we compare a security’s ratio of risk premium, given its beta, to that of the market (and the market’s beta is 1), we would have E(ri ) − rf E(rm ) − rf = βi 1 and by cross-multiplying, we obtain: E(ri) − rf = i [E(rm) − rf ]. Finally, by taking the riskfree term to the right-hand side of the equation, we obtain E(ri) = rf + i [E(rm) − rf ]

(10)

or the CAPM as an expected return-beta relationship. The CAPM implies that the expected rate of return of a security is equal to the risk-free rate plus a market risk premium adjusted by the security’s systematic risk measure (its beta). Stated differently, the investor should expect a rate of return from a risky security that is higher than the riskfree rate by a risk-adjusted market premium. Let us study the model with an example. Assume that the market is expected to return 8% and the risk-free rate is 3%. If the investor is considering adding a security to a market portfolio whose beta is 1.2, what would be the impact on the security’s expected rate of return? The answer is: E(ri) = 3 + 1.2 (8 − 3) = 3 + 1.2 (5) = 9%, which would be the expected return on the stock. What if its beta was 0.80? In this case, E(ri) = 3 + 0.8 (8 − 3) = 7%. Thus the lower the stock’s risk, the lower its expected return. Similarly, each stock’s risk premium would be 9% − 3% = 6% and 7% − 3% = 4%, respectively. In other words, the stock’s risk premium is proportional to its beta value as well as the market risk premium. What is the graphic illustration of the CAPM? Figure 8.7 shows the security market line (SML), which is the CAPM in a graph. We first saw it above, and it represents equilibrium in the market for a particular security (or a portfolio). Its slope is the market risk

E(r) SML + alpha (α) E(ri)

− alpha (α)

A’ A A’’

E(rm)

M

βm = 1

Figure 8.7 The security market line.

βi

beta (β)

Efficient Diversification and Capital Market Theory s 237

premium [E(rm) − rf] and its intercept the risk-free rate, rf. Point M shows the expected return on the market with a beta coefficient of 1. Before we move to the economic interpretation of the SML, let us differenatiate bteween the two lines we have just derived. The CML shows the relationship between the portfolio’s expected return and risk. Notice that in the horizontal axis we have standard deviation as a measure of portfolio risk. The SML characterizes the relationship between the security’s expected return and (systematic or market) risk. In this case, the graph’s horizontal axis measures risk by the security’s beta coefficient. Retain these distinctions, because later we will present another line, the security characteristic line. But we will discuss them one at that time. Now let us do some economic analysis on the SML graph (Figure 8.7) to understand (one reason) why investors buy/sell certain stocks. Any point on the line represents equilibrium in the market of that stock; that is, demand and supply equilibrate in order to generate the appropriate price for that stock. That price is known as the fair price. In other words, the stock is normally (fairly) priced; thus there is no reason for an investor to question whether he should buy, sell, or hold (more of) the stock (if he had it). Also on the SML, the stock’s expected rate of return is just equal to its required rate of return. This is very important and means that, again, investors expect to earn exactly what they minimally require from that stock. So whenever the CAPM holds, all stocks will lie on the SML, and thus the market will be in equilibrium. The above conclusions are implied by point A, for example, on the SML. Now assume that for some reason the stock’s expected rate of return exceeds its required rate of return. Graphically it lies directly above point A, say at point A. In this case, investors see the stock as a bargain (we say that it is underpriced or undervalued) because they require less return (given its beta) from it. So if they had it, they would want more of it but, if they did not have it, they would want to buy it. Therefore excess demand for that stock would raise its price and depress its expected return. This buying frenzy would stop when the stock’s excess return reverted back to point A, the equilibrium point. The difference between the expected return and the required return (or the fair return) is also known as the alpha () of the stock. In this case, the alpha will be positive. By contrast, if the stock’s expected return happened to be less than its required return, it would plot directly below point A, say at point A. In this case, investors would find the stock unattractive and there would be an excess supply of that stock (as investors would rush to dump it), thus lowering its price and raising its expected return. Such a stock is said to be overvalued or overpriced. In this case, its alpha would be negative. Again, when would this selling frenzy stop? It would stop when its expected return was equal to its required return or reverted back to point A, the equilibrium point. At this point, the stock would be fairly priced again. Think of this market dynamic for a moment. Investors go through security analysis (and perhaps company analysis) in order to detect undervalued and overvalued stocks on a daily basis for exclusion or inclusion, respectively, in their portfolios. Why do asset prices move inversely with their expected returns? Consider the formula for the security’s rate or return (or holding period return) from Chapter 3:

Holding period return =

ending price − beginning price + dividend × 100 beginning price

238 s Portfolio Theory

where ending price can be the new (or selling) price and beginning price the purchase price. Also, we can recast the equation above in expected terms as follows: Expected (HPR) =

Selling price − purchase price + dividend × 100 purchase price

Thus you see that as the purchase price increases or decreases, the expected return decreases or increases. We mentioned (positive and negative) alpha coefficients in the preceding analysis. But what is another way of interpreting alpha? When  is greater than 0, the investor realizes abnormal returns, but when  is less than 0, the investor suffers negative abnormal returns. In general, an abnormal return is the difference between the actual return and the expected return. Naturally investors prefer positive alphas because their portfolio performance is better than what the CAPM would predict (in theory). Such abnormal returns can be realized by superior selectivity of stocks (better stock-picking ability or skill) on the part of the portfolio manager. Portfolio managers would implement strategies such as market timing, according to which the portfolio manager places bets on assets before the expected market move takes place. We also mentioned beta coefficients, and we associated them with market risk. What is another way of interpreting risk using betas? We know that the CAPM framework provides a convenient way of assessing a stock’s (asset’s) contribution to overall portfolio’s risk. When we combine two assets, the risk of the new two-asset portfolio will simply be the weighted average of the betas of the two assets. Algebraically and generalizing to nth-asset portfolio, βp =

n

∑ wi βi

(12)

i =1

where wi is the proportional weight of asset i in the portfolio. A statistical expression and estimation of the CAPM yields the security characteristic line (SCL), which shows the (regression-like) relationship between a security’s excess returns and the market’s excess returns. This is shown below. rit − rf = it + i (rmt − rf ) + eit

(13)

where rit is security i’s return at time t, so that rit − rf shows the security’s excess return, the intercept is the alpha, it, and the slope is the beta, i, and eit is the error term (or the disturbance term). What do these terms actually mean? The intercept term implies the expected return when the market does not change (or when i = 0). We learned above that when alpha is greater than 0, investors earn positive abnormal returns, and when alpha is less than 0, they realize negative abnormal returns. The slope coefficient shows how much a security’s return would change if the market changed by a given (or anticipated) percentage. We also learned earlier that if  is greater than 1, the security’s return would be greater than that of the market. Finally, the error

Efficient Diversification and Capital Market Theory s 239

term means that the expected return on the security is determined by both alpha and beta and the market’s expected return. A more condensed version of Eq. 13 is given by Rit = i + i Rm + ei

(13a)

where Rit and Rm refer to the security’s and the market’s excess returns, respectively. Appendix B at the end of this chapter further discusses the significance of this regression equation (in Appendix A of Chapter 7 we formally discussed regression). Uses of the CAPM What is the CAPM’s usefulness? The CAPM is now widely accepted in both academia and the business world. It is considered a benchmark for assessing the fair prices (or expected rates of return) of many risky assets. The CAPM is also used by companies in setting a fair rate of return on investment projects. For example, utility companies usually earn a fair price or return on their investments (on plant and equipment) and thus employ the CAPM to guide them in their evaluation of that rate of return. In practice, what risk-free rate do we use? Alternatives are the Treasury bill and the Treasury note. The use of the riskless rate will depend on the investor’s expected investment period or the time period for the expected return. Typically, if it is the long-term, then he would use the 10-year Treasury; but if it is the short-term, then the 3-month Treasury bill would be appropriate. What about the market risk premium? In practice, investors compute the historical market risk premium because the expected market risk premium is unobservable. Besides, the use of historical data yields estimates of the stocks’ beta coefficient, which is easily obtained via regression analysis (see Appendix B at the end of this chapter). What is an alternative interpretation and use of the CAPM? Recall that in equilibrium, the firm’s expected return is equal to the required return. Thus we can interpret the CAPM as giving us an approximation of the firm’s required rate of return on equity, ceteris paribus. In other words, what would be one estimate of a company’s discount rate for a project (investment)? The CAPM can be used to determine this. Here’s an example. Assume that you run regression and obtained the following beta estimate for a company: 1.25. Given a risk-free rate of 3% and an estimate of 5% of the market’s excess returns, the firm’s estimated discount rate or required rate of return would be required rate of return = discount rate = 3 + 1.25 (5) = 9.25% Criticism of the CAPM What are the CAPM’s limitations? There are two. First, there is a problem with the definition of the market portfolio. As defined above, it includes all the available public assets (domestic and international). However, many assets are not traded, other assets cannot be bought by investors, and still others cannot be measured exactly (such as human capital). Thus, the real-world market portfolio cannot be exactly identified. The second problem is that the model is cast in expected returns, which are not observable, and not in actual returns. We observe only the realized or actual (historical) holding-period returns; thus moving from the CAPM to the SML represents a discontinuity in the model’s applicability. The result is that when we try to record investors’ expectations, we must accept that these would be simply estimates.

240 s Portfolio Theory

Additionally, critics point to the model’s simplistic assumptions and suggest that the model be extended by adding more variables; at worst, some scholars have indicated that because the model’s market portfolio cannot be observed, the model cannot be tested.4 An even harsher blow to the CAPM was given by Fama and French (1992), who suggested that once one accounts for a firm’s size and its market value-to-book ratio, the firm’s beta adds nothing to the prediction of the firm’s expected returns.5 Later, Fama and French (1996) published a follow-up paper proposing a three-factor model that has become a standard approach in empirically estimating asset returns (which include the two factors above and the market index).6 The model’s unrealistic assumptions notwithstanding, its usefulness still stands because it explains investor behavior and provides rational consequences from movements in asset prices and expected returns as they pertain to market equilibrium. See Box 8.1 on the real-world troubles of the CAPM. A way to reconcile the theoretical predictions of the CAPM with empirical applicability is to re-cast the CAPM in terms of actual market returns. Appendix B discusses that model, known as the single-index or single-factor or market model. The Arbitrage Pricing Theory The above-mentioned limitations of the CAPM prompted yet more research in the issue in an effort to find a similar model but one derived with fewer and most importantly realistic assumptions. This effort led to the construction of the arbitrage pricing theory (APT) by Ross (1976).7 We begin with the important concept of arbitrage. An arbitrage opportunity is created when you (the arbitrageur) can buy an asset cheaply and then immediately sell it dearly, thus making a riskless profit. Alternatively stated, going short on the expensive market and long on the cheap market will result in a sure profit. Arbitrage arises when the law of one price is violated. This occurs when the same commodity sells at different prices in different markets or when these prices are misaligned. In arbitrage activities, traders force the price of the asset back into alignment so as to close off any further arbitrage opportunity.

BOX 8.1 The 2000 Stock Market Crisis and the CAPM In 2000, the United States witnessed the collapse of the tech sector bubble and economists began revisiting their favorite model’s predictions, notably the capital asset pricing model (CAPM). The key ingredient of the model is the beta coefficient, which measures the security’s systematic risk (or the risk emanating from the overall market). The bursting of the bubble sharply increased new firms’ betas but decreased old firms’ betas (so that the average or the market beta is equal to 1). Beta is useful for comparing among stocks because it reflects the stock market risk premium. Investors began worrying about the stock market as an asset class because the crash rekindled investors’ interest in what happened to the equity risk premium. Although betas can be used for building risky portfolios, they tell us nothing about the stock’s price performance (in absolute terms). As a result, many market participants have given up on beta. Source: Financial economists wonder what is left of their favourite models, The Economist, June 7, 2003.

Efficient Diversification and Capital Market Theory s 241

What are the conditions for arbitrage opportunities? sThe same asset does not trade at the same price on all markets (i.e., the law of one price is violated). sTwo assets with same cash flows do not trade at the same price. sAn asset’s current price is different from its known future price (discounted at the risk-free rate). What are the implications of the absence of arbitrage opportunities? sThe market is in equilibrium, otherwise one could make a certain profit by buying the relatively undervalued asset and selling the relatively overvalued asset. In other words, there would be excess demand for the former and excess supply of the latter. sThere is no relative over- or undervaluation of the asset. The asset’s price is fair. sThe price of a derivative asset is related to the price of the underlying asset. Ross, in developing his model, assumed a well-functioning capital market, which is in equilibrium, and precluded any arbitrage opportunities. That is the first important assumption. The model’s other important insight centered on the construction (existence) of the market portfolio. In fact, he considered a well-diversified portfolio one that would have no residual (or firm-specific) risk. Taking this further, when only one risk factor exists in the world, that factor must be the market portfolio. Thus, Ross expressed the expected return/risk relationship in a market format (as we show in the Appendix B of this chapter)—unlike the way in which the CAPM expressed that relationship—as follows: Ri = i +i Rm + i

(14)

where Ri = ri − rf, implying the excess return on stock i, and Rm = rm − rf, implying the excess return on the market, as before. Rm is known as a (single) factor. Parameters i and i again represent the stock’s alpha and beta, respectively. Now if we assume that the well-diversified portfolio’s return, Rp, has zero nonsystematic (or firm-specific) risk, then we would obtain Eq. 14 without the last term: Rp = p + p Rm

(15)

Here is the important result. Ross was able to construct a capital asset pricing model with two completely different theories about asset pricing. This model is, of course, identical to the CAPM and the SML. But let us interpret the above equation. We have said that firm-specific risk is absent owing to efficient diversification. Also, if the portfolio’s beta coefficient is zero, then Rp = p. This means a riskless rate of return. If we substitute the expression for Rp in the above, we obtain rp − rf = p or rp = rf + p which simply implies a risk-free return augmented by the amount p. But given the assumption of no arbitrage opportunity, this alpha amount must be zero, otherwise an

242 s Portfolio Theory

arbitrage opportunity would emerge (see also the SML graph in Figure 8.7, above)! As you already know, if the alpha is positive, then the well-diversified portfolio would be a good investment to buy. Consequently the trader would borrow at the risk-free rate (go short on it) to purchase the well-diversified (and zero-beta) portfolio (or go long on it), thus profiting the riskless differential of p. The basic, one-factor APT assumes that the rates of return for all assets are affected by the same risk factor, the well-diversified market portfolio, as illustrated in Figure 8.8. In that figure, the stock’s beta is the same as that of the well-diversified portfolio’s beta. However, there is one fundamental difference between the two graphs in the figure. The security characteristic line (panel a) falls exactly on the dots, for the well-diversified portfolio, because there is no firm-specific risk. But for the individual stock (panel b), the line goes through the dots but never through each and every one, which suggests presence of firm-specific risk. In fact, the vertical differences between any dot and the straight line are examples of such risk. The APT can be extended to include more and different risk factors that work together to determine an asset’s market price. If we were to generalize Eq. 14 and denote a factor as Fni , we could express it as follows for three factors: Ri = i + 1i F1i + 2i F2i + 3i F3i + i

(16)

where F1, F2, and F3 are the factors. Their corresponding beta coefficients (known as the partial regression coefficients) measure the sensitivity of the security’s return to changes in a factor, assuming the other factors remain constant. These APT factors must be highly relevant to a security’s expected returns and must be unpredictable to the market in general. For example, unexpected inflation (or the difference between actual and expected inflation) is an APT risk factor. In addition, risk factors reflect broad economic and financial conditions but not firm-specific conditions. Other examples of such factors could be unexpected changes in industrial production, interest rates, unanticipated changes in dividend payouts, exchange rates, and so on. In general, the APT risk factors fall into three broad categories:

(a) Return on stock

Return on welldiversified portfolio

0

Return on market

Figure 8.8 Security and portfolio characteristic lines.

0

(b)

Return on market

Efficient Diversification and Capital Market Theory s 243

Company Risk Factors. These relate to a company’s business nature such as its return on assets, size, level of indebtedness, and the like. Industry Risk Factors. These pertain to the economic status of the industry in which a company operates, such as the industry’s sales level, size, and so on. Macroeconomic Risk Factors. These deal with macroeconomic magnitudes such as GDP, unemployment, inflation, deficits, and the like. Comparing the CAPM and the APT Why did the CAPM make so many assumptions and the APT, with just two, arrive at the same expected return/risk relationship? The fundamental differences involve the underlying theories and the market proxy. The CAPM relies on utility theory (see again the box titled Applying Economic Analysis), whereas the APT relies on the economics of arbitrage. Also, the CAPM assumes the full market portfolio, but the APT assumes a well-diversified one. However, neither theory offers any suggestions on the optimality of the market portfolio. The APT assumes that the actions of a few powerful investors (meaning institutional investors) are just enough to restore equilibrium in the market, unlike the CAPM’s assumption of all investors’ actions being required to restore market equilibrium. Further, with the APT, the return-risk (beta) relationship must approximately hold, because even if it was violated it would be virtually impossible for all well-diversified portfolios to satisfy the relationship. Now if many securities violate this relationship, even well-diversified portfolios would not be able to bring back equilibrium, thereby giving rise to arbitrage opportunities. However, both the CAPM and the APT serve as benchmarks for finding an asset’s fair price (or rate of return), but the APT is more direct in emphasizing the difference between factor risk (for which a premium is needed) and unique risk (for which is not). Additionally, the APT uses more factors in evaluating the security’s rate-of-return sensitivity to changes in other magnitudes (factors), in contrast to the CAPM, which assumes only one measure of risk, the market risk premium. In fact, the CAPM relationship would be exactly the same as that derived from the APT if there were only one factor influencing security returns. In that sense, the APT is more general than the CAPM. The bottom line is that both models are important and neither one surfaces as “superior” to the other, because both models are in agreement on the expected return/risk (beta) relationship. Perhaps the only difference is in the way people invoke such models, as they tend to view the CAPM as an “elegant” model with more real-world applications than the APT. What about the empirical verifications of the above two models? Empirical tests of the CAPM are tests of the SML. It is important to realize that the CAPM is an ex ante model as investors form beliefs about expected returns on the market and the risk premium. Thus, in order to test the model (theory), we rely on past data (returns) on the variables of relevance. Implicitly then, we assume that the beta values obtained are true estimates of the past betas and that the market index used to measure historical market premiums is the correct market portfolio. Some early studies of the SML reported some anomalous findings on the SML.8 Specifically, it was found that some other variables—such as firm size, book value, market/equity ratio, and earnings/price ratios—surfaced as statistically significant, but the beta coefficients had

244 s Portfolio Theory

very little explanatory power over an asset’s (or portfolio’s) returns. Overall, what do these test results mean for the CAPM? In general, critics (including Roll) point out the deficiencies of these studies in terms of using different or inappropriate models (methodologies), data periods, and frequencies that may be too small, and so on. Although there is little empirical verification of the CAPM, it may be impossible to test the theory accurately. How about the empirical evidence on the APT? Empirical tests of the APT have generally followed the same approaches as those for the CAPM. A major study by Ross and Roll (1980) analyzing 1,260 NYSE-listed stocks for a decade of daily returns reported that no more than four risk factors were statistically significant. These were changes in inflation, the growth rate of industrial production, the yield spread between high- and low-grade corporate bonds, and changes in the slope of the term structure of interest rates as measured by the difference between long-term government bond yields and T bills.9 An extension of the Ross and Roll study was undertaken by Chen, Roll, and Ross (1986), who found that the SML seemed to be misspecified and the APT was able to explain some of the SML’s unexplained variation. By contrast, the SML could not be successful in explaining any of the residual variation from the APT.10 Of course no study has been unnoticed by critics who suggested that there are still serious doubts as to whether the APT can be empirically tested. Dhrymes et al. (1984) noted that in the Roll and Ross paper the number of factors would increase as the number of securities in their sample increased with the time frame.11 Overall then, other studies have been done and have reported different risk factors as important in the APT model. Thus this evidence is to be taken as informative rather than conclusive. Portfolio Performance Evaluation In plain terms, portfolio performance evaluation entails the evaluation of an active portfolio manager’s style of investing and measures the value of the services (in terms of risk-adjusted returns) he or she has provided. The emphasis is on risk-adjusted returns, because in the past a portfolio’s performance was solely judged on its return compared to some benchmark portfolio. In the following discussion we introduce some classic performance measures and some new ones. We begin with two absolute risk-adjusted measures, that is, measures with no reference to some benchmark: Sharpe’s and Treynor’s ratios. Quantitatively speaking, how can one compare the performance of portfolios (and managers who manage them) on a risk-adjusted basis? Sharpe (1966), Treynor (1965), and Jensen (1968) were among the pioneers who recognized the importance of the CAPM in evaluating the performance of managers.12 The Sharpe measure is simply the ratio of the average portfolio’s excess return over the sample period by its standard deviation: Sharpe measure =

Rp − R f σp

(17)

Its interpretation is simply the reward-to-volatility ratio (as we have seen also in Eq. 6), with the difference being that here we have averages (the bars over the returns). This ratio is suitable for evaluating the performance of a (not very diversified) portfolio that reflects an investor’s overall investment portfolio.

Efficient Diversification and Capital Market Theory s 245

By contrast, the Treynor measure replaces the portfolio’s standard deviation with its beta as follows: Treynor measure =

Rp − R f (18)

βp

In other words, the difference between the Sharpe and the Treynor measures is that the latter uses systematic risk instead of total risk. One obtains the portfolio’s beta (from the characteristic line) and uses it in the formula above. The Treynor ratio is appropriate for evaluating the performance of a well-diversified portfolio and thus suitable for assessing the performance of a part of an investor’s overall (total) portfolio. There have been several generalizations and extensions to the above two measures in an effort to capture more information coming from the market. For example, a modification of the Sharpe ratio would be to replace the risk-free rate with a benchmark such as the market portfolio. Finally, other relative risk-adjusted measures have been developed, such as the value-at-risk (VaR), which (without getting into technical issues) measures the risk of a portfolio as the maximum amount of loss the portfolio can sustain given some predetermined confidence level. A third popular performance evaluation measure is the Jensen measure (alpha), a relative risk-adjusted measure because it is computed in reference to a benchmark (the market index). The measure focuses on the alpha of the equation (or the intercept of the regression), which is derived as follows: α p = R p − { R f + β f ( Rm − R f )}

(19)

This alpha is also known as an investment’s alpha. This measure is the average excess return on the portfolio over what the CAPM would predict given the portfolio’s beta and the average excess market return. As we have seen above, alpha can take positive, negative, and zero values. Let us illustrate with an example so we can point out some caveats about the main three measures.

Average return Standard deviation Beta coefficient Sharpe measure Treynor measure Jensen’s alpha

Portfolio (p)

Market (m)

Risk-Free (rf )

30% 45% 1.2 (30 − 5)/45 = 0.555 (30 − 5)/1.2 = 20.83 30 − {5 + 1.2 (25 − 5)} = 1.0%

25% 30% 1.0 (25 − 5)/30 = 0.667 (25 − 5)/1 = 20.00

5%

25 − {5+1(25 − 5)} = 0

In this instance, by Treynor’s and Jensen’s measures but not by Sharpe’s measure, portfolio (p) outperformed the market. In addition, Jensen’s alpha happened to give a result similar to Treynor’s. The point is this: All three measures have their own merit and, in theory, they should all point to the same conclusion. In reality, however, they do not provide consistent estimates because, for example, Jensen’s alpha is not risk-adjusted, as the other two measures are.

246 s Portfolio Theory

As with the previous performance measures, there are several extensions of Jensen’s alpha measure based on relaxing some assumptions of the CAPM. For example, Black (1972) showed that the CAPM could still hold even if the risk-free rate was not part of the investor’s portfolio.13 Instead, he proposed replacing the risk-free rate with the efficient portfolio that investors choose (based on their risk preferences) and combine it with their risky portfolio (p), assuming that these portfolios are uncorrelated. Then this portfolio would be called the zero-beta portfolio. In general, over the last 30 years or so, numerous other measures, new and extensions of existing ones and too many to mention here, have been proposed. Specifically, the extensions or modifications to existing measures called the validity of many CAPM assumptions into question, such as the risk-free rate, the market portfolio, the chosen benchmark, and so on in an effort to derive more precise portfolio performance measures. New measures focused on the impact of downside risk (based on investors’ degree of risk aversion), the higher distribution moments such as skewness and kurtosis of returns, the derivation of conditional (on information) portfolio betas, the managers’ market-timing capacity (without reference to a market index), and finally on various factors as potential predictors of portfolio returns. For some good surveys of all these portfolio performance measures see Ferson (2010) and LeSourd (2007).14

CAPM, APT, AND INVESTMENT DECISIONS Given the above criticisms of both models, it might be better to rely on alternative (or extensions of the) CAPM frameworks such as the multifactorial CAPM, the consumption CAPM, or the APT. Market-neutral strategies attempt to balance the market risk by going short on some securities and long on others. In essence, this entails the construction of a portfolio long on positive alpha (for undervalued securities) and short on negative alpha (for overvalued securities). Such a strategy is sometimes known as a double-alpha, no beta strategy. With a well-diversified portfolio, its risk (volatility) would be low. Hence a zero-beta portfolio is formed and, although risky, it does not add any risk to the market portfolio and thus should not require a risk premium (over the riskfree rate). The returns of such strategies are usually compared against the T-bill rate, which serves as a benchmark. Read the box titled Lessons of Our Times to learn about the alpha-beta debate. Practitioners are concerned with how they can evaluate and enhance their investment performance. Burmeister et al. (2003) offer some guidelines that can be easily implemented to those investment managers.15 We present some of them below. How to Evaluate Macroeconomic Risk Exposure and Attribution Return. The authors suggest that the manager determine his or her APT style. Find the risk exposure profiles of your portfolios and determine the appropriate benchmark for their return comparisons. For example, if you are a small-cap manager, you should know whether and how your portfolio differs in its exposure to macro risk factors from an appropriate index of small-cap firms. Only if you find that your risk exposures are the same as the index can you attribute ex post superior performance to your APT selection (that is, those stocks that yielded more than would be expected on the basis of risks undertaken). Index Portfolios. The APT provides important tools for tracking any index portfolio. Your ex post APT alpha can be made small by making your tracking portfolio well

Efficient Diversification and Capital Market Theory s 247

diversified, so that your portfolio-specific return is near zero. One way you might do this is to form your tracking portfolio by random sampling from the benchmark constituent stocks. Making a Factor Bet. If you believe, for instance, that the economy is going to recover from a recession faster than most market participants believe that it will and you are correct, the stocks you selected that have greater risk exposure to the risk factor “business cycle risk” will outperform, ceteris paribus. In general, multifactorial models help portfolio managers construct portfolios that have certain desired risk characteristics. There are several types of multifactorial models, such as fundamental, statistical, and macroeconomic ones. Analysts often favor fundamental factor models since they focus on explaining the returns of stocks from observable fundamental factors that describe the characteristics of the stocks themselves or their issuers. Use of such models allows analysts to separate the sources of active returns (defined as the portfolio’s return minus the benchmark return). We end this discussion of investment strategies by mentioning two and discussing only one of them here. These are noise-trading behavior and momentum investment strategy. We reserve the latter for the next chapter. A noise trader is a naive investor or a professional investor who makes continuous errors in the evaluation of information about a company compared with a smart trader (or smart money), who correctly assesses the characteristics of a company and its prospects. In other words, noise traders are irrational and follow trends (or the crowd), thus unnecessarily driving stock prices up or down irrespective of the underlying company’s fundamentals. For example, during the financial crisis of 2008, such investors panicked and ended up selling stocks at very low prices. Recent research has shown that smart money, represented mainly by institutional investors, is better at forecasting future prospects as well as at collecting and interpreting information.16

CHAPTER SUMMARY In this chapter we extended the simple diversification strategy using many risky assets and illustrated the Markowitz principle of efficient diversification. This analysis is known as mean variance analysis and is based on the construction of an efficient portfolio of risky assets. Then we examined two very important theorems in finance and investments that involve specifying the expected return/risk trade-off; these are the CAPM and APT. We then presented some empirical evidence on both frameworks and highlighted their advantages and disadvantages. We concluded that the CAPM is attractive because it is (1) simple and sensible and bridges modern portfolio theory with market equilibrium and (2) relatively easy to implement and interpret. On the other hand, the CAPM’s disadvantages were difficulties in (1) testing the theory, (2) identifying the market portfolio, and (3) estimating expected returns and betas. The APT’s appeal rested on the following characteristics: (1) there are fewer assumptions to be made in deriving it; (2) it uses a well-diversified, observable portfolio of stocks; and (3) it can be extended to multifactorial specifications. The APT’s disadvantages were (1) that only a few risk factors may be relevant in explaining returns and (2) that not all factors were identified by more research. We concluded the chapter by offering some investment strategies suggested by these two models.

248 s Portfolio Theory

APPLYING ECONOMIC ANALYSIS USING UTILITY THEORY TO MAKE A DECISION INVOLVING RISK Economic theory postulates that every person (investor) attempts to maximize his utility (satisfaction) given his constraints. Implicit in this statement is that investors’ level of utility changes when their wealth or their investments’ rates of return change. Therefore positive/ negative returns increase/decrease utility. In an uncertain world, investors try to maximize their expected utility from risky assets since, being risk-averse, they would invest in them only if they received higher returns. Investors possess various levels of utility, and these can be represented by their indifference curves. An indifference curve is one that shows the same level of utility along that curve. For risk-averse investors, indifference curves slope upward and their steepness reflects the degree of risk aversion (that is, the steeper the curve, the more risk-averse the investor). The indifference curves of risk lovers slope downward, and those of the risk-neutral are horizontal. So to maximize his utility, the investor must select the optimal investments—that is, those that offer the maximal return given their risk. We have shown this using the tangency point between the investor’s capital allocation line (CAL) with the efficient frontier (EF), or point O in Figure 8.3 in the text (see also that point in the figure below). What this graph does not tell us is which portfolio of risky assets (lying along the CAL) is the best one. That is where utility theory comes into play. The investor’s indifference curves will show exactly where that best investment would be to maximize his utility. The graph below is very illustrative for the risk-averse investor. The two sets of the indifference curves (I1, I2, I3 and Ia, Ib, Ic) are called indifference maps, and they show how investors, with different degrees of risk aversion, reach different investment decisions. An investor makes a decision by finding his highest-sloping indifference curve, which is just tangent to the CAL. One such highly risk-averse investor (with I1, I2, I3) is shown reaching a decision at point Z. At that point, the investor is aggressively borrowing at the risk-free rate to leverage out to the risky assets. Another less risk-averse investor reaches a utility-maximizing point at D, since his indifference curves are less steep. Perhaps this investor would allocate his funds 50:50 to the risky and risk-free assets.

I3 I 2 I 1

expected return

CAL

Z Ia

Ib

Ic

EF

O

D rf risk (σ)

Efficient Diversification and Capital Market Theory s 249

THE 130/30 STRATEGY The Investments & Pensions Europe (July/August 2008) magazine asked three pension services— in Denmark, the Netherlands, and the United Kingdom—the same question: What is your approach to 130/30 strategies? Here are excerpts from their answers. Ramon Tol, fund manager at Blue Sky Group (the Netherlands): We do not believe in launching a search for 130/30 or similar strategies because first of all we want to find a skillful manager. Only when we have confidence in the manager and he or she has experience and skill in shorting, will we then discuss the opportunity of 130/30. We run two enhanced equity portfolios with a 130/30 extension on top. The relaxation of the long-only constraint is theoretically sound and very appealing. One portfolio consists of US equities and the other concerns Canadian equities. So far most of these strategies have only launched on top of US equities, although more providers are now emerging that also apply to these international equities. Nevertheless, shorting stocks in the US is still easier from a liquidity and cost points of view compared with, for instance, Europe. The risk is that your underperformance is going to be bigger than the corresponding long-only strategy if the manager is not skillful enough or the underlying model does not work. The credit crunch has had a substantial impact on most quant and thus 130/30 strategies are run by quant managers. It turns out that most of the quant managers use the same quant factors, a practice known as “crowding.” It also had an impact on our 130/30 strategies though the influence on the total equity portfolio is limited because of manager diversification benefits. From a manager selection point of view it is, therefore, very important to find the managers that are doing things differently from the mainstream quants. Mike Taylor, chief executive at the London Pensions Fund Authority pension fund (United Kingdom): Currently we do not apply 130/30 or similar strategies to our investment portfolio because we are not convinced that they would be any better for us than long-only equity investments. A long-only approach comes with a track record and has a better certainty of achieving returns at a reasonable price. However, if the fees and the track record of this strategy were to change and become similar to traditional long-only equities we might look at 130/30 again. In addition to that, 130/30 strategies come with a different risk compared with long-only. We are not even sure that managers [good at picking shorting stocks] exist yet and are not convinced that 130/30 strategies offer higher returns than long-only equities. Nils Ladefoged, portfolio manager at PKA (Denmark): We currently have three long-short strategies: a 130/30 for UK equities, a 120/20 for Japanese equities and another 130/30 for North American equities. The difference between 120/20 and 130/30 are mainly the subject of theoretical discussion. The investment manager was more comfortable with the 120/20 strategy for Japan. Once you understand the theory behind taking short positions and the whole concept of extension strategies, 130/30 or 120/20 is simply just a natural step to take, as quantitative managers use signal source factors and a 130/30 strategy can get better exposure to those signals than a long-only strategy can. Unfortunately, the timing of moving to extension strategies could have been better. We, like everybody else, did not foresee the quant deleveraging that took place last year and so the portfolios suffered because with 130/30 strategies investors get more exposure to the factors they want to bet on. In other words, with such strategies in place, when things go against you they get even worse. There are two sides to the coin; when things are good, you will reap even higher rewards as we have seen some signs of in recent months. However, the counterparty risk in these strategies is often overlooked. Investors use a prime broker to lend them shares, which they then sell short. In order to borrow those shares, investors must put up some collateral and initially we did not feel comfortable with PKA being in a collateral relationship with a financial institution. But we found some solutions where our counterparty risk is extremely limited and have had no problem. According to consultants we are so far the only pension fund in Denmark that applies a 130/30 or 120/20 strategy.

250 s Portfolio Theory

LESSONS OF OUR TIMES THE ALPHA-BETA DEBATE These terms are known from the capital asset pricing model. In a regression framework of the CAPM, alpha is the constant or the intercept and beta the slope (see also the Appendix A of Chapter 7 to learn about regression). These two parameters have attracted a lot of attention, and that attention is not new. Recall that we learned in the text that various academics have criticized the CAPM since the 1970s. In addition, recent research has also questioned the validity of beta, asking “Is Beta Dead?” and “Is Beta Dead Again?” But as you already know from reading the chapter, beta suddenly became anathema after the stock market crash of 2000. More recent research (by Kritzman and Page, 2003) has tried to “rescue” beta and concluded that beta is still useful but, alone, is not sufficient to manage portfolios. The debate has centered on the assumption that it is not possible to forecast the market and thus not predictable for the active portfolio manager. This means that an active manager would not have earned “alpha” returns. Alpha is loosely interpreted to mean realizing returns from the manager’s skill, since these returns are independent of the returns due to beta. Which investors attempt to capture alpha? Typically such investors are hedge fund managers and rely on the realization of “absolute returns.” If absolute returns are the goal, the portfolio’s beta exposure would probably be low. Thus one might see the alpha-beta debate as a trade-off: returns realized from pure market movements—beta—and returns captured by the skill or investment style of the manager—alpha. In order to attract investors, many funds advertise their managers’ skill in earning superior returns on their managed portfolios. But beware of such advertisements. Recall that we learned in a previous chapter that the performance of the mutual fund industry was disappointing because fund managers could not, on average, beat the market. Sources: Anise Wallace, Is beta dead, Institutional Investor, July 1980. Richard C. Grinold, Is beta dead again? Financial Analysts Journal, 49, July/August 1993, pp. 28–34. M. Kritzman and S. Page, The hierarchy of investment choice, Journal of Portfolio Management, Summer 2003.

KEY CONCEPTS The investment opportunity set includes all available portfolio risk/return combinations. The capital allocation line shows the combinations of risky portfolios and the risk-free rate. The optimal point for the investor is found by the point of tangency between the highestsloping CAL and the opportunity set. The efficient frontier represents the set of assets (or portfolios) that offer the highest possible risk/expected return combinations. The property that implies that the investor’s portfolio choice can be separated into technical and personal parts is known as the separation theorem. The capital market line suggests that the expected return on an efficient portfolio is composed of the minimum compensation required plus a risk premium for bearing risk in the portfolio.

Efficient Diversification and Capital Market Theory s 251

The security market line relates an individual security’s (or a portfolio’s) expected return to the risk-free rate and the relative risk of the security (or portfolio). A market portfolio is one that includes all publicly available traded assets. A security’s relevant risk is measured by the extent to which a particular security (stock) moves with the market—that is, by its beta coefficient. The capital asset pricing model implies that the expected rate of return of a security is equal to the risk-free rate plus a market risk premium adjusted by the security’s systematic risk measure. The difference between the excess return and the required return (or the fair return) is also known as the alpha of the stock. Market timing involves placing bets on assets before the expected market move takes place. An arbitrage opportunity is created when you (the arbitrageur) can buy an asset cheaply and then immediately sell it dearly, thus making a riskless profit. The Sharpe measure is simply the ratio of the average portfolio’s excess return over the sample period by its standard deviation. The Treynor measure replaces the portfolio’s standard deviation with its beta. The Jensen measure (alpha) is based on the characteristic line and on the alpha of the equation. Value-at-risk measures the risk of a portfolio as the maximum amount of loss the portfolio can sustain given some pre-determined confidence level.

QUESTIONS AND PROBLEMS 1. Assume that you have the following hypothetical data on assets: the risk-free rate is 3%; the expected return on the investor’s optimal (tangency) portfolio is 10%; and the risk of the tangency portfolio is 18%. Now answer the questions below (which are related to the capital allocation line): a. How much extra return does the investor want per unit of risk in order to invest in the risky asset? b. Assume the investor requires a risk level for the portfolio of 14%. What fraction of assets should he invest in the optimal portfolio and what would be its expected return? c. What expected return should the investor demand for a portfolio with standard deviation of 25%? Discuss the result. d. What would be the investor’s optimal mix of risky portfolio and the risk-free rate so that he could have a portfolio with an expected return of 15%? e. Related to part (d), if the investor has $100,000 to invest, what fraction of must he borrow (at the risk-free rate) to have a portfolio with an expected return of 15%?

252 s Portfolio Theory

2. Assume that you are a financial consultant to a pension fund and are asked to discuss the capital market theory with the fund’s representatives. You also have access to the following data. Answer the questions that follow below. Correlation Matrix Asset Class Market Value A $100,000 B $ 50,000 C $ 10,000

Standard Deviation 15% 20% 30%

A 1.0 1 1

B 0.5 0.2

C 0.3

a. Given the three asset classes above, please compute: 1. The portfolio’s weights 2. The portfolio’s standard deviation b. If the risk-free rate is 3% and the market risk premium is 5%, give an expression for 1. The capital market line (CML) 2. The security market line (SML) c. If a fund representative states that their fund should have a long-term expected rate of return of 10%, how should you obtain it? d. Another fund representative tells you that the beta coefficient of a stock the fund is interested in purchasing is 1.25. What would the stock be expected to earn? e. If the same fund representative stated that they would like to earn a minimum of 11% on that stock, would you advise him to purchase the stock? 3. You are given the following data on two stocks, the risk-free rate and the market index. Asset N H Risk-free Market index

Returns 10% 15% 3% 11%

Standard Deviation 15% 20%

Beta 1.0 1.2

Now answer the questions below: a. Compute each asset’s expected return and alpha. b. Which stock would be suitable for inclusion in the investor’s well-diversified portfolio? Would he hold it as a single-asset portfolio? 4. Answer the questions below based on the following statements: sEarly in 1998, Apple was in huge trouble and its shares were more volatile than those of a rival, IBM. Yet Apple’s cost of equity was lower than IBM’s. Later on, Apple’s cost of capital rose even though its financial situation improved. sThe fundamental insight behind the CAPM is that investors require higher (expected) returns for bearing more risk. Risk is decomposed into two parts, alpha and beta. sThe extent of a stock’s volatility is picked up by the beta coefficient. Apple’s beta was 0.50 and that of IMB’s 1.1.

Efficient Diversification and Capital Market Theory s 253

sGoodbye CAPM? Not so fast! As long as investors are able to construct welldiversified portfolios, they will be able to be concerned only with market risk. a. Which statement above implies “market risk” and “Apple’s average return”? b. How volatile is Apple’s stock and how volatile is IBM’s? Compare the two stocks. c. Can you explain why Apple’s shares did not move as much as the market, and if so, what were investors reacting to? d. Should one discard CAPM? In answering this question, read once again the box titled Lessons of Our Times. Is beta relevant in this case? Discuss. 5. Read the following paragraph and answer the questions below: Many investors wish to earn hedge-fund type of returns (that is, absolute or superior returns) but are concerned about the high fees that hedge funds typically charge and, of course, the greater risks that they take. An alternative approach is the “130/30” strategy, in which managers go short on falling prices and using leverage (borrowing). For example, if a fund has $10 billion in assets, it will purchase $13 billion of assets financing the difference by selling $3 billion of short position. As another example (such as merger arbitrage), a hedge fund manager can buy the shares of a target company (or all target companies) if they are bid on and short the shares of the potential acquirer. Thus, according to this strategy, a portfolio manager has more flexibility by using his or her own skills to produce such superior (risk-adjusted) returns. A useful benchmark (130/30 index) to compare the performance of managers was constructed by Lo and Patel in 2007. The index incorporates several factors, such as valuation ratios and business prospects. It is composed of long positions in best stocks and short positions in worst stocks. The index was tested during the 1996–2007 period and produced returns that beat the S&P 500 by more than a percentage point per year (with similar volatility). Critics say that the index is not a benchmark, rather a stock-picking strategy, and as such there is no guarantee that managers using it will perform well in the future. What about those active portfolio managers who charge high fees because they tell you that they can realize superior returns? Are these excess returns due to alpha or their skill? Or are they due to simply mechanical investment strategies? (Andrew Lo and Pankaj Patel, 130/30: the new long-only, Journal of Portfolio Management, Winter 2008, pp. 12–38.) a. What is the 130/30 strategy? b. Associate the merger arbitrage strategy mentioned in the article to the pairs trading strategy that you learned in Chapter 5. c. What is the new 130/30 index and how can it be used? What are its caveats? d. How can one use the 130/30 index to measure performance? What is the difference between that index and the alpha? 6. Interpret the following statements (from the financial news): sIf your assets in your portfolio move in tandem, then you will either be all right or all wrong. sCorrelation has become more important over the last couple of decades because the world has become more linked.

254 s Portfolio Theory

sChanges in correlation reflect how often you buy bonds, when you shun stocks, and how often you sell bonds to buy stocks. sInvestors choose assets that are negatively correlated in order to hedge risk. 7. Assume that you use the same weighting scheme as used in Table 8.1. Now you have the following information about your two risky assets, X and Y: E(rx) = 10%, E(ry) = 12%, 2x = 200, and 2y = 300. Reproduce a graph like Figure 8.2 with the three values of xy: +1, −1, and 0. 8. We learned that portfolio managers can easily compute the optimal risky portfolio (and efficient frontier) for all investors. Thus they economize on administrative costs (savings that are passed on to clients). Do you think that, in reality, all managers will derive the same optimal risky portfolio for their clients? What do you think the role of security analysis is in this case? 9. Along with the above question, why do you think that optimal risky portfolios may vary across investors? 10. Answer the following questions. a. What happens to an investor’s (degree of) risk tolerance during good economic times and bad economic times? What do you think happened during the recent financial crisis of 2008? b. Which issue (concern) would constrain investors from buying low and selling high? c. During the third quarter of 2010, interest rates were at record lows. What risks were you facing with your savings or money market accounts? d. Given that currently interest rates are near zero, what would than mean about reaching your desired financial goals in the future? In other words, if the interest (compounding) rate is low, what would you have to do (adjust) in order to reach your financial goals? (Hint: relate this to asset allocation.)

APPENDIX A How to Find and Graph the Optimal Two-Asset Portfolio Using EXCEL The first four rows of the table are the inputs to EXCEL. Specifically, RF is the risk-free rate, ASSET 1 and ASSET 2 are the two risky assets, and CORR is the correlation coefficient between the two assets (computed as shown in Appendix B). Above these inputs are each asset’s expected return, standard deviation, and expected return minus the risk-free rate. Column B shows some weights for both assets. For example, in column B and row 13 (henceforth B13), we see that 0.0% is invested in asset 1 or 100% in asset 2. That is why in column C the expected return is 15% and in column D the standard deviation is 8.00%. Similar interpretations apply to the other weights in column B. Columns C and D record the computed expected returns and standard deviations of both assets when the weights are changed.

1 2

A

B exp ret

C st dev

D exp ret-rf

RF ASSET 1

6.00% 14.00%

0.00% 20.00%

0.00% 8.00%

E

Efficient Diversification and Capital Market Theory s 255

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

ASSET 2 CORR

8.00% 0.00%

15.00%

2.00%

Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off Trade-off OPTCOMB EFFTROFF EFFTROFF EFFTROFF

−60.00% −50.00% −40.00% −30.00% −20.00% −10.00% 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 100.00% 110.00% 120.00% 130.00% 140.00% 0.692307692 0.00% 100.00% 200.00%

0.268328157 0.246221445 0.224722051 0.204022058 0.184390889 0.166207701 0.15 0.136473441 0.126491106 0.120933866 0.120415946 0.125 0.134164079 0.147054412 0.162788206 0.180623919 0.2 0.220510771 0.241867732 0.263865496 0.286356421 0.145951277 0 0.145951277 0.291902553

4.400% 5.000% 5.600% 6.200% 6.800% 7.400% 8.000% 8.600% 9.200% 9.800% 10.400% 11.000% 11.600% 12.200% 12.800% 13.400% 14.000% 14.600% 15.200% 15.800% 16.400% 12.154% 6.00% 12.15% 18.31%

To compute the value in cell B28, the following formula is used: = (D2*C3^2−D3*C4*C3*C2)/(D2*C3^2+D3*C2^2−(D2+D3)*C4*C2*C3) The weights in cells B29 to B31 are user inputs. To compute the values in column C, from C7 to C27, the following formula is used and carried all the way to cell C28: = SQRT(B7^2*$C$2^2+(1−B7)^2*$C$3^2+2*B7*(1−B7)*$C$4* To compute the optimal combination (OPTCOMB portfolio) value in cell C28, the following formula is used: = SQRT(B28^2*$C$2^2+(1-B28)^2*$C$3^2+2*B28*(1-B28)*$C$4*$C$2*$C$3) For the remaining values in column C (C29 to C31), the following formula is used and carried to cell C31:

256 s Portfolio Theory

= B29*$C$28 For the values in column D, from D7 to D28, the following formula is used and carried all the way to cell D28: = B7*$B$2+(1-B7)*$B$3 Finally, to compute the values in cells E29 to E31, the following formulas are used: = $D$28*C29+$B$1*(1-C29) = $D$28*B30+$B$1*(1-B30) = $D$28*B31+$B$1*(1-B31) To derive the graph below, highlight the C7:E31 area and insert a graph pattern (XY scatter) from the Insert menu.

20.000% 18.000% 16.000% 14.000% 12.000%

Series1 Series2

10.000% 8.000% 6.000% 4.000% 2.000% 0.000% 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

APPENDIX B The Single-Index Asset Model We have discussed the fact that the firm’s total risk is composed of firm-specific risk and market risk. We also discussed that market risk largely emanates from the macroeconomy, affecting all securities, and one such magnitude or factor is the market index, proxied by the S&P 500 index. Here is an equation specification of such a factor model: ri = i + i rm + i

(A1)

where the dependent variable, ri, measures stock I’s return; the independent variable or factor, rm, measures the market return (or the return on the index); and i is the random variable measures fluctuations not explicitly specified in Eq. A1—that is, the

Efficient Diversification and Capital Market Theory s 257

unexplained fluctuations of asset i. The alpha (i) and beta (i) terms are statistical estimates of the equation’s intercept and slope, respectively. In finance, we interpret the beta as the nondiversifiable risk and i as the diversifiable risk (the firm-specific risk). A statistical and graphic representation of Eq. A1 is known as the characteristic line and is used to measure an asset’s beta and residual variance. Finally, Eq. A1 is also known as the single index model because the only influence to the asset’s return comes from the market index. To see this, rearrange the equation to separate the diversifiable from the nondiversifiable risk as follows: ri = βi rm ↓ ↓ total rate market of return risk

+ εi + αi ↓ diversifiable riskk

Since the firm-specific risk is uncorrelated with the market return, we can take the variances of each term as follows: Var(ri) = Var (α i ) + Var (βi rm ) + Var (εi ) = 0 + β2i σ 2m + σ 2 (εi ) = systematiic risk + nonsystematic risk

Now let us give an example of how to estimate this equation (please review again the appendix to Chapter 7, on regression). Regression analysis is used to derive the estimates for alpha and beta. We now examine the Bed, Bath & Beyond (BBY) company’s stock price against the S&P 500 index (SP) on a monthly basis from 1997:1 to 2008:12. The estimated regression equation for BBY’s stock against SP is: BBYt = 2.552 + 0.2625 SPt (1.991) (0.131) (1.279) (2.001) R-squared = 0.2698 Cov(rBBY, rSP) = 3.4675

(A4) standard errors t-ratios Standard deviation of independent variable (SP) = 3.650 Standard deviation of dependent variable (BBY) = 1.841

Let us now interpret these results. The stock’s alpha is 2.552% or the equation’s intercept. This number measures the stock’s return if the market is neutral—that is, if the market is not changing. Note that you could also measure the returns of the stock and the market as excess returns and interpret them accordingly. The stock’s beta is 0.2621 or the slope of the characteristic line. The beta coefficient reflects the sensitivity or the responsiveness of the stock’s return changes to movements by the market. It also shows the market or nondiversifiable risk. In addition, the value of the beta coefficient indicates the nature of the stock. In other words, if beta is greater than 1, the stock is an aggressive one; if beta is less than 1, the stock is a defensive one; and if beta equals 1, the stock is an average one (just like the market). In this case, BBY’s beta is 0.2621 is less than 1, and thus the stock is considered defensive, which means that it is less volatile than the market. So if the market were to advance by 10%, the stock’s return would advance by only 10% ×

258 s Portfolio Theory

0.2621 = 2.621%. How else can we estimate the stock’s beta coefficient? The formula is as follows: Beta =

Cov( rBBY , rSP ) 3.4675 = = 0.262 Var( rSP ) ( 3.650 ) 2

How else can we compute the value of alpha? An alternative way is to plug in the numbers for the beta coefficient and the average returns of both the stock and the market in the following rearranged equation: BBY = RBBY − BBY (RSP) where R represents the average return. If the average return of the BBY is 2.6565 and that of the S&P 500 is 0.3987, along with above-found beta coefficient, we obtain: BBY–s The statistics immediately below the estimated equation (A4) are the standard errors of the coefficients and the corresponding t-ratios. The t-ratios are found by dividing the estimated coefficient by its standard error. So, for example, for the beta coefficient we have: 0.2621/0.131 = 2.00. These ratios tell us whether a particular variable, here the S&P 500, is statistically significant; that is, does it exert any significant impact on the stock’s return? The rule of thumb is that for any t-ratio (in absolute sense) equal to or greater than 2, the conclusion is that the variable is statistically significant. The same, however, cannot be said for the intercept term since its t-ratio is less than 2. Finally, the R-squared value (or the coefficient of determination) of 0.2698, tells us that about 27% of the variation is the stock’s return is attributed to (or explained by) the simultaneous variations (movements) in the stock market. The rest, 100 − 27% = 63%, is due to other factors that we have not explicitly accounted for or due to unknown factors. Let us cast a more detailed look at the last measure and partition it into the two types of risk discussed above. The fraction of the total risk that is nondiversifiable is measured by the R-squared. Given the market’s variance (3.65)2, we can express the R-squared as follows, using Eq. A3 from above: R2 =

nondiversifiable risk β2 var( rSP ) ( 0.2621) 2 ( 3.65 ) 2 = = = 0.268 = 27% total risk of asset var( rBBY ) ( 1.841) 2

Naturally the nondiversifiable portion is Diversifiable risk Var( ε) = = 1 − R 2 = 1 − 0.268 = 63% Total risk Var( rBBY ) If we extend the above analysis to a portfolio, rather than an individual security, what would be the systematic and nonsystematic variances of the portfolio? The beta of the

Efficient Diversification and Capital Market Theory s 259

portfolio (p) is now the simple average of each of the securities betas in the portfolio. Therefore the portfolio’s systematic variance would be β2P ×  2m . Regarding market risk, low-beta securities within the portfolio will result in low-beta (or market risk) portfolio. The number of securities within the portfolio is irrelevant. However, in the case of diversifiable risk the number of securities in the portfolio is important because of efficient diversification. The risks among the securities are offsetting each other and thus the portfolio will end up with a very small level of such (nonsystematic) risk. You realize that comprehending the difference above is crucial in understanding the role of diversification in portfolio construction.

NOTES 1. 2. 3. 4. 5. 6. 7. 8.

9. 10. 11. 12.

13. 14.

15. 16.

See E. S. Browning, The herd instinct takes over, Wall Street Journal, July 12, 2010. James Tobin, Liquidity preference as behavior towards risk, Review of Economic Studies, 25(1), 1958, pp. 65–86. William F. Sharpe, Capital asset prices: a theory of market equilibrium under conditions of risk, Journal of Finance, September 1964, pp. 425–552. This seminal article won Sharpe the Nobel Prize in Economics in 1990. Richard Roll, A critique of the capital asset theory tests: part I: on the past and potential testability of the theory, Journal of Financial Economics, 4, 1977, pp. 129–176. Eugene Fama and Kenneth French, The cross-section of expected stock returns, Journal of Finance, 47, June 1992, pp. 427–465. Eugene Fama, Multifactor explanations of asset pricing anomalies, Journal of Finance, 51, 1996, pp. 55–84. Stephen A. Ross, Return, risk and arbitrage, in I. Friend and J. Bicksler, eds., Risk and Return in Finance (Cambridge, MA: Ballinger Press, 1976). Fisher Black, Michael C. Jensen, and Myron Scholes, The capital asset pricing model: some empirical tests, in Michael C. Jensen, ed., Studies in the Theory of Capital Markets (New York, Praeger, 1972). Sanjoy Basu, Investment performance of common stocks in relation to their price-earnings ratios: a test of the efficient market hypothesis, Journal of Finance, 32, 1977, pp. 663–682. Marc R. Reinganum, Misspecification of the capital asset pricing: empirical anomalies based on earning yield and market value, Journal of Financial Economics, 9, 1981, pp. 19–46. Eugene F. Fama and Kenneth R. French, The cross-section expected stock returns, Journal of Finance, 47, 1992, pp. 427–465. Eugene F. Fama and Kenneth R. French, Common risk factors in the returns on bonds and stocks, Journal of Financial Economics, 33, 1993, pp. 3–56. Richard Roll and Stephen A. Ross, An empirical investigation of the arbitrage pricing theory, Journal of Finance, 35, December 1980, pp. 1073–1103. Nai-Fu Chen, Richard Roll, and Stephen A. Ross, Economic forces and the stock market: testing the APT and alternative asset pricing theories, Journal of Business, 59(3), July 1986, pp. 383–403. Phoebe Dhrymes, Irwin Friend, and Mustafa Gultekin, A critical reexamination of the empirical evidence on the arbitrage pricing theory, Journal of Finance, 39(2), June 1984, pp. 323–346. William F. Sharpe, Mutual fund performance, Journal of Business, 39(S1), 1966, pp. 119–138. Jack L. Treynor, How to rate management of investment funds, Harvard Business Review, 43(1), 1965, pp. 63–75. Michael C. Jensen, The performance of mutual funds in the period 1945–1964, Journal of Finance, 23(2), 1968, pp. 389–416. Fisher Black, Capital market equilibrium with restricted borrowing, Journal of Business, 45, July 1972, pp. 444–455. Wayne Ferson, Investment performance evaluation, Federal Reserve Bank of Atlanta, CenFis Working Paper 10–01, January 2010. Veronique LeSourd, Performance measurement for traditional investment: literature survey, EDHEC Business School, France, January 2007, http://faculty-research.edhec.com/research/ edhec-publications/2007/performance-measurement-for-traditional-investment-literature-survey-50343. kjsp?RH=1295357652827. Edwin Burmeister, Richard Roll, and Stephen A. Ross. Using macroeconomic factors to control portfolio risk. Working paper, 2003, http://web.econ.unito.it/nicodano/roll_ross_apt_portfolio_management.pdf. Roger M. Edelen, Alan J. Marcus, and Hassan Tehranian, Relative sentiment and stock returns, Financial Analysts Journal, 66(4), 2010, pp. 20–32.

9 MARKET EFFICIENCY AND BEHAVIORAL FINANCE

CHAPTER OBJECTIVES When you finish studying this chapter, you should be able to sKnow what market efficiency is and its three forms sUnderstand the implications of efficient markets for investment strategies and analyses sExplain the impact of efficient markets on investment managers, investors, and asset pricing models sDefine the anomalies of market efficiency and their implications for trading sKnow what behavioral finance is and why it is gaining popularity sUnderstand the implications of behavioral finance for investors and investment strategies

INTRODUCTION Imagine for a moment that investors could accurately predict the future movement of stock prices. How lucky they would be! They would immediately reap profits by simply purchasing those stocks whose prices they knew would go up and selling those whose prices they knew would fall. This situation assumes that all investors had access to the same costless information and interpreted it accurately. But, as we will see later, even if it were true, this situation could not persist for long. In an informationally efficient market, investors cannot make abnormal profits. Recall that economists want to see an economy (or market) that is allocationally efficient, which means that financial capital should be channeled efficiently to its best uses. For example, the securities of high-risk industries will command higher prices (returns) in anticipation of higher profits and securities of lower-risk industries will command lower expected rates of return. Thus investors in such an economy expect to pay and receive fair prices for their traded assets. So in order to understand that, we must first explain what is meant by market efficiency. This is the 261

262 s Portfolio Theory

main task of this chapter. Once we define it, we shall then trace the implications of market efficiency with respect to some of the investment strategies we have learned so far and then present some empirical evidence of market efficiency. The second part of this chapter deals with the relatively new field of behavioral finance. We first mentioned this in Chapter 2, but here we will take a more detailed look into its tenets and implications for investment decisions.

THE EFFICIENT MARKET HYPOTHESIS The Notion of Market Efficiency We said above that investors who possess and use the same information cannot make abnormal profits indefinitely in an informationally efficient market. That is because if all investors purchased a given stock, its price would immediately be bid up to the level where no one would want it anymore! In other words, the stock’s price would jump to its fair price, given all available information. This situation best describes an efficient market, in which all assets are fairly priced at all times with no opportunities for excess returns (or profits). But, what if stock prices were indeed predictable? That would be first-class evidence of market inefficiency! Stated differently, if prices could be predicted, it would mean that the already available information was not effectively and fully incorporated into these current prices. In an efficient market, only normal (fair) profits must be earned, because prices should reflect the interaction between supply and demand. Why do stock prices change? In this context, we say that it is due to the arrival of new information, which, by definition, is unpredictable. Therefore stock prices respond to such information only, which means that stock prices (in an efficient market) behave as a random walk. The random walk theory postulates that asset price movements are unexpected, since they do not follow any particular trend or pattern. However, this does not mean that prices behave irrationally. In fact, quite the opposite! Because new information arrives randomly, price changes occur randomly, sometimes in a positive and other times in a negative manner. Thus, price changes are random but rational. Figure 9.1 illustrates market efficiency. The current price (P0) of a given stock before a major, favorable announcement (at time T) simply behaves normally; but right after the announcement is made public, it settles in its new, higher level (P1). stock price P1 P0

T−10

T−5 T+5 T+10 T Days before and after the announcement (T)

Figure 9.1 An example of market efficiency.

Market Efficiency and Behavioral Finance s 263

It is interesting to note that the efficient market hypothesis (EMH) stresses only that given the supply of information, investors will continue trading until there are no further gains to be made or an equilibrium is reached. It does not tell us anything about the sources, quality, or frequency of information. Why should we expect that all available information will be reflected in the current prices of assets? Shouldn’t your extra time, money, and effort put together all that information for a given stock pay off? The reality is that you would spend those resources to analyze the stock only if you were able to (or certain that you could) earn a higher (than average) return. Therefore, in market equilibrium, such additional information-gathering efforts should bear fruit. However, what may also be true is that the crucial (or all pertinent) information on that stock may not be uncovered or evaluated properly by you but, perhaps, by another investor. In fact, you, the average, amateur investor, do not possess all the information that Wall Street analysts, who specialize in that stock, possess; therefore it is the competition among them that forces a stock’s price toward its equilibrium price (as shown in Chapter 8). Thus, at any point in time in an efficient market, all available information (we will qualify this shortly) should be embedded in the current price of the stock. To generalize: sMany rational, wealth-maximizing investors (analysts) exist in the market who analyze and trade in stocks, thus forcing stock prices to their fair levels. sInformation is widely available, instantaneous, and relatively costless (for those analysts). sInvestors react quickly to news, thus causing stock prices to immediately adjust. sIndividual investors are price takers; that is, they cannot influence asset prices. If all these conditions are met in reality, asset prices would always be at fair levels and no one would have any incentive to go “bargain hunting.” Everyone would make only normal profits. But since in reality these conditions do not always strictly apply, asset prices may not adjust instantaneously to new information. Instead, over the long run, the actions of speculators will cause them to adjust and wipe out any speculative profits. This is sometimes known as an economically efficient market to distinguish it from the perfectly efficient market. Grossman and Stiglitz (1980) argued that “because information is costly, prices cannot reflect the information which is available, since if it did, those who spent resources to obtain it would receive no compensation.”1 Thus, there is some sort of conflict between the extent (and speed) with which markets disseminate information and the benefits of acquiring such information. Now let us turn to the three different forms of market efficiency to see how efficient the stock market is. The Forms of Market Efficiency Investors look for pricing inefficiencies because these would open up profit opportunities. Such profit opportunities in investment assets can be categorized into three forms of pricing efficiency based on the amount of all available information investors have and use in their asset valuations. All three forms imply that excess profits can be made only by chance (or luck) and unrelated to available (public or private) information.

264 s Portfolio Theory

Weak Form This type of market efficiency assumes that an investor cannot earn excess profits by using all past information on an asset because that information is already reflected in the current price of the asset. Thus any historical market data (price and trading volume) on the asset are incorporated into the current price of the asset and should have no value in predicting the asset’s price in the future. Past data are now part of public information and useless. If such data in the past had any profit value, that value would have been exploited at that time and no significant residual value would remain in the present. Semistrong Form The semistrong type of market efficiency states that, in addition to all past information, all current publicly available information should already be reflected in the current price of the asset. Some examples of such public information would be a firm’s earnings forecasts, quality of management, financing status, and the like. The instant such information is released in the market, the asset’s prices should immediately adjust to reflect that information. Such information can be obtained either from the firm’s web page (for free) or from your broker (for a fee). Therefore if all investors can access that information, no one should be able to make abnormal profits. Strong Form The last type of market efficiency is the strong form, where on top of all past and currently publicly available information, all private information is incorporated into the current price of the asset. By private information we mean whatever is available to company insiders and CEOs. This type is an extreme one because the SEC restricts the use of inside information by corporate officers for trading based on their privileged status. Thus, when people refer to efficient markets (in the United States), they typically mean the semistrong form, because the use of inside information is illegal in the United States. Recall, however, that insider trading is not always easy to define and punish (we first discussed that issue in Chapter 5). Figure 9.2 illustrates the three forms of market efficiency and their relationship. Implications for the Efficient Market Hypothesis Below we will present and discuss the trading and investing implications of the existence of market efficiency in general terms and then comment on the usefulness of some specific investment analyses.

strong form

Figure 9.2 The three forms of market efficiency.

semi strong form

weak form

Market Efficiency and Behavioral Finance s 265

We said above that in an allocationally efficient market security prices provide true signals for capital allocation and thus investors are rewarded more for taking on more risk and less by taking on less risk. Also, in an efficient securities market, abnormal (or speculative) profits do not exist, on average. In other words, there should not be any mispriced security available and any speculator (or trader) who believes that he has found such a security would necessarily reduce his (and his clients’) wealth by an amount equal to transaction costs and taxes. Speculation is a zero-sum game because for every lucky buy there is an unlucky one. Finally, we said earlier that each individual investor has no power in affecting the price of a security when acting alone. Besides, since all investors possess the same information and have homogeneous expectations, they should all agree on the same price of the security. These conditions imply a perfectly elastic demand curve for that security or a horizontal curve at the market consensus price (contrast this to the demand schedule for an asset we first discussed in Chapter 2). Now, we present the implications of efficient markets for some investment analyses and strategies. We begin with the main two types of investment analysis—specifically with technical analysis. Implications for Technical Analysis Recall that technical analysis attempts to uncover recurrent patterns in the history of the asset’s price in hopes of using them in the future. Technical analysts (often called chartists and their analysis chartism) focus exclusively on the stock’s price, ignoring any information about the firm’s prospects for growth (i.e., the firm’s fundamentals) or the general economy. Such analysts employ charts (or graphs) of past stock prices and try to discern market shifts before their impact catches up with the asset’s price. As the market adjusts to the new equilibrium, the analysts can position themselves correctly and ahead of time so as to profitably exploit this price trend. Alternatively put, if the stock’s price responds with a lag to changes in market conditions, such as demand and supply, the analysts would be able to exploit such a sluggish response in the next period. It is important to note that technical analysts do not discard their rival “fundamentalists” because they believe that eventually the asset’s price will be in par with the fundamentals. What are some of the conventional technical or chartist strategies? One early (classic) one is the Dow theory, named after its creator, Charles Dow (who also created the Wall Street Journal ). This technique attempts to distinguish short- and long-term trends in stock market prices. There are three forces that affect stock prices simultaneously: Primary trends, or the long-term movements of prices (reflecting bull markets, rising prices, and bear markets, falling prices) Secondary or intermediate trends, caused by short-term deviations of prices (within a couple of months) from the underlying trend and said to be technical corrections that reduce excess profits Tertiary or minor trends, which are the daily ripples occurring randomly around the basic or secondary trends The Dow theory includes the notions of “support” and “resistance” levels and “head and shoulders” patterns in stock prices. A support level is a price level below which prices

266 s Portfolio Theory

are unlikely to fall, whereas a resistance level is a level above which the stock’s price is unlikely to rise. These two levels are determined by the recent past of stock prices as seen in a graph of past prices (we will see an example of these shortly). A head and shoulders pattern is a pattern to predict stock prices. The left shoulder is built on a rally in the stock’s price and then profit taking reduces the stock’s price, thus completing the shoulder. The next (or similar) pattern of price increase (with high volume and price rise) above the left shoulder is followed again by profit taking, but on a more moderate level than the left shoulder (that would be the “head” pattern). Finally, the right shoulder pattern is formed on high volume but indicates an impending weakness to sustain the previous two price rallies (the left shoulder and the head). Thus, if the stock’s price on the right shoulder falls below (breaks through) the line connecting the low points in the last two technical corrections (the neckline), the technician would call for a sell signal. One important technical indicator that we hear about every day before the markets open is a futures index. Such an index gives an idea of the direction of the markets, up or down, as they open for trading. Examples of such indexes are the S&P 500 futures index, which indicate the overall short-term direction of the market, and the Nasdaq futures index, which is the best indicator of the direction of technology stocks. So if a futures index is up/down, there is an expectation that the market will open up higher/lower. Usually the rises or declines in futures contracts are calculated as differences from their fair value. Fair value is simply the equilibrium (theoretical) price of the futures contract based on the futures underlying cash price (index) and accounting for short-term interest rates and dividends (based on a formula). Box 9.1 explains in a nontechnical manner how a futures contract’s fair value is computed and used by professional investors (we will see the fair value concept again in Chapter 15). Finally, one more technical analysis tool is the moving average technique, which computes the average price for the past n days; thus analysts can see the pattern of such prices over time. See Box 9.2 for an example of how a moving average technique is used by traders. But, what is the implication of market efficiency for technical analysis? The answer is simple: Market efficiency is at odds with technical analysis. The theory predicts that such analysis is useless because no pattern in the past record of a stock’s price is left unaccounted for by the current stock price. If investors look at the history of stock prices, they simply drive up stock prices to levels where they might be neither good nor bad bargains, simply fairly priced. The weak form of market efficiency flatly dismisses technical analysis. However, we will return to this issue in the further on in the chapter. Implications for Fundamental Analysis Recall that fundamental analysis looks at the economics or the fundamentals behind the firm—such as expectations about future growth, earnings, and other quantitative and qualitative information—in an effort to determine the appropriate (fair) level of its stock price. Analysts pore through a company’s financial statements along with the economic environment of its industry and the economy as a whole, hoping to uncover some insight that other analysts have either overlooked or missed in order to determine the security’s theoretical (fair) price. This price is known as the intrinsic value, which is then compared with the stock’s current market value in order to make a buy or sell decision. Fundamental analysts or fundamentalists believe that a thorough financial analysis of a security can identify mispriced securities where information is not yet incorporated into the security’s current market price.

Market Efficiency and Behavioral Finance s 267

BOX 9.1 Fair Value Explained Fair value is the theoretically correct relationship between stock index futures and the underlying stocks (cash). In other words, fair value reflects the theoretical price at which the futures should trade based on the actual stocks that make up the index. If there is a spread (discount or premium)—a difference between the futures and the stock index prices (values)—it means that there is a divergence between what these prices should be; thus markets can be expected to advance or decline on that day. Specifically, when the fair value is up/down in the preopening market hours, the stock market is expected to open higher/lower. When the spread is at fair value, obviously there is no incentive for professional traders to own the futures or the cash index. When we hear that fair value is “plus 5,” it means that the futures contract must be 5 points above the cash index’s closing price (index value) of the previous day so as to be at its fair value. Although the index’s (like the S&P 500 stock index) value remains known the next day before the market opens (because it closed the previous day), the futures value fluctuates because of after-hours trading (at the Chicago Mercantile Exchange, or CME) until 15 minutes before the market opens at 9:30 a.m. Thus, the spread changes during those hours owing to the changes in supply and demand for futures at CME’s trading pit. In addition, fair value changes once the market opens and continues to change throughout regular market trading hours. What does fair value mean for professional and individual investors? For professional (institutional) investors, fair value means the possibility of generating profits (by buying/selling each instrument) at the blink of an eye. But for the average investor, this concept means nothing! For institutional investors (arbitrageurs), who can move billions of dollars in seconds, the spread indicates a buy opportunity, as is typically the case; but for the average investor, it amounts to simply placing an order at the open for a buy or a sell and nothing else. For example, if futures trade at above the fair value to the underlying index, the arbitrageur would sell the contract (at a future date) in hopes that the price would fall. If his bet pays off, then he will reap a profit from the difference between the sale of the higher-priced futures contract and the purchase of the cheaper one. Individual investors should also bear in mind that fair value does not refer to a company’s fundamentals, such as earnings or dividends. It is strictly an indicator of the market’s direction every day before the opening of trade.

Fundamental analysis takes on various forms (or steps), as implied above. For example, the analyst must understand the general macroeconomic environment by looking at several economic indicators in an effort to assess the economy’s health or weakness. Then an economic and financial analysis of the industry in which the company operates is needed to see how the firm in question fares relative to its peers in the industry. Finally, the company itself must be researched in detail to identify any information that may have been missed or ignored by other analysts and compute the stock’s fair price. We will look at all that in detail in Chapter 10. Once again, what does the efficient market hypothesis say about fundamental analysis? As in the case of technical analysis, fundamental analysis is without merit in the eyes of solid believers in market efficiency. The company’s financial reports are all publicly available for anyone to see and assess; thus no analyst would have any less information. Besides, the hypothesis is that all analysts would interpret the information in the same way and thus act in the same way. Since all analysts are well trained, well funded,

268 s Portfolio Theory

BOX 9.2 An Example of a Moving Average Moving averages (MAs) are very popular technical indicators and provide a powerful visual trend-spotting tool. Let us take a look at this indicator and how it can help traders follow trends toward greater profits.

MOVING AVERAGE CONSTRUCTION Below are some real and recent data on IBM stock, from 1/4/2010 to 10/31/2011. The third column shows the constructed 5-week MA, which was done as follows for the 2/1/2010 date:

5-week MA =

126.77

+ 127.67 + 121.58 + 118.57 4

= 123.6475

The remaining numbers to the last data point were computed accordingly. Date

IBM

5-week MA

1/4/2010

126.77

1/11/2010

127.67

1/19/2010

121.58

1/25/2010

118.57

2/1/2010

119.66

123.6475

2/8/2010

120.67

121.87

2/16/2010

123.77

120.12

2/22/2010

123.74

120.6675

3/1/2010

123.83

121.96

....

...

...

10/3/2011

182.39

169.6425

10/10/2011

190.53

174.8975

10/17/2011

181.63

179.2825

10/24/2011

187.45

182.355

10/31/2011

186.38

185.5

The plot of the three columns below shows the path of IBM’s stock and the 5-week MA. You see that the MA tracks the stock’s path closely, sometimes above and other times below the stock’s values. Notice that when the stock moves up or down abruptly, the MA follows these trends rather smoothly. You correctly guessed that this is because of the averaging of previous values in the construction of the MA. Notice also that 8/1/2011 (not shown in the data) is a bearish point according to the MA rule, which says that when the price crosses the MA from above to below it, it signals the beginning of a downturn in the price of IBM stock. In general, a trend is simply a price that is continuing to move in a certain direction. There are only three real trends that a security can follow: an uptrend, or bullish trend, which means that the price is moving higher; a downtrend, or bearish trend, which means the price is moving

Market Efficiency and Behavioral Finance s 269

lower; and a sideways trend, where the price is moving sideways. It is important to remember that prices rarely move in a straight line. Therefore MA lines are used to help a trader more easily identify the direction of the trend. 250

200

150

100

IBM 5-week MA

50

1/4 /20 2/4 10 /2 3/4 010 /20 4/4 10 /20 5/4 10 /20 6/4 10 /20 7/4 10 /20 8/4 10 /20 9/4 10 /2 10 010 /4/ 2 11 010 /4/ 20 1 12 /4/ 0 20 1/4 10 /20 2/4 11 /20 3/4 11 /20 4/4 11 /20 5/4 11 /20 6/4 11 /20 7/4 11 /20 8/4 11 /20 9/4 11 /2 10 011 /4/ 20 11

0

Finally, support and resistance refer to downward and upward trends, respectively. Support is established when a price is trending downward. There then comes a point at which the selling pressure subsides and buyers are willing to step in. In other words, a floor is established. Resistance occurs when a price is trending upward. There then comes a point when the buying strength diminishes and the sellers step in. This would establish a ceiling.

and highly competitive, it would be extremely difficult to find mispriced securities in the marketplace. The idea behind fundamental (as well as technical) analysis is for the analyst to find firms that are better than what the average market thinks they are. This naturally depends upon the skill and ability of the financial analyst, which would have to be better or superior relative to that of his or her peers. That is why fundamental analysis is very difficult and challenging at the same time. Implications for Active and Passive Investment Strategies We have said in previous chapters that active investment strategies involve stock-picking activities and frequent trading, and that they incur trading costs. One wonders why these financial analysts (advisers) would do all these things within an efficient market. Perhaps only serious and uncommon active analyses can generate sufficient excess profits to justify the salaries (and jobs) of those active portfolio managers. For example, a manager who manages $1 million and earns 1% above the market return would hardly justify his salary with a $10,000 extra return annually. However, for another with $1 billion under management, the same 1% annual return above the market would be enough to compensate him, his firm, and perhaps his clients. Perhaps the stock market is not fully

270 s Portfolio Theory

efficient after all. But we will return to these issues later. So, if active investment strategies should not pay off under market efficiency, which strategy is the best? The passive! The passive investment strategy involves buying a well-diversified portfolio with no regard to whether the securities that make it up are mispriced (under- or overvalued). Unlike active portfolio managers, passive portfolio managers do not try to beat or outsmart the market. They will just earn whatever the market earns and incur very little in transaction costs, which would eat out their profits. One very popular passive investment strategy is indexing (or investing in index funds, as we saw in Chapter 6), which is a fund set up to replicate the performance of a broadmarket index. In general, if you are a strong believer in efficient markets, then some reasonable investment strategies for you would be the following: sDiversify. An example would be an index fund mentioned above. sBuy and Hold. Do not attempt to guess the market or beat it. sConsider Costs and Taxes. Try to lower the investment costs as well as tax liabilities. An interesting perspective on the active and passive investment strategies can be offered at this point. It is important to know that before the 1960s, passive investment strategies were largely nonexistent. But with the publication of Markowitz’s portfolio theory (the modern portfolio theory, as is also known), the theory of efficient markets, diversification principles, and capital asset pricing models, attitudes regarding active investment strategies began to change. Many large investors (including mutual funds) started to question the efficacy of active strategies and shifted increasingly toward passive investment ones. Both camps, however, have their own arguments regarding each other’s investment philosophy. Active management strategists postulate that markets are inefficient enough to justify the time and money spent searching for mispriced securities. By contrast, passive investment strategists do not think that there are any meaningfully exploitable opportunities available and merely point to luck when they see that an active strategist was able to beat the market. Despite this ongoing debate on the two investment strategies, the reality is that most equity and debt portfolios are actively managed, albeit to varying degrees, by institutional investors. In general, given the above evidence of market (in)efficiency, what can we finally say about the active and passive portfolio managers? Technicians and fundamentalists are still persuaded that they can outperform the market or at least justify their efforts and salaries. The presence of anomalies neither refutes the EMH nor justifies the existence of so many active managers. Empirical evidence has shown that many problems plague those managers who try to beat the market, and if they do, that would be mostly due to luck rather than regularity. So in the final analysis, we can accept that the market is reasonably efficient, but not perfectly so. New information appears to be incorporated in asset prices quickly and effectively. Recall also that if you wish to perform fundamental analysis to uncover new insights that others may have missed, your marginal benefit would be zero, because other investors have done that as well. Your marginal cost, perhaps, would be greater than the marginal benefit. Behavioral finance came along to explain the persistence of anomalies, suggesting that investors behave less than optimally, or irrationally. But the behaviorists do not give any guidance as to how to exploit such anomalies. The bottom line for investors is that they have to choose between passive and active investment strategies. The box titled

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Lessons of Our Times features Jeremy Siegel, the author of Stocks for the Long Run, and discusses the EMH and the new paradigm for explaining the functioning of the markets, which he calls the noisy market hypothesis. Implications for Investment Managers The efficient market hypothesis (EMH) clearly states that stock prices are fair and that therefore all past, current, public, and private information is incorporated in the current price of the stock. If that is the case, what is the role of professional investment managers and analysts? It turns out that even in an efficient market, professional investment advisers and analysts still have reasons to exist. We list and discuss some of these reasons below. Need to Diversify Recall that investors must diversify in order to eliminate firm-specific risk and reduce market risk. Therefore even under a fairly priced market, the need for efficient diversification is there (as we showed in the previous chapter). Normally, an individual amateur investor would be unable to achieve such a diversification on her own; thus she would need the services of a professional. That is, in choosing their relevant risk/return profile, investors can hire a professional investment advisor to manage their funds and offer advice. Unique Investor Needs Not all investors have the same unique needs from investing. As we have discussed in previous chapters, investors differ in terms of age, money, status, risk tolerance, and the like. Therefore a professional adviser can help the investor to meet her objectives and tailor a portfolio to her unique needs. The investor’s degree of risk aversion is important for constructing an overall portfolio, and only a professional manager can help the investor with this task. Tax Considerations Rational investors need to care about the tax implications of their investment portfolios. Investors in high income tax brackets would want to invest in tax-exempt securities, which investors in low income tax brackets may find unattractive. Furthermore, depending on their degree of risk aversion, some may want to tilt their portfolios toward higherincome securities that would provide capital gains instead of interest income, because the capital gains tax is lower and because they may have the option to defer taxes. Overall, there is still a need for professional advice for investors, small and large alike, in order to build customized portfolios that would help investors to realize their investment plans. Implications for Asset Pricing Models The two capital market models we have learned, the capital asset pricing model and the arbitrage pricing theory, assumed (or were built upon) market efficiency. Their prediction is that the security’s price is fair, or in equilibrium. The paradox is, however, that both the CAPM and the APT imply market efficiency, but the reverse is not important. In other words, an efficient market can exist even when the models do not hold, suggesting that the efficient market hypothesis does not imply applicability of either the CAPM or the APT. Moreover, as we noted earlier, in view of the EMH being silent on the sources

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of information in determining the risk/return trade-off of a security (using either the CAPM or the APT), if a shock occurs in the real economy, investors would not be able to derive either model’s parameters consistent with efficient pricing. Thus asset pricing models (and modern finance theory in general) do not help us to trace the implications of significant changes in the real sectors of the economy. Finally, in view of existence of several anomalies (see further on), both asset pricing models need to be updated to reflect some of these anomalous situations. Finally, what do people say about EMH and the 2008 financial crisis? The short answer is that it is widely believed that EMH caused it. Read Box 9.3 to find out if that is true or not.

ANOMALIES AND TESTS OF MARKET EFFICIENCY The EMH worked relatively well during the 1970s and 1980s and asset prices were found to follow the random walk. During the 1990s, research focused on other issues, such as

BOX 9.3 The Efficient Market Hypothesis and the Crisis of 2008 Several prominent market investors such as Warren Buffett and Jeremy Grantham; and wellknown financial reporters such as Justin Fox; as well as other people say that EMH was responsible for the financial crisis of 2008. Some of the reasons they gave boil down to the following: regulators relied too much on efficiency of assets and slacked on regulation, and financial executives overextended themselves financially because they underestimated the dangers of asset bubbles. In general, they argue that market participants assumed, incorrectly, that asset prices were correct all the time and thus they failed to verify whether prices indeed reflected their true values. But how can one think that the EMH has caused the financial crisis when Almost all investment money is actively managed despite the fact that active managers are, on average, unable to beat the market? Mutual fund money flows follow past performance even though they caution that past returns is not a guarantee of future returns? Most of the losses of institutional investors originated at their proprietary trading desks applying strategies to profit from price misalignments? Investors who continuously poured money into real estate saw asset prices climbing fast but still believed that their prices were correct? These questions are at odds with the claims that reliance on the EMH had caused the crisis of 2008. It is important to bear in mind that the EMH is just a theory and as such it has many limitations. No one should take the theory (or any theory for that matter) literally. The real world is so complex that no model can capture its intricacies. You cannot construct a clean mathematical model (such as one for pricing new derivative products that failed in the crisis of 2008) to capture market activity or price financial assets. Did people assume validity of EMH when creating such complex instruments? Perhaps, but you cannot blame the theory for people’s misuse of it! Source: Ray Ball, The global financial crisis and the efficient market hypothesis: what have we learned? Journal of Applied Corporate Finance, 21(4), Fall 2009, pp. 8–16.

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the reaction of stock markets to earnings announcements, mergers and acquisitions, and other events. Although many studies seemed to validate the efficient market hypothesis, others were more careful in addressing the issue and began asking questions such as: Can announcements really affect stock prices? What other factors affect stock prices? For example, Roll (1988) and Cutler et al. (1989) noted that most of a stock’s price (or the aggregate market’s) movements cannot be solely attributed to regular public announcements.2 The real question is not if earnings announcements have or have not any impact on stock prices but whether expected or unexpected announcements have any impact on prices. Evidence suggests that prices appear to adjust to unexpected announcements. However, the speed with which this happens is still an empirical question. If there is a lag, speculative profits may be earned (in the very short run). In sum, current evidence suggests that stock prices can be predicted fairly well and is based on two competing theories: by the EMH, where the equilibrium in expected returns is generated by rational pricing as investors seek extra return for additional risk, and by psychological factors and irrational (and speculative) investors in the market. Therefore, in view of this evidence, we will briefly discuss the current debate (the issues and/or anomalies, as they are also known) on the EMH and then conclude with more of the empirical evidence. Market Anomalies A market anomaly is a behavior that is not normal or that departs from the predictions of the EMH. We will present some of them and discuss them briefly. Return Patterns If the EMH holds, there should not be any persistent and consistent patterns in the securities’ rates of return. Such consistent patterns are as follows. Day-of-the-Week Effect This effect has several interpretations. For example, it has been observed that trading on stock prices increases dramatically during the last 15 minutes or so of trading at the end of the day. Research also reports that the stock market records unusual trading behavior during Mondays relative to the other days of the week. Specifically, Monday’s returns seem to be lower, on average. Theoretically, if daily returns are positive over the long run and given that stock returns advance on good news, Monday’s returns should be even greater. But that is not observed in reality. Sometimes this behavior is known as the weekend effect, because Monday comes after Friday’s close and there is a weekend in between. This effect is also present in international stock markets except for the Japanese market, which is open on Saturdays, when western markets are closed. In addition, there is the holiday effect, which occurs on official national holidays. Research has uncovered that returns before a holiday tend to be at least 10 times larger than the average daily return. In sum, it is not known why these anomalies exist, but they do not appear to refute (the weak form of) market efficiency. Finally, recent evidence points to some predictable intraday and time-of-day return patterns (persistence) following institutional trades.3 In other words, there seems to be evidence that institutional investors choose certain times of the day to execute trades (or hand trades to the trading desk). Obviously, if such trades were fully anticipated by investors, such effects would not be present under market efficiency.

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January Effect This anomaly refers to the observation that January returns are (up to five times) greater than returns in other months. Additionally, recent research indicates that from 1927 to 2004, small stocks beat large stocks by 2½ times, on average, during January.4 This empirical regularity is consistent and large relative to the day-of-the-week effect and can generate net profits if you buy stocks late in December and sell them in January. In addition, portfolio managers tend to invest in riskier stocks (smaller firms) in the beginning of the year and shift to more defensive (stable) stocks toward the end of the year to secure the gains. Keim (1983) estimated that nearly 50% of the excess return on small firm returns comes from just the first five days in January.5 Although this empirical regularity is still a puzzle, the tax hypothesis is the most prevalent one. This hypothesis states that individuals sell stocks whose prices declined late in the year in order to realize capital losses for tax purposes. Another explanation centers on the observation that mutual fund managers sell losing stocks to avoid reporting them in their annual reports and quietly buy them back in January. What are some of the dangers of this empirical phenomenon if the average investor tries to exploit it? First, recognize that you will need to spend time and effort to identify stocks that could exhibit such (January) behavior. Second, even if you are successful at listing these stocks, do not forget the transaction costs, which could be higher for the stocks of smaller firms than for those of larger firms. Third, the stock portfolio may be volatile, meaning that there is no guarantee that you will end up earning an abnormal return following (playing) the January effect strategy. Finally, if you and other investors decided to do the same thing, can you guess what would happen to the strategy’s effectiveness? You guessed it correctly, it would be drastically reduced. What is the evidence of the January effect internationally? It appears that the effect is stronger internationally than in the United States (see Gultekin and Gultekin, 1983; and Brown and Luo, 2006).6 Finally, the January effect has also been documented for noninvestment-grade bonds. Read Box 9.4 on some evidence of these effects. Short- and Long-Horizon Returns Recall that technical analysts examine the history of stock prices to uncover predictable and recurrent patterns so that they can exploit them in the short run. Do security prices have memory? Are current stock returns correlated with past stock returns? If these are positively or negatively correlated, profits can be made. Some research has found positive autocorrelation (that is, positive returns followed by positive returns) over short horizons. Despite this evidence, however, it is questionable if any profits can be made. Another, related effect is the momentum effect (trading), which refers to the tendency of poorly performing and well-performing stocks in one period to continue their “anomalous” behavior in the next period. Thus, although individual stock returns are independent or each other, portfolios of the best-performing stocks appear to outperform other stocks, thus offering potential profit opportunities. Profitable momentum trading also occurs in international stock markets.7 But even if returns over short-range horizons (daily, weekly, or monthly) are uncorrelated, this does not attest to the validity of the EMH. Researchers examining the returns over longer horizons found that they are negatively correlated. Negative correlation means that positive returns in one period are followed by negative returns in the next. If such dependence is present, bubbles (which are differences between market prices and

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BOX 9.4 Some Instances of Return Effects According to a recent article in the Wall Street Journal, companies may apply some techniques that will paint a rosy picture in their books before closing them for the year in December 31. Some firms (such as banks and investment companies) simply engage in “window-dressing techniques” in order to make their financial statements sound at year-end. For example, they sell many of their riskier holdings at that time in favor of safer (or higher-quality) assets like government securities. Other firms adhere to holding large-cap stocks and avoid buying small-cap stocks during the last few days of the year in order not only retain to quality but also show robust gains (the “painting the tape” effect). In that way, investors can avoid losing money at year’s end. Finally, mutual funds compare their year’s return with a benchmark (index) that suits their needs, meaning selecting an index that they have already beaten. However, that index may not necessarily be the correct one against which these funds should compare their returns. In that way, they show that the beat the market and justify their fees and other money they have earned from clients. Keep in mind that smaller stocks have outpaced market returns in recent years, but during the late 2000s the market has beaten them. So, keep an eye on your (mutual) fund’s benchmark over time and look for changes in these benchmarks. Source: J. Zweig, The intelligent investor, Wall Street Journal, Sat/Sun Dec. 20–21, 2008, B1.

1,600 1,400

S&P 500

1,200 1,000 800 600 400 200

19 68 19 70 19 72 19 74 19 76 19 78 19 80 19 82 19 84 19 86 19 88 19 90 19 92 19 94 19 96 19 98 20 00 20 02 20 04 20 06 20 08

0

Year

Figure 9.3 The S&P 500 Index, January 1968 to October 2009.

fundamental values) or fads (which refer to overreactions by the stock market to relevant news, or the overreaction hypothesis) may occur. Examples of recent bubbles and subsequent crashes include the tech bubble of the second part of the 1990s and the real estate bubble of 2007–2008. Figure 9.3 shows the path of the S&P 500 index from January 1968

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to October 2009 and its two distinctive bubble and bust periods. Are bubbles at odds with the EMH? Well, if such bubbles are irrational (or as Shiller [2006] put it, “irrational exuberance”), they refute the EMH; but the problem is to categorize between “rightful” bubbles, or periods of large market advances accompanied by fundamentals, and irrational bubbles.8 However, most bubbles are irrational. Overall then, despite the important results of long-horizon studies, the evidence against the EMH is far from conclusive. Finally, another interesting effect is the reversal effect, which refers to the tendency of winner and loser stocks in one period to reverse their performance in the next. DeBondt and Thaler (1985) have suggested this effect and interpreted it as the stock market overreacting to pertinent news.9 Another important strand of research has been on the volatility of the stock market. Volatility can be defined as big changes (increases or decreases) in stock prices over time. Volatility can be measured by the standard deviation of stock returns (as we showed in Chapter 3 and Eq. 11a). Volatility tests were designed to test the market’s rationality by examining the fluctuations in stock prices relative to the volatility of the fundamental variables that affect them. Shiller (1981) tested a model in which stock prices are the present discounted value of future dividends.10 He found evidence of significant volatility in the stock market (as well as the bond market). Since fluctuations in stock prices appeared to be greater than those implied by the fundamentals, Shiller inferred that they were due to waves of optimistic or pessimistic market psychology. Size and P/E Effects Early research (in the 1970s) suggested another type of effect, the small-firm or the size effect. Analysis revealed that excess returns would have been earned by holding stocks of low-capitalization companies. A more robust study by Basu (1977) for the 1957–1971 period, within the context of the CAPM, also showed that stocks of companies with low price/earnings (per share) or P/E ratios earned a premium for investors.11 In other words, if an investor held a portfolio with a low P/E ratio, he would earn higher returns than another investor who held the entire sample of stocks. This evidence contradicts the EMH. Reinganum (1981) confirmed Basu’s findings but suggested that the cause may not be a low P/E ratio but a small-firm effect.12 Announcement Effects The semistrong form of market efficiency implies that all past and current public information (news) should be reflected in the current price of the stock. Thus when a favorable announcement is made by the firm, the firm’s stock price should sharply increase, and when an unfavorable announcement is made, the opposite should be true. Consequently, there should be no postannouncement movement (drift) in the stock price or returns, either positive or negative; but even if there is one, it should be completely random (or not related to the news). Earning announcements, for example, can either be on target, that is, as the market had expected, or miss the target, in which case we have an “earnings surprise.” Earnings surprises can also be positive when earnings announcements prove to be better than expected. Thus when asset prices jump to a new level following an earnings announcement, it does not violate the efficient market hypothesis. Such announcements contain valuable economic information that is regularly expected by the market. What would be a puzzle, and a violation of the EMH, would be a situation where asset prices did not move following serious earnings surprises (or deviations from expected

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outcomes). Moreover, if prices following earnings announcements appear to continue to drift for several days (that is, there is leakage of information), it would be evidence of a violation of the EMH. The implication of such unexpected moves can be measured by the cumulative abnormal return (CAR) of stock i, as follows: CAR i =

n

∑ ARit

(1)

j =1

where abnormal return, AR, for stock i at time t, is defined as ARit = Rit − E(rit)

(1a)

where Rit is the actual returns of the stock and E(rit) is the (risk-adjusted) expected rate of return of the stock at time t. Naturally the expected return can be obtained from the security’s characteristic line (SCL), which can be used to estimate the abnormal returns (as we learned in Chapter 8). To make the above more concrete, the computation of this cumulative abnormal return (or residual) is based on the difference between a stock’s actual return and the predicted market’s return from estimating a market model. Such a market model would be like Eq. 13a in Chapter 8, which we reproduce here for convenience: Rit = i + i Rm + ei

(2)

where Rit and Rm refer to the security’s and the market’s excess returns, respectively. Thus, by taking the difference between the security’s return and the estimated market’s return, we obtain the residual component, ei: ei = Rit − (i + i Rm)

(2a)

Thus the residual can be interpreted as the security’s return above and beyond the return that would be predicted by general market movements (given the security’s market sensitivity). So the cumulative abnormal return would be the sum of each of these residuals from one period to another. For example, if the market goes up by 2% on a given day and the stock’s actual return was 3% on that same day, what would be the stock’s predicted (estimated) return and its abnormal return for the day? Assume that i = 0.03% and i = 1.35. The stock’s estimated return would be: e1 = 0.03% + (1.35 × 2%) = 2.73% The stock’s abnormal return would be: 3% – 2.73% = 0.27% Obviously the stock’s cumulative abnormal return would be the sum of all such abnormal returns during some time frame (window).

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Another interesting announcement effect is a stock-split announcement. It is well known that stock splits do not alter the market value of the firm; thus it should not have an impact on the value of the firm (we will discuss stock splits in more detail in Chapter 10). A stock split is simply a break of a share into more shares. For example, a 2-to-1 (two-forone) stock split means that the investor now owns two shares instead of one, but the total value of the two shares is equal to that of the earlier one share. Thus there should be no postannouncement stock price drift. However, many investors may believe that such splits are good news because the company cares about small investors (who now can afford to purchase shares since their price is cut in half), and thus they may buy more of them. Such actions create a rise in the company’s stock price. Other Effects The neglected-firm effect refers to the tendency of less-known, less-researched firms to produce abnormal returns. The January effect is larger for such firms. The book-to-market effect refers to the tendency of firms with high ratios of book-to-market value to generate excess returns. Recall that Fama and French first suggested this effect in comparing it to the stock’s beta coefficient (which they found largely irrelevant). These findings challenge the notion of market rationality since beta, which should affect returns (the systematic risk), does not really matter, while a variable (book-to-market ratio) does! Finally, there are other lesser known or used anomalies, one of which is the presidential election cycle effect, which postulates that the stock market, on average, has performed weakly during the first 2 years of a presidential term while it showed strength during the last 2 years of that term. Summary of Market Efficiency Tests Tests of market efficiency were conducted on each type of market efficiency. Let us summarize some of the most important findings. Weak Form of Market Efficiency Very early tests of the weak form of market efficiency (such as evidence of correlation of returns and other statistical tests) failed to find evidence that abnormal profits could be earned by using past information. This evidence simply casts doubt on the usefulness of technical analysis. More recent tests have suggested that investors may overreact to some types of information and if so, some profits can be made in the short run. Brock et al. (1992) tested several technical trading rules and found that they had predictive ability of the DJIA from the 1897 to the 1986 period. Specifically, they found that sell signals had greater predictive ability than buy signals. Hudson et al. (1996) also found good predictive ability of technical trading rules (using UK data) translating into excess returns for investors but cautioned that the level of excess returns hinges on the costs of trading. Thus these authors support the weak form of market efficiency.13 Finally, Pukthuanthong-Le and Thomas (2008) examined whether the weak form of market efficiency existed in currency markets and found conflicting results (along with other studies). Specifically, they reported that the profitability of momentum-based technical trends eroded over time for major currencies around the mid-1990s, suggesting that market inefficiency improved or that the currency market became weak-form efficient.14 However, the jury is still out on the empirical front.

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Semistrong Form of Market Efficiency There is also mixed evidence on this form of market efficiency. Some studies support this form despite presence of the above-mentioned market anomalies, transaction costs on futures indexes, as well as stock splits and dividends. Specifically, if an investor can predict stock splits and dividends, he may earn abnormal gains; but the average return is zero after the announcement date for such events. However, the presence of some other anomalies such as the size effect may weigh against that type of market efficiency. For example, Chordia et al. (2004) found that market order imbalances (defined as the total daily market purchase orders minus sell orders for stocks in the S&P 500 index) are highly predictable from day to day.15 Thus some sort of persistent buying/selling activity appears to exist that can be profitably predicted by astute traders. In general, market anomalies typically arise from empirical tests that perform joint hypotheses that the market is informationally efficient and the assumption of a market equilibrium model (such as the CAPM) is valid. If the joint hypothesis is rejected, we conclude that the market is inefficient. This conclusion is incorrect because, perhaps, we may not have used the correct equilibrium (benchmark) model. Strong Form of Market Efficiency This form deals with trading on inside information and it has been shown that insiders (such as corporate officers and stock exchange specialists) have earned abnormal returns relative to outsiders.16 But this uneven playing field has been “flattened,” at least in the United States, because insider trading is made public (inside trading information and activity, for instance, is registered with the SEC and published in the Wall Street Journal). Also, and even more powerful, is the fact the mutual funds have not been able to beat the stock market, which flatly implies that these professional managers are not able to uncover valuable information that is not already embedded in the current prices of stocks. Is the Stock Market Efficient? So what is the final verdict on stock market efficiency? The extant evidence is conflicting, and many traders and researchers alike seem to lean toward market inefficiency. Bogle (2009) noted that the market is inefficient because traders and investment advisers no longer engage in traditional investing activities; that is, for the long run and on behalf of their clients. Rather, they focus on speculative activities to make as much money as possible as fast as they can. Moreover, Bogle cautioned that innovation in the financial services industry, such as new derivative instruments, did not help to improve market efficiency but instead elevated market risk.17 Many traders and investors believe that the stock market is not efficient for various reasons. Just think of the following questions: sWhy are so many active portfolio managers serving the investment needs of investors? sWhy is technical analysis so widespread in Wall Street? sWhy do traders exploit anomalies or are on the constant lookout for new ones? sWhy do so many ways of valuing stocks exist (as we will see in Chapter 11)? Don’t investors think a given stock’s price is fair at any given point in time? sWhy are some investors able to earn abnormal returns or to beat the market while others are not? sWhy do financial crises pop up?

280 s Portfolio Theory

sDo all investors acquire and process information at the same time and in the same way? Despite these considerations, evidence suggests that, overall, the stock market in the United States is reasonably efficient (or semistrongly efficient), which means that the marginal benefit (profits) of acting on information are less than the marginal costs. Thus investors cannot expect to find bargains on a consistent basis and to profit from them. That is also because “there is no such thing as a free lunch” (known as TINSTAAFL) and because of transaction and other research costs involved in frequent trading. But this does not mean that there are not or will not be any new opportunities to profit from. Nonetheless, because the fact that these anomalies exist and perhaps will continue to exist does not necessarily mean that the market is inefficient. The debate will surely continue to be lively, with one group of researchers explaining these anomalies as manifestations of risk premiums (Fama and French, 1993) and another group seeing them as evidence of market inefficiency or due to systematic errors in the analysts’ stock price forecasts (Lakonishok, Shleifer, and Vishny, 1995).18 Finally, even Fama (1991) himself declared that “the extreme version of market efficiency hypothesis is surely false” (because of trading and information costs) and that “market efficiency per se is not testable,” meaning that it must be tested jointly with a market equilibrium (he named this the “joint-hypothesis” problem).19 Specifically, he now focuses on the following three issues instead of the three forms of market efficiency: Tests for return predictability using other variables and not just past returns Event studies giving the most direct evidence of market efficiency Tests of private information that corporate insiders possess which can yield profits In general, the point is that the market is neither extremely efficient, so that no shortterm excess profits can be made at any point in time on any investment asset, nor extremely inefficient, where abnormal profits are made on a consistent basis. The truth is always in between. So if anyone brags about his superior investment strategy (skills), he or she should be listened to with a grain of salt. Market competition and costs ensure that only those with a special insight or luck can earn abnormal returns, but they do so only briefly. In conclusion, in view of the above debate on the EMH, is there an alternative theory that takes into account how people (investors) behave? Yes, and it is explained in the following discussion. Read Box 9.5, which discusses an insight from a professional analyst on revisiting the EMH.

BEHAVIORAL FINANCE A new theory has attempted to explain the (persistence of the) above anomalies by relying on a psychological view. Evidence suggests that investors are not “rational” when they attempt to make complex decisions because they have limited information-processing capabilities and frequently exhibit systematic bias in processing that information. Despite the counterargument that a large number of investors behave in a rational manner, empirical observations cannot fully confirm this statement. Additionally, observations imply that investors often rely on the suggestions of other investors or simply follow

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BOX 9.5 Revisiting the Efficient Market Hypothesis In 2003, the stock market has put on one of those frequent demonstrations that show exactly why smart investors buy stocks and hold on to them. The economic news has not been good, with unemployment rising to a nine-year high and the Fed warning of deflation and new corporate accounting scandals have surfaced. By conventional measures, stocks appear overvalued, with the price-to-earnings ratio for the benchmark Standard & Poor’s 500-stock index exceeding 30. Yet stock prices keep rising. Since March 11, the S&P is up by about one-fourth, the Nasdaq composite index by nearly 30 percent. These numbers reinforce my market credo: “In the short term, no one knows anything.” That motto is also a crude way of expressing the Efficient Market Hypothesis (EMH), first formally presented in the 1964 dissertation of Eugene F. Fama but dating back more than a century, to the work of Louis Bachelier. Here is how Fama put it: In an efficient market, competition among the many intelligent participants leads to a situation where, at any point in time, actual prices of individual securities already reflect the effects of information based both on events that have already occurred and on events which, as of now, the market expects to take place in the future. In other words, millions of people, with vast incentives to learn every scrap of information about companies, are buying and selling billions of shares every day. Therefore, prices reflect the best knowledge of the present and predictions of the future. From today’s perspective, tomorrow’s prices are utterly unknowable. As a result, prices tomorrow move in a phrase made popular by Burton G. Malkiel: a random walk. The problem with the EMH is that it denies our ability, as investors who think we are extremely cunning and perspicacious, to see the future. If you believe in the EMH, you understand that highly successful stock selections are really just lucky guesses. More important, all of that forecasting you hear on TV and read in the newspapers is just blather—as is “technical analysis.” According to John Allen Paulos, author of “A Mathematician Plays the Stock Market,” that’s all to the good. The paradox, he told me in an interview last week, is that, if all investors were convinced that markets were efficient, they would simply sit on their holdings, never buying or selling. In such a world, new information about stocks would never enter the market, moving the prices of stocks in an efficient way. Daniel Kahneman with the late Amos Tversky with their work on behavioral foibles earned the Nobel Prize in economics. But even Richard H. Thaler, one of the leading behavioral economists, warns investors not to try to profit from behavioral analysis. “While behaviorists think that it is theoretically possible to beat the market,” Thaler was quoted saying, “individual investors do not have the time or training to do that on their own, and finding superior skills among active mutual fund managers is not easy, either.” It’s a better strategy simply to trust in the EMH. Even if the hypothesis isn’t perfect, Malkiel says, “you ought to act as if the markets are efficient.” In an efficient market, we can’t tell the future simply by looking at the past. Such an admission of ignorance is the beginning of wisdom. If we can’t know the future, we can stop spending time on trying to pick the precisely correct stocks at the precisely correct times. We can forget about market timing and simply take advantage of the market’s broad tendency to rise. The average returns to U.S. stocks—both price increases and dividends—over long periods are remarkably consistent: about 10 percent annually, or roughly 7 percent after inflation. And for good reasons: first, the companies that issue shares increase their profits at roughly the rate of economic growth, or about 6 percent (including inflation) annually, and, second, the market pays investors for taking risks. Even Thaler agrees that you should “settle for the average returns and low fees offered by index funds.” As super-investor Warren Buffett once told his shareholders, “observing that the market was frequently efficient, [the EMH enthusiasts] went on to conclude incorrectly that the market was always efficient. The difference between the propositions is night and day.”

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So let’s be clear: There are inefficiencies in the market. Investors do get carried away. Buying shares of a company because you think they are cheap is not an irrational act. Investing in mutual funds run by managers who aspire to beat the market is not insane. But the EMH must be the default position, the pole, the home base of your investing life. When you think you can “beat” the market, you need to examine your assumptions and your hubris. Still, the quest to beat the market is gloriously human. Don’t deny it. Just put it in the proper perspective. Source: James K. Glassman, Revisiting the Efficient Market Hypothesis, Capitalism Magazine, June 29, 2003 (excerpt).

the crowd (the so-called herding behavior). Finally, another interesting situation is the debate over the October 1987 stock market crash, which still plagues the proponents of the EMH. The market’s decline of more than 22% was almost impossible to account for by the theory, since the crash did not occur because of fundamental shifts (for instance, in risk or expected earnings). Thus opponents of the EMH are given credence to their argument that the market includes a significant number of speculative investors who are guided by “nonfundamental” factors. But before we attempt to discuss this theory, a brief historical contrast will be useful. John M. Keynes (1936) hypothesized that investors have short-run investment horizons (or speculative motives) and that therefore their activities are guided by “animal spirits” (recall also his famous motto “in the long-run we are all dead”). This essentially means that investors are not interested in assessing the long-run value of assets but rather concentrate on their short-term behavior. Thus, it is clear that investors are faced with uncertainty regarding these issues where no probabilities can be assessed (derived) to guide the decision-making process. Keynes also suggested that uncertainty is different from risk, because in a risky environment probabilities of outcomes can be derived. Hence he emphasized the speculative motive of investors, suggesting that they do not really buy stocks so that they can keep them for the long run; instead, their motive is to resell them in the very near future in the hope of making a quick profit. The box titled Applying Economic Analysis discusses Keynes’s “beauty contest” and its relevance to investors’ behavior. By contrast, the EMH is based on investor rationality and on a longrun investment horizon. Thus, implicit in this definition is that investors possess complete information or knowledge of all factors affecting the behavior of assets. This, in turn, means that investors should have an accurate picture of the future cash flows of the assets they are trying to value, and the appropriate discount rate at which they discount those cash flows. The EMH is based on a risky environment, contrary to Keynes’s assumption of the capital markets, and assumes that investors are always guided by knowledge of the factors to evaluate assets. Behavioral finance argues that when investors attempt to solve complex problems (for instance, how to assign probabilities to uncertain outcomes or to their corresponding rates of return), they tend to use cognitive heuristics, which, unfortunately, leads them to several biases. An alternative way to define behavioral finance is to understand that it is a special branch of (micro) economics that is based on bounded rationality (which occurs

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when the decision maker has limited knowledge or cognitive biases). As a result, the objectives of profit maximization or the maximization of shareholder wealth fall short. Some of those biases are listed and briefly explained below. Biases in Information Processing The major attack on the assumption of human rationality was put forth by the pioneering work on prospect theory of Kahneman and Tversky (1973, 1984).20 Their findings suggest that individuals violate the expected utility theory because they evaluate situations (such as gains and losses) relative to some prior beliefs (or irrelevant reference points). Stated differently, people tend to place too much emphasis on recent situations (in making forecasts) and thus fall into what is known as the memory bias, leading them to behave on the basis of extremes. For example, investors tend to overreact to new information (the overreaction hypothesis mentioned above), ignoring the base situation. DeBondt and Thaler (1990) have suggested that the P/E effect can be explained by extreme behavior of investors when they expect high earnings in the future and concluded that high P/E ratios often tend to be poor investments.21 Another human frailty is overconfidence, which occurs when people tend to overestimate their knowledge or abilities. This bias can explain why we sometimes observe a high volume of trading and why unprofitable trades in securities are sometimes very high relative to profitable ones based on unsubstantiated forecasts of recent trends in those securities. Thus this irrational behavior causes the value of securities to diverge from their fundamental value. For example, Odean (1998) and Wang (2001) show that investors who are overconfident tend to believe that they can earn large returns and thus trade often, but they also underestimate the associated risks.22 Yet another example of overconfidence is the observation that there are more active portfolio managers than passive portfolio managers. Despite the advances in passive investment strategies, such as index funds and ETFs, mutual fund managers hold only a fraction of their managed assets in passively managed accounts. Yet one more bias in information processing refers to peoples’ ability to wrongly infer a pattern (or behavior) either fast or slowly. For example, if investors are slow in revising their beliefs (or expectations), they may underreact to some news and only gradually adapt to the new situation. By contrast, when investors are quick to extrapolate future trends, it may initially lead them to overreact and then initiate a correction. This means that favorable events may generate buying pressure and unfavorable ones selling pressure. Finally, some people tend to state that they would have been able to predict an event only after that event has taken place and been explained to them. Such a bias contributes to overconfidence and, naturally, leads investors to make erroneous decisions. The box titled International Focus discusses whether central banks create bubbles and the issue of whether investors learn from their mistakes or not. Biases in Behavior An important bias is observed in people when they are not able to judge economically equivalent choices if these choices are presented to them differently. This bias is known as the framing effect. Let us present it with a simple example (which we first encountered in Chapter 2). Suppose that on your way to the movies you discovered that you had lost your ticket, for which you had paid $10. The question is this: Would you pay another $10 to buy another ticket? Now assume that you had not purchased the ticket in advance but

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have $10 in your pocket to buy the ticket at the box office. On your way to the box office you discover that you have lost the $10 bill. Would you spend another $10 to buy the ticket? Economic theory says that these two events are the same (and thus you should buy the ticket in both cases), but they are presented differently. Observation has indicated that people would buy the ticket in the first case but not the second. Thus, people seem to “frame” these choices differently and to separate them into various “accounts.” For example, in peoples’ minds, “cash balances” is one account and “entertainment budget” is another. Sometimes this bias is referred to as mental accounting, which refers to the separation of assets into independent accounts rather than (rationally) considering them as part of an overall portfolio. Research by Shefrin and Statman (1985) found that investors are more likely to sell stocks with gains than with losses; they called this the disposition effect, which runs contrary to the objective of profit maximization.23 This effect simply refers to the tendency of investors to sell winners stocks, so that they hang onto gains (cash accounts), and to hold on to losing stocks so that they do not realize losses. Box 9.6 explains why investors sometimes make irrational decisions.

BOX 9.6 Instances of Irrational Decisions There are some mistakes investors make when reallocating/revising/rebalancing their portfolios.

CHASING WINNERS Are you buying stocks when the stock market is rallying? Are you influenced by recent events and that is why you act like that? Often, investors are bullish/bearish at the wrong time. If one asked you what you would expect the stock market to do in the near future while it is rising, what would be your answer? Obviously you would say that you expect it to advance.

CHASING HISTORICAL PERFORMANCE This refers to the bias mutual funds investors tend to have when putting money into funds that have historically performed better than the previous year. Such behavior rarely results in betterthan-average performance (and even beating the market). This is like “driving on the highway and, instead of looking through the windshield, you are looking in the rear-view mirror.”

STATUS QUO BIAS Investors sometimes do not act because they are afraid that they will regret it. So, if the market is doing very well and your portfolio is doing very well, you tend to think that you are a smart investor. This makes you more and more complacent (confident), and thus you take more risks (you “suffer” from overconfidence). But when the market tumbles, you are afraid of taking more risk and thus you may be overreacting. Such overreaction may make you lose a bunch of money (unless you are lucky). Source: M. Cooper, H. Gulen, and R. Rau, Changing names with style: mutual fund name changes and their effects on fund flows. Journal of Finance, 60(6), 2005, pp. 2825–2858.

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Finally, another behavioral bias is regret avoidance. This effect refers to the inclination of people to blame themselves or feel more regret for having made a wrong decision when the decision was not conventional. For example, if you lose on a stock of a wellknown company, you would not feel more pain (regret) than if you lost on the stock of a relatively unknown firm. Just think of what Markowitz does with his asset allocation: he has confessed (in an interview with a finance writer at the Wall Street Journal) that he allocates his retirement contributions 50:50, or 50% in stocks and 50% in equities.24 He explained that he does this because he wants to avoid feeling sorry for being absent when the market goes up and present when the market goes down. In general, the implication of the regret avoidance effect is that smaller firms or neglected firms tend to be out of favor by investors and thus may be in difficult financial positions. If investors focus on individual stocks (and particularly on losses) rather than portfolios, they may unnecessarily become more risk-averse for poorly performing stocks and thus require a higher risk premium. Models of Human Behavior Behavioral finance, while still in its infancy, provides a powerful alternative interpretation of market inefficiency (anomalies) and investor behavior. Its premise is also based on relaxing the strict assumption of investor rationality, a fundamental assumption under EMH and other rational expectation models. Shiller (1984, 1991), in a series of papers, proposed a new framework for explaining stock price movements that includes investor (social) psychology. Shiller (1991) concluded that excessive market volatility is caused by fads and is not guided by objective, fundamental factors.25 He emphasizes the October 1987 market crash, when there was no news about the fundamentals and yet investors traded because of price changes. Summers (1986) also challenged the EMH and suggested that asset pricing should contain a random walk component and a “fad” variable component.26 This variable is modeled as a mean-reverting stationary process. Mean reversion means that prices would revert back to their “normal” levels once investors had corrected for their initial overreaction. This phenomenon occurs when asset returns exhibit negative autocorrelation. Other decision-making models explicitly recognize that investors exhibit loss aversion. Loss aversion occurs when investors assess opportunities in terms of losses and gains instead of uncertainty with respect to their final wealth. In other words, potential losses carry more weight (in the minds of investors) than potential gains, but that preference changes as the investor’s wealth changes. This is contrary to conventional utility theory, and thus investors are led to make inconsistent and erroneous forecasts. For example, if investors are confronted with a choice between a certain loss and an uncertain outcome whose expected value is a loss (negative) but which might also produce a smaller loss (less negative), investors might chose the uncertain alternative (that is, exhibit loss aversion). Thus, they would exhibit risk-loving tendencies. A possible implication of this (special case of the mental accounting effect we mentioned earlier) is that potential losses may raise the investor’s level of risk tolerance in the future. If the investor cannot (learn to) accept losses, then his future trades may be riskier than otherwise. Thus, if investors follow such strategies, we would expect significant losses to be accompanied by higher risktaking behavior. Therefore, although risk aversion, a central assumption in traditional finance, would dictate that investors should choose the certain outcome (or the loss in the above example), loss aversion would push them choose the uncertain outcome.

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Numerous other nonrational investor (or human, in general) behaviors exist and are routinely taught in various economics and business curriculums (to say the least). Let us illustrate with three examples. Malkiel, one supporter of efficient markets (and index funds) and father of the random walk theory, admits that he does not hold all of his money in index funds; rather, he allocates a quarter to one-third to actively managed funds.27 Thus his actions indirectly imply that he does not believe 100% in efficient markets. As another example, let us examine the “prisoners’ dilemma,” which demonstrates the irrationality of a rational strategy. Briefly, the prisoners’ dilemma refers to the irrational choices faced by two prisoners who care for each other and have committed the same crime. Specifically, the choices for each prisoner (H and N) given by the prosecutor are shown in Table 9.1. The dilemma here is that regardless of what the other prisoner does, each is better off (or the rational outcome would be) remaining silent because they would both get lesser sentences (of 3 months each). However, the outcome obtained is not the ideal one (the above one) but the one where they both confess, which gives them each 6 months in prison. Thus the puzzle shows the conflict between individual decision making and group rationality or, by extension, the difference between individual selfish behavior (choice) and socially desirable outcomes. Finally, the winner’s curse is important; it occurs during a bidding process. Recall that Treasury bills are purchased in an auction where investors submit competitive bids. These investors run the risk of being shut out of the allocation of bills if they bid too low but increase their chances of being allocated the bills they wish to purchase if they bid too high. Once the bidding process is over, the average price would have been paid by the investors and thus those who overpaid to get the bills would realize that they had “paid too much.” Hence they are winners but cursed at the same time because higher prices imply lower yields. The implication of this situation is that in order to bid optimally, you should have had adequate information on the number of bidders, the true price of the security, and the like. But in reality, since this information is not available, potential bidders can arm themselves with valuable experience in the biding process so that they can avoid this phenomenon in the future. Noncompetitive bidders, like you and me, do not bid but pay the average price of the T bill (therefore we should not complain). Implications for Technical Analysis As long as market anomalies exist, there will be justification for the existence of active management strategies and, in particular, technical analysis. Technical analysts, as we have said earlier, examine the past behavior of stock (or index) prices and volume data in an effort to infer future price movements. Technical analysts believe that stock prices are slow to adjust to market fundamentals or changes because of irrational investor behavior, noise, or market power. This means that technical analysis may be a suitable strategy following the implications of behavioral finance. As we saw above, certain effects and Table 9.1 The Prisoner’s Dilemma

Prisoner H remains silent Prisoner H confesses

Prisoner N remains silent

Prisoner N confesses

each gets 3 months H goes free; N gets 1 year

H gets 1 year; N goes free each gets 6 months

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specific investor behavior (over- and underreactions, momentum trading, and so on) may be exploited by astute technical analysts. The technicians assert that the study of past price movements and volume patterns would allow them to identify times when a stock (or a portfolio of stocks) is either over- or underpriced. A more appealing version of technical analysis is that price patterns constantly develop and are never the same; thus only those analysts with superior skill and insight may be rewarded by devising or uncovering new trading patterns. This further implies that trading is never quite able to bring about efficiency in asset prices and that therefore technicians will be able to profit from these price discrepancies. However, early studies have found little evidence that technical analysts were able to “beat the market” on a consistent basis based on these traders’ rules. Ample evidence exists to the contrary, that the professional managers’ performance does not support technical analysis. Several studies, however, citing momentum and contrarian strategies, have offered empirical evidence supporting that technical analysis may be useful to investors. A contrarian investor simply does the opposite of what other investors do. In other words, he buys/sells when others sell/buy, believing that investors tend to overreact to news. Why do contrarian investors buy/sell when others sell/buy? Their logic centers on the notion that they buy when others dump a stock because they think that its price might have fallen too far. Once the other investors realize that they have overreacted to the bad news, the stock’s price rebounds toward its fundamental value. An alternative way to see a contrarian strategy is to recall that owing to the reversal effect (when loser and winner stocks in one period revert into winners and losers in the next, respectively), a contrarian investor would invest in recent losers and shun recent winners. Contrarian strategists also suggest that these returns are marked enough to generate profits. Evidence on the success of contrarian strategies is scant and at best mixed. Most studies, however, have concluded that errors were made in determining benchmark portfolios or investor behavior (such as overreactions), and thus their validity is questioned. Finally, both momentum and contrarian strategies would involve substantial transaction costs because of frequent trading, and whether such trades are indeed profitable is still an empirical question.

CHAPTER SUMMARY In this chapter, we discussed at length the efficient market hypothesis (EMH) and behavioral finance. We began with the notion of market efficiency and continued with the explanation of its three forms namely, weak, semistrong, and strong. Then we traced the implications of market efficiency for technical and fundamental analyses by concluding that these two investment analyses are useless within an efficient stock market. Similarly, we examined the implications of efficient markets on the use of active and passive investment strategies and concluded that the optimal investment strategy is passive and not active. Finally, we explored the consequences of investors employing professional managers to invest on their behalf and concluded that the services of such managers are still needed even within an efficient market. Next, we examined several anomalies, such as return patterns, the size of P/E effects, the calendar, and other effects and ended with a summary of some tests of market efficiency and their implications. The presence of so many market anomalies seems to refute market efficiency according to some researchers, but according to others it does

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not. It appears that some short-run profits can be made exploiting these anomalies, but it is still a puzzle why their exploitation by so many investors did not help reduce the effectiveness of trading strategies or even eliminate these anomalies altogether. The second part of the chapter dealt with a competing discipline to understand the behavior of financial markets, behavioral finance. We examined investor behavior from the perspectives of biases in information processing and other biases in behavior and discussed some models of human behavior. Finally, we explored the implications of behavioral finance doctrines on technical analysis.

APPLYING ECONOMIC ANALYSIS KEYNES’S BEAUTY CONTEST AND INVESTOR BEHAVIOR Keynes suggested that the stock market behaves like a “beauty contest” in the sense that investment decisions are driven by expectations of what other people think and not by expectations about the fundamentals of the particular investment. In other words, he coined the term animal spirits in view of investors’ behavior as a herd. The beauty contest parallel is as follows. Among the 100 young women featured in a London newspaper during the 1900s, you had to make your choice of the six prettiest women. Everyone who managed to pick the most popular woman would win a prize. So, here’s the situation. If you had selected the women that you thought were prettiest, you would not win, because your selections would have to match the popular one. So you would not pick the women that you thought were prettiest but those that you thought the judges or everyone else would pick. In other words, in order to win, you would have to “go with the herd” or pick those that you would think the average person would pick. Keynes noted that the goal of the entrant would be to pick the girls that others thought prettiest rather than the ones he thought prettiest. So the contestant conformed to the average, which would be an irrational behavior. Thus, in applying this principle to the stock market, we see that volatility increases because fundamental values become irrelevant and because waves of optimism and pessimism occur owing to the perceptions of (ignorant) investors. So, for example, if average opinion expects a company’s P/E ratio to go up, investors would also believe that it would go up. It is no wonder that almost 70 years ago, Keynes described the stock market as a casino, with musical chairs and the mass psychology of ignorant investors, in addition to the terms mentioned above. In Keynes’s words, “We have reached the third degree where we devote our intelligence to anticipating what average opinion expects the average opinion to be.” To conclude, the whole idea is to understand that an investor would have to move before the average investor moves in order to exploit a future situation (if, of course, you believe in market inefficiency). Adapted from John Maynard Keynes, General Theory of Employment, Interest, and Money, Chapter 12 (Cambridge University Press, 1936), p. 155.

INTERNATIONAL FOCUS DO CENTRAL BANKS CREATE BUBBLES? Yes, according to J. Grantham, GMO’s fund manager, and no, according to A. Posen of the Bank of England. Grantham argues that the Fed’s former and current chairmen had acted or continue to act to stimulate the economy through asset price inflation because of the greater sensitivity of

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the financial sector of the economy relative to the real sector. He says that when the stock market experienced serious declines, the two chairmen acted “to goose prices.” Thus they viewed market declines and advances as asymmetric, which caused serious economic distortions and led to the creation of bubbles. Currently, Ben Bernanke is inflating asset prices in an effort to bring the US economy out of the hole created by the previous chairman’s monetary policy. Posen, on the other hand, argued that accommodative monetary policy does not create asset bubbles. Loose money and asset price bubbles are just a coincidence, he says, citing the Japanese case. Even if the money supply is expanded, investors would not proceed with buying real estate if they never expected higher returns from such buys. Thus he blames investor expectations for the creation of bubbles. So what is the verdict? It is clearly understood that expectations matter. It is argued that investors perceive futures moves by the central bank and thus act accordingly. Investors are cognizant of the fact that their past experience of pain from not participating in a rally may be greater the pain of getting out of a bubble too late. Behavioral finance implies that once individual investors have been hit hard twice, they should stop playing. By contrast, professional investors would continue playing because they think of themselves as being better than the rest of investors and thus may come out on top after the bubble has burst. Source: Central Bankers and Bubbles, wsj.com, October 28, 2010.

LESSONS OF OUR TIMES THE “NOISY MARKET” HYPOTHESIS We are on the edge of a new way of building broad-based indexes that can offer investors a better risk/return mix than the traditional indexed funds. These new indexes are weighted by fundamental variables like dividends and sales, in contrast to the usual indexes, which are capitalization-weighted (with the exception of the DJIA). The new approach finds support from the academic community, which cherishes the notion of market efficiency. Under this notion, capitalization-weighted indexes offer investors the best risk/return combination. Research has proven that capitalization-weighted portfolios have offered disappointing results since (mutual fund) active portfolio managers have not been able to beat the market. Thus, indexed investing has gained popularity and cracks have begun to appear in the efficient markets hypothesis (such as small stocks earning higher returns than what their risk indicated and stocks with low P/E ratios having more returns than stocks with high P/E ratios). These are described as anomalies in the market. Efficient market proponents maintain that these stocks contain risks hidden in historical data and predict that one day, when a crisis hits and investors frantically seek to liquidate their portfolios, small and value-based stocks will crumble while large growth stocks will shine. However, this is not true, given that in the past 10 years we witnessed a huge tech bubble, 9/11, a recession, major corporate scandals, and wars. The new paradigm can help us understand how markets function and claims that prices of securities are not always the best estimate of the true underlying value of the firm. They can be influenced by traders like speculators and momentum traders as well as by insiders. Siegel calls such temporary shocks (which may last for days or years) as noise that hides the true value of security prices. Thus, he calls this paradigm “the noisy market hypothesis.” Siegel argues that this hypothesis explains the size and value anomalies: “If a stock price falls for reasons unrelated

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to the changes in the fundamental value, then it is likely—but not certain—that overweighting such a stock will yield better than normal returns. On the other hand, stocks that rise in price more than their fundamentals become ‘large stocks’ with high P/E ratios that are likely to underperform. It can be proved that if stock prices are subject to noise, then capitalization-weighted indexes will offer investors risk-and-return characteristics that are inferior to those of fundamentally weighted indexes. Dividends are the only fundamental variable that is completely objective, transparent and unable to be manipulated by managers who tinker with accounting assumptions.” According to Siegel’s research, dividend-weighted indexes outperformed capitalization-weighted indexes. His data also indicate that the outperformance by fundamentally weighted indexes was even greater among midsized and small stocks. In addition, dividend-weighted indexes outperformed “value cuts” of the popular capitalization-weighted indexes such as the Russell Value. Thus, Siegel proposes that devotees of value investing, who are searching for a simple, lowcost indexed portfolio in which to hold their stocks, should switch to fundamentally weighted indexes. These indexes will influence the next wave of investing. Source: Jeremy J. Siegel, The “noisy market” hypothesis, www.jeremysiegel.com

KEY CONCEPTS An efficient market is one in which all assets are fairly priced at all times with no opportunities for excess returns (or profits). The random walk theory postulates that asset price movements are unexpected since they do not follow any particular trend or pattern. The weak form of market efficiency assumes that all past information on an asset is already reflected in the current price of the asset. The semistrong type of market efficiency states that, in addition to all past information, all currently publicly available information is already reflected in the current price of the asset. The strong form of market efficiency postulates that on top of all past and currently publicly available information, all private information is incorporated into the current price of the asset. Technical analysis attempts to uncover recurrent patterns in the history of the asset’s price in hopes of using them in the future. The Dow theory technique attempts to distinguish short- and long-term trends in stock prices. A support level is a price level below which prices are unlikely to fall. A resistance level is a level above which a stock’s price is unlikely to rise. A futures index gives an idea of the direction of the markets, up or down, before they open for trading.

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Fair value is the equilibrium (theoretical) price for the futures contract based on the futures underlying cash price (index) and accounting for short-term interest rates and dividends. The moving average technique computes the average price for the past n days; analysts simply see the pattern of such prices over time. Fundamental analysis looks at the economics or the fundamentals behind a given firm— such as expectations about future growth, earnings, and other quantitative and qualitative information—in an effort to determine the appropriate (fair) level of its stock price. The intrinsic value of an asset is the fair price of the asset based on investor beliefs. The passive investment strategy involves buying a well-diversified portfolio with no regard to whether the securities that compose it are mispriced (under- or overvalued). Indexing (or investing in index funds) is an investment technique set up to replicate the performance of a broad market index. A market anomaly is a behavior which is not normal or one that departs from the predictions of the EMH. Volatility can be defined as big changes (increases or decreases) in stock prices over time. Behavioral finance argues that when investors attempt to solve complex problems they tend to use cognitive heuristics, which, unfortunately, lead them to several biases. Loss aversion occurs when investors assess opportunities in terms of losses and gains instead of uncertainty with respect to their final wealth. Regret avoidance refers to the inclination of people to blame themselves a wrong decision or feel more regret when the decision was not conventional. Mean reversion means that prices would revert back to their “normal” levels once investors had correct for their initial overreaction. A contrarian investor simply does the opposite of what other investors do. The prisoners’ dilemma refers to the irrational choices faced by two people who care for each other and have committed the same crime.

QUESTIONS AND PROBLEMS 1. Haris is pondering whether to invest in a new project that has a positive net return (net present value). He can borrow and lend from a bank at the risk-free rate (for simplicity also assume no risk). He states that he prefers more wealth to less. a. If Haris declines to invest in the project, even though it has a net positive return, because he claims that the initial outlay of cash would reduce his current level of consumption, is his decision rational? b. What would you advise Haris to do if he could finance the project and earn its net present value by borrowing from the bank? Could he increase his current level of satisfaction without sacrificing his future level of satisfaction (or consumption)?

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2. We discussed in the text that economists documented that the market generates systematic biases (such as overreactions) for winner or loser stocks. If investors were rational, what would competition among investors (traders) do to these biases? 3. Assume that investors search for information about asset prices to determine if they are over- or undervalued. While searching for such mispriced stocks, they uncover information and quickly act on it by buying or selling. What would be the implication for the market’s functioning if competition for such information were fierce and continuous? (Hint: Be sure to read Box 9.3.) 4. What can the EMH and behaviorists say about the Internet bubble of the late 1990s and the subsequent stock market crash? 5. The following sentences are from an article that appeared in the Wall Street Journal of November 24, 2008, titled “Fear and Frustration: Some Calling it Quits.” After you have read them, answer the question below. “Rational or not, many investors say they have no choice but to bail. They are losing income elsewhere and can’t afford to risk more erosion of stocks and bonds. Many professionals are trying to counteract the trend. Investment firm Gerstein Fisher held a seminar at the Museum of Natural History Tuesday for 400 clients titled ‘Managing the Fight or Flight Reflex.’ Standing under the museum’s famous blue whale exhibit, a behavioral finance expert discussed how to stay rational in the current market and discussed how emotions can impact such decision making.” If you were a financial consultant, how would you advise your clients to fare during the current credit crisis? Would you invoke the EMH and/or behavioral finance? Discuss. 6. Are continuous stock price movements following an announcement by a firm evidence of market inefficiency? 7. Suppose that you had examined the economic performance of a company over the last few years and observed that it earned large profits. Does this contradict the efficient market hypothesis? 8. Assume that you went to a casino to play and began betting with $20. After a while, you won big (say $100). If you then continued playing, why would you have done that (ignore playing for pleasure or for killing time)? (Hint: Think of the answer in terms of mental accounting or framing.) 9. Below are some actual reports on some companies’ quarterly results (as of January 25, 2011). Predict the subsequent change in each company’s stock price. a. Before the opening bell, DuPont reported results that beat expectations. b. Verizon’s earnings missed by a penny and revenue fell from a year earlier. c. After the bell, American Express reported earnings a hair short of analysts’ estimates. 10. What are the implications for technical analysis under the theory of behavioral finance? 11. Assume that you have estimated the following (market) model for a stock x: Rx = 0.05% + 1.1 Rm where Rx and Rm are the stock’s and market’s excess returns, respectively. If the market happens to advance by 2% during a given day and the stock’s return rises by 1% during the same day, what would be the stock’s predicted and abnormal return?

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NOTES 1. 2. 3. 4. 5. 6.

7. 8. 9. 10. 11. 12. 13.

14. 15. 16. 17. 18.

19. 20.

21. 22.

23. 24. 25. 26. 27.

Sanford J. Grossman and Joseph E. Stiglitz, On the impossibility of informationally efficient markets, American Economic Review 70, June 1980, p. 405. Richard Roll, R2, Journal of Finance 43, 1988, pp. 541–566. David M. Cutler, James M. Poterba, and Laurence H. Summers, What moves stock prices, Journal of Portfolio Management 15, 1989, pp. 4–12. Steven L. Heston, Robert A. Korajczyk, Ronnie Sadka, and, Lewis D. Thorson, Are you trading predictably? Financial Analysts Journal 67(2), 2011, pp. 36–44. Mark Haug and Mark Hirschey, The January effect: http://papers.ssrn.com/sol3/papers.cfm?abstract_id = 935154 Donald B. Keim, Size-related anomalies and stock return seasonality: some further evidence, Journal of Financial Economics 12, June 1983, pp. 12–32. Mustafa N. Gultekin and Bukent N. Gultekin, Stock market seasonality: international evidence, Journal of Financial Economics 12, December 1983, pp. 469–481. Lawrence D. Brown and Liyu Luo, The January barometer: further evidence, Journal of Investing, Spring 2006, pp. 25–31. Gaert Rouwenhorst, International momentum strategies, Journal of Finance 53(1), 1998, pp. 267–284. Robert Shiller, Irrational Exuberance, 2nd ed. (Princeton, NJ: Princeton University Press, 2005). William F. M. DeBondt and Richard H. Thaler, Does the stock market overreact? Journal of Finance 40, 1985, pp. 793–805. Robert Shiller, Do stock prices move too much to be justified by subsequent changes in dividends? American Economic Review 71, June 1981, 421–436. Sanjoy Basu, Investment performance of common stocks in relation to price/earnings ratios: a test of the efficient market hypothesis, Journal of Finance 32(3), June 1977, pp. 663–682. Marc R. Reinganum, Misspecification of the capital asset pricing: empirical anomalies based on earnings yields and market values, Journal of Financial Economics 12, 1981, pp. 89–104. William Brock, Joseph Lakonishok, and B. LeBaron, Simple technical trading rules and the stochastic properties of stock returns, Journal of Finance XLVII(5), 1992, pp. 1731–1764. Robert Hudson, Michael Dempsey, and Kevin Keasey, A note on the weak form efficiency of capital markets: the application of simple technical trading rules to UK stock prices—1935 to 1994, Journal of Banking and Finance 20, 1996, pp. 1121–1132. Kuntara Pukthuanthong-Le and Lee R. Thomas III, Weak-form efficiency in currency markets, Financial Analysts Journal 64(3), May/June 2008, pp. 31–52. Tarun Chordia, Richard Roll, and Avanidhar Subramanyam, ‘Evidence on the speed of convergence to market efficiency, Journal of Financial Economics, 72, 2004, pp. 485–518. Nejar H. Seyhun, Insiders’ profits, costs of trading and market efficiency, Journal of Financial Economics, 16, 1996, pp. 189–212. John C. Bogle and Rodney N. Sullivan, Markets in crisis, Financial Analysts Journal, 65(1), Jan/Feb 2009, pp. 17–24. Eugene F. Fama and Kenneth French, Common risk factors in the returns of stocks and bonds, Journal of Financial Economics, 33, 1993, pp. 3–56. Joseph Lakonishok, Andrei Shleifer, and R. Vishny, Contrarian investment, extrapolation, and risk, Journal of Finance, 50, 1995, pp. 1541–1578. Eugene F. Fama, Efficient capital markets: II, Journal of Finance, 46(5), Dec. 1991, pp. 1575–1617. Daniel Kahneman and Amos Tversky, On the psychology of prediction, Psychological Review, 80, 1973, pp. 237–251. Daniel Kahneman and Amos Tversky, Choices, values, and frames,” American Psychologist, 39, 1984, pp. 341–350. William E. F. DeBondt and Richard Thaler, Do security analysts overreact? American Economic Review, 80, 1990, pp. 52–57. Terrance Odean, Volume, volatility, price, and profit when all traders are above average, Journal of Finance, 53, 1998, pp. 1887–1934. Albert F. Wang, Overconfidence, investor sentiment and evolution, Journal of Financial Intermediation, 10, 2001, pp. 138–170. Hersh Shefrin and Meir Statman, The disposition to sell winners too early and ride losses too long, Journal of Finance, 40, July 1985, pp. 777–790. Jason Zweig, Investing experts urge “Do as I say, not as I do,” Wall Street Journal, January 3, 2009. Robert J. Shiller, Stock prices and social dynamics, Brookings Papers on Economic Activity 2, 1984, pp. 457– 498; Shiller, Market Volatility (Cambridge, MA: MIT Press), 1991. Laurence H. Summers, Does the stock market rationally reflect fundamental values? Journal of Finance, 41, 1986, pp. 591–601. Zweig, 2009.

Part IV EQUITY PORTFOLIO MANAGEMENT

In this part we present and discuss in depth equity portfolio management and describe the various strategies that money managers pursue. Specifically we elaborate on the topdown and bottom-up approaches to investment as well as active and passive investment strategies. Additionally, we explain further the two main investment approaches— namely, fundamental and technical analysis—that equity portfolio managers might apply to satisfy the risk-return profiles of their clients. Finally, we provide an in-depth analysis of the equity valuation process and discuss several strategies that both individual and institutional investors can implement. In general, when an equity manager pursues an active strategy to selecting stocks for his clients, he can follow the top-down or the bottom-up approach. If he applies the former, he would start with the asset allocation step of the investment process and conclude with security selection. The bottom-up approach reverses these steps. Within the two approaches to active investing there are two investment analyses with the goal of deciding what information is useful in selecting (undervalued) stocks. These are technical and fundamental analyses. In general, an active equity manager does not believe in market efficiency. However, if the portfolio manager adheres to concept of the efficiency of markets, he will follow a passive investment strategy, such as indexing, to build equity portfolios. In sum, this part of the textbook “puts everything together” in the sense that you will learn how to apply the investment process and how to execute each step of it, depending upon your risk tolerance and stock market beliefs. We begin with an overview of equity investments and conclude with fundamental equity analysis.

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CHAPTER OBJECTIVES After studying this chapter, you should be able to sDescribe the two types of equity and the differences between them sConstruct a simple equity portfolio and conduct fundamental analysis sExplain the difference between active and passive investment management strategies sAppreciate the significance of macroeconomic analysis sUse the business cycle to exploit profitable opportunities sBe aware of the importance of examining the industry in regard to forming various investment strategies

INTRODUCTION In this chapter, we will present the fundamentals of equity securities, focusing on common and preferred stock and highlighting the fundamental differences between the two. To further clarify the reading of stock quotations, we will present some representative stock information from the Wall Street Journal and explain it. Then we will discuss the way individual and institutional investors create and manage a position in equities (or in a portfolio) using active and passive investment management strategies. We then discuss fundamental analysis in some detail. The purpose of fundamental analysis is to understand how the company fares within its industry, how the industry fares within the economy, and finally how the general economy affects the firm. Within the context of industry analysis, we discuss the sensitivities of industries to the state of the economy and extend our discussion to the industry life cycle. Finally, we examine basic economic analyses and the business cycle. Once security analysts have this knowledge, they can value a security—in this case a stock—to determine its intrinsic value (price). This, however, will be further explored in Chapter 11. 297

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EQUITY SECURITIES In this section, we present and discuss in detail the characteristics of the two main forms of equity, common and preferred stock; in the next section, we explain some stock quotations. Common Stock Characteristics As previously defined, common stock represents an equity (ownership) position in a corporation. Common stock is issued by a corporation, which is a (legal) form of business organization chartered (or recognized) by the state, with the principal feature of limited liability. This means that the corporation’s owners (the common stockholders) cannot lose more than their initial investment. Ownership is typically represented by a single certificate, which denotes the number of shares held by the investor. If one investor wants to transfer her stock certificates to another investor, the issuing corporation’s transfer agent cancels the old stocks and issues new ones to the new owner. The rate of return of a share for a common stockholder is derived from the dividends received and the capital gain or loss realized if she sells that share. SEC regulation states that before a share of stock is sold to the public it must be registered with the agency. We saw this rule (the shelf registration) when we discussed an initial public offering (IPO) in Chapter 6. Under certain conditions, unregistered stock may be sold directly to private investors under a private placement arrangement, but its subsequent sale is prohibited. Finally, existing (or outstanding) stock can be traded in the secondary market, but new or additional issues by public companies are traded in the primary market. Shareholder Equity When a corporation is formed (chartered), a fixed number of shares of stock are issued and valued at par. The par value is usually set below the stock market value or the value at which the stock is sold initially. The par value is recorded under the “common stock” account and its value equals the number of shares outstanding times the par value per share. When the market value of the stock exceeds its par value, this excess is recorded in the corporation’s books as paid-in capital. Over time the sum of the firm’s retained earnings (or earnings that are not distributed to shareholders as dividends), paid-in capital, and common stock is recorded in a separate account named book value of the equity. To express the book value of the equity on a per share basis, the account is simply divided by the number of shares outstanding. Thus the book value of equity per share (BVPS) is computed as follows: BVPS =

value of common equity number of shares outstanding

(1)

Investors use this metric to evaluate the value (worth) of a firm. Shareholder Rights Stockholders, as owners of the corporation, hold the right to elect its directors. The directors can elect the management team or the officers who manage the corporation. In a large firm, stockholders have the right to fire the managers if they believe that they do not act in their best interests (recall the agency problems first discussed in Chapter 1).

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In a small firm, by contrast, major stockholders typically hold some key positions in the firm. Thus, stockholders have control of the firm, whether small or large. Such control is stipulated by state and/or federal laws. The question of control has become a major issue in a corporation (as well as in academic circles) in recent years because managers who do not get majority control may attempt to gain it by other methods, as we will see below. Other shareholder rights include: sSharing dividends according to the number of shares they hold sSharing the remaining assets of the corporation in case of liquidation (shareholders are the residual claimants) sPurchasing proportionally any new stock issued by the corporation before any new investors (known as the preemptive right) The purpose of the preemptive right is twofold: (1) to allow current stockholders to retain control of the corporation and (2) to protect existing shareholders against earnings dilution. To see how earnings are diluted, consider the following example. Assume that the company currently has 1,000 shares outstanding, each valued at $100; thus their market value is 1,000 × $100 = $100,000. If the firm sells an extra 1,000 shares at $50 a share, it would reduce existing shareholder value to $75 per share. This value is found by dividing the new total market value of $150,000 ($100,000 old shares + $50,000 new shares) by the total number of shares, 2,000, or losing $25 per share. This earnings dilution also transfers wealth from existing (old) shareholders to the new ones. Voting Privileges The corporation’s board of directors is elected each year at the firm’s annual shareholders’ meeting. Usually, majority voting is required to elect these directors by the shareholders who are present or are represented by other shareholders. The idea is one share, one vote. There are several types of voting privileges of shareholders. Cumulative voting is a procedure by which a shareholder may cast all votes for a single director, thus permitting minority participation (that is, by shareholders who have few shares). Therefore the total number of votes by each shareholder is determined first. Under straight voting, each shareholder may cast his votes for each member of the board, thus enabling the shareholders to elect the directors one at a time. For example, if shareholder N has 70 votes and shareholder H has 20 votes in a case of only two shareholders in the firm, the firm’s directors will all be elected by shareholder N. This type of voting can render minority voting redundant. For this reason, several states impose mandatory cumulative voting. When shareholders cannot be present at the meeting for elections, they usually transfer their votes to other shareholders under proxy (voting). This means that the absent shareholders allow their designated shareholders to vote on their behalf. Typically in a large public firm with millions of shareholders scattered throughout the world, having all shareholders at the same physical place is impossible; thus proxy voting is the norm. Management usually solicits such votes and typically obtains them. However, if shareholders do not view management as performing satisfactorily, an outside group may attempt to capture those votes in order to have the power to remove the ineffective management team in a so-called proxy fight. The outside group’s attempt to remove that team is known as a hostile takeover. Because management is highly concerned with

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proxy voting, it tries to get shareholder approval for charter changes so as to minimize that external threat. The other side of the story is that shareholders, usually large or institutional ones, counter these management actions in an effort to remove it before more harm comes to their firm. Types of Common Stock Although common stock is one type, some companies issue classified stock or stock given some special designation, such as class A, B, and so on. These classes often have unequal (including voting) rights relative to the main type of common stock, where all shareholders have the same rights. The issuance of that type of stock can serve some special needs of the company, such as mergers and acquisitions (M&A), or enable one group (typically the firm’s owners) to maintain control (owing to the higher voting status of such stock classes). For example, GM issued class E (“GME”) and class H (“GMH”) stock in the mid-1990s to meet the need for some acquisitions (such as the Hughes Aircraft company). Google’s board of directors issued class A and B common shares by year-end 2009 to allow executives to keep control of the company.1 Investors were unhappy about the fact that class B shares were reserved for the firm’s founders and principal owners (with each share carrying 10 votes) in order to maintain control of the company, whereas class B shares were sold to the general public (with one vote). Finally, a more recent example is the creation of a dual-class stock by Facebook designed to give the company’s founder and existing shareholders control over the company. Similarly, the company’s existing shareholders will get class B shares (by converting their class A shares), which carry 10 times the voting power of class A shares and remain so unless their owner sells them at the initial public offering, in which case they will convert into class A shares (with the power of one vote). The New York Stock Exchange (NYSE) voiced its concern with these types of stock and had warned that it was not allowing listed companies to create such multiple stock classes, especially nonvoting ones. However, under pressure from GM, it changed its rules and permitted GM and others to issue stock classes and still be NYSE-listed. Although controversy around this issue still exists in the United States, in other countries, such as the United Kingdom, such stock types are very common. Dividends and Splits Cash payments paid by a corporation to its shareholders are called dividends. In the United States, dividends are authorized and typically declared quarterly at the discretion of the company’s board of directors. The dividends that shareholders receive represent a direct or indirect return on their investment in the company. There are also other types of cash dividend payments: extra dividends (which may or may not be repeated in the future), special dividends (which similar to extra dividends but they will not be repeated in the future), and liquidating dividends (which are issued only when the company is liquidated). To identify the potential shareholders who are to receive dividends, companies employ the stockholders of record on the ex-dividend date because shares are constantly traded and changing hands. The ex-dividend date is specified as 2 business days before the date of record, which is the date that the board of directors states for payment of the dividend. Investors who buy a share before an ex-dividend date are entitled to receive the next dividend, while those who purchase a share after the ex-dividend date are not. Here’s a real example from GE’s website:

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On September 2, 2011, the company declares a dividend payable on December 25, 2011, to its shareholders. The company also announces that shareholders of record (on the company’s books) on or before September 19, 2011, are entitled to the dividend. Thus the stock would go ex-dividend 2 business days before the record date, or 9/15/2011. Note that in this example the record date falls on a Monday; thus 2 business days back, excluding weekends and holidays, the ex-dividend is set on Thursday, September 15, 2011. These dates are summarized below. Declaration Date 9/2/2011

Ex-Dividend Date 9/15/2011

Record Date 9/19/2011

Payable Date 10/25/2011

Dividend payments have three important features: sThey are not a liability of the company unless are explicitly declared by its board of directors. sThey are not tax-deductible for a US corporation and are paid out of after-tax profits; however, US corporations receiving dividends from other corporations are permitted by law to deduct 70% of the dividend amount from taxes. sDividends received by shareholders are considered ordinary income and are taxed as such. Firms may offer stock repurchases instead of cash dividends. Also, firms may use a combination of cash dividends and share repurchases, which effectively means paying out reduced dividends from retained earnings. The effect of this combination is to cause reverse dilution of the earnings per share (EPS). Occasionally, the board of directors may decide to pay shareholders a stock dividend rather than declaring cash dividends. A stock dividend comprises an amount of additional shares and is represented by a percentage. For example, a 2% stock dividend means that the existing shareholders, who, say, have 100 shares, will receive two additional shares. The effect of a stock dividend is to increase the number of shares each shareholder has and thus dilute the value of each share outstanding. Stock dividends raise the common stock and paid-in capital account entries by an amount equal to the market value of the stock at the time of the payment times the numbers of new shares issued. The book value of the shareholders’ equity remains the same by equivalently reducing the retained earnings account. A stock split is similar to a stock dividend except that it is expressed as a ratio rather than a percentage and its effect is to raise the ownership of shares. For example, a twofor-one stock split means that each old share owned is split to create two new shares. Thus the old shares are destroyed and the new ones are issued with a new par value. A stock split does not change the percentage of the entire firm that each shareholder owns. The other impact of a stock split is to change the par value of each share (which is cut in half in this example). By contrast, a reverse stock split reduces the number of shares and raises the par value of each share. For instance, a one-for-three reverse split means that each investor receives three additional shares for each one owned. In this case, the par value is tripled. Why do companies declare stock dividends or stock splits given that they are costly but result in no apparent change in the company’s revenues? Much debate surrounds the

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motivation for such actions by the corporation. Some researchers find that neither one of these actions changes firm or shareholder wealth. Perhaps one reason for a stock split is to keep the firm’s price within a reachable price limit for small investors (known as the “normal” or “optimal” trading range, although it cannot be defined precisely). Thus a stock split may represent a signal to investors that the firm’s stock price is undervalued. These reasons notwithstanding, evidence suggests that the validity of such actions may be questionable. For example, many companies have high share prices and these do not appear to pose a problem for new investors. A prime example is Buffett’s Berkshire Hathaway common stock, which closed at $116,235 on December 9, 2011, and never had a stock split. What about the evidence on the debate that stock splits incur substantial transaction costs and may be associated with inefficiencies within the corporation? The evidence is mixed. For example, some studies suggest that stock splits decrease the liquidity of the firm’s shares (Lakonishok and Lev, 1987) and others report exactly the opposite (Schultz, 2000).2 What does this evidence mean? If market quality actually declines after a stock split announcement, volatility and bid-ask spreads increase. Thus if these spreads after a stock split actually increase, that would be good evidence that liquidity declines as well. Preferred Stock Characteristics Unlike common stock, preferred stock implies a preference (or a senior status) in the dividend payment and usually occurs with a fixed dividend rate. Stated differently, preferred stockholders receive dividends before common stockholders. Preferred stockholders typically do not have voting rights but come before the common shareholders in the rights of asset distribution upon company liquidation. This nonvoting structure enables management to obtain additional financing without diluting the control of existing shareholders. Preferred stock has a stated liquidating value and its dividend is usually expressed in terms of dollars per share. As noted above, preferred stockholders receive dividends before common stockholders. The dividend is generally fixed and expressed in dollars or as a percentage of the par value. Unlike common stock, the par value of his or her stock is important to a preferred stockholder because dividends are expressed in terms of the par. The par value represents the holders’ claims in the event of liquidation. For example, a 6% preferred means that its annual dividend would not be higher than 6% of the par value. Dividends on preferred stock are either cumulative or noncumulative. Cumulative dividends are paid before any common stock dividends are paid. If dividends are not paid, say during the previous quarter, they cumulate and must be paid before the company pays any dividends to the common stockholders. This is typically the common practice of corporations. Noncumulative dividends are mute when it comes to the accumulation of dividends but are declared by management when the financial status of the company is adequate for dividend payouts. As in the case of convertible preferred stock, investors who anticipate the rapid growth prospects of small companies prefer cumulative preferred stock. Preferred stock is a hybrid security because it has features of both equity and debt. Like a bond, preferred stock has a par value and generally pays a fixed amount of dividends. Preferred stock can carry credit ratings just like a bond. Preferred stock can also be converted into common stock and can carry call features. The convertibility option

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of preferred stock is designed to attract investors when company financial difficulties do not allow for cash distributions. A preference for such stock is often expressed by investors when the company has good growth potential. The call feature of preferred stock (callable preferred stock) gives the company the right (option) to retire (buy back) the preferred stock. Preferred stock is also like equity owing to its legal and tax advantages. For example, the US tax code allows a receiving corporation to withhold (deduct) up to 70% of the qualified dividends issued by another corporation from taxation, as mentioned above.

STOCK MARKET QUOTATIONS How should a typical stock’s quotation be read? Let us provide a real stock quotation and explain it. In Table 10.1 shows Alcoa (AA) corporation’s stock quotation as of Tuesday, January 25, 2011, as reported in the Wall Street Journal online. Alcoa’s Symbol at the NYSE is AA. The Open column shows the firm’s stock price at the opening of that day’s trading. The High column indicates the highest price during that trading day, and the Low column indicates the lowest price during the same trading day. The Close column simply contains the closing price of the stock that day. The next column, labeled Chg, shows the change in the (closing) stock price from the previous day. This was $16.43, because the change is negative (–0.19) and the %Chg column shows the rate of change [($16.24 – $16.43) / $16.43]. The Vol column indicates the number of shares traded during that day. The next two columns, 52-Week High and Low, record the stock’s highest and lowest prices during the year. The Div column indicates the dividend paid, $0.12, on an annual basis. The Yield column computes the stock’s current dividend yield ($0.12 / $16.24). The next column shows the stock’s price-earnings (PE) ratio, and the last column, YtD %Chg, shows the year-to-date percentage change in the stock’s price (which must have been $15.39 in order to experience a 5.52% change). Besides the above explanations, some numbers (in the Table 10.1) and in the rest of the table (which is omitted) might have some letters attached to them that further explain the entries. These letters are (and are also taken from the Wall Street Journal): a: Extra dividend or extras in addition to the regular dividend. b: Annual rate of the cash dividend, indicating that a stock dividend was paid. dd: Loss in the most recent four quarters. e: A dividend was declared in the preceding 12 months, but that there is no regular dividend rate. The amount shown may have been adjusted to reflect stock split, spinoff, or other distribution.

Table 10.1 ALCOA’s Stock Quotations 52-wk YtD Symbol

Open High Low Close Chg. % Chg.

Volume

High Low Div Yield

P/E %Chg.

Alcoa AA 16.33 16.36 16.06 16.24 –0.19 –1.16 32,918,890 16.72 9.81 0.12 0.74 77.33

5.52

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f: Annual rate, increased on latest declaration. g: Dividends and earnings are expressed in Canadian currency. The stock trades in US dollars. No yield or P/E ratio is shown. i: Amount declared or paid after a stock dividend or split. j: Indicates that a 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: 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.

MANAGEMENT OF AN EQUITY PORTFOLIO The creation and management of an equity portfolio is both an exciting and a daunting task because it involves knowledge on the specifics of each stock (its risk and return) as well as the general economic, industry, and company situations. In this section, we compile what we have learned thus far on diversification, indexing, and the two approaches to the investment process in discussing equity portfolio management. We also expand the analysis to the international aspects of managing an equity portfolio and present some strategies associated with the management of such a portfolio. We begin with the two types of management (strategies) of an equity portfolio, passive and active. Passive Equity Portfolio Management A passive investment strategy is simply a long-term buy-and-hold strategy where the equity portfolio manager purchases stocks that closely match or replicate the relevant index. Also, in constructing a passive equity portfolio, a plausible (albeit not always true) assumption is that the manager believes in the efficient market hypothesis (EMH). Thus the creation and management of an equity portfolio has as its objectives broad diversification, tax liabilities, and index replication. We discuss each of these objectives below from the perspectives of both individual and institutional investors. Individual Investors Individual investors differ in the way they construct and manage (actively or passively) an equity portfolio. However, they can still create a broadly diversified portfolio by spending less time and money as well as knowledge. So, the question is: How can an individual investor create a diversified passive equity portfolio? Regarding diversification, several issues are relevant: the risk of individual securities, volatility of returns, and tax considerations. Individual investors can diversify in one of the following three main ways: buy and hold, indexing, and personal portfolio construction. Let us explain each of these briefly. Buy-and-Hold. This strategy simply involves purchasing stocks to build a well-diversified (across and within sectors to reduce or eliminate unsystematic risk) portfolio and

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holding them for the long run. The advantages of such a strategy are economizing on (minimizing) transaction costs by trading infrequently; not attempting to beat or time the market, which can prove dangerous; and enjoying the long-run growth of the portfolio because the investment is for the long run. Invest in an Equity Indexed Mutual Fund. Numerous funds track a market index such as the S&P 500 or the broader Wilshire 5000 index. These funds have broad diversification and are low-cost alternatives (such as actively managed portfolios). For even greater diversification, an individual investor can also purchase a foreign equity index such as the Emerging Markets; Europe, Australia, and the Far East (known as EAFE); and other developing markets. Two offsetting factors exist for the lower return of index funds (because of management fees) relative to an index such as the S&P 500: first, some index funds receive a higher price for some stocks than implied when their return in the index is computed and, second, because the S&P 500 does not always adjust for dividends, thus understating its total return. For these reasons, some mutual funds have been able to “beat the market” at times even though more than 50% of them have received a belowmarket return. Invest in Several Actively Managed Mutual Funds. This method differs from the pure passive strategy (above) because of higher transaction costs and tax liabilities. Further, the investor faces the following two issues. First, she must be careful to pick those funds that have broad diversification among stocks, large and small alike. Second, she must know the specific investment philosophy or style of the portfolio manager (more on further on), which refers to what types of stocks the manager prefers (such as value or growth stocks or a blend). Personal Portfolio Construction. Although admittedly this is the costliest approach for an individual investor owing to transaction costs and other factors, the investor may proceed with this strategy on his own only if he can control his tax liabilities. This is true especially when differential tax rules are in place for dividends and capital gains. Recall that when the investor invests through a mutual fund, he cannot control his tax liabilities and thus the mutual fund’s actions. But if he invests (passively) on his own, he can apply efficient tax management techniques by timing his tax liabilities (to the extent possible, of course). An example of such a strategy is to purchase an exchange-traded fund (ETF). Institutional Investors Institutional investors can construct passive equity portfolios in one of the following ways. Indexing and Sampling. Several problems are associated with the creation of index funds. One is that they may not exactly match the index they are supposed to replicate yearly (we will discuss this problem shortly). This is due to several factors including the fund’s yearly activity, such as the cash inflows and outflows from investors, payments of dividends, removal of securities for the index, and so on. Thus, sometimes index funds perform slightly better in declining and a bit worse in advancing markets. However, consistent and substantial deviations of the portfolio’s return from the index’s returns are a serious cause for concern. Index funds are also constructed based on the CAPM market equilibrium idea because managers care about the value of alpha. A fund’s positive/ negative alpha value means that the manager of that fund has been able to over/underperform the market. But, simply paying attention to alpha values over the long run is perilous. Let us see why. If a fund earns 10% per year on average, then a $1 investment over 40 years (using the geometric rate of return method) would result in $44.2; but if it

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earned 8% (or 2% less), the investment’s terminal value would be only $20.7. That is, it would be less than half the return for a 2% reduction in the yield. A potentially more serious problem with index funds is that they are supposed to exactly replicate the relevant index. Box 10.1 discusses the qualities of a benchmark index and applies them to the S&P 500 index. There are three techniques for creating an index portfolio: full replication, replication, and quadratic optimization. Full replication implies that all securities in the index are purchased according to their proportions (weights) in the index. But this method has the disadvantage of incurring high transaction costs, which reduce overall return. The second method, replication, alleviates the above problem because the manager purchases only a representative sample of securities from the relevant (benchmark) index. There are two ways to replicate a portfolio: capitalized sample and stratified sample methods. The capitalized sample method centers on the largest capitalization stocks in the index. Consider the following example. As of January 28, 2011, the S&P 500 Index had approximately the following characteristics: Percent of Index Market Value 18.97% 81.03%

No. of Stocks Top 10 largest 490 remaining

Total Index Capitalization (adjusted) $11,607 (in billions)

A capitalization-based sample would be constructed by selecting the top 10 largest companies and weighting each one according to their weight (percentage) within the index. Therefore if Alcoa (a company in the S&P 500 Index) had a market cap of $16.49 billion (as reported in Yahoo! Finance on January 28, 2011), a passive investment manager would invest 0.14% in the company (or $16.49/$11,607). Overall, 18.97% of the indexed fund’s market value would be allocated to the 10 largest stocks, with each stock identically weighted to the index. The remaining 81.03% of the fund’s assets would be invested across a sample of the remaining 490 stocks in the index (perhaps at random). The stratified sample technique selects stocks from the index based on some predetermined variable such as the price/earnings ratio or the debt-to-equity ratio categorized within a matrix. Assets of this type of replicating portfolio are invested so that the portfolio has a similar mix. Stratified sampling allows the portfolio to match the basic characteristics of the index without full replication. The more dimensions within the matrix, the more closely the portfolio will match the index (but the greater the possibility of underperformance due to transaction costs). Frequently factor models such as the APT are employed to select stocks from the index in this type of replicating portfolio. What are the problems with these sampling techniques? Because the entire index is not purchased, there will always be a difference between the replicating portfolio’s return and that of the index. This deviation, which is called the tracking error, is defined as follows: 2 = [1/(n – 1]) (xi – yi)2

(2)

where  is the tracking error, n is the number of periods over which it is measured, x is the percentage return on the portfolio in period i, and y is the percentage return on the benchmark. To make the tracking error comparable across methods, it must be annualized. For example, if the error is based on monthly returns, it should be multiplied by the square root of 12 (months) to annualize the number. The tracking error may be

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BOX 10.1 Features of the S&P 500 Index as a Benchmark Index A valid benchmark should be a passive representation of the manager’s investment process and possess the following qualities: Unambiguous Investable Measurable Appropriate for the manager Specified in advance In order for an index to work as an investment benchmark, it must provide an unbiased model of the market segment it is intended to represent. The S&P 500 was designed as a sample drawn from that pool to represent the market performance of the leading companies in the leading industries in the United States. The academic community quickly adopted the S&P 500 as the benchmark used in the evaluation of investment theories. For example, modern portfolio theory as embedded in the CAPM and the APT uses the notion of the market portfolio, one of the major characteristics of which is that each asset in that portfolio is held in exact proportion to its market value. This happens to be the basis upon which the S&P 500 is constructed. Equity managers strive to compare their portfolios performance to the S&P 500. Some companies, such as Fidelity, even make a portion of their management fees contingent on whether their funds outperform the S&P 500. However, an investment management firm can no longer simply claim that it beat the index. The adoption of performance presentation standards by the CFA Institute has focused attention on the need for properly defined and utilized investment benchmarks. The firm must use a benchmark that parallels the risk or investment style that the client’s portfolio is expected to track.

calculated from historical data (called the ex-post tracking error) or estimated for future returns (called the ex-ante tracking error). What are the causes of tracking error? These causes are, first, trading and management costs, and, second, the differences in the composition of the portfolio and the benchmark. A trade-off exists between selecting the sample of stocks and transaction costs. That is, the larger the sample, the better the portfolio’s representation of the index but the higher the transaction costs. Therefore if portfolio managers want to minimize this error, they need quantitative (statistical) analysis (see next). At this point, the question of index rebalancing must be noted. Although stocks in the index (such as the S&P 500) can never become too large, some have become relatively small. A prime example is the 2008 credit crisis, which changed the capitalization of many companies as well as industries (as we saw in Chapter 6). Rather than periodically removing such outliers from the index, Standard & Poor’s attempts to keep portfolio turnover at a minimum. Every change in a benchmark’s components adds costs for the investment managers replicating it without necessarily adding value. Finally, the third technique in constructing an indexed portfolio of stocks is quadratic optimization. This is relevant to the construction of the composition of stocks for the

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replicating portfolio that minimizes the tracking error. A disadvantage of this technique is that it is based on historical data (correlations) which may not be representative of the index in the present or the future. This would have serious consequences for the performance of the portfolio relative to the benchmark index. Enhanced Indexing. Other issues, and related to the use of the CAPM in constructing a passive equity portfolio, refer to the orientation of the index fund toward more dividend-paying stocks and tax considerations. In other words, the dividend-tilted index fund and the investor’s tax bracket are related when there are differential taxation rules for dividends and capital gains. Often this method is known as enhanced indexing because it bets on certain factor risks called tilts. If such a strategy is successful, the portfolio manager would earn somewhat more return without much extra risk. Another example of such a strategy is index arbitrage, where the manager of the indexed portfolio also trades option and futures contracts when he believes that the value of the derivatives does not match the value of the index. Other innovations of passive strategies have emerged as well. For example, a variation of holding the index fund is for the portfolio manager to hold T bills and a futures contract on the index and still maintain the same risk position. If the futures are underpriced, this portfolio will beat the market. Such a strategy attempts to capitalize on the temporary mispricing across the types of markets and simultaneously increase the return on the index fund. Active Equity Portfolio Management The goal of active equity portfolio management is to earn a net return that exceeds the return of the relevant benchmark (passive) portfolio. The active portfolio manager does not “believe inefficient markets but believes that his abilities and skills give him a comparative advantage over other managers (or investors). Also, active investment management is based on forecasts of future financial variables such as interest rates. As before, we will discuss active equity portfolio management for both individual and institutional investors. Individual Investors Individual investors apply active equity portfolio management by picking individual stocks and forming a portfolio or by trading equity mutual funds. One simple way to select stocks is to see the relevant companies in action, if possible, by visiting their stores, talking to people, or reading the news. Alternatively, if the investor has a broker, the broker can supply additional and perhaps more detailed information (perhaps for a fee) for a more informed decision. Further information can also be obtained (for a fee) from various professional information sources such as Moody’s, Standard & Poor’s, or Value Line. Therefore once the investor has decided to examine a particular stock, learning more details on that stock should be enough for him to decide on the stock for eventual purchase (or sale if he owns it already and decides to get rid of it or replace it). What are some practical issues of active management and stock selection by the individual investor? One issue refers to the timing of a purchase or a sale. For example, how would the investor know when to buy or sell a stock when its price goes up or down? Second, does an individual investor have the quantitative, economic, and financial knowledge to value a stock and determine if it is underpriced for purchase or overpriced for sale? Also, what about the trading costs if frequent purchases/sales take place? Third, can

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the investor use the stop-loss method to protect any gains? This might be risky if the stop-loss price is set close to the prevailing market price of the stock. An alternative strategy is to select among mutual funds instead of individual stocks. In that way, the individual investor economizes on transaction costs and obtains, at the same time, broad stock diversification. The investor can do this either by buying a mutual fund that is actively managed or switching among mutual funds in an effort to pick the one(s) that would perform better than others. Obviously the investor must be knowledgeable about the specifics of each mutual fund in which he is interested because the manager’s philosophy, trading costs, past performance (although past performance is not a guarantee of future performance), and the like may differ. Finally, he should be able to select those funds that closely match his investment objectives and constraints. Institutional Investors An important issue for active portfolio managers is the construction/selection of the appropriate benchmark or the normal portfolio. We saw in Box 10.1 some desirable qualities of such a portfolio. Also, the normal portfolio must be consistent with the needs (or desires) of the client(s). If an appropriate benchmark is unavailable, the manager must construct (customize) a benchmark portfolio that would be aligned with both the manager’s skills and the clients’ wishes (or requirements, including risk tolerance). The job of an active equity portfolio manager is highly challenging. For example, the portfolio manager should be able to beat the benchmark portfolio by an amount in excess of the yearly transaction costs. In other words, if the annual transaction costs are 2%, the total return on the managed portfolio must be at least 2% higher than the passive benchmark portfolio. This is directly related to the bets or risks the manager takes because the higher the risk, the larger the potential (expected) return should be (above the passive benchmark). Alternatively, the manager might attempt to reduce (minimize) the transaction costs by reducing the portfolio’s trading activity. Less frequent trading might be justified because, if the manager exploits short-term price forecasts, the overall return would suffer (if things went wrong). Active management styles vary but can be classified into three main categories: security selection, sector rotation, and market timing. Style investing entails creating portfolios in a manner that captures certain equity security characteristics. This style was developed to exploit the anomalies present in the market (Chapter 9 contained a discussion of the anomalies). Let us briefly discuss each one of these general investment styles. We will also discuss some of these issues again in Part V. Security Selection. Active portfolio managers search for underpriced stocks and attempt to buy low and sell high. Such managers are betting that the market’s weights on stocks are not the optimal ones to hold in each security. Thus they attempt to overweigh or make a positive bet (forecast) for undervalued securities and underweigh or make a negative forecast for overvalued securities. Sector Rotation. Instead of simply picking stocks at random, the manager may attempt to shift funds among sectors or industries (such as technology or consumer durables) and make bets on the sector(s). The manager is usually guided by the Standard Industry Classification (SIC) codes, which define industries according to some characteristics (see also below). This type of strategy selects stocks among various sectors with more or fewer weights according to the manager’s bets (or forecasts of the sectors’ future expected performance). Sector rotation is also associated with the manager’s particular

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investment style in a hunt for a “hot item” before the market notices it. Below are some examples. The manager may: sRely on a theme, such as changes in demographics or new technology sFocus more on growth stocks, with above-average growth prospects, and purchase stocks with high P/E ratios sFocus more on value stocks, with prices below their economic worth, and buy such stocks with low P/E ratios sSelect among large and/or small capitalization stocks according to how he defines the market The above strategies refer to specialized managers because they do not rotate frequently among sectors but concentrate on those sectors about which they feel more comfortable or in which they have a comparative advantage. Sometimes managers of that sort construct customized passive portfolios, called completion portfolios or funds, which complement active portfolios that do not cover the entire market (or just one or a few sectors). In this case, the active portfolios are overweighted in the sector(s), but the manager wants the remaining funds to “fill the hole” of underweighted market sectors. Market Timing. Market timers try to move funds in and out of stocks (as well as other securities) upon forecasts of the broad market movements. Specifically, they change the risk premiums of their overall portfolios by either altering the beta on the equity portfolio (for example, by swapping stocks) or changing the amount invested in short-term securities. An example of market timing involves the forecasting of interest rates. If a particular manager, not the general market, expects interest rates to increase, he should alter the composition of his equity portfolio to include more interest-insensitive stocks and fewer interest-sensitive stocks. Managers of bond portfolios also widely practice market timing. The bottom line is that each portfolio manager must select the strategy that meets his comfort level and is consistent with his investment style and his clients’ needs. Further, the extent to which these approaches work and the general investment approach selected (top-down or bottom-up) depends on sound fundamental analysis. We will examine this further below. Finally, an important point to emphasize is that professional managers typically advocate active investment strategies, while academics (and some notable professionals such as John Bogle and Warren Buffett) advocate passive (fundamental) strategies. Besides, as we have noted elsewhere in the textbook, in general, passive investment strategies have outperformed active investing. Ultimately, however, you should be able to determine which strategy works best for you given your objectives and constraints. The box titled Lessons of Our Times highlights the dangers of investing and emphasizes some things an investor needs to know. We conclude this discussion by looking at international investing. International Equity Investing Active or passive portfolio managers must include in their portfolios international equities as part of the strategy for reducing their holdings’ total risk. For the passive manager, simply purchasing an international index such as the EAFE (Europe, Australasia, and the Far East) is enough to diversify globally. For the active portfolio manager, the choice is more involved because he might want to identify equities that are under- or overvalued

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before including or excluding them from a portfolio. Investing in international equities involves several problems for an equity portfolio manager. The two major problems are: sThe requirement that the manager be familiar with the specifics and complexities of the foreign markets (such as operations, costs, trading structures, accounting standards, and the like) sThe ability of the manager to apply the same domestic stock or portfolio-picking techniques to international equities The equity portfolio manager must also be able to address the following issues in her analysis, which should be consistent with her objectives: sWhich international equities (along with other securities) to select sWhich national currencies to invest in sWhich sectors or industries to consider in his global portfolio sKnowledge of how to hedge such a global portfolio Because corporations are now multinational and cross national borders easily, it may be necessary to conduct equity analysis at both the industry and country levels (for the need to forecast global economic trends). In sum, investing internationally is very challenging (finding the best equities in terms of optimal risk-return profiles) and risky (because of the increased comovement/correlations among global equity markets); it requires adequate knowledge of international factors (political, economic, and social) as well as good forecasts of future movements of international money and capital markets. Box 10.2 highlights the benefits and risks of investing in international equities.

FUNDAMENTAL ANALYSIS We noted earlier that a portfolio manager must be able to evaluate the company, industry, and general economy before attempting to value a firm’s stock. Specifically, the analyst must be able to forecast the company’s earnings and dividends as well as the appropriate discount rate, because these are the fundamental inputs in the stock valuation model. The analyst should also examine the “big picture”—the national and international economy—in order to identify the firm’s prospects for growth and how it would affect the “small picture”—the firm and the industry. As we will see, certain firms (and industries) are more sensitive to macroeconomic developments than other firms or industries. In this section, we will not discuss in detail the various monetary and fiscal policies (and their prescriptions) to avoid getting involved in disagreements that exist within academia and the professional world. Instead, we will briefly present the broad aspects of economic and industry analyses and examine some of the economic forecasting tools that professionals use. Classic fundamental analysis is based on the top-down approach to investing because it begins with the general (the economy) and ends with the specific (the firm). The idea underlying fundamental analysis is to evaluate all the factors that could potentially affect an estimate of a company’s fair stock price or its intrinsic value. Intrinsic value is the risk-adjusted discounted present value of the firm’s future dividends (we will see this notion in detail in the next chapter). The bottom-up approach, by contrast, starts with

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BOX 10.2 Risks and Benefits of Investing in International Equities BENEFITS Diversification potential to home equities Historically have earned higher returns relative to US stocks Opportunities to participate in sector/regional outperformance relative to the US stock market Exploiting market inefficiencies given that emerging markets, for instance, are deemed inefficient Exposure to sectors that home investors find thin or absent in the home market

RISKS Higher risk of foreign markets (emerging and mature) Currency volatility or exchange-rate exposure Higher investment costs and other barriers to investment Other risks such as political and social Benefits reduced owing to increased correlations among global equity markets

Macroeconomic Analysis Gross domestic product Inflation Unemployment Deficits (budget and trade) Interest rates Technology Business cycle Consumer sentiment International economy

Industry Analysis Product market Industry life cycle Industry forecasts Competitive structure International influences

Company Analysis Products Competitive forces Financial statements Forecasts Global influences Share valuation

Figure 10.1 Top-down equity fundamental analysis.

the micro aspects of the firm that are expected to influence security prices and seldom ends with the macro economy. In this case, the analyst tries to rationalize why the firm’s specifics matter most, in selecting stocks, independent of the general economy. In this section, we will focus on the top-down approach to fundamental analysis. Figure 10.1 shows an example of the various components of the top-down approach to fundamental security analysis which culminates in forecasts and evaluation of the possible estimates of the stock’s intrinsic value. We begin with macroeconomic analysis. Macroeconomic Analysis A discussion of the macroeconomy comprises the study of both the national and international economy. The security analyst looks at several magnitudes in order to assess the

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economy’s health or weakness as well as to evaluate the likely impacts of the two main economic policies, fiscal and monetary. Finally, the analyst should be able to understand the working and the impact of the business cycle on the viability of firms and industries. Let us list and briefly explain some of these elements of economic analysis. Macroeconomic Magnitudes Gross Domestic Product. GDP refers to the total market value of all goods and services produced in the economy during a year. When GDP increases, the economy grows and with it the industries and firms’ sales and when GDP decreases the economy slows down and with it both industries and firms’ sales. GDP includes consumption expenditures, investment expenditures, government spending, and export and import activity. The country analyst should examine each component closely in order to identify sectors that are possible investment targets. A related but more narrow measure of the economy’s output is industrial production, which measures only the manufacturing activity within the economy. Inflation. Inflation is the change in the average price level of goods and services in the economy. Higher price levels signify rapidly growing and overheating economies, which could be harmful to all market agents. Higher prices would benefit a firm by increasing its sales (and, perhaps, profits), but continuous price increases would decrease sales and profits. Unemployment. This refers to the number of workers of the labor force not working (or being able to find work but actively seeking work). Higher unemployment implies operation at less than full capacity by the general economy thus adversely impacting the firm’s sales and profits. Interest Rates. Interest rates affect a firm’s ability to invest because they directly influence (the present value of) its (future) cash flows needed for deriving the firm’s stock intrinsic value. Some firms and industries are more sensitive to interest rate changes than other firms and industries and the analyst must be able to distinguish between the two in developing an equity portfolio. We will discuss the role of interest rates later within the context of economic policies. Deficits. There are (potentially) two types of deficits in any economy: budget and trade deficits. A budget deficit arises when the government’s expenditures exceed its revenues, while a trade deficit occurs when the nation’s (value of) imports exceed (the value of) its exports. Both deficits are important parts of economic analysis because they do not only affect interest rates (although there is still debate on how much, if at all, deficits affect them) but also reduce business investment (and consumer) spending. Expectations. Expectations (or sentiment) involve consumers’ or producers’ optimistic or pessimistic feelings about the prospects of the economy. If these agents have more confidence on the future status of the economy (perhaps by looking at their own income levels, employment opportunities, and the like), they would be more willing to spend and invest. Higher spending and investing would benefit firms by raising their prospects for sales and profits. Box 10.3 contains the latest information on the state of consumer confidence from The Conference Board, the official source of such surveys. Exchange Rate. Firms are also affected by competition from foreign firms; thus examining how much impact that competition has on the firm’s future sales and profits is important. The health or weakness of foreign agents (consumers, firms) will definitely influence domestic firms and industries (and their imports and exports). The exchange

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BOX 10.3 The Consumer Confidence Index The Conference Board Consumer Confidence Index Falls to a New All-Time Low in October 2011 The Conference Board’s Consumer Confidence Index, which had increased moderately in September, declined to a new all-time low in October. The Index now stands at 39.8 (1985 = 100), down from 46.4 in September. The Consumer Confidence Survey is based on a representative sample of 5,000 US households. The monthly survey is conducted for The Conference Board by TNS. TNS is the world’s largest custom research company. Says Lynn Franco, director of The Conference Board Consumer Research Center: “Consumer Confidence is now in levels last seen during the 2008–2009 recession.” Consumers’ appraisal of current conditions deteriorated further in October 2011 and their expectations were also low. Source: Consumer Confidence Survey, The Conference Board, October 2011.

rate is the price of one currency in terms of another. If the US dollar weakens relative to the euro, for instance, imports from a European country may decline because the goods from that country would be dearer when expressed in US dollars. Thus importing sectors and firms may suffer but other domestic sectors and firms may benefit. Further, a weakening dollar may contribute to higher domestic inflation. Several factors affect the exchange rate, including differences in interest and inflation rates, income levels, and economic policies (notably monetary via central bank interventions). The above (and other) factors are embedded into the two sides of the market, the demand and supply sides, which at the national level become aggregate demand and aggregate supply (curves). Thus, one way to examine the influence of these factors on the growth prospects of firms and industries is to see how these curves change (shift) and trace the implications of such shifts. Some factors that shift the aggregate demand are income level changes, tax rate changes, changes in the government spending, changes in the money supply, changes in investment spending, and changes in net exports (the difference between exports and imports). Some factors that shift the aggregate supply curve are changes in prices of inputs of production (such as raw materials, labor, and capital), acts of god, and changes in the population or labor force (as well as the educational levels of workers). In a general (economic) equilibrium, the forces of aggregate demand and aggregate supply equilibrate to determine the equilibrium level of prices and output in the economy. Figure 10.2 illustrates the general economy equilibrium (point A) for the general price level, PL*, and the national output, Q*. Shifts in any curve change both the price level and national output along with a host of magnitudes (like those mentioned above). In the following text we will illustrate some of those shifts and discuss their implications for investment analysis. In general, the portfolio manager (and analyst) needs to identify those industries and firms that are less likely to be hurt/favored by an economic swing (expansion or recession, as we will below) and avoid/seek including them into his portfolio. Economic Policies The two main economic policy bodies in the US economy are the government, which conducts fiscal policy, and the Federal Reserve (Fed), which conducts monetary policy.

Equity and Fundamental Analysis s 315 price level

AS

A

PL*

AD Q*

national output

Figure 10.2 Macroeconomic equilibrium.

(a)

(b)

price level

AD

AS

AS AD’’

b

PL’ a

PL*

a

PL* PL” b AD’ AD

Q*

national output

Q* national output

Figure 10.3 Macroeconomic equilibriums.

Both of these bodies’ policies attempt to directly influence economic activity and the financial markets (which is of interest here). Let us discuss each of these policies in brief. Fiscal Policy. Fiscal policy is performed by the federal government by using its two main tools: government expenditures and tax rates. Manipulation of either tool results in changes in personal and corporate income levels and thus aggregate demand. For example, if the government reduces personal tax rates, then higher (disposable) income is in the hands of households that, in turn, are able to buy more goods and services. Consequently higher sales and profits are recorded by companies that, in turn, step up their investment expenditures, thus increasing national output and the general price level (or inflation). Panel (a) in Figure 10.3 illustrates this process where the aggregate demand (AD) curve shifts up (or rightward) to AD’, ceteris paribus, thus raising both the price level (PL’) and national output (Q’), from the initial economy equilibrium (PL*, Q*). By contrast, if the government reduces its expenditures, perhaps to avoid further overheating of the economy, less income will be in the hands of people who, in turn, will curtail their expenditures and consequently reduce companies’ sales and national output. In this case, the AD shifts down (or leftward) to AD’’ reducing the general price level (PL’’) and output (Q’’), ceteris paribus. This is shown in panel (b) of Figure 10.3.

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One final note about fiscal policy is warranted. Fiscal policy is very direct and can have an immediate impact on the economy (stimulating or slowing it down). However, because fiscal actions must go through various channels, at the legislative and executive branches of the government, it can take time (measured in several months) to be implemented (the three lags associated with fiscal policy are the recognition lag, the time it takes to recognize a problem; the implementation lag, the length of time to decide on a policy and implement it; and take-effect lag, the time it takes for the policy to show an impact). In fact, it has been argued that sometimes by the time it is implemented the economy may not have the problem anymore thus potentially harming the economy. For that reason, fiscal policy cannot be used effectively to fine-tune the economy. Monetary Policy. This policy refers to the manipulation of the nation’s money supply by the Fed using three main (quantitative) tools: open market operations, the discount rate, and reserve requirements. Economists and professional portfolio managers believe that the growth of the money supply has broad implications for economic activity, inflation, and interest rates (primarily); thus they closely watch any move by the Fed. Let us focus a bit more on the interest rates, since their level and future path are extremely important to investment managers. The interest rate is a crucial input in any asset valuation model. For example, if you expect interest rates to go up in the future, you would be tempted to favor some and shun other securities (as we will show in the next couple of chapters). At this point, just think of higher interest rates as good news for some groups of investors (such as savers and those holding some long-term instruments) but bad news for other investors and instruments (such as equities) because of the inverse relationship between interest rates and prices of securities. That is why forecasting the future level and path of the market interest rate is very difficult (in reality, there are several different interest rates, but we will refer simply to “the the interest rate” in our discussion for convenience). But what are some of the factors that determine the interest rate in an economy? Here are some important ones: sActions by the government and the Fed sThe demand for funds by the other three economic agents (households, firms, and the rest of the world) sThe supply of funds by households primarily (and businesses secondarily) sExpectations about inflation In Figure 10.4, panel (a), the equilibrium real interest rate (i*) is shown when the supply of funds (S) intersects the demand for funds (D). Recall that the real interest rate is found by subtracting expected inflation from the nominal interest rate (the socalled Fisher equation). The demand curve slopes downward because lower interest rates (or lower financing costs) make more business investment projects more profitable. The supply of funds slopes upward because a higher interest rate entices savers to save more (and give up or postpone current consumption) so they earn a higher return. Shifts in the two curves are initiated by the government’s and the Fed’s actions as well as actions by the other agents. Economists argue that monetary policy cannot affect the real interest rate (but it can influence the nominal rate) because in the long-run the ultimate impact of changes in the money supply will be inflation (and the nominal interest rate) with no real effect on economic activity. By contrast, in the short-run, the potency of monetary

Equity and Fundamental Analysis s 317 (a) interest rate

(b) D

D

S i*

i*

i’ S Qf*

quantity of funds

S” Qf’

Figure 10.4 Equilibrium interest rates.

policy is high. Now let us discuss each one of the three tools of monetary policy very briefly. Open-Market Operations. OMOs involve the buying and selling government securities by the Fed in the open market (that is, the public). OMOs are conducted daily at the trading desk of the New York Fed and represent the most frequently used tool of monetary policy. Let us see how OMOs work and affect economic activity. When the Fed purchases securities in the open market, it receives these securities in exchange for cash. That cash, in turn, is deposited in the sellers’ banks, thus increasing the banks’ reserves (and the money supply). These funds will then be loaned out to other people (individual and institutional investors) who, in turn, will deposit the loan amounts in their banks and son on. Thus, through this multiplying process, the money supply is expanded, stimulating economic activity in terms of consumption and investment. In this process, the interest rate plays a central role. Expansionary monetary policy lowers interest rates to i’ because the supply of money (S) increases or shifts out (right) to S’, ceteris paribus. Panel (b) of Figure 10.4 illustrates this result. Naturally, sales of government securities have the opposite effect since the supply of money curve decreases or shifts down (left) to S’’, thus raising interest rates to i’’. The impact of OMOs can be evaluated in terms of changes in the federal funds rate. Recall that the fed funds rate is the rate that banks charge each other for very shortterm (or overnight) loans. The Fed can directly affect the funds rate through OMOs. Fed watchers pay close attention to the fed funds rate for direction of future interest rates and forecasts of monetary policy. The Fed funds rate is also a function of market demand and supply forces for bank loan demands. Discount Rate. The discount rate (or discount window) is the rate the Fed charges member banks when they borrow from it on a short-term basis. When the Fed reduces or raises the discount rate, it signals an easy (expansionary) or a tight (restrictive) monetary policy. That is, with a lower discount rate, banks can borrow from the Fed cheaper and thus pass on those costs savings to their clients who are asking for loans. In that way, the investment activity picks up which stimulates general economic activity. Reserve Requirement. The reserve requirement is the ratio of the reserves to total deposits the bank is required to keep in its vaults as cash or at the Fed as deposits. The purpose of retaining a fraction of deposits is to meet daily operations (demand) by agents. For example, if the reserve requirement ratio is 10%, then for every $100 in deposits, the

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bank must keep $10 in cash and the rest ($90) can be lent out to agents. The lower/higher the ratio, the greater/lesser the money supply expansion within the economy. Thus lower ratios stimulate economic activity, whereas higher ratios contract it. What is the relevance of monetary policy to investment management? First, recognize that monetary policy works through its effects on interest rates, which change up or down as the money supply decreases or increases. As the economy’s quantity of money increases, investors find that they hold too much money in their portfolios relative to the other assets and thus will rebalance them by purchasing more assets (such as stocks) and reducing their cash balances. This reallocation of assets forces their prices up (owing to excess demand) and their yields or interest rates down in the short run. In the long run, they may also include real assets in their portfolios comprising financial assets, all of which enhance the consumption and investment activity and thus general economic activity. The difference between fiscal policy and monetary policy, in terms of the speed at which they affect the economy, is that the latter’s impact is more immediate than that of the former. However, as with fiscal policy monetary policy, there are lags, including a recognition lag along with the implementation lag. Second, recall that another objective of monetary policy is to promote economic growth. By exercising monetary policy, the Fed influences forecasts for corporate earnings and profits and thus the market value for stocks. However, for best policy effects, economists recommend the use of both fiscal and monetary policies. Finally, a few words on the global monetary policy are needed. The central banks of other countries have similar goals to those of the Fed and thus conduct very similar policies. What differs among the countries’ monetary policies is that some may have more resource constraints and thus focus more on one or another goal than other countries. Several country regions, such as the European Union, have eliminated their own national currencies and adopted a common currency (the euro) thereby eliminating exchangerate risk for their investors when they are investing in countries other than their own within the Union. Also, because of the ever-increasing pace of global (financial) integration, the central banks of countries need to coordinate their policies (and consider their different economic conditions) before proceeding with a global policy move (although sometimes they act unilaterally). Such coordination takes the form of intervention in the foreign exchange market to stabilize a currency (or restore confidence in economic activity). A related goal would also be to reduce (mainly short-term) capital flows from one country to another, which could destabilize financial markets and thus endanger economic conditions. The Business Cycle One objective of the equity investment manager is to understand why and how economies alternate between expansions and contractions in an effort to decide on the broad asset allocation of his portfolio. These (irregular and recurring) expansions and contractions in economic activity are known as the business cycle. They are irregular because they differ in amplitude and duration and recurrent because they happen every so many years (the number is still subject to debate but a range can be from 5 to 30 years). The business cycle has four distinct phases; expansion, peak, contraction, and trough. The peak is the point between the end of an expansion and the beginning of a contraction, where economic activity is at its highest level. The trough is the point between the end of a recession and the start of an expansion, where economic activity is at a very

Equity and Fundamental Analysis s 319 economic activity

1. Expansion 2. Peak 3. Contraction 4. Trough 2

3 1

4

time

Figure 10.5 The business cycle and its phases.

low level. During each phase, the above-mentioned macroeconomic magnitudes change as they contribute to the overall business activity. For example, during expansions incomes rise, consumption and investment spending increase, the price level increases, and unemployment decreases, thus enhancing business activity. During contractions, the opposite occurs and the economy slows down. Figure 10.5 shows a graph of the business cycle and its phases. The ups coincide with economic expansions and the downs with economic recessions. Table 10.2 records the National Bureau of Economic Research (NBER) classification of business cycle expansions and contractions from the postwar period to the present. How can portfolio managers use the different stages (phases) of the business cycle in creating/managing their portfolios? As we will see in the following discussion on industry analysis, the analyst must know if the industries move with or opposite to the business cycle. That is, whether an industry (and the firms comprising it) is cyclic, if it moves in sync with the business cycle, or defensive (or countercyclic), if it moves counter to the cycle. Stated differently, a cyclical industry has greater sensitivity to the business cycle (or the state of the economy), and during expansions it tends to outperform other industries. Some examples of such industries are the automotive industry and other durable- or capital-goods industries. By contrast, a defensive industry is one that has below-average sensitivity to the business cycle and tends to outperform other industries during recessions. Examples of such industries are public utilities and the health care sector. Therefore the portfolio manager, armed with such knowledge, can construct and/ or position his portfolio so as to capitalize on the current as well as the expected phases of the state of the economy. Let us tie the significance of the industries’ relationship to the business cycle with the CAPM (or APT). Recall the notion of systematic (market) risk (or economic trends, in this discussion) in the CAPM specification relating to beta. Defensive industries have a beta coefficient of less than 1 and cyclic industries greater than 1. Thus, the defensive companies’ stock prices will rise less than the cyclic firms’ stock prices during expansionary periods because they are less responsive to expansions. As a consequence, active

320 s Equity Portfolio Management Table 10.2 NBER Classification of Recessions and Contractions Business Cycle Reference Dates (Quarters) Peak

Trough

Nov 1948(IV) Jul 1953(II) Aug 1957(III) Apr 1960(II) Dec 1969(IV) Nov 1973(IV) Jan 1980(I) Jul 1981(III) Jul 1990(III) Mar 2001(I) Dec 2007(IV)

Oct 1949(IV) May 1954(II) Apr 1958(II) Feb 1961(I) Nov 1970(IV) Mar 1975(I) Jul 1980(III) Nov 1982(IV) Mar 1991(I) Nov 2001(IV) Jun 2009(II)

Duration in Months Contraction Expansion Peak to Trough Previous Trough to this Peak 11 10 8 10 11 16 6 16 8 8 18

37 45 39 24 106 36 58 12 92 120 73

Cycle Trough Peak from previous 48 55 47 34 117 52 64 28 100 128 91

45 56 49 32 116 47 74 18 108 128 81

Source: NBER.

portfolio managers must be able to predict the next phase of the business cycle (better and faster than the general market) in order to choose between the two types of industries and engage in, for example, sector rotation or other strategies. However, as we have pointed out earlier, such forecasting is very difficult, and setting up strategies based on such forecasts is risky. We will expand our industry analysis to gain more insights in the next section. But how do we create forecasts of the future state of the economy? One important source of economic information that can help forecast future economic activity is The Conference Board (which was first introduced in Box 10.1). The Conference Board publishes detailed information on economic indicators, which are economic magnitudes that tend to move before, with, and counter to the business cycle. There are three types of economic indicators: leading, coincident, and lagging. Table 10.3 exhibits the components of each type of indicator. Let us explain each one of them briefly. Leading Indicators. These indicators tend to move up or down ahead of the aggregate economic activity (as measured by GDP). For example, if the index of new housing starts (which is a leading indicator) increases, it can be assumed (expected) that the general economic activity will pick up, because other sectors such as furniture, appliances, and construction materials (all intended to furnish/improve the new homes) will be stimulated. The stock market itself is a leading indicator, as stock markets are forward-looking predictors of company profitability. In all, 10 economic series make up the index of leading indicators as seen in the table. Although these series are considered leaders in predicting economic activity, they occasionally give off uncertain signals. For example, in Figure 10.6, we see that the leading indicators failed to decline before the start of the 2007 recession. Also, some observers (and critics) argue that the index of leading indicators falsely signaled a downturn in 1995 (not shown in the graph). The leading indicator approach to economic forecasting

Equity and Fundamental Analysis s 321 Table 10.3 Components of Economic Indicators Leading Index 1 Average weekly hours, manufacturing 2 Average weekly initial claims for unemployment insurance 3 Manufacturers’ new orders, consumer goods and materials 4 Index of supplier deliveries–vendor performance 5 Manufacturers’ new orders, nondefense capital goods 6 Building permits, new private housing units 7 Stock prices, 500 common stocks 8 Money supply, M2 9 Interest rate spread, 10-year Treasury bonds less federal funds 10 Index of consumer expectations Coincident Index 1 Employees on nonagricultural payrolls 2 Personal income less transfer payments 3 Industrial production 4 Manufacturing and trade sales Lagging Index 1 Average duration of unemployment 2 Inventories to sales ratio, manufacturing and trade 3 Labor cost per unit of output, manufacturing 4 Average prime rate 5 Commercial and industrial loans 6 Consumer installment credit to personal income ratio 7 Consumer price index for services Source: The Conference Board.

5.00 4.95 4.90 4.85 4.80 4.75 4.70 4.65 00

01

02

03

04

05

06

Figure 10.6 Leading Indicator Index for the United States, 2000–2011.

07

08

09

10

11

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is based on purely statistical grounds (patterns) and makes no assumptions about economic behavior and/or its causes. Coincident Indicators. These economic series simply tell us where we are in the business cycle, and they change path whenever the economy moves from one phase, say peak, to another, contraction. In other words, coincident indicators share the same timing of the business cycle and rise in expansions and decline in contractions. Industrial production is a coincident indicator because it is affected by the current state of the economy. Lagging Indicators. Lagging indicators trail economic activity and tell us where the economy has been over the last few months. For example, the (average) duration of unemployment (rate) is a lagging indicator because as unemployment patterns change, they are recorded and become public in the next period(s). Forecasting turning points is one of the objectives of the leading indicator approach, but predicting the timing of the turning points is one of the most challenging activities in economic forecasting. An active portfolio manager needs to diversify internationally and include other countries (and their sectors) in his asset allocation scheme. Economies that are expected to grow faster than others (such as emerging economies) may need to be overweighed in his portfolio, ceteris paribus. Also, the correlations among countries and foreign sectors are an important consideration in a global asset allocation strategy. Therefore studying the international arena is important and rewarding. The box titled International Focus discusses the manner in which the Organization for Economic Cooperation and Development (OECD) uses the leading indicator approach to forecast the business cycle for various countries. Industry Analysis Why does the analyst (or portfolio manager) need to perform industry analysis? The simple answer is that the analyst thinks that she can uncover profitable investment opportunities. Specifically, an analyst seeks to address the following basic questions: sDo returns in industries vary and, if so, do they move together or opposite to each other? sDo industries (and their firms) exhibit consistent performance over time? sDo risk factors change from one industry to another and over time? We have already discussed the link between industries and the general economy in terms of the two types of industries, cyclic and countercyclic. Naturally, returns among industries (and among firms within an industry) are different according to the phase(s) of the business cycle and risk levels, which also vary across industries. Thus, company analysis (which is briefly explained in Chapter 11) should supplement industry analysis. In this section, we will discuss the sensitivities of an industry to the business cycle as well as the competitive structure and the life-cycle of an industry, which might serve as forecasting tools for industry sales and prospects. In the appendix to this chapter, we present briefly how industry analysis is done and provide some sources of industry analyses that professionals consult. We begin with the degree of responsiveness of an industry to economic activity. Industries’ earnings have sensitivities to the state of the macroeconomy in terms of their sales and their financial and operating leverages. For example, sales of cyclical

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industries will vary directly with the state of the economy, but sales of defensive industries will show very little reaction to it. Consumer staples industries will do much better during downturns than capital goods industries. The entertainment industry, for example, might do much better than durable goods industries during contractionary economic periods. Operating leverage (the extent to which a firm has more or less fixed assets relative to variable assets and thus costs) is also a factor determining how responsive an industry is to the state of economic activity. Specifically, firms with high overhead costs (or fixed assets) relative to variable costs will do worse during economic downturns, but firms with more variable than fixed costs will do better during the same economic times because of their quick downsizing ability. Therefore profits for high-fixed-cost firms will vary more sharply (even if the downturn is mild) than those of high-variable-cost firms and, consequently, their stock prices. Finally, financial leverage (the extent to which a firm has more debt or borrowing relative to equity) is important for industries (and firms alike) because interest payments must continually be paid even though sales and profits fall during economic contractions. Therefore firms with lower financial leverage (or less debt) will do much better during lean times than firms with high debt. What do these three factors imply about selecting industries for inclusion in one’s portfolio? Perhaps the investment practitioner should include industries that are less sensitive to the business cycle, as they would have a less than average beta value and are less risky. But although they may fare better during downturns, they may be inferior to the more sensitive ones (with higher than average beta values and thus riskier industries) during good economic times. The bottom line is that the analyst and manager should always consider the industries’ expected returns, given risk, in a fairly competitive (efficient) market. Although the macroeconomic influences on industries are important, the microeconomic forces affecting industries and their competitive structure (position) within the economy are equally important. Stated differently, from a microeconomic point of view, industries are classified into various market structures: perfect competition, monopolistic competition, monopoly, and oligopoly. Although observing the perfectly competitive outcome is difficult, the other market structures such as the monopolistically competitive outcome (retail trade), monopoly (utilities), and oligopoly (automobiles) are very much alive and present. For that reason, the investment professional needs to understand how they compete (that is, based on price, on volume of sales, or on other methods) and what would be their long-run profit potentials. The box titled Applying Economic Analysis highlights the various factors that affect the intensity of competition among industries and their consequences for portfolio management. The analysis is based on the microeconomic aspects of Porter’s five factors of industry competitive strategy. Finally, another tool to predict industry trends (or sales) over time is to understand the time path of an industry and its stages of development. This analysis refers to the industry life cycle and comprises four stages: (1) start-up stage, (2) rapid growth, (3) stabilization and maturity, and (4) slow growth and decline. Figure 10.7 illustrates these stages. Let us briefly explain each of thm. Start-up Stage. During this stage, the industry innovates technologically and becomes a pioneer of its kind. For industries that modify or launch a new version of an existing product, sales may initially be very slow and cash flow may be negative or very low. By contrast, for a revolutionary industry with an entirely new product (such as one in biotechnology or entertainment), sales may be hurt initially, as people are only beginning to

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1

2

3

4

1. Start-up 2. Rapid growth 3. Maturity 4. Decline

stages (over time)

Figure 10.7 The stages of the industry life cycle.

become acquainted with the industry and its products, but over time they become robust and generate a positive cash flow. During this stage, it is difficult to identify leading firms as new firms attempt to find their niche and/or form alliances in an effort to exploit their technology. Rapid Growth. During this stage, also known as consolidation, leader firms are beginning to emerge and the market for their products is developing. Consequently rapid growth of sales and high(er) profit margins begin to take shape. Their products also become ubiquitous. Such a rapid growth, however, may attract new entrants, and over time old and new entrants will find their way either to remain in the industry or to exit. At this stage, it becomes easier to identify profitable firms, as they offer attractive investment opportunities, but these firms still pose high risks. For example, their stocks may be overpriced and over time they may be unable to keep up with demand or competition. Maturity. Beyond a certain point, when excess demand for a product has been satisfied, sales will stabilize and grow slowly. Future sales growth may follow that of the growth of the general economy, leading to normal profit margins (depending upon existing competition) and normal dividend payouts. These industries simply exist to satisfy normal demand and do not necessarily promise high growth prospects. At this stage, the investment professional will need to reexamine her investment position in such industries and change her weighting schemes accordingly. Decline. If the company wants to remain profitable within its industry or the industry wants to be healthy, given that its products have become saturated, the firm needs to extend its growth. At this stage, the industry either grows in pace with the economy or trails it and profit margins are squeezed, resulting in low rates of return. The solution for the industry is to innovate in order to remain in business, otherwise it will fade or disintegrate as firms become bankrupt and/or exit the industry. Investment professionals can easily estimate growth rates and determine whether continued investing in the industry is still worthwhile. Overall, what is the purpose of knowledge of the industry life cycle for the active equity portfolio analyst? The analyst must be able to distinguish between the stages of

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growth and invest accordingly. Although conventional investment practices would dictate investment in high-growth and/or high-dividend industries, such a recipe is not always foolproof. Recall the Internet bubble of the late 1990s. If portfolio managers believe in efficient markets, they will recognize that rapid growth and high profits immediately entice new competitors, thus depressing both profit margins and rates of return (see again the box titled Applying Economic Analysis for additional insights). This dynamic of each stage in the life of an industry is important and should be seriously considered by the active portfolio manager.

CHAPTER SUMMARY This chapter discussed general equity analysis and fundamental analysis. The characteristics of common and preferred stock were compared and contrasted focusing on common stock’s voting rights, limited liability, and residual claims. We differentiated among the various types of common stock and examined the significance and the impact of dividends and stock splits. Next, we explored the nature of preferred stock, emphasizing its cumulative dividend structure, and we explained why it is a hybrid security or a mix between equity and debt. Finally, we explained how one can read off stock quotations from the financial press. We also presented some ways in which individual and institutional investors can create and manage an equity portfolio using active and passive management approaches. Under each approach, we stressed the differences between individual and institutional investors and highlighted the different strategies for each investor group. We concluded the section with a brief look at the risks and benefits of international equity investments as well as the challenges faced by the equity portfolio manager. Next, we examined classic fundamental analysis from the top-down approach to investing. The main objective of fundamental analysis is to examine the economic situation of the firm and extend this analysis to the industry and the national economy. Specifically, we discussed macroeconomic analysis, focusing on the basic macroeconomic magnitudes designed to assess the health or weakness of the economy, highlighted the roles of the two main economic policies (fiscal and monetary), proceeded with the presentation and discussion of the business cycle, and concluded with a presentation of the three economic indicators (leading, coincident, and lagging). Finally, we presented industry analysis and included a discussion of the industry life-cycle model and discussed the implications for portfolio management of the different stages within the life cycle.

APPLYING ECONOMIC ANALYSIS Porter’s analytical approach to analyzing and evaluating company risk within the context of industry structure is important for industry analysis from a financial perspective.* The competitive strategy of a firm is to find its niche or a favorable competitive position within its industry, since its profitable competitive strategy is based on the inherent industry profitability. Porter suggests five competitive factors that determine the intensity of competition (and structure) of an industry:

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s s s s s

2IVALRYBETWEENCOMPETITORS 4HREATOFNEWENTRANTS "ARGAININGPOWEROFCUSTOMERS "ARGAININGPOWEROFSUPPLIERS 4HREATOFSUBSTITUTEPRODUCTS

The five forces are based on microeconomic analysis because they incorporate insights from supply and demand for substitute and complementary products, costs of production, and market structures. Let us highlight very briefly each one of these forces from the economics point of view. Rivalry. Internal industry competition may occur via price or nonprice methods and depends upon the following factors: perfect competition or imperfect competition (monopolistic, monopoly, or oligopoly), homogeneous or nonhomogeneous products, and capacity utilization (for example, monopolistically competitive industries usually have excess capacity). Entry. Firms enter an industry when they see a potential for economic profits. The economic profit is analogous to excess profit (above the fair or normal profit which is included in the total cost function to be subtracted from total revenues or sales). New entrants reduce sales (and market shares) and profits of existing industries and generate higher rivalry among existing and new entrants. There are also barriers to entry categorized into structural or regulatory: limited access to basic resources, economies of scale (or the production of a good at the declining part of the average cost of production), patents and licenses, and other costs. Customers. Customers may have bargaining power to lower prices if there are a few of them (a structure known as monopsony), especially for similar or homogeneous products and when there is a close relationship between seller and buyer. In either case, buyers eat out of the profits of sellers. Suppliers. Inputs of production (human and nonhuman) are controlled by suppliers who may have negotiating power in the case of noncompetitive structures. Unions also are important in creating seller-supplier relationships and pricings. In a perfect competitive structure, the inputs of production prices are set by demand and supply forces; no one party has advantage over the other. Substitutes. Substitute products embed new technologies (e.g., VHS vs. DVD, analog vs. digital) and pose a serious threat to existing firms in an industry. Relevant pricing formulas are cross-price elasticity (of demand), firm- and industry-level price elasticities of demand, and function of customers’ willingness (and ability) to switch to new products. In sum, the professional investor must be able to identify the forces that affect industries and firms in order to determine the concentration of competition within an industry and across industries and evaluate their long-run profit prospects. *M. Porter, How competitive forces shape strategy. Harvard Business Review, May–June 1979, pp. 137–145.

INTERNATIONAL FOCUS PREDICTING THE BUSINESS CYCLE For economic policymaking and other economic agents’ decisions, it is necessary to correctly assess the current and especially future state of the economy. Several leading indicators have been developed to signal the movements of future economic activity before they occur as well

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as to provide some indication of the magnitude of those movements. One of the best-known composite indicators worldwide has been developed by the OECD.

PURPOSE AND CHARACTERISTICS OF THE OECD’S COMPOSITE LEADING INDICATORS (CLIS) The OECD system of leading indicators is based on the “growth cycle” approach, which measures deviations from the long-term trend. A contractionary phase signals a decline in the rate of growth of the reference series though not necessarily an absolute decline in economic activity. This is different from classic cycles, which are defined as a succession of periods of absolute growth and decline in economic activity. The peaks and troughs of growth cycles tend to appear earlier in time than those of classic cycles. The index of industrial production is used as the reference series for aggregate economic activity because, besides constituting the most cyclic subset of the aggregate economy, OECD CLIs are calculated by combining component series in order to cover the key sectors of the economy. These component series cover a wide range of shortterm indicators such as observations or opinions about economic activity, housing permits, financial and monetary data, etc. The final set of component series is selected in order to maximize the performance of the CLI with respect to the reference series, which is evaluated in terms of missing or extra cycles, homogeneity of leads at turning points, and cross-correlation. The aggregation of component series to form the CLI reduces the risk of “false signals,” which are defined as changes in the indicator due to irregular movements that do not correspond to any later developments in the reference series. The component series need to be transformed and “standardized” in various ways before they can be combined into one single composite indicator. This entails: s s s s s

Detrending: The growth cycles (i.e., the deviations from the long-term trend) of each component series are derived. Periodicity: All component series are transformed to monthly periodicity. Smoothing: In order to reduce the irregularity of the final composite indicator, component series are smoothed using well-established statistical techniques. Normalization: The cyclic movements are expressed in a comparable form, and so the cyclical amplitude is homogenized. Weighting: In general for each country, component series of the CLI have equal weights.

IMPROVING THE PERFORMANCE OF THE OECD CLIS As with most statistical indicators, CLIs are subject to revision. Although revisions are necessary, they are not very much appreciated by users, especially when signals provided by indicators about the cyclic situation change over time. The following factors give rise to CLI revisions: s s s s

Timeliness/availability Frequency Smoothness Other factors

HOW HAVE THE OECD CLIS PERFORMED IN PRACTICE? In general, the historical record of the composite indicators both with respect to turning points and closeness of fit has been rather good. The average lead of the composite indicator, as

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measured by the lag at which the closest correlation occurs, should not be too different from the median lag at all turning points if the composite indicator is to give reliable information both about approaching turning points as well as during the evolution of the reference series. Source: R. Nilsson and E. Guidetti, OECD Statistics Brief, February 2008, No. 14, by excerpt, http://www.oecd.org/ dataoecd/35/38/40182804.pdf.

LESSONS OF OUR TIMES SOME DANGERS OF INVESTING We often hear from people that the economy and the stock market will collapse, the dollar will collapse, unemployment will skyrocket, and so on. It appears that everybody knows what is about to happen and tells us about it. People give you advice all the time about managing your money and investments: buy this “hot stock,” sell this “loser stock,” stick with winners, and the like. Thus if you really listen to such talk and trade on such advice, chances are that you are going to lose. Think about it for a moment: would you listen to these infomercials on TV or to these “young gurus” of finance who want to give you their winning strategy so that you can reap (their) profits too? You know that these strategies are surely losing propositions once they are out and followed by other naive people. Hot stocks end up becoming vastly overvalued, leading to their demise (by offering lower returns). Winner mutual funds would struggle to remain on top year after year. Similarly, if you read the financial pages on the Internet, you will definitely come across articles that advise you to pay attention to this, avoid that, and the like, or that even tell you the top 10 things to know before the markets open. Then, another article pops up instructing you to take action on certain things based on the writer’s interpretation of the news. What are you going to do? Are you going to follow one writer’s advice and ignore another’s? Too much information might confuse you or even lead you to despair! If you read the research that you obtained after paying a fee, what are the real chances (or guarantees) that your investments will earn better returns than the average if you follow that advice? Should you expect to beat the market just because you paid a consultant to manage your investments better? Do you recall the sentence that all funds state at the end of their investment brochures? Past returns do not guarantee future ones! So, what are the lessons? Hard work and prudence are important. Be smart! Be vigilant! Do not be too trusting! Invest wisely, within your limits and understanding. Be conservative but not too conservative. Be aggressive but not too aggressive. You decide.

KEY CONCEPTS Common stock represents an equity (ownership) position in a corporation. A stock’s par value is usually set below stock market value or the value at which the stock is sold for initially. Cumulative voting is a procedure by which a shareholder casts all votes for one director, thus permitting minority participation.

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When shareholders cannot be present at the meeting for elections, they usually transfer their votes to other shareholders under proxy (voting). A classified stock is given some special designation such as class A, class B, and so on. Cash payments paid by a corporation to its shareholders are called dividends. The ex-dividend date is specified as two business days prior to the date of record, which is the date that the board of directors states for payment of the dividend. A stock dividend represents an amount of additional shares and is represented by a percentage. A stock split is similar to a stock dividend except that it is expressed as a ratio rather than a percentage and its effect is to raise the ownership of shares. A reverse stock split reduces the number of shares and raises the par value of each share. Preferred stock, unlike common stock, implies a preference (or a senior status) in the dividend payment and occurs with a fixed dividend rate. Preferred stock is a hybrid security because it has features of both equity and debt. Cumulative dividends are paid before any common stock dividends are paid; if not paid during a previous year, they cumulate and must be paid before any dividends are paid to the common stockholders. Passive equity portfolio management is a long-term buy-and-hold strategy where the equity portfolio manager purchases stocks that closely match the relevant index. Enhanced indexing involves bets on certain factor risks called tilts. Index arbitrage occurs when the manager of the indexed portfolio also trades option and futures contracts where he believes that the value of the derivatives do not match the value of the index. Active equity portfolio management involves earning a net return that exceeds the return of the relevant benchmark (passive) portfolio. The normal portfolio is the appropriate benchmark in active investment strategies. Fundamental analysis is based on the top-down approach to investing because it begins with the general (the economy) and ends with the specific (the firm). Fiscal policy is performed by the federal government by using its two main tools: government expenditures and tax rates. Monetary policy refers to the manipulation of the nation’s money supply by the Fed using three main (quantitative) tools. Open-market operations refer to the buying and selling government securities by the Fed in the open market. The discount rate (or discount window) is the rate the Fed charges member banks when they borrow from it on a short-term basis. The reserve requirement is the ratio of the reserves to total deposits the bank is required to keep in its vaults as cash or at the Fed as deposits.

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The irregular and recurring expansions and contractions in economic activity are known as the business cycle. The peak is the point between the end of an expansion and the beginning of a contraction where economic activity is at its highest level. The trough is the point between the end of a recession and the start of an expansion where economic activity is at a very low level. Leading indicators tend to move up or down ahead of the aggregate economic activity. Coincident indicators share the same timing of the business cycle and rise in expansions and decline in contractions. Operating leverage is the extent to which a firm has more or less fixed assets relative to variable assets and thus costs. Financial leverage is the extent to which a firm has more debt or borrowing relative to equity. The industry life-cycle refers to the time path of an industry and its stages of development.

QUESTIONS AND PROBLEMS 1. If an investment professional approached you and began telling you a story about how good (or hot) certain stocks were and would be, hoping to entice you to purchase them for your portfolio, that analyst would be following which general approach to security analysis? 2. If a particular sector in the economy is expected to grow faster and generate higher cash flows than other sectors, what impact would that have on analysts’ perceptions about the sector and its companies’ stock prices? What would be the impact on stock prices (of the same firms) if the market had already anticipated this growth? 3. Explain the link or the chain of events from a falling (value of the) dollar to business investment spending. 4. Propose a policy for an overheating economy and a contracting economy. Include both economic policies in your discussion. 5. How can an investment practitioner use the information contained in the economic indicators? 6. Why should investors worry about federal budget deficits and trade deficits? 7. Explain the effect on the price level and output of an economy when there is an increase in investment within the economy. 8. What is the relevance of monetary policy to investment management? 9. How is the CAPM related to the business cycle? 10. Scour the Wall Street Journal to find articles on the issue of foreign governments (such as China) holding US dollars and how this situation sparks heated debates on the US budget and trade deficits. 11. Search the Wall Street Journal to find articles on stock-split announcements and follow the path of the firm’s stock price. What do you see? 12. How can you, the retail investor, apply active portfolio management and what practical issues could you face in doing so?

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13. If an industry is growing faster than the overall economy and the threat of new entrants is real, which stage of the life cycle is the industry in? Can you provide an example of such an industry? 14. Can you identify some advantages and disadvantages of dual-class stocks? 15. What is the impact of operating leverage on a company during the business cycle?

APPENDIX Guidelines for Conducting Industry Analysis The purpose of this appendix is to provide a general framework for conducting industry analysis following Porter’s guidelines.3 This framework can help an analyst develop a complete set of factors to consider in evaluating an industry from the economic and competitive perspectives. We will also blend the analysis with the life-cycle theory so that the analyst can have a comprehensive picture of the industry’s past, present, and future. We will present this general framework in a question-and-answer format.

QUESTIONS AND SUGGESTED ANSWERS How can the analyst determine the relevant stage of the industry life cycle? The analyst must identify the following: sCustomer behavior sProduct characteristics sAdvertising and marketing strategies sManufacturing and distribution sCompetitive strategies sResearch and development efforts How can the analyst develop an overview of the relevant industry? sIdentify the industry (by SIC) sRead analysts’ information sRead companies’ annual reports and financial statements sEvaluate management performance sRead industry publications sCollect information on global industry factors What are some sources of industry information? sStandard & Poor’s Industry Surveys sStandard & Poor’s Analysts Handbook sValue Line industry surveys sIndustry publications sTrade Association publications sInternational industry magazines

332 s Equity Portfolio Management

NOTES 1. 2.

3.

Google 10-K report, Feb. 2010, http://www.faqs.org/sec-filings/100212/Google-Inc_10-K/. Joseph Lakonishok and Baruch Lev, Stock splits and stock dividends: why, who, and when. Journal of Finance, 62, 1987, pp. 913–932. Paul Schultz, Stock splits, tick size and sponsorship, Journal of Finance, 55, 2000, pp. 429–450. Michael Porter, Competitive Strategy (New York: Free Press, 1980).

11 EQUITY VALUATION AND INVESTMENT STRATEGIES

CHAPTER OBJECTIVES After studying this chapter, you should be able to sCompute a stock’s expected and required rates of return and interpret them sValue a stock using several methods sUse and interpret several relative equity valuation measures sKnow how to apply some ad hoc investment strategies to picking stocks

INTRODUCTION Valuing an equity security is simultaneously challenging and exciting. The analyst must have knowledge of such areas as economics, statistics, finance, and accounting in order to extract and use the relevant information for a company. In the previous chapter, we discussed fundamental analysis, which included analyses of the macroeconomy and the industry. In this chapter, we add company analysis and discuss various equity valuation models. Specifically, we discuss the dividend discount model—the basic equity valuation model— and its variants and explore the information content of the cash flow and the cash dividend magnitudes. In these analyses, we use real data on IBM and illustrate how these models can be used to derive a company’s fair stock price. Next, we examine some other equity valuation techniques including an options valuation approach. We then extend our analysis to include some discussion of some issues on equity valuation, such as the impact of inflation on stock values and the significance of dividend signals. Finally, we conclude with the presentation of some equity trading strategies and highlight their advantages and disadvantages.

EQUITY PRICES AND RETURNS This section illustrates the relationship between prices and returns and addresses the issue of when an investor should buy, sell, or hold a stock based on prices and returns. Let us begin with a basic question: Why do investors buy a stock? The answer is because they 333

334 s Equity Portfolio Management

expect future cash dividends and capital appreciation (if and when they sell the stock). Therefore, the now familiar expected holding period return (HPR) from the stock is reproduced here for convenience: Expected HPR =

D1 + ( P1 − P0 ) P0

(1)

where D1 is the next period’s dividend, P1 is the next period’s stock price, and P0 is the current stock price. Recall that D1/P0 is the dividend yield and (P1—P0)/P0 is the capital gain/loss yield. As an example, assume D1 = $1.20, P0 = $25, and P1 = $28. The stock’s expected HPR or E(rs) is: ($1.20 + $28—$25)/$25 = 0.168 or 16.8%. This number means that the stock is expected to yield (earn) 16.8%. However, this information is insufficient for the investor to decide whether he should buy, sell or hold the stock. He also needs to know the stock’s (or her) required rate of return, k. One method to compute the stock’s required rate of return, ks, is the capital asset pricing model (CAPM); its specification is: ks = rf + s [E(rm)–rf ]

(2)

where rf is the risk-free rate, s the stock’s beta coefficient, and E(rm) is the expected return on the market. Remember that this method derives the investor’s (minimum) or required rate of return in order to invest in (buy, sell, or hold) the stock. Also, recall that the CAPM derives the investor’s expected rate of return. Figure 11.1 plots the security market line (SML), on which both the expected and required returns are equal at point A. This is so because the market is in equilibrium. As an example, assume that the stock’s beta coefficient is 1.5, the risk-free rate is 4%, and the expected return on the market 10%. The stock’s required rate of return would be: ks = 4% + 1.5 (10%–4%) = 13%. Also, you can see that with the derived return data above, the stock’s expected return lies (vertically) above the stock’s required return, at point A (the required return point is A and lies on the SML). Now the investor has enough information to decide whether to buy, sell, or hold the stock. In general, there are three choices:

return (%) 16.8%

13%

A’

SML

A

4%

1.5

Figure 11.1 Expected and required return from a stock.

beta

Equity Valuation and Investment Strategies s 335

1. If the stock’s expected return is greater than the stock’s required return, buy the stock. 2. If the stock’s expected return is less than the stock’s required return, sell the stock (or sell the stock short). 3. If the stock’s expected return is the same as the stock’s required return, buy or hold the stock. Given the above results from our example, the investor should buy the stock, because it would return more that what she minimally requires from it. This extra return is also called abnormal return or pure profit (or alpha, as we saw in Chapter 8), which is the additional return above the stock’s expected risk-adjusted return. Such divergence between the two returns would be impossible in an efficient market because the prices of assets would always be fair. Now let us conduct a similar analysis from a different perspective, the stock prices. We need to introduce a new concept, the stock’s intrinsic value, and compare it with the stock’s (current) market value. But before we do that, let us illustrate and explain how market prices are determined. We have seen in a previous chapter that the market price of a stock is determined by the forces of demand and supply. Given the available supply of shares (hence a vertical supply of shares of a firm), the market-clearing stock price will be determined at the point of intersection between the supply and the (downward-sloping) demand curve for the firm’s shares. Figure 11.2 shows this equilibrium and the market price of the stock at point A. Let us derive some insights from this simple graphic illustration: sThe equilibrium price is what the marginal investor thinks the price of the stock is and does not necessarily reflect the market consensus price. sAt higher prices, investors would want to hold fewer shares; and at lower prices, they would want to buy more shares. sChanges in equilibrium prices occur as new information comes into the market that affects either curve. sNot all investors may agree on the security’s price (as shown in the Figure 11.2).

Supply security price

P*

Demand

S*

Figure 11.2 Market Clearing Stock Price.

quantity of shares

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In fact, some investors may end up deriving a different price for the stock (given that they obtain different information and interpret that information differently). Thus, we are interested in establishing what the individual investor thinks the value (price) of the stock is (and is willing to pay) rather than accept the market price of the stock. We will term this price the intrinsic price and explain it below. The intrinsic value (price) of a stock is the present value of the firm’s total expected net cash flows discounted by the firm’s (risk-adjusted) required rate of return. Denote V0 as the intrinsic value. Using the total cash flows as expected dividends (D1), the proceeds from the sale of the stock as next period’s price (P1), and the required rate of return (k), we derive the basic (initial) valuation formula below: V0 =

D1 + P1 1+k

(3)

The investor can compare the stock’s intrinsic value with its current market value to decide whether to buy, hold, or sell the stock. Using the hypothetical data from above, we calculate the stock’s intrinsic value to be V0 = ($1.2 + $28)/(1 + 0.13) = $25.84. Now since the intrinsic value (or price) of the stock of $25.84 exceeds its current price (P0 = $25), the investor concludes that the stock is undervalued (underpriced or marginally fairly priced ); thus she should buy the stock. To put the discussion within an active investment strategic context, the investor should overweigh that stock in her portfolio relative to what a passive investment strategy would dictate. This is the same conclusion as was reached above in comparing the stock’s expected and required returns. Table 11.1 summarizes these findings using the two ways of making a buy/sell stock decision. Box 11.1 contains an actual example of equity valuation as perceived by Warren Buffett and his company, Berkshire Hathaway Inc., using the notion of the intrinsic value of a stock. As previously noted, in market equilibrium the current market price of the stock would reflect the market’s consensus price. Any (marginal) investor’s intrinsic price that differed from the market’s rate would mean that he would not agree with the values of

Table 11.1 Stock Price and Returns Decisions to Buy or Sell a Stock Using Returns Comparison of Returns

Stock is

Decision

expected return > required return expected return < required return expected return = required return

undervalued overvalued fairly valued

buy the stock sell the stock buy/hold stock

Using Prices Comparison of Prices

Stock is

Decision

intrinsic price > market price intrinsic price < market price intrinsic price = market price

undervalued overvalued fairly valued

buy the stock sell the stock buy/hold stock

Equity Valuation and Investment Strategies s 337

BOX 11.1 Intrinsic Value in Practice Warren Buffett strongly defended the valuations of some stocks that he holds (among them Wells Fargo and Kraft stocks) given recent declines in their prices. Specifically, following a prompt by the SEC that the company should have recorded a lower value for these stocks, Buffett’s company, Berkshire Hathaway Inc., told the agency that it had no immediate plans to sell these stocks and believed that they were all undervalued and expected to rebound soon. The company’s officials told the SEC that they were confident that these stocks were not trading at their true (price) levels—which should be higher—and expected that in due course the stocks’ market prices would reach their intrinsic value, which existed when they were first purchased. These officials also remained confident that these companies had good prospects for growth, despite their having been hurt by the recent credit crisis, and strong earnings power. Source: J. Funk, Buffett’s firm defends valuation of 5 stocks, Associated Press, March 28, 2011.

the (expected) cash flows or the discount rate. The latter is also known as the market capitalization rate, or the market cap rate, because it represents the market’s consensus (required) rate (or return).

SOME GENERAL VALUATION MEASURES Besides the basic valuation models discussed in the next section, investors and analysts have historically used several other relative methods for valuing stocks. However, some of these approaches suffer from shortcomings that limit their use in practice. Let us present and briefly discuss some of these methods. However, we withhold discussion of one of these approaches (the price/earnings ratio) until a later section. Book Value The total book value of a security is the net worth of the company as recorded in the company’s balance sheet. As an example, Table 11.2 presents selected items of IBM’s balance sheet for December 31, 2010. To compute the stock’s book value per share, simply divide the total value of stockholder equity ($23,046) by the number of shares outstanding 1.22 billion (as of early 2011, source: Yahoo! Finance) and obtain $18.89 (while the actual, as of early 2009, also from Yahoo! Finance, was $18.77). As of January 10, 2011, IBM’s stock price was approximately $147.67, which is much higher than the book value number. Using the above analysis, can we conclude that IBM stock is greatly overpriced? This method is a poor indicator of a stock’s value for several reasons. First, book value reflects a set of arbitrarily applied accounting rules that makes comparisons difficult, such as inventory valuation methods including first-in first-out (FIFO) and last-in first-out (LIFO) across firms. Second, book value reflects historical (or the initial dollar investment) valuation, whereas the market value reflects an ongoing concern (or is forward-looking). Third, book value can be considered the minimal value for a security, whereas the market value can (theoretically) decline to zero. Given that some firms’

338 s Equity Portfolio Management Table 11.2 Selected Balance Sheet Items for IBM, December 31, 2010 Assets (in millions) Total assets

Liabilities and Equity $113,452

Total liabilities Total stockholder equity

$90,405 $23,046

Source: Yahoo!Finance.

stocks have book values above or below their current market prices, the book value does not reliably represent a floor in the stock’s price. Price/Book Value As its name indicates, the price/book value is found by dividing the market price per share by the book value per share for the stock. This derivative measure addresses some of the problems highlighted above. Whereas stock book values are determined by accounting conventions (and economic factors), market stock values are determined by investors’ assessments of the firm. IBM’s price/book value was 8.20 (approximately computed by dividing an average share price of $151 by the book value per share of $18.77). This information was obtained and derived from Table 11.3, which exhibits some valuation measures and other selected financial information on IBM as of December 31, 2010. Price/Sales Value Another multiple is Kenneth Fisher’s price/sales (P/S) ratio, where S represents the past sales (total revenue) per share for the firm. In general, the smaller the ratio (less than 1), the better the investment is. So if the P/S ratio is 1, it means that you are paying $1 for every $1 sales the company makes. Despite its volatile history, some analysts believe this ratio to be important because sales of a company are a primary factor for growth. However, the analyst must be cautious in comparing firms across industries because sales volumes and financial leverage differ dramatically from industry to industry. Using Table 11.3 again, IBM’s P/S ratio was 1.95 (approximately computed by dividing an average [of past quarter’s] price of $153 by the actual revenue per share of $78.71). Notice also the discrepancies in deriving these figures when data are taken from different (or multiple) sources. Liquidation Value This measure represents the cash value an investor would receive if the company were to be liquidated (by selling its assets, paying off all parties, and distributing assets by priority). Because liquidation means the end of a company, liquidation value may be regarded as the minimum (or floor) value of the firm’s security. Two issues arise in the estimation of a firm’s liquidation value. First, using the book value of assets to determine the terminal value of the firm requires an assumption about the value of these assets as well as the expected inflation rate. Second, if one uses the expected cash flows of the firm’s assets up to a future liquidation point in time and discount these cash flows to the present, then estimates of both the flows and the discount rate must be provided. Despite the difficulties in deriving the liquidation value, some investors use their estimates to determine whether the company would be a takeover target. For example, if the liquidation value

Equity Valuation and Investment Strategies s 339 Table 11.3 Selected Financial Information on IBM Beta: Revenue per share: Price/sales: Price/book: Book value per share: Shares outstanding (in billions): Forward annual dividend rate: Payout ratio:

0.73 $78.71 1.95 8.20 $18.77 1.23B $2.60 21%

Source: Capital IQ For the fiscal period ending in December 31, 2010

exceeds the current value of the firm (that is, as a going concern), an investor (raider) may buy the company and then liquidate it to achieve a positive return. Replacement Value Replacement value, by contrast, refers to the cost incurred to reproduce the firm (and its existing assets) at market prices. As with the liquidation value strategy, some analysts contend that the firm’s replacement value should not get too far apart from its market value, because this might attract corporate raiders. For example, if the replacement cost were less than the firm’s current market value, competitors would try to replicate the firm and earn a positive profit (given that the market value exceeds the replication cost). The replacement value measure also suffers from problems including estimation and the realization that expected cash flows cannot be used in (or are unrelated to) the firm’s replacement value. This concept was elegantly proposed and extended by Tobin (1969) and is known as Tobin’s q.1 The ratio is as follows: q=

market value of capital in place replacement cost of capittal

According to Tobin’s analysis, the firm’s replacement value or ratio of firm market price to replacement cost should not differ from 1. Firms with a q value greater than 1 would tend to be attractive investment opportunities. To see this, consider the alternative expression of q using book values rather than market values: q=

equity market value + liabilities book value equity book vallue + liabilities book value

In sum, these measures focus on a firm’s balance sheet or suffer from drawbacks. A better measure would be to find the present value of the future benefits (cash flows) the investor (shareholder) expects to receive from investing in the firm. This notion forms the basis for the next section, where the fundamental dividend discount model is presented.

340 s Equity Portfolio Management

THE DIVIDEND DISCOUNT MODEL AND ITS VARIANTS To reiterate, valuing an asset involves estimating its expected stream of payments during the ownership period and then converting this stream of payments into a (present) value by discounting this stream using the investor’s required rate of return. In general, the stock’s stream of payments can take various forms, including dividends, earnings, cash flows, and capital gains (or losses). Because these payments occur in the future, the investor must be able to forecast them to derive an accurate value for the stock. The general required rate of return on an investment is typically composed of three factors: Required rate of return = real risk-free rate + inflation premium + risk premium The last factor depends on the uncertainty of the payments for the investment asset, which, in turn, depend on various factors (such as business risk, liquidity risk, and default risk), which were discussed in Chapter 3. The Dividend Discount Model To link our previous discussion on the stock’s intrinsic value (price) to the present discussion, let us start with Eq. 3: P0 = V0 =

D1 + P1 1+k

(3)

Based on the above, the next period’s price, P1, can be expressed as follows: P1 =

D2 + P2 1+k

(4)

Substitute Eq. 4 into Eq. 3’ and obtain the following expression: P0 =

D1 D + P2 + 2 1 + k (1 + k )2

(5)

By continuously substituting successive versions of Eq. 4 for any future price into Eq. 3’, we can obtain (in infinity) the following expression: P0 =

D1 D2 D3 + + +… 2 1 + k (1 + k ) ( 1 + k )3

(6)

This expression is the general form of the dividend discount model (DDM), which states that the current price of a stock should equal the present value of the expected dividends in infinity (or in perpetuity). Two important questions arise at this point. First, where is the stock’s price in the above equation? Recall that the value of the stock is determined by its expected cash flows; thus any price paid for it must reflect that expectation. Therefore, in expressing this into infinity, we end up with an equation that has only dividends (to be discounted). The second question involves stocks that do not pay dividends. This notion is the same,

Equity Valuation and Investment Strategies s 341

but perhaps we can omit dividends in the early periods. Recall again that we use the expected dividend stream in the model, which means that investors expect dividends to be paid at some future time. Besides, some companies (such as insurance companies as well as pension funds and some state enterprises) are required to invest in dividend-paying stocks; thus if a stock is not expected to pay some dividends (even in the distant future), its value cannot be calculated (using this approach) and would be zero. Second, remember that if a firm does not pay dividends now, it must reinvest the earnings for future growth, and this would form investors’ rational expectations for dividends. Finally, one can use a similar company in the industry to estimate the dividend payout ratio and the company’s free cash flows to derive a comparable stock price. Let us illustrate Eq. 6 with actual data. Assume that you have a 1-year holding period (investment horizon) and you buy IBM stock today (at $93 early in 2009) for only 1 year, and at the end of the year you sell it. Let us use some of the information contained in Table 11.4 to derive the investor’s intrinsic price. We see that the annual total dividend for 2009 was $2.15. Specifically, the annual dividend growth was 13.15% (from $1.90), while the quarterly dividend increased by 10%, or from $0.50 to $0.55, and it is expected to continue at that rate. Next, scouring the Internet for a consensus of analysts’ predictions on the expected rate of return of the S&P 500 for 2009, we arrived at an average of 20%. Naturally you would have to derive your own estimates (that is the purpose of security/fundamental analysis after all), but here let us use that number. Finally, the rate of the 1-year Treasury bill is estimated, on average, at 1.00% for 2009 (in 2008, it was 1.6%). Now, let us compute P0. To find the required rate of return, k, we first use Eq. 2 and the beta input from Table 11.3. Therefore, k = 1.00% + 0.73 (19.00%–1.00%) = 14.14% One way to find an estimate of next period’s price, P1, is simply to multiply the current price, P0, by the annual growth rate of dividends, 13.15% (as we will show later): P1 = $93 (1 + 0.1315) = $105.23 Finally, using the above values for D1, k, and P1, we derive an estimate of the stock’s current price, P0, using Eq. 3: P0 =

$2.15 $105.23 + = $1.883 + $92.19 = $94.08 1 + 0.1414 1 + 0.1414

Table 11.4 Selected Data on IBM Magnitude

2008

2009

2010

Dividend per share Quarterly dividend Average share price

$1.90 $0.40–$0.50 $95.5

$2.15 $0.50–$0.55 $93

$2.50 $0.55–$0.65 $134

Sources: IBM annual reports, Yahoo!Finance

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Box 11.2 Actual Uses of the Dividend Discount Model by Firms Goldman Sachs uses the dividend discount model (DDM) to predict the future values for the S&P 500 Index (by deriving a multiple or a number by which the current index value is multiplied). For example, their 2009 year-end price target of 1,060 for the S&P 500 Index was derived from their DDM and implies a multiple of 13.1 for the index (by year end) based on other inputs such as an earnings per share estimate of $81, a cost of equity or a discount rate of 8.5% and a long-run earnings growth rate of 6.7%. Thus the year-end (2010) estimated fair value for the index was 1,130. The actual, average value of the index during 2010 was 1,250. Source: Goldman Sachs Portfolio Strategy Report, October 1, 2009. Alcoa also uses a DDM—or the discounted cash flow (DCF) model, see Eq. 11 in the text—to estimate the current fair value of parts of its business, including forecasting its operating cash flows. A number of important assumptions and estimates enter the calculation of the values, including markets and market share, sales volumes and prices, costs, and a discount rate. Source: Alcoa’s 2008 Annual Report. Finally, IBM used the DDM (or the DCF model) to find the fair value of investments (late in 2008). The valuation inputs included an estimate of future cash flows, expectations about possible variations in the amount and timing of cash flows, and a discount rate based on the riskadjusted cost of capital. Various results from the model were assigned probabilities in order to arrive at a most likely discounted cash flow fair value for these investments. Source: IBM 2009 Annual Report.

Thus, the investor’s intrinsic value today (early in 2009) for an IBM share is estimated to be $94.08. The stock’s actual average price in early 2009 was $93, which may imply that the stock was undervalued and thus a good bargain. Note that the above analysis can be extended to multiyear holding periods simply by adding more discounted dividend terms before the (discounted) sale price term. However, this is much harder because estimates of both dividends and required returns can be difficult to obtain. Box 11.2 includes various applications of the DDM by three firms, so you can see potential uses of the model. For example, Goldman Sachs uses it to estimate the future value of the S&P 500 equity index, Alcoa to value parts of its operating business, and IBM to find fair prices of investment projects. The Constant Growth Model We said above that Eqs. 3’ or 6 are not always useful in valuing a stock because forecasts of future dividends (into perpetuity) are required and also because we assume a constant required rate of return. In this section, we will rearrange Eq. 6 in order to derive a very important variant of the DDM. Start with estimates of the future dividend, D1. The current dividend, D0, is known, but to find future D’s, we need to multiply D0 by the growth rate of dividends, g. This is done as follows:

Equity Valuation and Investment Strategies s 343

D1 = D0 (1 + g) D2 = D0 (1 + g) (1 + g) = D1 (1 + g)2 D3 = D0 (1 + g) (1 + g) (1 + g) = D1 (1 + g)3 and so on Thus, substitute each of the above into Eq. 6 to obtain the following expression: P0 =

D0 ( 1 + g ) D0 ( 1 + g ) 2 D0 ( 1 + g )3 + + 1+k (1 + k )2 ( 1 + k )3

(7)

Continuing in this way to infinity, the formula reduces to the following, more compact expression: P0 =

D1 k−g

(8)

This equation is known as the constant growth model or the Gordon model (after Myron Gordon, who first proposed it). This version of the DDM is the infinite-period model, which is more compact and easier to apply than the above specifications. Let us interpret this important stock-valuation model. The denominator is the difference (spread) between the stock’s required rate of return and the growth rate. For the model to be useful, we must impose k > g. If the investment practitioner derives a value for g greater than k, it means that the sck’s growth rate (and perhaps the company’s) might be unsustainable in the future. However, though k < g currently, this does not mean that we have a violation of the requirement of k > g! Also, a firm cannot permanently have its required return greater than its growth rate because competitors would enter this lucrative business and force the firm’s profit margins and thus its growth rate. Recall that what we derived above is a long-run equilibrium (infiniteperiod variant) that can differ from short-run variations; thus Eq. 8 is still valid. Let us apply this variant to price IBM stock. Using the previously derived and obtained values for D1, k, and g, we have: P0 =

D1 $2.15 = = $215 k − g 0.1414 − 0.1315

As you see, this model variant gives an unusually different price for a share compared with the general model variant.2 In this case also, the investor should buy the stock because it is considered undervalued. The constant growth model has four implications for the stock’s price (ceteris paribus). The stock price is: sHigher when expected dividend is greater sHigher when growth rate is higher sLower when the required rate of return is higher sGrowing according to the growth rate of dividends

344 s Equity Portfolio Management

Let us elaborate on the fourth implication, because we can derive additional insights and more versions of the model. First, if the growth rate of dividends is zero, then Eq. 8 reduces to the perpetuity formula: P0 = D1/k

(9)

The investor can use this formula to price preferred stock that pays a fixed dividend. Again, the same analysis (that is, to compare the intrinsic value to the stock’s market value) can be done to see if it is worthwhile to buy the stock that gives those fixed dividends. Rearranging Eq. 9 to solve for k (k = D1/P0) results in the derivation of the stock’s promised yield (a concept we will encounter in Chapter 12, on bond valuation). Now, let us manipulate Eq.8 by substituting an earlier expression for future values of the dividend. The next period’s price, P1, can be expressed as follows: P2 =

D (1 + g ) D2 D1 = 1 = ( 1 + g ) = P0( 1 + g ) k−g k−g k−g

(10)

Thus, the constant growth model implies that the stock’s price grows steadily according to the growth rate of dividends, g. Note that we used this expression in the IBM stock valuation example above. Which factors affect the dividend growth rate? We learned in the previous chapter that the overall macroeconomic and the global economy affect it in general. A company would not pay dividends at the start-up stage but might pay dividends during the growth stage. Yet, another version of Eq. 8 is derived when we solve for k, k=

D1 +g P0

(11)

which is interpreted in various ways: as the dividend yield plus the growth rate or as an expected rate of return in equilibrium when the expected rate of return equals the required rate of return, with components of the dividend yield and the growth rate of dividends. Some authors call Eq. 11 the discounted cash flow (DCF) approach to stock valuation. Applying this variant to the IBM data above, we obtain a new value for k: k = ($2.15/$93.00) + 0.1315 = 15.46% which is higher than the one derived using the CAPM. If we apply the above number for k to the IBM data above to find P0, we have: P0 = $2.15/(0.1546 – 0.1315) = $93.07 which is slightly higher than the stock’s (average) current price ($93); this would again mean that the investor should buy the stock because (based on this analysis) it is currently underpriced. The DCF approach is mostly employed by utility companies, which are set to earn a fair profit (on top of costs) in order to estimate their required rate of return.

Equity Valuation and Investment Strategies s 345

A caution is warranted at this point. Firms have three choices with respect to earnings payouts: dividends, stock repurchases, or special dividends. Thus if a firm uses any of the last two choices, the investor cannot use the dividend models that we learned about to value the firm’s stock. Also, some firms that have high growth prospects retain their earnings for reinvestment and pay no dividends. Thus problems in valuing these firms’ stocks arise in this case as well. Finally, some firms that do not have growth prospects (the socalled declining firms) do not pay dividends; it would be optimal for them to liquidate their companies and pay investors large liquidating dividends. The Multistage Dividend Growth Model Recall from the previous chapter, on industry analysis, that firms go through various growth stages such as the following: sStages with different growth rates, gi, over time sOne stage with positive (g greater than 0) and another with negative growth rate (g less than 0) sA stage with zero growth For example, IBM’s 2009 stock price growth rate from 2008 was negative (–2.6%, see Table 11.2), but for the year before that it was positive (not shown in Table 11.2). In general, however, young companies typically do not pay dividends when they are in their infancy (at the start-up stage of industry life cycle, from Chapter 10) because they reinvest their earnings for future growth. Even for mature firms, dividend growth may vary as they move with or counter to the business cycle. Therefore, given that the models above (Eq. 3’ or 8) assume constant growth forever, they can have a limited use when a firm has multiple growth rates. For that reason, analysts employ a variant of the DDM that incorporates high (and variable) growth rates for some years and then revert to the basic DDM (or constant growth model) for steady-growth years. This variant is known as the multistage growth model and is expressed as follows: P0 =

D1 D2 D3 D + Pn + + +…+ n 2 3 1 + k (1 + k ) (1 + k ) ( 1 + k )n

(12)

where Pn represents the forecasted stock sale price at period n. The idea behind this model variant is that you analyze (discount) each year in the firm’s business (when supernormal growth takes place) separately. Once growth becomes steady, you can use the conventional DDM for the remaining years. Let use a different source of information on IBM stock. We choose the free Value Line Investment Survey (VLIS) for 2008 to derive some data and apply the multistage DDM (Eq. 12).3 We seek to determine IBM’s intrinsic stock price for 2009 (P2009), in view of the reported average price of $81.25 for 2008. We obtain or infer the following data from the survey: sCurrent dividend forecast, D2009 = 2.30 sDividend growth rate, g, years 2011–2013 = 21% Let us derive the expected dividends from the above data:

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D2010 = $2.30 (1 + 0.21) = $2.78 D2011 = $2.78 (1 + 0.21) = $3.36 D2012 = $3.36 (1 + 0.21) = $4.07 D2013 = $4.07 (1 + 0.21) = $4.93 Again, we are presented with a challenge in computing the stock’s price for 2012 because we need an estimate for k. For example, if we employ the CAPM, we need estimates for the 3-year Treasury bill and, most importantly, the market’s return. The stock’s beta coefficient is given in the VLIS as 0.85, which, incidentally, differs from that given by Yahoo! Finance or from other sources and employed earlier in our analysis. But, if we use Eq. 11, we can, perhaps, get a better estimate for k. k = ($2.78/$81.25) + 0.21 = 24.42% We can now derive an estimate for the stock’s price in 2012 using Eq. 8: P2012 = $4.93/(0.2442 – 0.2100) = $144.15 The general model formulation is as follows: P2009 =

D2010 D2011 + P2012 D + + 2012 3 2 (1 + k ) (1 + k ) ( 1 + k )3

Therefore IBM’s intrinsic stock price for P2009 is as follows: P2009 =

$2.78 $3.36 $4.07 + $144.15 = $81.36 + + 2 ( 1 + 0.2442 ) ( 1 + 0.2442 ) ( 1 + 0.2442 )3

Thus we find a price of $81.36 for early 2009, which is slightly above the reported market price of $81.25. This means that the investor should consider buying the stock because it is undervalued. This finding also agrees with our previous conclusions that the company’s stock was undervalued. Using Earnings Instead of Dividends We begin with the relationship between a firm’s earnings and dividends. In general, a firm has three options with regards to disposing of its earnings: sRetain and reinvest it (denoted as rr as the retention ratio) sDistribute its earnings in the form of dividends (denoted as dr as the dividend payout ratio) sUse a combination of both (note that rr + dr = 1 by definition)

Equity Valuation and Investment Strategies s 347

Let us do some basic economic analysis for these three options. A company should decide to retain and reinvest all of its earnings only when it can earn a rate of return that is higher than its shareholders’ investment rate of return. This means that if the firm’s expected rate of return from investment (call it rate of return on equity, or ROE) exceeds the shareholders’ required rate of return (k), it would be optimal to retain and reinvest the funds. Why? Because future growth would generate higher firm value and thus higher dividends. By contrast, if shareholders can earn a return higher than the firm can offer, then paying out the earnings as dividends would be optimal for the firm. A company that does not have growth opportunities (but has a considerable amount of cash and distributes 100% of its earnings or free cash flow in the form of cash dividends) is known as a “cash cow.” In this case, its stock value can be determined by Eq. 9. The firm would not grow because no new investment (of capital) takes place, and its dividends would not grow either. But what would happen to the firm’s stock price if it retained some funds and distributed the rest as cash dividends? As we will see shortly, this situation would arise because future growth would be reflected in today’s stock price (the discounting factor). Following the above discussion, sustainable growth in dividends per share is determined by the firm’s return on equity (ROE) and retention ratio (rr) as follows: g = ROE × rr

(13)

As a reminder, ROE is computed as follows: ROE = profit margin × total asset turnover × financial leverage where profit margin is defined as the ratio of net income to sales, total asset turnover as the ratio of sales to total assets, and financial leverage as the ratio of total assets to equity. An investor must be able to create forecasts (estimates) of all three components of ROE in order to arrive at a reasonable estimate for his analysis. Let us redo the above analysis using the new long-run growth rate for the firm, as computed above. The dividend data remain the same as above. From the VLIS we see that the firm’s ROE is expected (forecasted) to be 45% and its dividend growth rate to be 26%.4 Thus the firm’s retention ratio, rr, can be computed as follows: rr = 1 – dr = 1 – 0.26 = 74%. Now we can derive the estimate for g: g = 45% × 0.74 = 33.33% Next, we need to compute or derive an estimate for k. Recall that employing the CAPM requires estimates for the 3-year Treasury note and, most importantly, the market’s return. Using Eq. 11 again, we obtain: k = ($2.78/$81.25) + 0.3333 = 36.75% As previously, we can reestimate the stock’s price in 2012 using Eq.8: P2012 = $4.93/(0.3675–0.3333) = $144.15

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Therefore the P2009 price for IBM stock is as follows: P2009 =

$2.78 $3.36 $4.07 + $144.15 = $61.79 + + 2 ( 1 + 0.3675 ) ( 1 + 0.3675 ) ( 1 + 0.3675 )3

Thus we find a price of $61.79 for 2009, which is much lower than the reported price of $81.25. This means that the stock is overvalued and the investor should not buy it (and should sell the stock if he has it in his portfolio). This is in contrast with what we found earlier, when the company’s price was undervalued. This analysis offers a powerful lesson. Given the different conclusions—albeit some marginal and one vastly lower—reached from the various equity valuation models, which one should the investor trust and use? Recall also that we made several assumptions in using each of these models that may not hold in the distant future. Also, different sources give different estimates. For example, the Yahoo! Finance source gives an estimate of future dividend growth of 13.15%, while the VLIS gives 21%. The starting or average price also differs between the two sources. Finally, consider the significance of sensitivity analysis (which you first learned in the corporate finance course), entailing a change in one model parameter and a redo of the entire analysis. For example, a small change in the firm’s required rate of return (k) may yield different results and conclusions regarding buy or sell decisions. Also, firm decisions as to what to do with earnings (reinvest or pay out as dividends, as we will see below) can have a tremendous impact on expected dividends as well as the firm’s required rate

S&P500 Price/Earnings Ratios 1902–2003 50 45

Linear Regression Channel 2-Year Simple Moving Average 5-Year Simple Moving Average

40

Prize/Earning Ratio

35 30 25 20 15

Median P/E - 15.17

10

0

20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02

5

Year

Figure 11.3 The S&P P/E multiple as a trading tool.

Equity Valuation and Investment Strategies s 349

of return. The bottom line is that the investor is presented with several challenges in estimating his own intrinsic stock value (if he wants to differ from the market’s consensus) and that he should not expect to identify easy bargains. Table 11.5 summarizes the above models and their predictions for IBM’s stock price. Therefore, once again, we conclude that the investor is faced with many uncertainties and challenges in equity valuation, which, at the same time, underscore the importance of having good and accurate inputs to valuation and selecting among competing asset valuation models. Now we continue with the general discussion of the use of earnings in lieu of dividends. Let us apply these concepts and Eq. 13 with an example. Assume that we have two firms, N and H. Both firms have a current dividend of $1 and a required rate of return 10%. If neither firm has growth prospects and both distribute all earnings as dividends, Eq. 9 would be applicable to determine their stock price: PN or PH = $1/0.10 = $10 Now, assume that firm H retains some funds, say 60% (so rr = 0.60), because some new capital opportunities have emerged; but it can reinvest in them with the expectation of earning 15% on its equity investment (that is, ROE = 15%). In this case, the firm’s growth rate (of capital) can be determined by Eq. 13 as follows: g = 15% × 0.60 = 9% Since firm H now has some growth opportunities, we can apply Eq. 8 to see what would happen to its stock price (relative to firm N, which does not have any such growth opportunities): PH = $1/(0.10 − 0.09) = $100 As you see, its price increased to $100 from $10! The rationale, again, for this sharp increase is that intended investments by the firm generated a rate of return (15%) greater than that of its shareholders (10%). This, in turn, enabled the firm to generate 9% more (future) income and 9% more dividends. Therefore growth prospects are positive for both the firm and its shareholders. The relationship between expected earnings per share, EPS1, and dividends can be algebraically defined as follows: D1 = EPS1(1–rr)

(14)

Note that EPS is derived by dividing the firm’s net income by the average (for the year) number of shares outstanding. Now let us substitute Eqs. 13 and 14 into Eq. 8 to derive two important conclusions.

P0 =

EPS1( 1 − rr ) k − ( ROE × rr )

(15)

350 s Equity Portfolio Management

If we assume that a firm has ROE = k, and this is possible for a firm that has an internal rate of return equal to its required rate of return or a (normal) firm that does not have growth opportunities. Therefore g is zero and we obtain the following expression: P0 =

EPS1 k

(16)

This equation simply implies that the firm’s value does not depend on its dividend policy. In other words, for a firm that has ROE = k, dividend policy is irrelevant for the firm’s value. This is the celebrated Modigliani and Miller (1958, 1961) dividend irrelevance theory in corporate finance.5 Their assumption was that investors already incorporate dividend information in the current prices and thus this would have no impact on the firm’s price. Only growth firms, firms that have ROE greater than k, can maximize their value by retaining all their earnings and reinvesting them. The implication is that paying dividends does not increase the value of the firm (or reduce the firm’s true stock value). What is the economics behind dividend payments? Economic theory suggests that growth firms that pay dividends do not maximize their stock values. Reality, however, tells us a different story. Growth firms such as IBM, Microsoft, and Coca-Cola do pay dividends. Some observers explain such behavior on market imperfections or other government-imposed restrictions (which requires some firms to invest in dividend paying firms, as mentioned earlier). At this point, you should read the Applying Economic Analysis box to learn other reasons companies have for paying (or not) dividends as well as to understand the opportunity cost of a dividend policy. Now let us further manipulate Eq. 15 to derive more insights. Taking EPS1 to the lefthand side of the equation, we obtain the following: P0 =

EPS1 k

(17)

Alternatively, by dividing both sides of Eq. 15 by EPS1, we obtain the following expression: P0 D /EPS1 = 1 k−g EPS1

(17)

where both of above equations represent the well-known price-earnings ratio (that is, the P/E ratio). This is another commonly approach used to value a stock. This is a multiple magnitude, which reflects the amount of dollars investors are willing to pay now for $1 of (future) earnings by the firm. IBM’s P/E ratio is reported to be 9.10 (per the VLIS) or 9.56 (per Yahoo! Finance). A high P/E ratio indicates a firm with high growth prospects, whereas a low P/E ratio indicates a firm with few growth opportunities. We can derive three insights from the above two equations: sFirst, we can obtain the expected dividend payout ratio, D1/EPS1 (which is equal to 1–rr) sSecond, that the P/E ratio rises with increases in ROE sThird, that the P/E ratio increases when rr increases (assuming that ROE is greater than k)

Equity Valuation and Investment Strategies s 351

Continuing with a blend of Eqs. 17 and 17’, we derive a mechanism of how cash dividend payout ratios affect the stock’s P/E ratio: P0 1 − rr 1 − rr 1 − rr 1 = = = = EPS1 k − g k − (ROE × rr ) k(1 − rr ) k

(18)

for ROE = k (or normal firms with a fair rate of return). This equation states that a firm’s cash dividend policy has no effect of the P/E ratio. This conclusion is similar to that derived above (the dividend irrelevance proposition, a rearrangement of Eq. 16. Investors must determine if they agree with the prevailing P/E ratio’s number before purchasing a company’s stock (that is, they must see if it is too high or too low, according to them) and compare it to other firms within the industry. Although this earnings multiple (or multiplier) is easy to obtain and interpret, it offers several additional challenges. First, the investor must have good estimates for the firm’s expected earnings. Second, what if a company’s earnings are negative? In this case, you would get a negative multiple which is not useful. Third, beware of earnings management (or manipulation) by companies when reporting their earnings figures. In general, we saw in the previous chapter the enormous amount of information the investor needs to consider (macro, industry, and now firm conditions) before attempting to forecast a firm’s earnings. Thus one needs to be cautious when using multiples (or relative valuation measures). How can we derive a firm’s P/E ratio when the firm does not pay any dividends? One way to avoid this problem is to recast dividends in terms of earnings (per share). Besides, companies that pay no cash dividends typically have earnings and, hence, price/earnings ratios. Therefore if you know the firm’s P/E ratio, required rate of return, k, and growth rate, g, you can derive the firm’s implied dividend payout ratio (D1/EPS1). Let us illustrate this it with actual IBM data. We will use information and numbers from our previous analyses also. We need to compute the current price, P2009, first. Using the above inputs for k and g and applying the constant growth model, we obtain a price of $67.25 (which again, is different from the previously obtained stock prices as summarized in Table 11.5) as follows: P2009 = $2.30/(0.2442–0.2100) = $67.25 Now we need to see if the alternative models, based on earnings, can give us an approximate value for the company’s price found above. We start with the P/E ratio. P0 /EPS1 =

D1/EPS1 $2.30/7.25 = = 9.2 times k−g 0.2442 − 0.2100

This P/E value is vey close to the actual figure (of 9.1) as reported in the VLIS. Then we multiply IBM’s P/E ratio found above by the estimated EPS1, 7.25, as given by the VLIS, to derive an estimate for the company’s price: Estimate for IBM stock price = EPS1 × (P/E) = $7.25 × 9.2 = $66.70 which is very close to the value found above, $67.25. Thus getting around lack of expected dividends with expected earnings can yield satisfactory estimates.

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To conclude this section, let us demonstrate the relationship between the constant growth model and the price/book value (PBV) general valuation model. Start with Eq. 15 and substitute the expressions for the expected dividend, D1, using Eq. 14, and replacing EPS1 with an expression with current EPS, EPS0, just as we do in deriving future dividends (that is, an expression similar to the one in the numerator in the first term of Eq. 7) and then rearrange: P0 =

EPS1(1 − rr ) (1 − rr ) (1 + g )EPS0 = k−g k−g

Since EPS0 equals book value (BV0) per share times ROE, we substitute this expression above to obtain: P0 =

(1 − rr )(1 + g )(ROE/BV0 ) k−g

Thus, dividing both sides by BV0, we obtain the PBV ratio as follows: (1 − rr )(1 + g )(ROE) P0 = k−g BV0

(19)

This equation states that as ROE increases, ceteris paribus, the higher the PBV ratio for the firm. Also, the higher the firm’s dividend payout ratio (1–rr), ceteris paribus, the higher the firm’s PBV ratio. What is the interpretation and significance of Eqs. 16 and 19? The important principle is that stocks (given similar growth rates, payout ratios, and risk) with high P/E ratios are overvalued and stocks with low P/E ratios are undervalued. The investor can carry out her analyses of valuing stocks relative to other stocks in their industry based on their P/E ratios. The conclusion she should reach is to buy the stocks with low P/E ratios (because they are undervalued), and sell the stocks with high P/E ratios (because they are overvalued).

OTHER EQUITY VALUATION TECHNIQUES In this section, we present some other stock-valuation methods that are not based on dividends or earnings, but on the firm’s cash flows or other magnitudes. We stated in the beginning of this chapter that, in theory, the value of an asset is determined by its future cash flows. The determination of cash flows, however, needs a more careful analysis because of items such as noncash expenses and also because we need to understand which type of cash flow we are analyzing. Let us begin with a discussion of the firm’s operating cash flows and free cash flows. Present Value of Free Cash Flows In general, a firm’s cash flow from assets can be decomposed into three parts: operating cash flow, change in working capital, and capital spending. Operating cash flow (OCF) refers to the cash flow (in and out) occurring in the firm’s daily operations. Specifically

Equity Valuation and Investment Strategies s 353

operating cash flow equals earnings before interest and taxes (EBIT) times (1–tax rate) plus depreciation. In accounting practice, unfortunately, OCF is often defined as net income plus depreciation. However, we will employ the former definition in our analysis. Operating cash flows to the firm are the cash flows including any debt obligations (financial leverage). In other words, there can be leveraged firms (those with debt obligations), and unleveraged firms (those with no debt obligations). There are two types of free cash flows, free cash flows to firm and free cash flows to equity. Free cash flow to the firm (FCFF) is the cash available to all of the firm’s investors, share- and bondholders alike, after the firm has paid for operations and (short-term and capital) investments. A firm’s free cash flow to equity (FCFE) is derived by subtracting the firm’s debt obligations from FCFF. These cash flows are termed free because they reflect the bottom line in the firm’s cash flows (after all obligations to other investors have been accounted for). Hence these free cash flows are available to equity owners (in the form of dividends, for instance). Once these flows (FCFE and FCFF) have been computed, the analyst discounts them at two different costs of capital (discount rates). Specifically, for the FCFE the appropriate discount rate is the firm’s usual (risk-adjusted) cost of equity, k. Thus, to find the value of the firm, V0, the relevant formula is as follows: V0 =

n

FCFF

∑ (1 + k )ti

(20)

i =1

By contrast, the valuation using the firm’s FCF at time t must be done using the firm’s weighted average cost of capital (WACC) because it includes both equity and debt items, as in the following general formula: V0 =

n

FCFF

t ∑ (1 + WACC) i

(21)

i =1

In sum, whereas the value of a firm’s equity (FCFE) is discounted at the firm’s required rate of return on equity (or cost of equity, k), the FCFF to investors is discounted at the firm’s WACC. FCFE is best suited for companies whose capital structure is rather stable, whereas FCFF is the best choice for companies with negative FCFE and substantial debt burden. A less subtle and practical way to derive a firm’s share price when the firm does not pay any dividends is to use the firm’s free cash flows (as derived above). Then these cash flows are divided by the number of shares outstanding in order to derive a share value. Options Valuation Approach We know that when a firm goes bankrupt, its shareholders are paid last and with whatever is left of the firm’s assets. In case the firm’s liabilities fall short of the assets, shareholders (owners) have the right to sell these assets to the firm’s creditors (so that they get paid). Stated differently, shareholders have a put option on these assets with an exercise price equal to the payments to the creditors. In the case the liabilities exceed the assets, then shareholders get nothing and creditors get to keep these assets (as partial

354 s Equity Portfolio Management

payment). Stated differently, creditors own the company and sell a call option on these assets to the firm’s shareholders. The exercise price of this option is equal to the par value of the firm’s debt. If the firm’s assets are inadequate to repay all debts, the shareholders will let this option expire worthless and thus surrender all assets to the firm’s creditors. To summarize, shareholders and creditors are seen to hold options on the firm’s assets as follows: If assets are greater than liabilities, shareholders (owners) own a put option on assets If assets are less than liabilities, bondholders (creditors) own a call option on assets Shareholders might be able (or have an incentive) to exploit creditors from such an option clause on the firm’s assets. Specifically, knowing that the firm’s value is the discounted (or present) value of its assets (A), this value will be equal to the sum of equity (E) and debt (D). Then shareholders have an incentive to increase A by taking actions that decrease D, ceteris paribus. Because E is the value of a call option on A, actions that raise the value of E will have to lower the value of D. This discussion reminds us of the

Box 11.3 Economic versus Accounting Profit In general, profit can be defined in a variety of ways. For example, profit might be the difference between revenues and expenditures. Alternatively, profit might be the monetary gain or return from an investment after all costs (charges) have been deducted. However, the notion of profit takes on a different meaning in trying to compute an economic profit or an accounting profit. Accounting profit is the difference between a business’s total revenues and total expenses. Expenses include all explicit costs of making and providing the good or service as well as depreciation and taxes. Thus, accounting profit = total revenues–explicit costs of production. By contrast, economic profit is the difference between the total revenues minus the explicit and implicit costs of production or the opportunity cost of resources available to the operation of the business. For example, such costs include the value of the business owner’s time and labor services, if not explicitly accounted for, as well as the foregone interest in assets not tied with the business itself. Thus, economic profit = total revenues–explicit and implicit costs of production. Here is an example to show the different results in computing profit under the economic and accounting sense. Assume that you are employed as a delivery person earning $20,000 per year, you own a van that can be rented for $2,000 per year and earn $1,000 interest on your bank accounts. You decide to quit your job and make deliveries yourself, using your van and keeping all the profits. Assume that your business generated revenues of $70,000 in a year, while its expenses (such as the cost of items to be delivered, utilities, gas, taxes, and advertising expenses) totaled $50,000 in that year. Taking the difference between the total revenues ($70,000) and total explicit costs ($50,000) would give you an accounting profit of $20,000. But you forgot to include the opportunity costs of doing this business, which include the lost wages of $20,000, the van’s rental fee ($2,000), and the interest foregone ($1,000). Adding these up as well and subtracting from the total revenues would give you a loss of $3,000! Thus, you incurred a loss and not an economic profit. Such is the power of the opportunity cost of resources.

Equity Valuation and Investment Strategies s 355

agency problem we discussed in the first part of this book, and that is why creditors take protections from such undesirable actions by shareholders. We will discuss some of these protective covenants, embedded in debt instruments, in the next chapter. Economic Profit Another important metric for a firm’s value is the economic profit (EP) or economic value added (EVA) notion, trademarked by Stern Stewart & Co. EP is simply the difference between net operating profits after taxes (NOPAT) and the capital charge. Specifically, NOPAT is (adjusted) earnings before interest and taxes (EBIT) after subtracting cash operating taxes. For companies that have no debt and thus no interest expense, NOPAT is equal to net profit that would accrue to shareholders (after taxes). Note, however, that NOPAT includes the cost of debt and equity capital. The capital charge item is calculated by multiplying the firm’s invested capital by its weighted average cost of capital (WACC). This invested capital represents some “rental fee” the company pays for using capital (rented by both shareholders and debt holders). Stated differently, invested capital is what investors require in order to make their investment worthwhile. This, in turn, is adjusted by the firm’s WACC. Summing up, economic profit is expressed as follows: Economic profit (EP) = NOPAT – (invested capital × WACC) An alternative way to express EP is the following: EP = (ROIC – WACC) × I

(22)

where ROIC is the return on invested capital (I). The difference between ROIC and WACC known as the economic spread, which suggests that a firm adds value when ROIC exceeds WACC. Some professional investors also suggest computing EP based on expectations. This approach is known as Expectations-Based Management (EMB), trademarked by the MonitorGroup. EBM is defined as follows: EBM = actual EP – expected EP Finally, EP can also be viewed as the portion of the firm’s free cash flows (FCF) after subtracting the capital charge. Specifically, EP looks at the FCF valuation differently by discounting the expected (forecasted) FCF by WACC and adding back the invested capital: EP = (FCF/WACC) + invested capital One advantage of the EP approach is that it helps management to define a firm’s value and makes management realize that any additional invested capital that returns above WACC is desirable and adds value to the firm. At this point understanding the various definitions of the term profit and contrasting them with its uses among economists and accountants is important. Box 11.3 discusses the differences between “economic profit” and “accounting profit”.

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OTHER ISSUES IN EQUITY VALUATION In this section we explore some important issues that arise when an investor values assets (or stocks in this case) and discuss their impact on the derived values of the assets examined. The first issue is the impact of inflation on stock prices, the second deals with the information content of cash dividends, and third, other issues as to when to buy/sell a stock and what additional information (use) the P/E ratio contains when used to value the aggregate stock market. The Impact of Inflation on Stock Values During the past 30 years or so, researchers have generated much empirical evidence on the impact of inflation on equity prices. Inflation refers to the rise in general consumer prices in the economy during a year (as measured by the consumer price index, or CPI). In theory, the fundamental equation called the Fisher equation implies that nominal interest rates move in tandem with (expected) inflation. Remember that the nominal interest rate is approximated by the real interest rate plus expected inflation. Consequently, when inflation increases interest rates also rise and typically depress stock prices. Furthermore, in theory, stocks should be inflation-neutral, meaning that rising inflation should have no impact on their values. The rationale for this argument is that companies are able to set prices according to inflation and that the real interest rate investors use to discount cash flows remains unchanged with inflation (this also follows from the Fisher equation). The counterargument is that inflation does impact the real interest rate because rising inflation lowers expected earnings (and also increases the equity risk premium) and raises required (real) returns.6 Further, Fama and Schwert (1977) find that investors cannot use stocks as a hedge against expected inflation (proxied by the ex ante interest rate) and document a negative relationship between the two magnitudes.7 Further empirical evidence corroborates the above findings for other industrial countries. In the short run, stock prices generally move inversely with inflation, but in the long-run stock prices adjust to inflation, suggesting that inflation has no impact on asset growth. Inflation also inversely impacts the P/E ratio. The basic argument for this relationship is that during low inflation and interest rates, companies have more opportunities for growth and thus real earnings, making investors more willing to pay for the firm’s expected earnings. Thus the firm’s P/E ratio rises. Alternatively, when inflation is rising, investors require a higher rate of return (to maintain, at least, their purchasing power) meaning that the P/E ratio has to fall. Investors might think that inflation benefits companies (because they increase their earnings and profits) but reality is different. Corporations typically prefer stable prices because rising prices also mean rising costs, lower inflation-adjusted earnings, and erosion of their P/E ratio. Investors need to understand the impact of inflation on equity prices in order to apply appropriate (according to them) investment (or allocation) strategies. For example, from a strategic perspective, they might have to invest in stocks (securities) that preserve capital (or their purchasing power) such as inflation-indexed securities during inflationary periods. Information Signals/Content of Dividends In general, dividend decisions convey information about a firm’s future earnings prospects. Theoretically management’s dividend decisions should be based on the firm’s long-run (and sustainable) earnings capacity. Then, dividends may convey signals about

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the quality of earnings. Prior empirical literature has investigated the information content of dividends but little agreement on the findings has been reached. An early study by Lintner (1956) found that most corporations try to smooth out cash dividend payments consistent with their firms’ long-run earnings trends. Also, managers are hesitant to decrease dividend payments or, at least, change the regularity of such cash payments.8 Later studies also reached similar conclusions. For example, Miller and Rock (1985) found that changes in dividend policy conveyed information about the firm’s future cash flows (that is, if dividends increased then future cash flows would decrease). Benartzi et al. (1997) also found that firms that decreased dividends experienced increases in growth rates in the 2 years following the dividend decrease. However, this evidence contradicts the central theory of the dividend signaling hypothesis (see Grullon, Michaely, and Swaminathan, 2002).9 Grullon et al. related dividend changes to a firm’s life cycle and hypothesized that stock returns respond to changes in the firm’s systematic risk following a change in dividend announcement period. They found that firms that increase dividends experience a significant decline in their systematic risk. However, substantial changes have occurred in corporate dividend policy over the last 30 years. Fama and French (2001) report that the proportion of US firms paying regular cash dividends has declined dramatically since 1999. Grullon and Michaely (2002) also document a decline in the dividend payout ratio.10 Some authors attribute this to the lower information content of dividend announcements. Alternatively, investors are now more sophisticated and informed, which enables them to profitably exploit such dividend information. Others posit that the recent scandals that have erupted in major corporations, where managers falsely presented a rosy picture of their companies’ financial strengths, have made investors suspicious of dividend announcements. Finally, despite the Modigliani-Miller (1961) dividend irrelevance theorem, dividend news does carry meaningful information to investors. Since investors typically do not have more information than the company’s managers (that is, there is asymmetry of information), investors should pay attention to dividend announcements (signals) to infer future intentions of the company’s management. Besides, obtaining information on the company’s expected earning power is important for outside investors attempting to determine the company’s value and/or its stock price. The P/E Ratio and the Stock Market How else can we define the general P/E ratio? It is the ratio of the firm’s market price per share over the firm’s annual earnings per share: P/E =

market price per share annual earnings per share

(23)

Let us concentrate on the denominator of the ratio, the annual earnings per share. Recall the derivation of EPS, which is the ratio of the firm’s net income by the firm’s average number of shares outstanding. If the net income value used in the equation is for the most recent year (past four quarters), the ratio would be the trailing P/E. The trailing P/E ratio is the one most commonly used by analysts. By contrast, if the EPS figure was derived using a firm’s estimated net income (over the next year), the P/E ratio would show the forward or leading P/E. As an example, consider a company that has reported

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Figure 11.4 Value Line Investment Survey Report: International Business Machines. Source: Capital IQ

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an EPS of $1 over the past 12 months and the company’s current stock price is $20. The trailing P/E ratio would be $20/$1 = 20. If analysts predict an increase in the company’s EPS, say, by $0.25 per share next year, the forward P/E ratio would be $20/$1.25 = 16. Thus you see that the company’s stock is currently a bargain for investors, ceteris paribus. Which one of these two ratios or multiples should you use to value a stock or to decide whether to buy or sell a stock? First of all, each ratio has its own merits and drawbacks, and the ratio can be manipulated (via various accounting practices) by a company to show a different picture that what it actually is. Second, the trailing P/E ratio would give you a more accurate picture of a stock because it uses actual figures relative to the forward P/E ratio, which uses estimates or projected figures (these can be wrong or updated frequently). Third, it might be prudent to look at both ratios to see how they fared over time, and if you observe a divergence between them, you might want to learn more about the company’s valuation process. An interesting question arises at this point. If we can have P/E multiples for a stock can we also have one for the aggregate stock market? Yes, there is one for the equity market. Recently, economists have suggested that the average P/E ratio for the S&P 500 Index can help to predict long-term changes in the index. Specifically, they contend that a high/low P/E ratio was followed by rapid/slow growth in stock prices in the next several years. Figure 11.5 shows the P/E ratio for the S&P 500 Index from 1960 to 2008. We see the fluctuations in the ratio for several turning points in the economy. For example, the ratio rose to an all-time high in 2000 but then fell dramatically with the bursting of the tech bubble. The reciprocal of the P/E ratio is known as the earnings yield for the S& P 500, and we infer that it falls as the P/E ratio rises. For instance, during the 1980s, inflationary pressures eased and the earnings yield declined as the P/E ratio was increasing (see Figure 11.5). A rule of thumb for predicting the future level of the S&P 500 Index is to multiply the earnings yield by the earnings per share (EPS), assuming that the earnings yield, historically, runs a percentage point below the 10-year Treasury bond. For example, the S&P 500 EPS forecast in December 2009 was about $61 (based on S&P 500 data), while the forecast for the earnings yield was 4.6%. Such an earnings yield would imply a P/E ratio of about 22; thus a forecast of the future level of the index would be 22 × 61 = 1,342 points. The actual value of the index a year later (December 2010) was 1,258 points. As you see, several guesses entered the above calculation method; thus an investor must always be careful with the inputs or estimates he uses. A slight variation of the rule of thumb is the so-called Fed model, the name that Edward Yardeni of Prudential Securities gave to it. This model assumes that (in equilibrium) the real yield on the 10-year T bond should be similar to the S&P 500 forward earnings yield (as computed above). The forward earnings yield is the ratio of next year’s earnings forecast to the stock market value today. Thus differences between the two yields should indicate whether the stock market is undervalued or overvalued and thus suggest an investment strategy. Specifically, if the S&P forward earnings yield exceeds that of the T bond, this would imply that the stocks are undervalued and investors should buy more stocks (and dump Treasuries). The opposite would be true of the earnings yield was less than the T bond. The 10-year T-bond yield during the same period was about 3.84%. Thus, using the above figures, the model would suggest that the S&P 500 is undervalued because the S&P 500 yield, 4.6%, exceeds that of the 10-year T bond, 3.8%. The overall message from the analyses here and above is that equity valuation, based on fundamental analysis, is challenging and that other relative valuation measures are

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Box 11.4 Determining When to Buy and Sell Stocks USING THRESHOLDS Some people use thresholds or percentages of advances or declines of stock markets, measured by an index, to buy and sell. For example, one such threshold system (known as the common sense system) calls for buying stocks at thresholds of 10% declines and selling on 25% increases of the Nasdaq.* * See James B. Stewart, Wall Street Journal, January 14, 2009.

USING FUNDAMENTAL ANALYSIS Determine your objectives and constraints first. Then research the company you are interested in investing. This entails conducting fundamental analysis by examining the company, the industry, and the economy as a whole. If you are convinced this is a solid company, then purchase shares to include in your stock portfolio.

USING QUALITATIVE FACTORS Examine the company’s management. In other words, examine the five W’s for a company: who, where, what, why, and when.* Who is at the helm of the company? Where has he or she been before joining this company? What is the management’s philosophy and when did the management team take over the direction of the company? Finally, why is this team at the helm? In addition to the above factors, examine the company’s product as well. Is it a brand name Does it sell well? And so forth. * See Stock-Picking Strategies Tutorial, investopedia.com

USING OTHER CRITERIA Investors can select stocks based on multiples such as P/E ratios, PEG (P/E ratios divided by the stock’s growth rate) ratios, and other financial ratios such as liquidity, profitability, and asset and debt management. The objective is to see the path of a company’s financial health or weakness over time and in relation to its industry. Then the investor would pick stocks based on value, growth, or income investment objectives.

simply rule-of-thumb (heuristic) measures. The investor should be aware of these valuation measures’ shortcomings before applying them to value equities within the context of market efficiency. Such models have often failed to explain (or even predict), for example, the overall market declines in the late 1990s and the financial crisis of 2008. Kamstra (2003) discusses equity pricing (and most of the models presented above) on the basis of fundamentals and concludes that such analyses should be the start rather than the end to valuation. Malkiel (2003) also discusses the challenges posed by market efficiency and comments on the predictive power (or lack thereof) of some relative valuation models such as the dividend yield and P/E ratio over the past decade or so.11

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SOME STRATEGIES ON WHEN TO BUY/SELL EQUITIES In this section, we present (without endorsing) some common trading signals (guidelines) for equities that rely on technical and fundamental analyses. These refer to the timing of the stock market so as to earn the maximum possible return. Again, these guidelines should not be blindly applied, however, and should be properly evaluated before being adopted for consistency. After finishing reading the section, be sure to read Box 11.4, which offers some perspectives on when to buy and sell stocks these days. When to Buy/Sell a Stock You have heard the motto “ ‘buy low, sell high,” which financial advisers give their clients, and the occasional tips for “hot stocks,” implying that you should immediately buy these stocks because they are “good bargains.” The trouble is knowing what is low and what is high, and it may be too late to buy that “hot stock” because other investors have noticed it as well. As a result, a hot stock’s price would have risen and you might end up buying the stock at a higher price than otherwise. Further, jumping from one stock to another can be classified as anything but investing! Such short-run behavior by investors has both risk and tax consequences. Recognize that a low price of a stock (prompting you to sell it, if you own it) has to do with other factors than a trading signal or a rush to sell, which you habitually follow. In general, sound sell/buy decisions must be made on the basis of a comprehensive economic analysis and not just on the current price of the stock. Perhaps, a rising stock price may be a signal to sell and a falling price a signal to buy. These decisions rest with real investors who invest for the long run. Investors might also follow common yardsticks relative dividend yields and cash dividend (yields) as guides for a buy or sell triggers. For example, some investors calculate a stock’s dividend yield and compare it to the market’s dividend yield to decide whether to buy or sell it. Thus, if a stock’s yield is much higher (at least 50%) than the market’s, they may buy the stock. Other investors observe the path of the market’s cash dividend yield for trading opportunities and act upon it based on some predetermined levels. For example, when the yield reaches 5% or above, they tend to buy; but when it falls below 3%, they interpret it as a sell signal. The common belief is that the market’s cash dividend yield has a floor of 3% unless most of the stocks in the index must be overpriced. The S&P 500 Index’s average historical dividend yield ranged between 3% and 4% over the last 50 years or so. From December 1936 through March 31, 2008, the average yield for the S&P 500 was 3.83%.12 In any event, the above strategies ignore fundamental magnitudes such as past and expected earnings, the state of the industry and the economy as well as other indicators such as P/E ratios. A similar trading rule involves the market’s P/E ratio (as described in the previous discussion), and when stocks are selling for less than a certain critical multiple, investors think that the market is underpriced. If that multiple is more than the critical one, it suggests a buy. Optimists (i.e., bulls) have proclaimed that such ratios were irrelevant (in the 1920s and 1990s) and pessimists (i.e., bears) argued that they were relevant (in the 1930s and 1980s). In all instances they all had missed the target. One commonly used trading tool is the P/E simple moving average (first introduced in Chapter 9) because by averaging past values, any noise in the series (i.e., stock price) is smoothed out, allowing the user to see the big picture. As an example, the S&P’s P/E ratio based on Shiller’s data is used to construct a chart and a simple moving average path (or

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trigger) that would identify a buy or a sell opportunity.13 This graph is shown in Figure 11.4 for the P/E ratio, the 1-year moving average (MA1), and the 3-year moving average (MA3) for the period of January 1960 to October 2011. Buy signals are implied when the 1-year simple moving average (green line) crosses above the 3-year average (red line) and sell signals are suggested when the 1-year line crosses below the 3-year line. The median P/E for the period shown was 19.35. In general, based on these tests, a 1-year moving average signal was good at removing excessive noise in the series whereas the 3-year signal line was found to provide the same number of trades but with lower returns. In general, in using technical analysis to identify trading signals, two lines, an upper and lower, can be drawn within which a stock tends to trade. Specifically, the upper line, the resistance line, represents the price(s) where people bought the stock in the past. A technical analyst would look for a breakout upward through that line before producing a buy signal. The other line is the support line, which represents the series of closing prices that have not broken below it. Again, the analyst would look for a breakdown downward through the support line before issuing a sell signal (assuming, of course, that the movement was sustained). Although there are several other equity trading strategies and new ones are published in the media often, we chose to present three more here: the “dogs of the Dow,” “day trading,” and “swing trading.” The dogs of the Dow equity trading strategy emerged in the 1990s and is considered a contrarian strategy focusing on 10 value stocks of the DJIA Index that have the highest dividend yields and lowest P/E ratios. Some concerns about this strategy revolve around the use of the DJIA benchmark relative to another one like the S&P 500 Index, ignoring the risk aspects of the selected stocks and the investor’s assumed investment horizon. A day trader is one who trades stocks (or futures) within a day and frequently so. The advantage of this technique is that traders limit their exposure

70.00 60.00 50.00 40.00 30.00 20.00 10.00

03 /3 12 1/19 /3 6 09 1/19 0 /30 61 06 /19 /3 6 03 0/19 3 /31 65 12 /19 /3 6 09 1/19 7 /30 68 06 /19 /3 7 03 0/19 0 /31 72 12 /19 /3 7 09 1/19 4 /30 75 06 /19 /3 7 03 0/19 7 /31 79 12 /19 /3 8 09 1/19 1 /30 82 06 /19 /3 8 03 0/19 4 /31 86 12 /19 /3 8 09 1/19 8 /30 89 06 /19 /3 9 03 0/19 1 /31 93 12 /19 /3 9 09 1/19 5 /30 96 06 /19 /3 9 03 0/20 8 /31 00 12 /20 /3 0 09 1/20 2 /30 03 06 /20 /30 05 /20 07

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Figure 11.5 The S&P 500 Index's P/E ration, from March 1960 to June 2007.

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to any asset but incur substantial commission (trading) fees because of their frequent trading. Finally, a swing trader is a trader who trades in a stock (or options and/or futures) and attempts to capture the maximum gains in a financial asset that has a large gain potential within a few days. The advantage of this (technical) strategy is that the trader has no competition in the market and incurs fewer commissions, relative to day trading, whereas a disadvantage is the necessity to follow the market very closely and act quickly on it to avoid large exposures. What is an overall evaluation of these (or all, for that matter) trading strategies? These are not always “investment” strategies but rather short-term strategies designed to capture temporary deviations in the assets’ prices. As mentioned before, an investor is one who invests in the long run and does not care about the short-run ups and downs of the market. If investors purchased the stock, when should they sell it? In general, if one of the initial assumptions that led to the purchase of the stock in the first place is no longer valid, this may be time to sell the stock (after an evaluation of all parameters has been performed). One guide is the stock’s intrinsic value. If the stock’s current value moves away from its intrinsic value, it is time to reconsider the stock. You might also want to read again the Lessons of Our Times box in Chapter 10 to remember what it means to find a “hot stock” and what its implications might be.

CHAPTER SUMMARY In this chapter we presented methods to value an equity asset by focusing on company analysis. In this effort, we presented several valuation techniques including relative valuation measures (for example, book value, price/sales, liquidation, and replacement value measures) and the basic equity valuation model, the dividend discount model, and some of its variants, including the constant growth and the multistage dividend growth model. We recast the analysis using earnings instead of dividends in order to derive important relative valuation measures such as the P/E and the price-to-book ratios. We also examined the information content of cash flows, the option valuation approach, and the economic profit valuation metric. In all illustrations, we used real data on IBM and showed how these models can be used to derive a company’s fair stock price. We extended our analysis to include some discussion on some issues on equity valuation, such as the impact of inflation on stock values, the importance of dividend signals, and the use of the price/earnings ratio to predict stock market indexes. Finally, we concluded with the presentation of some equity trading strategies and highlighted their advantages and disadvantages. What is the overall message of this chapter? We showed that there are several equity valuation models, each of which yielded different results in valuing a stock. Thus an investor is faced with many challenges in trying to compute a stock’s intrinsic value with a view to deciding whether to buy or sell it. Additionally, if the investor wants to use relative valuation measures, he should also be aware of their shortcomings, especially within the context of fundamental analysis and market efficiency. Therefore the investor must exercise caution in attempting to value a firm’s stock or follow the presented strategies on when to buy or sell a stock. There are always many factors that affect the inputs in a valuation model, and these factors never remain constant.

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APPLYING ECONOMIC ANALYSIS TO GIVE OR NOT TO GIVE DIVIDENDS? TO CUT OR NOT TO CUT DIVIDENDS? Determining an appropriate dividend policy is not an easy task for a firm’s board of directors. The primary objective of management of a corporation is to maximize shareholder wealth. Research indicates that dividends serve as an indicator of the company’s present and future economic performance, given risk, and expected dividends are the main determinants of the market price of a share of stock. Management often views stability in dividend policy as necessary to remove uncertainty in investor expectations and misvaluation of their stock price with unpredictability in dividend payments. Often, a decrease in dividends results in a reduction in the firm’s stock price. For example, US auto manufacturers (e.g., GM) and giant financial firms (e.g., J. P. Morgan Chase) cut dividends during the financial crisis of 2007 and saw their share prices plummet. However, as earnings recovered a couple years later, both firms increased their dividends. Companies face an opportunity cost in deciding what to do with their earnings (or free cash). But there is no general agreement as to what they should do with that cash. There are several competing theories about dividend policy. The “dividend irrelevance” theory states that regardless of whether a firm pays dividends, the value of the firm’s stock will not change because a firm’s investment decisions are independent of its financing decisions. The “bird in the hand” theory states that investors have a preference for a certain dividend stream than to a future (and uncertain) price appreciation. The “tax-preference” theory maintains that investors prefer companies to retain funds rather than to give out as dividends so as to avoid unfavorable tax liabilities. The “signaling” hypothesis indicates that dividends offer signals about the firm’s future growth opportunities or lack thereof. The “agency problem” theory asserts that paying dividends many force firms to obtain external financing, which can result in a conflict between management and shareholders. Thus the question of whether a firm should to pay dividends or cut them is complex. These decisions are left to the firm’s board of directors’ discretion following management’s recommendations. In theory, another matter to consider concerns the opportunity costs of funds: if the firm’s expected rate of return on equity exceeds that of its shareholders, the company might be better off retaining and reinvesting the earnings. In the opposite case, the company might decide to pay dividends (or repurchase its stock). For more competing theories on this issue, see H. Kent Baker, Dividends and Dividend Policy (Hoboken, NJ: John Wiley & Sons, 2009).

INTERNATIONAL FOCUS FAIR-VALUE ACCOUNTING The financial crisis of 2007 unmasked several weaknesses in the application of fair-value accounting standards (which requires companies to mark assets to market value) as well as with the valuation and reporting of certain structured financial products. A dispute between the United States (US Financial Accounting Standards Board, FASB) and the London-based International Accounting Standards Board (IASB) threatens to disrupt efforts to achieve a global

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standards convergence affecting how trillions of dollars of financial assets are marked on the financial institutions’ balance sheets. The US FASB wants to expand the use of fair-value accounting to all financial assets, in contrast to the IASB, which wants to limit its use. For example, if the FASB gets its way, then 26 largest US banks could write down nearly $4 trillion worth of loans to $138 billion. According to Paul Volcker, a former chairman of the Federal Reserve and head of a group that oversees IASB, one common accounting standard would be better for global corporations. Thus, harmonization of such standards would enable investors and regulators to better compare lenders worldwide. Differences in fair-value accounting could skew banks’ calculations of risk-adjusted assets and equity ratios implying that European and American banks with identical loans could end up with different capital ratios. Moreover, during economic downturns, procyclicality of fairvalue accounting could force banks to recognize losses immediately, thus affecting their capital adequacy and triggering the sale of assets, thus turning prices and valuations down even further. By contrast, under traditional accounting, such losses would be registered in the books slowly. Both bodies are reportedly moving toward a middle ground by allowing banks that hold loans to maturity to be valued at their original price. Further proposals would allow banks move assets to a different part of their balance sheet so as not to mark them to market values. Sources: Fair-value accounting, The Economist, 2008. A. Novoa, J. Scarlata, and J. Solé, Procyclicality and Fair value accounting, BIS, working paper, 2009, https://www.bis.org/bcbs/events/cbrworkshop09/novoascarlatasole.pdf. Y. Onaran, Fight over fair value in global finance making Volcker rue FASB dissonance, Bloomberg online, 2010.

LESSONS OF OUR TIMES FINANCIAL CRISES: TIME TO BUY? There are many voices telling investors what they should do. Sell, so you limit your losses. Buy, because it is the right time to do so and buy low. Well, Warren Buffet announced that he is buying stocks. He gave a contrarian advice by saying that you should buy when others sell and vice versa. He also cautioned against trying to predict he market. He said that he had no idea as to what the market will do in a month or a year from now but one thing is almost certain: that the market will continue trending higher. What about market psychology? It is very important, Buffett contends. Look at the VIX or the volatility index, for example, which measures investor anxiety. This measure shows how much investors are prepared to pay to protect against future declines in the S&P 500. When its value becomes high, market anxiety is high. Another measure of anxiety is the Treasury bill yield. For example, on December 9, 2008, the 1-month Treasury bill yield turned negative. This effectively means that investors were willing to pay (a known amount) in order to keep their funds safe rather than risking losing much more by investing in riskier assets. Such extreme market conditions typically signal a rebound and thus, perhaps, a time to buy. How about the S&P 500 P/E ratio as a predictor of future bubbles? Shiller, in his book Irrational Exuberance, noted the very high values of that multiple right before the major stock market crashes, the 1930s and the 2000 tech bubble. The idea is to look at the profit cyclicality of the ratio when viewed over long periods of time. The predictability of that ratio was also good for the real estate bubble of the 2007–2008.

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A final measure signaling expansions or recessions is Tobin’s q ratio. This measure is simply the ratio of a company’s market value to its replacement value (cost). If this ratio is applied to the entire stock market, it would be the ratio of the value of the stock market over the corporate net worth. For example, if the company’s q ratio is less than 1, it would suggest that the company is undervalued and thus a good buy. Over time, the value of the company should tend to converge to 1. Sources: The New York Times, Oct. 16, 2008. Reuters, Dec. 15, 2008. John Authers, Bear market: time to buy? FT.com, November 9, 2008.

KEY CONCEPTS The intrinsic value (price) of a stock is the present value of the firm’s total expected net cash flows discounted by the firm’s (risk-adjusted) required rate of return. The total book value of a security is the net worth of the company as recorded in the company’s balance sheet. The price/book value is calculated by dividing the market price per share for the stock by the book value per share for the stock. The liquidation value measure represents the cash value an investor would receive if the company were to be liquidated. The replacement value, or Tobin’s q, refers to the cost incurred if the firm (and its existing assets) were reproduced at market prices. The dividend discount model states that the current price of a stock should equal the present value of the expected dividends in infinity. The constant-growth model (or the Gordon model) is the infinite-period dividend discount model. The price-earnings ratio is the ratio of the earnings per share over the stock’s price. Free cash flow to the firm (FCFF) is the cash available to all of the firm’s investors after the firm has paid for operations and (short-term and capital) investments. Free cash flow to equity (FCFE) is derived by subtracting the firm’s debt obligations from FCFF. The economic profit or economic value added notion is the difference between net operating profits after taxes and the capital charge. The resistance line represents the price(s) where people bought the stock in the past. The support line represents the series of closing prices that have not broken below the support line. The dogs of the Dow equity trading strategy focuses on 10 value stocks of the DJIA Index that have the highest dividend yields and lowest P/E ratios.

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A day trader is one who trades stocks (or futures) within a day and frequently. A swing trader is one who trades in a financial asset and attempts to capture the maximum gains in a financial asset that has a large gain potential within a few days.

QUESTIONS AND PROBLEMS 1. Based on the following paragraph, answer the questions that follow. I am upset that my favorite stock, which I owned for a very long time, has decreased in value. If its price continues to fall, I am thinking of selling the stock. Should I hold onto the stock hoping that it will quickly rebound? Should I sell it and invest the proceeds in another instrument such as a mutual fund? An index fund may do better than a single stock. What are other differences (such as risks and benefits) between owning a stock or even a small stock portfolio and investing in a broad (market) portfolio via a mutual fund? I think that a single stock or a portfolio is riskier (than the index of stocks) and it involves considerable time and effort (as well as money) to keep track of it. Can I beat the market with my stock portfolio? Besides, how do I know that I have picked the right (i.e., undervalued) stocks in my homemade portfolio? Am I better at picking winning stocks than other people, even professional managers? Finally, what do I believe about the market if I decide to build a stock portfolio and not simply go with the general market? a. Can you devise a “good time” to sell a stock, according to your beliefs? b. What are the pros and cons of owning a stock (or a small number of them) and investing in a stock mutual fund (such as an index fund)? Which approach is preferred and why? c. What is the purpose of individual stock picking, based on information contained in this chapter? d. If you engage in stock-picking activities, what would be the counterargument for stock investments? What are the advantages and disadvantages of each approach? 2. Based on the following paragraph, answer the questions that follow. “The time to buy stocks is when blood is running in the streets,” said one famous investor in the early nineteenth century. The market currently (i.e., in 2008) is down so, should I begin buying stocks, given that I am a long-term investor? It makes sense, despite the fact that my guts tell me “sell,” and also because down the road the market will rebound anyway and so I will not regret it. I should not fear the temporary market swings. My advisor also is recommending that I do not sell but start buying. My adviser also tells me that when investors are frightened, that is the good time to buy. Sometimes, however, he tries to sell me a “hot stock.” Should I believe him and follow his recommendation? But what is a hot stock, anyway? Why is he telling me that? Doesn’t he tell the same thing to his other clients? Am I so special? a. When would buying a stock not be prudent? b. Should investors listen to “market experts” on buy/sell recommendations or should they engage in sound stock-trading activities? Discuss. c. Should long-term investors fear volatility of the stock market? Explain.

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3. Based on the information below on the Coca Cola Company (obtained from Value Line online), answer the following questions. Data for Coca-Cola: D2007 = $1.36; D2008 = $1.52; D2009 = $1.64; P2008 = $42.88; Average stock price = $54.5; EPS = $13.8; P/E = 3.06; beta = 0.55 a. From the data on dividends (past, for 2008, and expected, for 2009), derive the dividend growth rate. b. Based on the above information and the company’s current stock price, derive the firm’s required rate of return. c. Using the current stock price and expected dividend figure, verify that the stock’s dividend yield is 3.8%. d. Using Eq. 11, recompute the firm’s required rate of return (Hints: Compute the growth rate of dividends for years 2007 and 2008 and then determine the 2008 price using Eq.10. Use an average price for 2007 based on the upper and lower prices given on the data above.) Does the new number resemble the one obtained in question (b)? e. Using an alternative methodology, can you derive Coca Cola’s current (2008) stock price? (Hint: Multiply EPS by the P/E ratio.) f. Given that the S&P 500 Index returned −1.97% during the year from March 2008 to March 2009 (according to Yahoo! Finance) and the 10-year Treasury bond (alternative proxy for the risk-free rate) yielded an average of 2.65% during the same period, recompute the company’s required rate of return using the beta information found on the company’s information sheet above. What conclusion can be drawn from this number? 4. An investor has the following information about a company: P0 = $43, EPS = $3.00, k = 12%, and ROE = 29% a. Compute the company’s retention ratio (rr). b. What would happen to the company’s P/E ratio if the ROE decreased to 25%? Explain. c. What would happen to P/E if rr increased? What is the implicit assumption in this case? Explain. 5. Assume that the market yields 10% and the dividend yield of an average-risk stock is 5%, what would be the market’s consensus forecast for the rate of growth (appreciation) on that stock’s price? 6. If a stock’s dividend growth rate is expected to be zero forever, what would be the stock price if the dividend was $1 and the firm had a required rate of return of 10%? 7. Suppose that an investor was considering whether to keep a stock in her portfolio, buy more of it, or sell it. The investor required a 10% rate of return from that stock. If the stock is expected to give a rate of return of 11%, what action should the investor take? What should happen if the stock’s expected rate of return is exactly 10%? 8. Assume that a stock has a beta coefficient of 1.2, the risk-free rate is 3%, and the market risk premium is 7%. Answer the questions below. a. What are the stock’s expected and required rates of return (assuming equilibrium conditions)?

Equity Valuation and Investment Strategies s 369

b. What is the implied expected return on the market? c. If, upon further analysis, an investor finds that the stock is expected to provide a 10% rate of return, is the stock over- or undervalued? Should the investor buy, hold, or sell the stock? 9. Use the information on the stock above to compute an estimate of its current price. Assume further that the stock’s expected dividend is $1.50 and the growth rate of dividends is 3.4%. 10. If the intrinsic value of a stock exceeds the market price of the stock, is the stock over- or undervalued? Explain. 11. You are given the following hypothetical information on a company: Total assets  $100,000,000 Total liabilities  $70,000,000 Total stockholder equity  $30,000,000 No. of shares outstanding  10 million Stock’s current price  $50 Total revenue per share  $35 Earnings per share  $2 Compute the company’s book (BV), price-to-book (P/B), price-to-sales (P/S), and price-earnings (P/E) values. 12. Assume the following hypothetical information on a stock: D0 = $1.00 g = 5% P0 = $45 P1 = $50 Compute the stock’s holding period return. If the stock is expected to yield 15%, would you buy or sell the stock? Explain.

NOTES 1. 2. 3. 4. 5.

6. 7. 8. 9.

10.

11.

12. 13.

James Tobin, A general equilibrium approach to monetary theory, Journal of Money Credit and Banking, 1(1), 1969, pp. 15–29. As of mid-December 2011, IBM’s stock price was about $195. Note that if you access the survey today, you will not find the numbers we obtained at that time. To obtain ROE from the survey, find the item referred to as “Return on Shareholder Equity”; to obtain the dividend growth rate, find the item referred to as “All dividends to Net Profits.” Franco Modigliani and Merton Miller, The cost of capital, corporation finance, and the theory of investment, American Economic Review, 48, 1958, pp. 261–297. Merton Miller and Franco Modigliani, Dividend policy, growth and the valuation of shares, Journal of Business, 34, 1961, pp. 411–433. S. A. Sharpe, Stock prices, expected returns, and inflation, Finance and Economics Discussion Series, 1999– 2002, 1999, p. 1. Eugene F. Fama and William G. Schwert, Asset returns and inflation, Journal of Financial Economics, November 1977, p. 129. John Lintner, Distribution of incomes of corporations among dividends, retained earnings and taxes, American Economic Review, 46(2), 1956, pp. 97–113. Merton Miller and Kevin Rock, Dividend policy under asymmetric information, Journal of Finance, 40(4), 1985, pp. 1030–1051. Schlomo Benartzi, Roni Michaely, and Richard Thaler, Do dividends signal the future or the past? Journal of Finance, 52(3), 1997, pp. 1007–1034. Gustavo Grullon, Roni Michaely, and B. Swaminathan, Are dividend changes a sign of firm maturity? Journal of Business, 75(3), 2002, pp. 387–424. Eugene F. Fama and Kenneth R. French, Disappearing dividends: changing firm characteristics or lower propensity to pay? Journal of Financial Economics, 60, 2001, pp. 3–44. Gustavo Grullon and Roni Michaely, Dividends, share repurchase and the substitution hypothesis, Journal of Finance, 57, 2002, pp. 1649–1684. Michael Kamstra, Pricing firms on the basis of fundamentals, Federal Reserve Bank of Atlanta, Economic Review, first quarter, 2003. Burton G. Malkiel, The efficient market hypothesis and its critics, Journal of Economic Perspectives, 17(1), Winter 2003, pp. 59–82. www2.standardandpoors.com http://www.econ.yale.edu/~shiller/data.htm

Part V DEBT SECURITIES

In this part, we explore in some detail the basics of the fixed-income or the debt securities sector of the capital market (or economy) in two chapters. Chapter 12 deals with the fundamentals of a bond—the main debt security—and its valuation. Chapter 13 explores the way bond portfolios are built and how they are monitored and evaluated. Why is the bond market important? Let us answer this question by addressing each sector of the bond market. Recall that bond sectors or issuers are governments (federal, state, and local), agencies, and corporate and foreign entities. When the federal government needs to finance its expenditures, such as running the government or building highways, it issues bonds by selling them to the public in exchange for cash. State and local governments or municipalities that need money to finance various operations and fund projects also issue bonds to raise the funds needed. Agencies (either belonging or related to the federal government) issue bond securities to support various operations such as financing home ownership, offering student loans, and providing agricultural assistance. Corporations also need funds and thus issue bonds in the open market to finance their daily operations and capital projects (investments). Finally, foreign entities such as governments, companies, and investors also tap the global bond market to finance various activities, both at home and abroad, so as to further develop/grow their activities. In general, the bond market’s role is to direct capital to its best uses toward building capital (and infrastructure) for productive purposes, expanding businesses, and promoting economic development and growth around the globe. In other words, the global bond market facilitates the efficient flow of capital for all users worldwide.

371

12 BOND FUNDAMENTALS AND VALUATION

CHAPTER OBJECTIVES After studying this chapter, you should be able to sUnderstand the international bond market sExplain what a bond is and describe its main features sIdentify the various issuers of bonds sPrice a bond sMeasure a bond’s price sensitivity to changes in interest rates sUnderstand the yield curve and its significance

INTRODUCTION In this chapter, we look in more detail at the capital market’s fixed-income segment, the bond market, by discussing the fundamentals and valuation of bond instruments. In general, a fixed-income security is one that pays an even, specified amount calculated by a specific formula over a predetermined period. Because a bond is the main fixedincome security, we devote special attention to it. Compared with equities, a bond is a relatively convenient and secure investment instrument and is often part of any investor’s portfolio. Why should an investor include bonds in his portfolio? There are several reasons. First, because bonds offer a stable (fixed) and predictable income to their holders, it makes them attractive investments. For example, the investor may be saving for her children’s education or to make a big purchase or even for retirement. Second, bonds provide additional diversification benefits to a stock portfolio because they tend to be less volatile than stocks and thus stabilize the portfolio’s returns in down markets. Third, some bonds are tax-exempt from federal, state, and local governments (such as municipal securities) or exempt from taxation at the federal government level (such as Treasury bonds). Understanding how bonds can add value to a well-diversified portfolio is even 373

374 s Debt Securities

more important in view of the recent changes many companies have made to their employees’ retirement accounts. Specifically, moving from defined-benefit retirement plans to defined-contribution plans such as a 401(k) or IRA means that the employee must be careful in selecting from various investment options. Inclusion of bonds in the retirement portfolio will help to secure the investor’s goals. We begin with an overview of the global bond market and continue with the basics of a bond and its valuation. We show how bond values change with the economic environment, such as interest rates, and examine several types of bonds ranging from the government to the corporate sector. An important element of a bond issue is default risk because it affects bond prices and yields. In some instances, we extend our bond valuation discussion to the international bond arena.

OVERVIEW OF THE GLOBAL BOND MARKET The International Bond Market The international bond market (first discussed in Chapter 4) is a 24-hour electronic market, facilitating the flow of capital around the globe; it is larger than the equity market. As of 2010, the value of global total debt outstanding exceeded $87 trillion, whereas that of the global stock markets was about $75 trillion, according to Bank of International Settlements (BIS) estimates. One feature of the international bond market is that it allows investors to broadly diversify their investment portfolios in their search for attractive returns worldwide. Table 12.1 highlights the growth of that market from 2007 to June 2011 by nationality of issuer. The bulk of the issues come from the developed world, followed by developing countries. Also, all issues are on the rise over time. Figure 12.1 shows the size of the international debt market as of 2009 (comprising both government and private issues), which was $92 trillion, focusing on specific countries/ regions of the world. The figure clearly shows that the Eurozone is second to the United States in the issuance of such instruments, followed by Japan. Moreover, according to a study by the European Central Bank, the European, US, and Japanese government bond markets together accounted for about 84% of all government bonds outstanding.1 According to the same study, nongovernment bond issuance was also on the rise but still lagging behind that of sovereign issuers. Japan now has the third largest government bond market in the world, behind the United States and the eurozone (see Figure 12.1). The Bank of Japan (BoJ) and the Japanese government guarantee yen-denominated bond issues, which makes such securities Table 12.1 The Evolving Size of the International Bond Market Amounts Outstanding (Billions of US$) Country Region

2011∗

2010

2009

2008

2007

By Nationality of Issuer Developed Countries Developing Countries Offshore Centers

26,612 1,715 282

24,080 1,532 257

23,695 1,326 245

21,781 2,192 235

20,638 1,185 231

Source: BIS Quarterly Review (various issues). As of June 2011, amounts rounded up by author.

Bond Fundamentals and Valuation s 375 Other 13.01% Euro zone 29.00%

Emerging 8.35%

Japan 13.04%

Canada 2.00%

USA 34.65%

Figure 12.1 The size of the global bond market, 2009.

very attractive worldwide. The Japanese corporate bond market resembles that of the United States, where private companies and banks issue bonds; it is regulated by the BoJ and the Japanese Ministry of Finance. The US Bond Market The details and composition of the US bond market were discussed in Chapter 4; thus in this section we will concentrate on the importance of the bond market for the country’s economy. Although the United States has traditionally dominated the world’s bond markets, bonds issued in the United States now account for less than half of the global bond market volume in the United States (as seen in Figure 12.1); individual holdings of bonds amount to about 6.9% of total financial holdings. What is the general (economic) importance of the development of a home bond market for the United States (or for any country, for that matter)? The chief benefit is that the presence of a bond market ensures efficient functioning of the country’s financial markets so as to effectively channel funds from those who have funds (savers) to those who need funds (investors). For example, the bond market provides the federal, state, and local governments with the capital needed to pay for development and infrastructure projects such as highways, bridges, libraries, and schools. Bonds also help governments to manage the in- and outflows of cash, passing, in turn, the benefits on to the taxpayers who financed the projects in the first place. For firms, this also means that they can borrow/lend at competitive interest rates that better reflect the true cost of capital (funds). Further, investors and other market agents can better manage their risks, which provides stability in the domestic financial markets. In countries with competitive bond markets, a diversified financial system is created, which, in turn, fosters the availability and variety of financial instruments. Moreover, firms need not borrow from the international bond market, as they may expose themselves to additional risks, such as exchange rate and political risks. Finally, the existence of an efficient domestic bond market aids the country’s economic policymakers, fiscal and monetary, to effectively operate their policies and smooth out any fluctuations in economic activity.

376 s Debt Securities

OVERVIEW OF BOND BASICS Features of a Bond A bond is a promissory note (security) that obliges the issuer of the bond to make specific payments to its holder during a specified period. In other words, these securities are IOUs and make payments on specified dates (once or twice per year). When the bond reaches the end of its life, the maturity date, the issuer repays the holder the bond’s full par or face value. The periodic payments are known as coupon payments (or coupon interest) and are computed on the relevant interest rate, called the coupon rate. The coupon rate is the nominal rate or the interest rate that the issuer agrees to pay each year. All these stipulations are included in the contract of the bond, known as the indenture of the bond. For example, a bond with a face value of (typically) $1,000 that can be sold to an investor for that price can carry a coupon rate of 10%, have a maturity life of 10 years, and make semiannual payments (as is typical). The bondholder in this case will receive $50 (or [$1,000 × 10%] / 2) every 6 months (or $100 annually) for 10 years; at the end of the tenth year, he will also receive the $1,000. Although we will use the term bond to denote a long-term security, some market participants refer to bonds with maturity between 1 and 5 years as short-term notes, between 5 and 12 years as medium-term bonds, and bonds with a maturity life of more than 12 years as long-term bonds. The bondholder should be interested in these maturity dates of a bond because the yields of the bonds, the number of coupon payments, and the price(s) of these bonds depend on these dates, as we will see later in the chapter. Bond Types and Characteristics Bonds come from different issuers, carry several features, and have varying coupon structures, such as a coupon bond or a zero-coupon bond. Bonds can be secured—meaning they are backed by real assets such as equipment or financial assets such as Treasury bills—or unsecured (also known as debentures)—which promise payments of interest and principal by the “full faith and credit” of the issuer. An example of unsecured bond is a Treasury bond; an example of a secured bond is a mortgage bond. Before embarking in the explanations of the above characteristics, let us distinguish between a coupon bond and a zero-coupon bond. A zero-coupon bond is one that makes no coupon payments. The investor pays for the bond up front at a discount from the face or par value and at maturity receives the full par value. This is the same as saying that the bond has a coupon rate of zero (percent). We will price such bonds in a later section. Let us continue now with the types of bonds by issuer. We begin with government bonds. By Type of Issuer Government Bonds A government bond is a security issued by a national government in its own currency. For example, the US government’s (at the federal level) bonds are known as Treasury bonds (T bonds) and notes (T notes), have denominations of $1,000 or more, and have maturities for up to 30 years. A T note is issued in terms of 2, 3, 5, 7, and 10 years and, like a T bond, pays interest semiannually; such interest is exempt from state and local taxes. The price paid for a bond or a note may be less than, equal to, or greater than its face value. In general, the prices and yields of T bonds and T notes are determined at auctions. Two types of bids are acceptable: a competitive bid, where investors agree to accept the interest

Bond Fundamentals and Valuation s 377

rate determined by the auction (this is usually for individuals who will get the bonds they want and the full amount they want), and a noncompetitive bid, where investors specify the yield that they are willing to accept (this is the norm for businesses, and it is not guaranteed that the investors will get everything they want). Bonds come in two formats, paper certificates (the old type) and electronic entries (the new type), which is the usual form today. Table 12.2 shows some of these bonds and notes as reported in the Wall Street Journal. The par value in these quotes is $100. The coupon rate is the interest rate of the bond, which specifies the coupon payment. For example, for the first-row bond, the coupon is 4.5%, which means that the payment will be $100 × 4.5% = $4.5 per year, or $2.25 per 6 months. Payments are usually made in April and October each year. The Bid price is the price that dealers are willing to buy the bond (or you are willing to sell the bond) and is quoted in fractions of 32nds (as also mentioned in the Table 12.2 notes). The Asked quote is the price that dealers are willing to sell the bond (or the price that you would pay to buy it) and is also expressed the same way as the bid quote. The Chg column simply denotes the change in the bid and asked quotes. Finally, the column labeled Asked yield refers to the bond’s maturity yield based on the asked price. Market participants often refer to that as the average rate of return (yield) an investor would earn if he bought the bond at the asked price and held it to maturity. A cautionary note is warranted before going further. The prices you read in the financial press, such as the Wall Street Journal, are not the ones that an investor actually pays for the bonds. This is because the actual prices paid need to be adjusted for interest accruals when the bond is traded (bought and sold) between coupon payments. Simply put, you would want part of the coupon interest if you bought the bond a few days after the bond paid its interest (to the previous bondholder and now seller of the bond). For example, assume that you bought the bond 30 days after the semiannual interest (paid every 182 days or 6 months) was paid then you are entitled to 152 days out of the 182 days or 83.5% of the, say, $50 semiannual interest, or $41.75. This also means that the seller of the bond, who owned the bond for 30 days, is also entitled of some coupon interest—in fact, the difference between the semiannual interest and the portion that you received: $50.00 – $41.75 = $8.25. This number will be added to the price that the

Table 12.2 Treasury Bonds and Notes Maturity 2009 Mar 31 2009 Apr 15 2009 Apr 30 2009 May 15 2009 May 15 2009 May 15 2009 May 31 2009 Jun 15

Coupon

Bid

Asked

Chg

Asked yield

4.500 3.125 4.500 3.875 4.875 5.500 4.875 4.000

100:03 100:05 100:14 100:17 100:22 100:24 100:28 100:26

100:03 100:07 100:15 100:17 100:22 100:26 100:28 100:27

unch. –1 –2 –1 unch. –2 –1 –1

–0.1379 –0.5069 0.1806 0.1899 0.1984 –0.0515 0.1912 0.3022

Notes: Treasury note and bond data are representative over-the-counter quotations as of 3:00 P.M. Eastern time. Figures after colons in bid and ask quotes represent 32nds; for example, 100:03 means 100 and 3/32, or 100.0935% of face value. For notes and bonds callable prior to maturity, yields are computed to the earliest call date for issues quoted above par and to the maturity date for issues below par (Wall Street Journal, March 20, 2009).

378 s Debt Securities

buyer will pay to buy the bond; if it was, say, $985, the full price paid for the bond will be $993.25. This price is known as the invoice price or the dirty price (which equals clean price plus accrued interest). In general, accrued interest is computed using the following formula

Accrued interest = coupon payment ×

days since last coupon payment days between coupon payments

(1)

where the coupon payment will be either annual or semiannual, depending on the bond’s payment schedules. Other Government and Government-related Bonds As we first saw in Chapter 5, municipal bonds (or munis) are bonds issued by states, cities, and counties to raise funds to pay various expenses incurred by state and local governments. These bonds bear interest at either a fixed or variable rate, which can be subject to a cap (the maximum legal limit). Munis are exempt from taxation at the federal level and (usually but not always) at the state and local levels. Therefore, because of their special status, investors accept lower interest payments than on other types of borrowing (of comparable risk). This makes the issuance of bonds an attractive source of financing for many municipal entities, as other borrowing rates available in the open market are relatively higher. According to the Securities and Exchange Commission (SEC), the Municipal Securities Rulemaking Board launched in March 2008 its Electronic Municipal Market Access (EMMA) program. EMMA provides free public access to disclosure documents, including official statements and refunding documents as well as real-time municipal securities trade price data. Other government bond issuers are known as agencies and come in two types: government-sponsored enterprises (GSEs), which are chartered by Congress but owned by investors (and whose shares trade on the New York Stock Exchange), and federally related, which are owned or controlled by the federal government. The objective of these types of agencies is to finance specific activities. Some examples of GSEs include the Federal National Mortgage Association (Fannie Mae) and Federal Home Loan Mortgage Corporation (Freddie Mac), both of which buy certain types of mortgages from banks and use them to create mortgage-backed securities. The Government National Mortgage Association (Ginnie Mae), on the other hand, although engaging in the same type of activities as Fannie and Freddie, is a government-owned corporation. Agency bonds come in a wide variety of structures, maturities, and coupon rates. Many make semiannual interest payments and require a minimal investment of $10,000 (with $5,000 increments thereafter). Unlike Treasuries, agency bonds are not backed by the full faith and credit of the US government. As a result, the yields on agency bonds are typically higher than those of Treasuries but lower than those of corporate bonds. However, the likelihood that the federal government would allow these entities to go bankrupt is quite low, so both Fannie Mae and Freddie Mac securities are generally considered “safe.” At this point, read Box 12.1 to learn why these agencies recently went almost bankrupt and why the US federal government had to bail them out to cope with the 2008 global financial crisis.

Bond Fundamentals and Valuation s 379

BOX 12.1 Fannie and Freddie to the Rescue In September 2008, the US government announced that it would take over Federal National Mortgage Association (Fannie Mae) and Federal Home Loan Mortgage Corporation (Freddie Mac) to back up some $5 trillion in home loans that they owned. The two agencies, which were created by the US government in the 1930s, had been severely hurt by the recent financial crisis and the drastic declines in home prices due to massive mortgage delinquencies and foreclosures. The takeover plan would work as follows: First, the two agencies would be taken into conservatorship, which means that a new regulator (the Federal Housing Finance Authority) would see that they returned to financial soundness. Next, the two agencies would have access to a loan facility (using their assets as backing) until 2009 so as to ensure an uninterrupted credit line. Then, the government (i.e., the Treasury) would purchase preferred shares of stock from these agencies in order to ensure priority of future revenue streams. Finally, the Treasury would become the “buyer of last resort” for the agencies’ bonds whenever demand by the private sector slackened. The main idea of the plan, according to Treasury Secretary Paulson, is to keep the two agencies working in the market for the soundness of the financial system. Note that the plan does not bail out the agencies’ common stockholders and limits the government’s financial investment to a minimum or until the agencies record a positive net worth. As of April 2011, Treasury Secretary Timothy Geithner proposed a gradual and careful reduction plan for the Treasury in its $11 trillion investments in Fannie Mae and Freddie Mac without reducing the government’s support during the transition period.

Examples of the types of bonds these agencies issue are mortgaged-backed securities (MBS), asset-backed securities (ABS), collateralized mortgage obligations (CMOs), and real estate mortgage investment conduits (REMICs), among other innovations in the bond market. Briefly, are created from pooling many mortgages (by homeowners) and creating a new security for sale to the general public. ABS are bonds created by the backing of financial assets such as credit-card receivables, auto loans, and home equity loans. The creation of a CMO begins with a mortgage loan extended by a bank to finance the borrower’s home or other real estate. A word on a special type of government bond is warranted at this point. Treasury Inflation-Protected Securities (TIPS) are marketable securities whose principal is adjusted for changes in inflation (as measured by the consumer price index). With inflation, the principal increases, but with deflation, the principal does not decrease below par. Also, interest is protected because investors receive fixed payments based on the inflationadjusted principal, thus guaranteeing a real rate of return that exceeds inflation. Let us see that through an example. Assume a newly issued bond with a 4-year maturity, face value of $1,000, and coupon rate of 3%. Also assume annual payments. Inflation is expected to be 2.5%, 3.0%, and 2.0% during the following 3 years. Table 12.3 exhibits the hypothetical data and shows how the coupon payments, the principal repayments, and the total payments are calculated. The total payment column is found by adding the coupon payment and the principal repayment. The first payment comes at the end of period 1. Inflation during that year was 2.5%; thus the face value of the bond will be $1,025. Because the coupon rate is 3%, the coupon payment will be $1,025 × 0.03 = $30.75. Thus the total

380 s Debt Securities Table 12.3 How TIPS Work Period

Inflation

Face Value

Coupon Payment

Principal Repayment

Total Payment

0 1 2 3

2.5% 3.0% 2.0%

$1,000.00 $1,025.00 $1,055.75 $1,076.86

$30.75 $31.67 $32.30

$0 $0 $1,076.86

$30.75 $31.67 $1,109.16

payment will be $30.75 (since there is no principal repayment but only a payment at the end of the third year). Following the same approach, you obtain the remaining values in the last column of Table 12.3. In general, the real rate of return on a bond is found as follows: Real rate of return =

1 + nominal rate of return 1 + inflation ra te

(2)

where the nominal rate of return is computed as: Nominal rate of return =

interest + price change initial price

(3)

In our example, the nominal and real rates of return are calculated below for the first period: $30.75 + ($1,025.00 − $1, 000 ) $55.75 = = 5.58% $1, 000 $1,000 1.0558 1 + 0.0558 − 1 = 0.030 , or 3.0% Real rate of return = −1 = 1.0250 1 + 0.0250

Nominal rate of return =

which is exactly 3% as the nominal coupon rate. Why does the federal government issue TIPS? Two reasons are typically cited in the press: first, to give access of various maturities and rates to a greater variety of investors (principally institutional ones) and, second, because the government believes that such issuance would reduce the cost of financing (or its interest cost) in the long run. What about the academic literature? Studies have argued that TIPS (or inflation-indexed securities in general) fill the gap between nominal long-term securities, which are not safe in real terms, and real short-term interest rates, which vary over time, by offering a truly riskless investment.2 Naturally the opposite side of academic research cites that TIPS issuance costs the government more than regular T bonds because the former are not as highly valued in the market relative to the latter.3 The general objective of TIPS is to compensate the investor for the loss of her purchasing power due to inflation—that is, to generate real return. That is why the face value adjusts with inflation. Furthermore, if

Bond Fundamentals and Valuation s 381

deflation occurs, the investor will not lose, because TIPS guarantee to pay (at least) the original principal at maturity. The semiannual interest received is taxable at the federal level, just like any other Treasury security, but exempt at the state level (exemptions vary from state to state, however). A disadvantage of TIPS is that taxes accrue (are due) when the security does not mature or investors have not yet received payment for the principal. Box 12.2 presents the methods of purchasing TIPS and some key facts on and auctions of TIPS.

BOX 12.2 TIPS in Depth HOW TO BUY TIPS TIPS are sold directly in TreasuryDirect and through brokers, banks, and dealers. Effective April 2009, TreasuryDirect allows accounts for entities such as trusts, estates, corporations, and individuals. The price of a TIPS can be less than, equal to, or greater than the face value. You can bid for TIPS is one of two ways: With a competitive bid, you specify the yield you are willing to accept (just as for other government securities, as we saw in the previous discussion). Your bid may be accepted in the full amount desired if the yield is less than the auction-determined yield, accepted in less than the full amount you want if the bid is equal to the high yield, or rejected if the yield you specify is higher than the auction-determined yield. To place a competitive bid, you must go through a broker, bank, or dealer. With a noncompetitive bid, you agree to accept the yield determined at the auction. In that way, you are guaranteed to receive the TIPS you wish and the full amount you want. To place a noncompetitive bid, you can use TreasuryDirect.

KEY FACTS TIPS are issued in terms of 5, 10, and 30 years, although the latter is gradually being phased out. TIPS are sold in increments of $100 (the minimum purchase). TIPS interest rates are determined at auction. TIPS are issued in electronic form. You can hold the TIPS to maturity or sell it before maturity. In a single auction, the investor can purchase up to $5 million in TIPS by noncompetitive bidding or up to 35% of the initial offering amount by competitive bidding.

AUCTION DATES TIPS are auctioned according to the following schedule: 5-year TIPS in April, August, and December 10-year TIPS in January, March, May, July, September, and November 30-year TIPS in February, June, and October Source: TreasuryDirect.

382 s Debt Securities

Corporate Bonds Corporate bonds are issued by public and private corporations in order to raise funds to finance expenses and expansions. Bonds are typically issued in multiples of $1,000 and $5,000. Bonds usually trade in the over-the-counter (OTC) market, although some bonds trade on the New York Stock Exchange (NYSE) and American Exchange (AMEX) as well. The US corporate bond market is large and liquid, with a daily trading volume estimated at $15.1 billion (in 2008). Corporate bond issuance for the first half of 2007 reached a record of $702.4 billion; but for the first half of 2010 it was under $480 billion.4 Global corporate bond issuance was about $1.8 trillion for 2009.5 Investors in corporate bonds include large financial institutions such as pension funds, endowments, mutual funds, insurance companies, and banks. Individuals also invest in corporate bonds because of the many benefits these securities offer. The interest received from corporate bonds is subject to federal and state income tax. If an investor sells a bond (at a profit) before it matures, he generates a capital gain; if the investor sells it (at a loss), he may incur a capital loss. If the bond is sold up to a year from purchase, the gains are taxed at the investor’s ordinary tax rate. If the investor sells the bond more than a year from purchase, his capital gains are considered long term and are currently taxed at a maximum rate of 15%. When bonds are issued at substantially less than par, the difference between the face amount and the initial offering price is known as original issue discount (OID). An example of that category of bonds is a zero-coupon bond.6 International Bonds and Eurobonds The international bond market comprises the foreign bond and the Eurobond markets. Foreign bonds are bonds issued by a foreign corporate borrower in a country other than its own residence and denominated in that country’s currency. For example, if a British firm issues and markets a dollar-denominated bond in the United States, this bond is considered a foreign bond. Recall that such bonds often have catchy names, depending on the country in which they are sold. For example, a pound-denominated bond that is issued in the United Kingdom by a non-UK company is known as a Bulldog bond. Dollar-denominated bonds sold in the United States by a non-US entity are known as Yankee bonds, yen-denominated bonds sold in Japan are referred to as Samurai bonds (Matilda or Kangaroo bonds sold in Australia and Matador bonds sold in Spain are other examples). If a bond is simultaneously offered in the foreign and the Eurobond markets and in various currencies, it is known as a global bond. The US market has been traditionally the major market for global bonds. Eurobonds are bonds issued in one currency but sold in other markets at that currency. For example, a bond that is denominated in US dollars and issued in the United Kingdom by a Japanese company would be an example of a Eurobond. London is one of the main centers of the Eurobond market, but Eurobonds may be traded throughout the world. According to the European Central Bank, euro-denominated international bonds amounted to 43.5%, dollar-denominated issues to 40.5%, pound-denominated issues to 7.6%, and then yen-denominated issues to 4.4% of the market.7 Major issuers in this market include supranational organizations such as the European Bank of Reconstruction and Development and the World Bank and as well as other major banks and corporations. Eurobonds are known as “bearer” bonds because they are not registered anywhere—that is, they are anonymous—thus whoever happens to own the bonds is their owner.

Bond Fundamentals and Valuation s 383

A sovereign bond is a bond issued by a national government in its home or in a foreign currency. Just like foreign bonds, sovereign bonds have colorful names like gilts if issued by the UK government and bunds if issued by Germany. Stable countries with stable currencies such as the United States, United Kingdom, and Germany issue such bonds in their home currency (dollar, pound, and euro, respectively). Countries whose currency or economy is unstable tend to denominate their bonds in the currency of a country with a stable economy—that is, a hard currency. Brady bonds, which are issued by governments in developing countries, are a popular example of such sovereign debt securities. Brady bonds were named after the former US Treasury Secretary Nicholas Brady, who engineered the effort (in the 1980s) to prop up and restructure many emerging markets’ external debt. The box titled International Focus discusses the current important sovereign debt crisis within the eurozone and its implications for the stability and viability of the euro. By Bond Feature Some bonds carry several provisions or embedded options in their indenture. Some of these provisions are explained briefly below. A call option is a provision that allows the issuer of the bond to buy back the bond at a predetermined price at some future time. Alternatively, the buyer of the bond has sold a call option (explained further below) to the issuer. Callable bonds are called only a few years after they are issued. This period is known as the lockout period. Why would an issuer embed such an option to the bond? The economics of that action is simple: if interest rates fall in the future, newly issued bonds will carry lower coupon rates and thus pay lower interest to the holders of those bonds. Thus a company may want to embed a call option to its bonds so that it can have the opportunity to retire those bonds, which carry higher coupon rates, and issue new ones with a lower coupon rate. So a call option benefits the bond issuer, not the bondholder. By contrast, a put option is an option that permits the bondholder to redeem (sell back) to the issuer a bond earlier than its maturity date. Again, what is the economics of a putable bond? If market interest rates rise, existing bondholders would like to have an option to get out of current, lower-rate bond holdings and replace them with higherrate bonds. Thus, they have the right (but not the obligation) to sell back their currently held bonds at a predetermined price so that they can buy new ones. Thus, with a put option, bondholders benefit. We will discuss what these callable and putable bond prices are later in this chapter. A convertibility option (or a convertible bond) gives bondholders the option to convert their bonds into a specified number of shares of common stock of the same company at a certain future time. Let us see how this conversion works and also clarify the economics of it via a simple example. Suppose that a bond issued at par ($1,000) is convertible into 50 shares of the firm’s stock. The conversion ratio is the number of shares for which a bond may be converted. The current stock price is $15 per share. Given this information, converting the bond into shares of stock is not profitable because, in multiplying the conversion ratio by the current stock price, the value of shares would be $750, which is less than the bond’s value. However, if the stock’s price rises to $25, then the shares value rises to $1,250; thus the bond can be profitably converted. The conversion premium is the difference (excess) between the shares value and the bond’s face value, or $250 here. Therefore, while bondholders benefit from price appreciation of the company’s stock,

384 s Debt Securities

they usually pay a price in terms of earning a lower yield on convertible bonds. A disadvantage for an investor exercising the convertibility option is that it results in ownership dilution. This occurs because investors will hold more shares of stock of the company and experience a decline in revenues per share or stock price per share. For the company, dilution may mean that the lower the stock price falls, the greater the number of shares the company must issue to obtain future financing. By contrast, an exchangeable bond is one that allows the holder to exchange the bond into shares of stock of another company, usually a subsidiary of the main bond issuer, again at a predetermined price and future time period. Exchangeable bondholders, like convertible bondholders, usually accept lower coupon rates because they have the chance to profit from the underlying stock’s increase. A disadvantage of an exchangeable bond is that the investor is exposed to a stock that has a different risk/return profile from that of the issuer’s stock. Exchangeable bonds typically mature in 3 to 6 years. A floating-rate bond (floater) makes variable (not fixed) interest payments; its coupon rate is tied to a market interest rate or a reference rate (such as the London Interbank Offered Rate [LIBOR] or the federal funds rate) plus a spread. GSEs and corporations typically issue such bonds (or notes) in the United States, while in Europe mostly banks do. Floating-rate securities are traded in the OTC market and investors usually hold them to maturity. Although such bonds suffer very little interest rate risk (as we will see later), their risk emanates from the financial condition of the underlying (issuing) company. If the company’s financial health deteriorates, investors will require higher yields (reflected in the spread), which would depress the bonds’ prices. An inverse floater bond resembles the floater but has an inverse relationship to the market or reference rate. That is, when interest rates increase, the bond’s coupon rate falls. As a result, this relationship magnifies the bond’s risk, as the value of the bond can drop substantially, yielding very little to the investor. The up side of this, of course, is that such investors greatly benefit when interest rates decline. Municipal and corporate issuers are the main sellers of inverse floaters. Finally, some new innovations in the global bond market include the so-called catastrophe bonds, which transfer a specific risk (catastrophe or total loss) from a sponsor (firm) to an investor. Investors in such bonds receive remuneration for accepting the risk in the form of higher yield. Other types are weather-linked bonds, bonds linked to insurance or commodities, and so on (the market’s ingenuity can never be questioned!). The idea behind such innovative instruments is that there is (or should be) little correlation with financial events (and instruments); thus investors achieve better diversification potential in their portfolios. Such instruments are also known as alternative investments. We will discuss them in Chapter 16. By Other Characteristics Default Risk One basic and very important characteristic of a bond is risk, particularly default (or credit) risk. Default risk refers to the risk that companies may not be able to fulfill in full and on schedule their contractual obligations. Thus if companies are unable to continue servicing their debt, the bondholders will not get all the payments they were promised, which renders the actual payments of a bond uncertain. Credit risk is rated by three main credit rating agencies, namely Standard & Poor’s, Moody’s, and Fitch & Associates (as we saw in Chapter 5). However, not all bonds carry this risk. For example, US Treasury

Bond Fundamentals and Valuation s 385

bonds are (typically but not always) free from default risk (because they are backed by the full faith and credit of the US government) but US (and world) corporate and other private bonds are risky. Recall (from Chapter 5) that in April 2011, Standard & Poor’s warned of a potential US sovereign debt downgrade. In August 2011, Standard & Poor’s actually lowered US long-term federal debt from its triple-A status to double-A+ grade. The box titled Lessons of Our Times provides more information about this downgrade move and its potential consequences for investors worldwide, given the “risk-free” or quality status of US Treasuries. How can an investor make sure (to the extent possible, of course) that if she purchases a bond, the company will continue honoring its obligations? One way is for the investor to seek additional information on the company from her financial advisor to determine the creditworthiness of the company. A prospectus may be found on the company’s website for all interested parties. Also, the credit-rating agencies continue monitoring the financial condition of the company over time and issue reports when a change is imminent. Additional information on the company’s bond issue may include a credit enhancement, which is an additional backing (guarantee) by an external agency such as a bond insurer like the Municipal Bond Insurance Association (MBIA) or the American Bond Assurance Association (AMBAC). Bond Determinants and Covenants Bonds have built-in mechanisms to ensure the bond’s safety based on the issuer’s financial status, as mentioned above. A company’s financial strength or weakness can be evaluated by constructing ratios that address the five aspects of the company’s operations (business): liquidity, asset management, debt management, profitability, and market value. For example, coverage ratios measure the company’s ability to pay its fixed obligations in the short run. Leverage ratios measure the firm’s capacity to service its long-term debt and may cast doubt on its ability to pay in the long run. Finally, profitability ratios measure the efficiency with which a company manages its assets and give a signal of the firm’s overall financial health. The bond’s contract, the indenture, specifies a series of protective covenants in order to market the bond effectively to prospective investors. For example, a sinking fund calls for the issuer to buy (repurchase) some fraction of the outstanding bonds periodically before maturity. Another protective covenant is the collateral, which is a specific provision on an asset pledged against a possible default of the bond. Examples of collateral are real assets (such as equipment) or financial assets such as Treasury bills. Finally, refunding means the replacement of a current, high-coupon bond issue with (the issuance of) new, lower-coupon bonds. If a bond is callable, refunding does not offer any protection to the bondholder, but at least he will have an idea when the bond might be called away. In general, the refunding provision is advantageous to the issuer when existing bonds need to be replaced with lower-coupon bonds. Junk Bonds A special type of a high-risk, high-yielding bond is a junk bond. Such a bond does not qualify as an investment-grade (the highest quality or AAA) bond but as a speculative issue (BB rating or lower) and thus has a higher risk of default. The junk-bond market flourished in the 1980s when this alternative means of financing (leveraged buyouts and hostile takeovers) became the fashion before it fell out of favor (and landed Michael

386 s Debt Securities

Milken, one of its originators, in jail). In the 1990s, interest in junk bonds grew rapidly because of the growing sophistication of investors (at home and abroad) in search for higher yields and the potential for capital appreciation. According to the Securities Industry and Financial Markets Association (SIFMA; visit www.investinginbonds.com), in 2003, $123 billion worth of junk bonds flooded the US market, which, by comparison, was more than nine times the new issue volume in 1990. In Europe, high-yielding bonds reached an all-time high demand in early 2010, according to the Financial Times. Additional risks from such bonds include declines in their values (perhaps more than straight bonds) due to economic slowdowns and the inability to dump them in a short period of time (owing to their illiquid status). In general, all sorts of investors, ranging from individual investors to pension funds, participate in this bond market. High-yield bonds offer similar features as straight bonds, such as fixed- and floating-rate coupons, convertibility options, and zero coupons.

BOND PRICING Basic Bond Valuation Formulas Before considering the basic bond valuation formula, let us begin with a basic question: Why do investors buy bonds? The simple answer (in this context) is that they receive a fixed (and even) cash flow (the coupon payments or interest) for some period, and at the end of the period, they receive the bond’s face value. Thus a bond provides two types of cash flows: an annuity and a lump sum. Both parts need to be discounted to the present in order to find the bond’s current price (or the price that investors are willing to pay). Guided by these two parts, we are ready now to derive the formula to value a straight or plain “vanilla” bond. First, denote as P0 the current bond price, CFt the cash flows at time t, r the discount rate, T the maturity date, and  the summation operator. Thus we derive the general cash flow formula: P0 =

CF1

(1 + r )

1

+

CF2

(1 + r )

2

+

CFt

(1 + r )

T

=

T

CF

∑ 1 + rt t t =1

(

)

(4)

or more compactly, P0 =

T

CF

∑ 1 + rt t t =1

(

)

+

M

(1 + r )T

(5)

where M is the par value and CFt the fixed cash flows, discounted at the same rate at time T. The current price of the bond is also known as the bond’s intrinsic price or value (just like a stock’s intrinsic price, as we learned in Chapter 11). The first part of the equation is the discounted cash flows (the annuity part) and the second term the discounted par value (the lump-sum part). These distinctions will come in handy shortly when we show a shortcut formula. Both equations above imply a promised yield to maturity of the bond. This yield (which is also known as the required yield) reflects the yield for alternative instruments

Bond Fundamentals and Valuation s 387

with comparable risk. Also, this yield is assumed to remain constant throughout the life of the bond where all cash flows are discounted. This is the traditional way practitioners value a bond. In reality, however, it is inappropriate to discount a bond’s cash flows at the same interest rate because of different cash-flow patterns. Instead, each cash flow must be discounted at a unique interest rate when the cash flow is received. This is accomplished by using a theoretical set of discount rates derived from a (theoretical) zerocoupon Treasury yield (or spot rate) curve (the yield curve is discussed further on). Its construction, however, is beyond the scope of this presentation. Let us show this with an example. Assume that a bond has a coupon rate of 10%, with a maturity date of 5 years and is making annual payments. What is the current price of that bond if the opportunity cost of holding it (the discount rate) is 10%? Recognize that the annual interest payment is $100 (par will always be $1,000 here). Therefore we have P0 =

$100

(1.1)

1

+

$100

(1.1)

2

+

$100

(1.1)

3

+

$100

(1.1)

4

+

$100

(1.1)

5

+

$1, 000

(1.1)5

= $90.90 + $82.64 + $75.10 + $68.30 + $62.10 + $620.10 = $999.99 or $1,000 which means that the bond’s current price is $1,000 or sells at par. Note that in using this approach we treat each cash-flow component as a lump sum and not as an annuity. Notice also that this approach can be tedious and time-consuming. That is why a shortcut approach exists that relies on the present value tables or a financial calculator.8 Let us illustrate both next. P0 = PMT (PVIFAr,T) + M (PVIFr,T)

(6)

where PVIFA is the present value interest factor of an annuity, with coordinates r and T and PVIF is the present value interest factor with the same coordinates.9 We will need the present value tables to find the numbers for these factors.10 The appendix at the end of this textbook contains these tables. Thus, using the above data as an example, we have P0 = $100 (PVIFA10%,5) + $1,000 (PVIF10%,5) = 100 (3.791) + 1000 (0.621) = $1,000 which is the same price that was found using Eq. 5.11 Using a financial calculator such as a BA II plus, you should follow the command sequence: N=5

I=5

FV = 1,000

PMT = 100

where N is the number of periods, I is the interest rate (entered as a whole number not as decimal), FV is the future value, and PMT the interest payment. Thus you enter these values (by entering the value first and then pressing the relevant key) and then press the keys CPT (compute) PV (present value) to obtain 1,000 (or – 1,000). What if the bond paid interest twice per year or semiannually, as is common for bonds? In this case, we need to make the following adjustments to the formula above: the interest and the coupon rates will be halved, the coupon payment will be halved, and the time

388 s Debt Securities

period will be doubled. Thus, in our example, r = coupon rate = 10%/2 = 5% and T = 2 × 5 = 10 periods. Applying these numbers to Eq. 6, we obtain: P0 = $50 (PVIFA5%,10) + $1,000 (PVIF5%,10) = $50 (7.722) + $1,000 (0.614) = $1,000 Naturally if the payments were quarterly, analogous adjustments would be needed to compute the bond’s price. The Inverse Relationship between Prices and Yields In the above example, we assumed that the interest (or discount) rate used to evaluate the bond was the same as the bond’s coupon rate. We also assumed that this interest rate would remain the same throughout the life of that bond. These assumptions make sense (only) when we try to find the bond’s price so it can be marketed and sold to investors. Corporate issuers typically set (issue) their bond offerings at par initially and try to approximate the bonds’ coupon rates to those of the prevailing market rates. When investors subsequently trade these bonds (in the secondary market), their prices fluctuate according to market forces (demand and supply) and particularly to interest rates. Because interest rates change frequently, either upward or downward, the bond’s price will change as well, but in the opposite direction. Let us prove this and explain the economics of it. Consider a newly issued bond with a coupon rate of 10%, with 10 years to maturity and making annual payments. Assume next that the market interest rates fell, a year after the bond was issued, to 8% (from 10% initially) and remained at that level. Note that the bond’s coupon rate is unaffected because it is set at contract and thus the bond will still pay $100 annually to the bondholder. Note also that the bond has 9 years to maturity left. In this case, what would be the bond’s current price? P0 = $100 (PVIFA8%,9) + $1,000 (PVIF8%,9) = $100 (6.247) + $1,000 (0.500) = $1,124.70 The bond’s price would be $1,125 (rounded up), which means that the bond would sell at a premium (from par). Thus, we derive the first insight: Insight 1. When the bond’s coupon rate exceeds the market interest rate, the bond should sell at premium. Let us find again the bond’s price 2 years after issuance, ceteris paribus: P0 = $100 (PVIFA8%,8) + $1,000 (PVIF8%,8) = $100 (5.747) + $1,000 (0.540) = $1,114.70 As you see, the bond’s price still trades at premium (the size of the premium in this case is $1,114.7 − $1,000 = $114.7, while before it was $124.7), but at a lower price than before (we will explain this shortly). What is the economics behind this result? If you had to choose between two bonds, one (currently) paying $100 per year and another (new one) paying $80 (recall that the coupon rate of new bonds will be 8% in accordance with market rates), which one would you choose? Naturally you would want to receive more per year; thus you would select the bond that pays $100 per year. But so would everyone else! Thus the excess demand

Bond Fundamentals and Valuation s 389

for such bonds will increase their prices and decrease their yields! That is exactly what we have shown above. Now, let us assume that market rates rose, a year after the bond was issued, to 12% and remained so for the life of the bond. What would be the bond’s current price in this case? P0 = $100 (PVIFA12%,9) + $1,000 (PVIF12%,9) = $100 (5.328) + $1,000 (0.361) = $893.80 So the bond’s price will be $893.80, which means that it will set at a discount from par (the size of the discount is $893.80–$1,000 = –$106.20). The second insight is then: Insight 2. When the bond’s coupon rate is less than the market interest rate, the bond should sell at discount. Two years after issuance, the bond’s price will be, ceteris paribus: P0 = $100 (PVIFA12%,8) + $1,000 (PVIF12%,8) = $100 (4.968) + $1,000 (0.404) = $900.80 Thus, again the bond trades at a discount from par, but at a higher price than before. Finally, for the sake of completeness, if we assume that the market rates remained the same 1 and 2 years after the bond was issued, then their prices would be (as you might have correctly guessed) $1,000: P0 = $100 (PVIFA10%,9) + $1,000 (PVIF10%,9) = $100 (5.759) + $1,000 (0.424) = $1,000 P0 = $100 (PVIFA10%,8) + $1,000 (PVIF10%,8) = $100 (5.335) + $1,000 (0.467) = $1,000 Thus, the third and last insight is: Insight 3. When the bond’s coupon rate is equal to the market interest rate, the bond should sell at par. Figure 12.2 illustrates the general inverse relationship between bond prices and yields at various interest rates (with an 8% coupon bond and making annual payments). We will discuss why the inverse relationship is not linear later in the chapter. Figure 12.3 shows the path of the bond prices (premium and discount values) until the time to maturity. As you see, premium/discount bonds decline/rise in value at maturity ($1,000). Naturally, in reality the bonds’ prices do not decay so smoothly because interest rates change continuously, thus altering the bonds’ prices. In this case, the graph would look more like a seesaw because of the increases/decreases in bond prices. To cast a more in-depth look into the relationship between bond yields and prices, Table 12.4 exhibits the price/yield combinations for various years and yields. What can we observe from this table? First, when the discount rate differs from the bond’s coupon rate (8%), the bond sells at a premium or at a discount (as we showed above). Second, for any given time to maturity, we find that the bond’s price either declines (when the market rate falls short of the coupon rate) or increases over time (when the market rate exceeds the coupon rate) toward the par value at maturity. Third, as the time to maturity increases and with a given discount rate, the bond’s price is higher (see the second

390 s Debt Securities bond prices

1,038.4 1,018.8 1,000.0 981.8 964.2

4%

6%

8% 10% 12%

yields

Figure 12.2 Bond prices and yields.

bond prices 1,124.7

@ 8% rate and remaining constant until maturity

0

$1,000 1

2

3

900.8

4

5

6

7

8

9

10

@ 12% rate and remaining constant until maturity

Figure 12.3 Path of bond prices over time.

column with a 4% rate for 1 to 30 years to maturity). For a higher discount rate, such as 6% (but still lower than the bond’s coupon rate), the bond’s prices are lower than the prices of those with a lower discount rate (say 4%). Let us look into these observations more carefully and interpret them. We noted that longer-term bonds are more price-sensitive to a given change in yield than shorterterm bonds. For example, for a 6% rate and 30 years to maturity, the bond’s price is $1,275.30, compared with the 10-year bond, whose price is $1,194.20 (relative to par values). Thus the increase in the price of the longer-term bond is larger than that of the shorter-term bond. Also, the price-sensitivity of a bond increases with its maturity, but

Bond Fundamentals and Valuation s 391 Table 12.4 Bond Prices and Yields Time to Maturity

4%

6%

8%

10%

12%

1 5 10 15 20 30

$1,038.461 $1,178.072 $1,324.435 $1,444.735 $1,543.613 $1,691.681

$1,018.867 $1,084.247 $1,147.201 $1,194.242 $1,229.398 $1,275.296

$1,000.000 $1,000.000 $1,000.000 $1,000.000 $1,000.000 $1,000.000

$981.818 $924.184 $877.108 $847.878 $829.728 $811.461

$964.285 $855.808 $773.991 $727.565 $701.222 $677.792

Note: 8% coupon rate, annual payments.

at a decreasing rate. Examine, for example, the differences in the bond prices for the 6% yield and for the 10- and 5-year bonds. The difference between the 10- and the 5-year bonds’ prices is $84.247–$18.867 = $65.38 and the difference between the prices for the 15-year and the 10-year bond is $62.95. Thus you see that the sensitivity in a bond’s price decreases as its maturity increases. All of the above conclusions have important implications for bond portfolio managers and the formation of bond strategies, as we will see further on. Let us now show how to price a zero-coupon bond, a special type of bond. A zerocoupon bond does not make any periodic payments but gives only one lump sum at the bond’s maturity. Thus, the first terms in Eqs. 5 and 6 are zero: P0 =

M

(1 + r )T

(7)

Thus, Eq. 7 states that the price of a zero-coupon bond is just the present value of its par value (at maturity). For example, for a 10-year zero-coupon bond with a required yield of 10% and semiannual payments, the price would be P0 =

$1, 000

(1.05 )

20

=

$1, 000 = $376.9 2.653

where the required yield was halved (10%/2) and the time to maturity doubled (2T). Now that you have learned how to price various bonds, let us determine what the total or holding-period return (or actual) on a bond is for an investor. Let us (re)define, first, the holding-period return. A bond investor can expect to earn the following dollar return from one of three sources: sThe fixed periodic coupon payments sAny capital gain/loss when the bond matures (or is retired, as we will see later) sAny reinvestment of interest income To keep this discussion simple, assume that the bond is not retired (that is, called before maturity) and that reinvestment of interest is made at the same discount rate. The

392 s Debt Securities

simple total return formula (or holding-period return formula, in this case) is expressed as follows: Total or holding-period return (HPR) on bond = coupon yield + capital gains/loss yield HPR =

interest income + price change interest income price change = + purchase price purchase price purchase price

(8)

where coupon yield is defined as the periodic interest income divided by the purchase price and the capital gain/loss yield is the rate of change in the (sell/buy) prices of the bond. Let us use the previous problem to apply the above formula. Assume that you bought the 10% coupon 10-year annual-paying bond 1 year after it was issued at $1,124.70. You kept the bond for 1 year and then sold it at $1,114.70. What was your 1-year rate of return? HPR return =

$100 $1,114.70 − $1,124.70 + = 0.0889 + (−0.0089 ) = 8% $1,124.7 $1,124.7

So as you see, your return on that bond was 8%, exactly the current interest rate. As an exercise, repeat the same analysis with the second example above and prove that your holdingperiod rate of return, if you had bought the (discount) bond at $893.80, kept it for 1 year, and then sold it at $900.80, would be 12% (the same as the prevailing interest rate). Let us look at one more example with the additional assumption that you hold the bond to maturity (along with the implicit same reinvestment rate). Compute the total return (since you hold it to maturity) of a 9% coupon bond with 7 years to maturity currently selling at par and making semiannual payments. The three components of the bond’s total return are: sCoupon interest (payments), PMT sInterest earned from reinvesting the payments (at reinvestment rate r) sPar value of the bond at maturity (M) So, PMT is $90/2 = $45, n = 7 years × 2 = 14, and r = 9%/2 = 4.5% or 0.045. The first two components can be computed as follows: ⎡(1 + r )n ⎤ (9) Coupon payment + interest from reinvestment = PMT ⎢ ⎥ ⎢⎣ r ⎦⎥ ⎡(1.045 )14 − 1⎤ = $45 ⎢ ⎥ = $851.95 ⎢⎣ 0.045 ⎥⎦ Then compute the semiannual total return (which includes the coupon payment + the interest from reinvestment and the par value of $1,000) as follows:

Bond Fundamentals and Valuation s 393

⎡total future dollars ⎤ Total semiannual return = ⎢ ⎥ −1 ⎣ price of bond ⎦ ⎡$1, 851.95 ⎤ =⎢ ⎥ − 1 = 4.5% ⎣ $1,000 ⎦

(10)

or doubling it to make it an annual total return gives us 9.0% Two additional risks exist in calculating the holding-period return of a couponpaying bond and holding it to maturity. The first is the interest rate risk, which emerges because the bond’s price moves inversely with the interest rate. This risk is implicit in the capital gain/loss component of Eq. 8. The second is the reinvestment rate risk, which occurs when the investor reinvests the proceeds of the bond (that is, the periodic cash flows or the final payment at maturity) at a different interest rate than the (implied) yield to maturity. In general, we can see that these two types of risk can offset each other. An increase in interest rate lowers the current price of the bond, but because the future cash flows will be reinvested at a higher rate, the future value of the bond’s proceeds will be increased. For an economic analysis of the reinvestment risk, read the box titled Applying Economic Analysis, which discusses an alternative way to compute a bond’s total return. Bond Yield Measures There are several yield conventions used in the market and quoted by several market traders and portfolio managers. In this section, we explain the different yields, show how they are computed, and highlight their advantages and disadvantages. Current Yield The bond’s current yield (CY) is the ratio of the bond’s interest or coupon payment to the bond’s current price. ⎡interest (coupon) payment ⎤ Current yield = ⎢ ⎥ current price ⎣ ⎦

(11)

For example, if the bond has a 10% coupon rate and currently sells for $985, its current yield, CY, is $100/$985 = 10.15%. A bond’s current yield is higher for a discount bond and lower for a premium bond. For example, using the above data, the CY for the premium bond would be 8.89% ($100/$1124.7) and for the discount bond 11.2% ($100/$893.8). The disadvantage of the current yield measure is that it ignores the time value of money (and everything else that comes from that, including the other potential sources of return from the bond); but it is a useful and simple measure. Yield to Maturity Contrary to the current yield, the yield to maturity (YTM) is the most quoted bond yield measure and is computed by equating the present value of the bond’s cash flows to its current full market price. The full market price includes accrued interest. YTM

394 s Debt Securities

is a special case of the internal rate or return (IRR) method, which solves the formula for the discount rate that sets the net present value equal to zero. The formula for YTM is the same as using Eq. 5 and simply replacing r with YTM and solving for it. YTM is a promised yield or a yield that the investor earns when he keeps the bond to maturity. Sometimes YTM refers to the average rate of return earned if the bond is held to maturity. For example, what would be a bond’s YTM if the bond has a coupon rate of 10%, has 9 years to maturity, pays interest annually, and currently sells for $1,124.70? Let us plug those numbers into Eq. 5, which is reproduced here for convenience: $1,124.70 =

9

$100

∑ (1 + ytm)t t =1

+

$1, 000 (1 + ytm)9

Or, using the shortcut formula (Eq. 6) $1,124.70 = $100 (PVIFAytm,9) + $1,000 (PVIFytm,9) Solving for YTM would give us the answer. But that requires a trial-and-error approach, which can be tedious. So how do you know which discount rate to use first? First of all, recognize that the bond’s price is higher than par, and this should give you the clue that your first guess must be a discount rate of less than 10%. If you try 8%, you will see that this is the YTM that is consistent with the actual (observed) price of the bond.12 An annualized YTM (using simple interest techniques) is also known in the market as the bond-equivalent yield (BEY). For example, a doubling of the semiannual yield is a bond-equivalent yield, based on this (erroneous) market convention. Recall (from Chapter 3) that the appropriate way to annualize (and compare among different yields) is to express them in an effective basis (that is, compute the effective annual rate, or EAR). The YTM is an improvement over the current yield because it takes into account the timing of the cash flows. The relationship between the bond price, coupon rate, current yield, and yield to maturity can be expressed as follows: Bond sells at Par Discount Premium

Relationship coupon rate  current yield  yield to maturity coupon rate  current yield  yield to maturity coupon rate  current yield  yield to maturity

Yield to Put As mentioned earlier, many bonds have embedded options in their indenture, such as a put option. A put option allows the bondholder to receive the principal (from the bond issuer) of the bond when she exercises the option. The yield to put (YTP) is the interest rate that makes the present value of cash flows to the (assumed) put date plus the put price on the date (according to the put schedule) equal to the bond’s price. Again, YTP would be calculated in a similar way as YTM, except that the date that the put is exercised is substituted for the maturity date because the bondholder receives the par value on the exercise date just as if the bond matured.

Bond Fundamentals and Valuation s 395

Yield to Call A bond can have put and/or call options. If a bond is callable, the investor cannot earn YTM. What would be the adjustment to the bond’s price under a call option? With a callable bond, the bond’s issuer can redeem the bond prior to maturity and pay the call price, which is typically higher than the face value (M), to the bondholder. Typically, bonds are not called before 5 or 10 years after issuance, and these dates are known as the call date(s). Thus the yield to call (YTC) is the rate of return the investor earns if he held the bond until the (first) call date given that the bond was called. Alternatively, YTC represents the discount rate that equates the discounted value of a bond’s future cash flows to its current market price given that the bond is called on the call date. The formula for the calculation of the YTC is the same as Eq. 5 with two changes: first, M now becomes the call price, and second, T becomes T*, to denote the number of periods until the call date: P0 =

T

CF

∑ (1 + r)t t t =1

+

call price (1 + r)T

(12)

The computation of YTC is the same as the one to find YTM. The call price is usually the par value plus 1 year’s interest.13 Let us do some economic analysis on callable versus plain bonds. If, after the callable bond was issued, interest rates are higher, there is no profit from exercising the call option by the bond issuer. Thus, ceteris paribus, the values of a straight (that is, a bond without call options) and a callable bond are similar. When interest rates decline, however, the possibility of a call away for these bonds is more real and the two bonds’ values begin to diverge. In this case, bond market analysts may be more inclined to look at a bond’s YTC rather than its YTM, especially under a declining interest rate environment. The YTC makes the same assumptions as the YTM plus the assumption that the investor will hold the bond to its call date. The actual (and true) yield of a callable bond is less than its YTM because the bond’s call provisions limit the potential of price appreciation (the price of the bond cannot be higher than its call price). The reason is that the issuer will call the bond away immediately. Thus bond investors in practice compare the yield to (any) call (date) and the YTM and select the lower measure as the more realistic indication of the bond’s return. In other words, investors calculate all three yields mentioned above and consider the lowest of them, which they often call the yield to worst.

DURATION AND CONVEXITY We saw above that interest rate risk is essential to understanding how a bond’s price responds to changes in interest rates and, as we will see in Chapter 13, how a portfolio manager formulates bond strategies (active and passive). For these reasons, examining a bond price’s sensitivity to the interest rate, which includes measures of duration and convexity, is important. Duration Thus far we have learned about the various bond yields, the relationship between them, and the interest rate. We also saw (see Table 12.4) that bond prices change differently

396 s Debt Securities

depending on the maturity of the bond and its the coupon. Specifically, the bond’s price change (or volatility) varies directly with maturity and inversely with its coupon. The next logical question is: Can investors consider both effects on the bond’s price volatility? The answer is yes, by computing the bond’s duration. Duration has several interpretations. On interpretation of duration is that it measures the approximate percentage change in the price of a bond for a 1% (100 basis points, where a basis point is 1/100 of 1%) change in the interest rate. In other words, duration shows how sensitive a bond’s price is to a change in interest rate. Another interpretation, the original one, is that it measures the number of years it takes to recover the cost of the bond (after taking into account all coupon and principal payments). Box 12.3 contains the original duration measure as derived by Frederick Macaulay as well as the definitions (and application) of other duration measures. We discuss next the former definition of duration. A quick (and approximate) way to compute duration14 is the following: Duration =

P+ − P− 2 P0 Δr

(13)

where P+ is the estimated price of the bond if the yield (infinitesimally) decreases by r P– is the estimated price of the bond if the yield (infinitesimally) increases by r P0 is the initial price of the bond r is the change in the yield of the bond in decimal form For example, consider a 5% coupon-paying bond with 10 years to maturity trading currently at $100 (current price). Suppose that the yield changes to 4.5% or by 50 basis points (0.005, in decimal form). Its new price would be $105.4113. If the yield increased to 5.5%, its price would be $94.9376. Substituting these numbers into Eq. 13, we obtain a duration value of Duration =

$105.4113 − $94.9376 = 10.47 2 $(100) (0.005)

Thus this bond’s price will approximately change by 10.5% for a 1 percentage point (100 basis points) change in interest rates (consisting of 50 basis points down and 50 basis points up). This measure of duration is also known as (average) effective duration and is useful when interest rates move in a parallel fashion up or down. Practitioners use a variation of the above formula, defined as the percentage change in the price of the bond, P/P, as follows: ⎡ Δ (1 + r) ⎤ ΔP / P = −D × ⎢ ⎣ 1 + r ⎥⎦

(14)

Eq. 14 shows that the proportional change in the price of a bond is equal to the bond’s duration times the proportional change in (1 plus the) yield. The negative sign implies the inverse relationship between price and yield changes.

Bond Fundamentals and Valuation s 397

BOX 12.3 Duration Measures Frederick Macaulay derived the duration formula in 1938 while he was working at the National Bureau of Economic Research (NBER). In simple terms, the duration formula is as follows:

Macaulay duration =

n

(PVCF ) × t

t ∑ price of the bond t =1

where (PVCFt) is the present value of the bond’s cash flows (interest income or payments), t is the time to each cash flow (in years) and n the number of periods to maturity. Let us illustrate with an example. Assume a 4-year bond with a 10% coupon rate and annual payments. The prevailing interest rate is 7%. What is the bond’s duration (in years)? First, we need to compute the price of that bond to yield 7%. So, P0 = $100 (PVIFA7%,4) + $1,000 (PVIF7%,4) = $100 (3.3872) +$1,000 (0.7629) = $1,101.62 or, using present values P0 = $100 / (1.07)1 + $100 / (1.07)2 + $100 / (1.07)3 + $1,100 / (1.07)4 = $93.45 + $87.34 + $81.63 + $839.19 = $1,101.62 Thus, the Macaulay duration (MD) would be MD = [($93.45 × 1) + ($87.34 × 2) + ($81.63 × 3) + ($839.19 × 4)] / $1,101.62 = 3.54 Thus it takes 3.54 years to recoup the true cost of the bond. An extension of MD is the modified duration, computed as Modified duration = MD / (1 + r/n) In our example the modified duration would be 3.54/(1.07) = 3.38. Thus, for a very small (infinitesimal) percentage change in market interest rates, the bond’s price will change (inversely) by 3.38%. Note that the yield here is assumed to be one period; otherwise divide it by the compounding frequency. For example, divide r by 2 if the bond makes semiannual payments. The effective (or empirical) duration measure can be a more complex measure when it takes into account a bond’s embedded features, such as call and put, along with the bond’s coupon payments, yield, and maturity. Finally, there are other measures of duration, such as dollar value of 1% (change in interest rates), spread or option-adjusted spread, key rate, and average duration, but they fall outside the scope of this textbook.

Two special cases of duration exist: one which applies to perpetuities (or perpetual bonds) and another on zero-coupon bonds. The latter is the easiest to find because the duration of a zero-coupon bond is simply equal to its maturity date. The duration of perpetuity is equal to the ratio of 1 plus the yield over the yield: Duration of a perpetuity = (1 + r) / r

(14a)

398 s Debt Securities

For example, what is the duration of a perpetuity that pays $50 a year forever at a yield of 5%? Its duration would be 25 years, or (1 + 0.05)/0.05. Finally, the duration of a bond portfolio is defined as the weighted average duration of each bond’s duration multiplied (weighted) by their weights in the portfolio. For example, consider a three-bond portfolio with the following characteristics, as shown in Table 12.5. The portfolio’s duration is 5.667 and implies that if interest rates changed by 100 basis points, the value of the portfolio would change by about 5.67%. Note that each bond in the portfolio would change by a different amount owing to their different durations. What are some principles (properties) of duration and what are their implications? We begin with its three properties: sAs a bond’s maturity increases, duration increases, thus making the bond’s price more sensitive to interest rate changes, assuming the coupon rate does not change. sAs interest rate change, duration changes in the opposite direction, thus making the bond’s price less sensitive to further interest rate changes, ceteris paribus. sAs the bond’s coupon rate increases, the bond’s duration decreases and the bond’s price becomes less sensitive to interest rate changes, holding maturity constant. There are several implications of the above properties of duration. First, duration allows a portfolio manager to formulate investment strategies by deriving quantitative estimates of how much an interest rate bet would harm/benefit the portfolio following hypothetical (or actual) interest rate changes. Second, duration shows the differential impact of (beginning, less sensitive; later, more sensitive) coupon payments of a bond on the average maturity of the bond’s payments (this derives from the third property above). Finally, the higher the bond’s or portfolio’s duration, the higher the risk of price changes following interest rate changes. To summarize, the typical duration measures the sensitivity of the bond’s price change to a change in the interest rate (yield). However, recognize that this is a linear measure, but the relationship between the price of the bond and its yield is nonlinear (see Figure 12.2). As a result, duration cannot be an accurate (and complete) measure of approximating a bond’s price change to a change in interest rates. Stated differently, in using duration (the first derivative of the bond’s price change to a change in interest rates), we try to approximate a convex relationship (as in Figure 12.2) with a straight line (as in Figure 12.4). This means that the estimated price change will underestimate the true (actual) price change, which will be on the curve, and not on the tangent straight line.

Table 12.5 Characteristics of a Hypothetical Bond Portfolio Bond

Market Value

Portfolio Weight

Duration

Weighted Duration

X Y Z Total

$100,000 $200,000 $300,000 $600,000

16.67% 33.34% 50.00% 100.00%

3 5 7

0.500 1.667 3.500 5.667

Bond Fundamentals and Valuation s 399 bond price

Actual bond price (Convexity)

P*

Tangent (Duration) r*

yield

Figure 12.4 Bond price-yield relationship and tangent line.

Thus we need an additional measure to complement duration that would provide a better approximation to the bond’s price change to yield changes. This measure is convexity, which we turn to next. Convexity Convexity is the measure of the curvature of the bond’s price-yield relationship or the rate of change of the rate of change of a bond’s price to changes in interest rates. Convexity is then the second derivative of the bond’s duration. Instead of deriving the full convexity measure, we opt to present and apply the shortcut or approximation formula15: Covexity measure = P+ + P− +2 -2P0 P0 (Δr)

(15)

where, as in the case of duration, P+ is the estimated price of the bond if the yield (infinitesimally) decreases by r P- is the estimated price of the bond if the yield (infinitesimally) increases by r P0 is the initial price of the bond r is the change in the yield of the bond Using the above bond example, we make an infinitesimal change in the yield say, by 0.2% (from 12%), or 20 basis points, and obtain the following prices for the two yield changes: r = 12.2%  P– = $91.942 r = 11.8%  P+ = $93.344 P0 = $92.64 (at r = 12%)

400 s Debt Securities

Thus we substitute these values into Eq. 15 and obtain Convexity measure =

$91.942 + $93.344 − 2($92.64) = 15 ($92.64) (0.002) 2

It is difficult to interpret this number because it was derived using square numbers (in the yield); thus we can say only this: the value of convexity lies in the fact that it provides an insight into how a bond’s price responds to changes in the yield. Such reactions are not symmetric, however, as is evident from Figure 12.5. Specifically, a bond’s price decreases less for a given increase in yield but increases more for the same decrease in yield. In other words, the increase is higher than the decrease in the price. This is exactly what investors seek in a bond: to have higher convexity (curvature). What is the implication of convexity for a bond? If two bonds have the same duration but different convexities, then the bond with the greater convexity will be more valuable to investors because its price changes will be greater and thus losses lower (for higher yields) relative to the bond with smaller convexity. Obviously convexity is not free, which means that investors will either pay higher prices or accept lower yields (to maturity) for bonds with greater convexity. Box 12.4 highlights the importance of a bond’s convexity with an application to the US mortgage-backed securities market.

THE YIELD CURVE A graph showing the relationship between yields to maturity of various securities and their corresponding maturities is known as the yield curve. Stated differently, the yield curve represents the cost of money for all market traders. When traders in the United States refer to the yield curve, they refer to the US Treasury yield curve (and in other countries as the government securities yield curve). The traditional yield curve is constructed from the actual (observed) yields and maturities of Treasury securities because such securities are perceived to have no credit (default) risk and are highly liquid. However, as we noted earlier, this yield curve is not an adequate measure of the relationship between yields and maturities because securities with different maturities carry different yields. That is why market participant construct a theoretical Treasury yield (spot rate) curve with on-therun (most recently auctioned) or selected off-the-run (existing) Treasury issues. In this way, a Treasury security is forced to be priced on these spot rates and not the observed yield curve so as to avoid arbitrage opportunities. There are four common types (shapes) of the yield curve; these are shown in Figure 12.5 in two panels. Panel (a) shows two yield-curve shapes: an upward-sloping or normal curve, which shows a positive relationship between yields and maturities, and downward-sloping or inverted curve, which implies that longer-maturity bonds have lower yields than shorter-maturity bonds (securities). Panel (b) depicts two more yieldcurve shapes: a flat curve, which denotes similar yields for all maturities, and a humped curve, in which short- and long-term yields are lower than medium-term yields.16 When the yield curve changes shape say, from a normal to an inverted, we say that it experienced a “twist.” This means that short-term yields are higher than long-term yields. On September 21, 2011, the Fed announced that it plannned to reshuffle its portfolio by selling $400 billion worth of short-term government securities and to use the proceeds

Bond Fundamentals and Valuation s 401

BOX 12.4 The Importance of Bond Convexity In recent months, various US agencies such as the Federal Reserve and the Federal Deposit Insurance Corporation have been trying to assess the potential damage of a sudden increase in interest rates. Currently (April 2011), rates in the United States are very low, and the bond market has been shaken by the recent announcement by PIMCO, the largest US bond fund, that it is shorting or selling its US Treasury bonds. The fund fears that a sudden jump in interest rates is imminent, especially when the US debt/deficit situation is worsening. Moreover, mortgage spreads recently widened and there was some convexity-related buying causing 10-year T bonds to move down to 3.5% (as demand rises, prices go up and yields down). But what does a sharp rise in interest rates mean for bond investors and especially for mortgage-backed securities (MBS) investors? If history is of value, it is worth noting that in 1994 the US bond markets suffered a major shock when Alan Greenspan, the former Fed chairman, unexpectedly doubled short-term interest rates to 6% in a year. That caused long-term rates to jump from 6% to 8%. The markets also suffered because the structure of the US mortgage market created a so-called convexity problem. This essentially means that when rates rise, the duration of fixed-rate mortgages typically lengthens. In 1994, portfolio managers tried to hedge that by selling long-term Treasuries; this caused big losses for many investors and banks because they had previously been so confident that Greenspan would keep rates low that they had not hedged their exposures. To understand the convexity effect, you must know that when rates go down enough, homeowners refinance their mortgages at lower rates. Those investors who held MBS—or packages (pools) of individual home loans or mortgages—experienced a sudden drop in cash flows and, in order to offset this reduction, were forced to buy T bonds (such as 10-year ones). Thus as more buying takes place, yields continue to go lower, triggering (perhaps) another round of mortgage refinancing. This happens because in the United States, a homeowner is allowed to pay off his mortgage as soon as he wants (without waiting for 15 or 30 years to pay it off completely. Thus, mortgage refinancing caused MBS owners to hold cash instead of long-term cash flows, which, in turn, was reinvested at lower rates. That is why MBS—unlike typical bonds— lose value when interest rates fall. Such bonds are known to have negative convexity. Negative convexity also arises when bonds are callable, meaning that the issuer can pay the bonds off when rates are low enough to justify such an action. Therefore the bond’s price increases, but not as much as if the bond were not callable. Such a price compression is also known as a negatively convex price-yield curve.

to purchase $400 billion worth of long-term government securities by June 2012. The move was dubbed “operation twist.” The idea was to push long-term rates down in order to give another push to the sluggish economy. A similar move had taken place as recently as December 2005. In both instances, the stock market reacted negatively and the 10-year Treasury bond’s yield tumbled. Theories Explaining the Shape of the Yield Curve Several theories have been proposed to explain the shape(s) of the yield curve. Let us present each one of them very briefly.

402 s Debt Securities (a) Normal (4/2/2009) and inverted (2/28/2007) yield curves (YC) 6 5 yield

4 YC: 2/28/2007 YC: 4/2/2009

3 2 1 0 1 month

1 year

3 year

7 year

20 year

maturity

(b) Flat (but not perfectly flat) (4/1/2007) and humped (4/1/2000) yield curves (YC) 7 6

yield

5 4

YC: 4/1/2007 YC: 4/1/2000

3 2 1 0 1 90 1 2 3 5 7 10 20 30 month days year year year year year year year year maturity

Figure 12.5 Four actual shapes of the U.S yield curve.

Market Expectations Theory Simply put, the expectations theory suggests that the shape of the yield curve depends on investor expectations about future (short-term) interest rates. For example, if investors expect the 1-year interest rate to increase next year, the 2-year interest rate will also be increased. Stated differently, the forward rate equals the (current) market consensus expectation of the future interest rate. This relationship (of the forward rate) is captured by the following mathematical expression in general terms: (1 + rn)n = (1 + rn-1)n-1 × (1 + fn)

(16)

(1 + rn)n = (1 + rn-1)n-1 × [1 + E(r)n]

(16a)

where r denotes the yield to maturity (YTM) of a bond, with n-period maturity, and f is the forward rate or expected rate, E(r), for which we solve. For example, if a 4-year zerocoupon bond has YTM of 6%, and a 3-year zero-coupon bond has YTM of 5%, then the 4-year forward rate (or expected rate) would be

Bond Fundamentals and Valuation s 403

1 + f4 =

(1 + r4 )4 ( 1.06 )4 1.2625 = = = 1.0906 (1 + r3 )3 ( 1.05 )3 1.1576

thus f4 = 1.0906 – 1 = 0.0906 or 9.06%. According to the expectations hypothesis, the YTM of the bond then would have exclusively been determined by the current and expected interest rates. In this case, an upward-sloping curve would be implied. What is the economics behind this yield curve theory? Assume that economic news leads market participants to expect interest rates to rise, thus yielding a rising yield curve. How would market participants be affected by such an expectation? Some market agents (such as long-term borrowers) would want to borrow now so as to lock in lower interest rates in their loans; therefore they will demand more funds now. Other market agents who would be interested in purchasing long-term instruments (bonds) would also defer such purchases because they would expect the yield curve (structure) to rise soon, thus resulting in a price decline (and a capital loss) on such instruments. These traders would rather invest in short-term instruments now until the rise in yield has occurred, so that they can invest later at higher yields. Therefore the actions of those market participants would add to the demand for funds now (on short-term instruments), raising their prices and lowering their yields. At the same time, the excess supply of (or less demand for) long-term instruments (bonds) would lower their prices and raise their yields. These two demand and supply forces would produce an upward-sloping yield curve, consistent with the expectations of the market participants. Liquidity Preference Theory One shortcoming of the (pure) expectations theory is that it does not account for interest rate risk, which occurs when one is holding a bond with longer maturity and interest rates change. What would induce investors to hold long(er)-term securities in view of the fact that they are faced with uncertainty about long-maturity bonds when they do not have (prefer) long-term horizons? A rival theory, the liquidity preference theory, suggests that investors will want a premium for holding longer investment instruments. This liquidity premium compensates investors for holding such instruments and for tying up their money for long periods. As a result, longer-term bonds will have higher yields than shorter-term bonds, producing an upward-sloping yield curve. Higher yields also contain other premiums for holding bonds (such as default risk). To link this theory (which is a variant of the expectations theory) to the expectations theory, note that the forward rate would also reflect a liquidity premium, which should be higher for longer-term bonds (or longer maturities). In terms of mathematical expression, the forward rate can be shown as fn = E(rn) + liquidity premium

(17)

where fn is the forward rate at period n and E(rn) the expected short rate. Again, what is the rationale behind the liquidity preference theory of the yield curve? Investors respond to incentives, and one such incentive is compensation in the form of higher yield on an instrument. For example, if you do not intend to park your funds for a long period of time, how would you be enticed to reverse your preference? A higher yield on your investment and for taking one additional risk of (potentially) not being able to

404 s Debt Securities

convert your investments into cash (if you needed it) within a logical time frame would, perhaps, be enough for you. Obviously, other investors have different preferences and thus the size of the liquidity premium would vary. Market Segmentation Theory Proponents of this theory argue that investors have preferred investment horizons, short- and long-term, depending on the nature of their liabilities and investment objectives. As a result, the market segmentation theory argues that these investors do not normally deviate from their stated investment horizons; consequently the shape of the yield curve is solely determined by the relative forces of demand for and supply of securities in these market sectors. For example, assume that there is an excess demand for long-term securities relative to short-term securities at a particular point in time. This would raise the prices of bonds and lower their yields while lowering the prices of short-term bonds and raising their yields. The end result would be an inverted yield curve, since the shortterm securities would have higher yields than long-term securities. Naturally the opposite would occur when there was an excess demand for short-term securities relative to longterm securities, producing a normal yield curve. In general, the theory predicts a normal curve, since it assumes that short-term yields are lower than long-term yields (a stylized fact of the market), but it does not recognize that the forces of demand and supply are independent in each maturity sector. Preferred Habitat Theory This theory also endorses interest rate expectations and a liquidity (or risk) premium and represents a compromise between the expectations and the market segmentation theories. The preferred habitat theory also postulates that investors have habitats or “preferred maturities” in mind when it comes to investing. The preferred habitat theory argues that some lenders/borrowers in the market may be induced to invest outside their preferred market if there is a mismatch (need) in the demand for and supply of funds in a particular maturity sector. Again, they will ask for additional compensation (risk premium) for bearing their aversion to such risks (interest rate and reinvestment rate risks). Proponents of this theory in general believe that short-term investors are more common in the bond market and that therefore longer-term rates tend to be higher than short-term rates, although, on occasion, short-term rates can be higher than long-term rates. Thus, the shape of the yield curve, according to this theory, can be upward-sloping, downward-sloping, or flat depending on the expectations of future (short-term) rates, risk premiums, and the forces of demand for and supply of funds in the maturity sectors. Significance of the Yield Curve In general the yield curve is important to both investors and policymakers. Investors use the US Treasury yield curve to price and determine future payments on all instruments and identify those securities that are more attractive to buy or sell. Additionally, they formulate future strategies and current trading opportunities on shifts in the general interest rate structure and its shape. Policymakers (monetary and fiscal authorities) recognize the vast amount of information bond prices carry and thus monitor them closely in an effort to judge the current state of the economy (about inflation expectations and output). For example, a tightening of monetary policy should be accompanied by higher rates and thus a higher yield curve.

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The shape of the yield curve plays an important role, as we will see now. When investors expect the economy to grow normally without any serious inflationary pressures, the yield curve has the normal upward-sloping shape. Thus investors who have invested in long-term securities expect to earn a higher reward than those who have invested in short-term securities. A variation of the normal curve is a steep curve, when the yields on higher-term (30-year) bonds are much above the yields of short-term (1- or 3-month) securities (Treasury bills). In other words, the yield curve spread widens. This could be an indication that the market expects a quicker recovery of the economy (as was also the case during the early stages of the 2010 expansion). Sharp and huge shifts out of shortterm into long-term bonds also contribute to the steepening of the curve as investors demand higher yields for long-term securities. An inverted yield curve implies that long-term investors seek (and settle for) lower yields than short-term investors because they believe the economy will worsen in the future. Thus they seek to lock in these (now higher) rates before they fall even further in the near future. Inverted yield curves occur during recessions (or slowdowns), when short-term rate are higher than long-term rates (see Figure 12.5). Another example of such a curve was in 2004–2005 when foreign investors actively sought to purchase US Treasury securities because they were backed by the US government. Therefore such a sustained demand for such long-term products allowed the issuers to offer them at lower yields. This situation, which runs contrary to the laws of demand and supply, enabled bond issuers to find buyers without paying higher rates because these global buyers were mostly concerned with an impending economic slowdown. In general, an inverted yield curve is (considered to be) a rare phenomenon and represents an “economic anomaly” because it ignores the risk premium as maturity (of a security) lengthens. Finally, a flat curve occurs when the economy moves from a recession to an expansion as interest rates begin to (slowly) rise, thus giving rise to a positive slope of the yield curve. A flat curve means that the short- and long-term yields are converging. Just like an inverted curve, it too does not happen very often (another example of a flat curve was in 1989), as short- and long-term investors roughly earn the same return on securities. In between these adjustments, a humped yield curve may also occur, which implies that short- and long-term yields are similar and lower than intermediate-term yields. It is believed that such a curve signals the beginning of a recession (or the end of an expansion) because a yield must flatten first before becoming inverted. However, its shape depends on investor (market) expectations about the future and the relative demand for and supply of long-term securities. Naturally, the latter becomes important in uncertain times, when investors flock to US Treasuries (in a so-called “flight to quality”), thus decreasing the yields of short-term securities (due to price increases following strong demand) and increasing those of long-term Treasuries. The net effect would be a steepening of the yield curve. Which other factors, besides monetary policy and inflation expectations, can affect the shape and slope of the yield curve? Fiscal policy and the value of the US dollar are also important determinants of the shape and slope of the yield curve. For example, if the government runs unsustainable budget deficits, as is the current case in the United States, investors would not invest in longer-term Treasuries for fear that they might not be repaid if the country is (expected to be) headed for default. However, if they are to invest long term, they might demand very high risk premiums, thus raising long-term

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yields and lowering short-term ones. These outcomes would steepen the yield curve. Finally, if a strong US economy reflects a strong demand by investors due to brightening economic prospects, the yield curve will start steepening (and rising) as longer-term rates rise relative to shorter term ones. Box 12.5 summarizes these factors. In general, the market looks at the yield curve for guidance on the future state of the economy (the yield curve is a leading economic indicator) and the empirical evidence on the success of the yield curve as predictor of future economic activity is good.17 A Simple Strategy Using the Yield Curve The yield curve is very important for bond portfolio managers who construct strategies based on its shape and direction in an effort to realize higher returns in various interest rate environments. Specific strategies will be presented and discussed in the next chapter. However, in this section we will present a simple strategy that fixed-income managers apply, known as riding the yield curve. Specifically, with an upward-sloping curve, bond portfolio managers value successive bonds, as they approach maturity, at lower yields and higher prices. So an investor holds a bond for a while until it appreciates in price and then sells it (before it reaches maturity) for a profit. The crucial assumption, however, is that the yield curve remain unchanged and normal (i.e., upward-sloping) throughout this bond swapping process. Let us illustrate with a simple example and using available T-bill information. 0n December 1, 2011, a 13-week T bill yielded 0.031% and sold for $99.9924 (per $100), while a 4-week T bill yielded 0.020% and sold for $99.9984. If you bought the longermaturity bill, held it for 4 weeks, and sold it at the prevailing (future) 4-week price, it would then generate the following profit, in dollars and percentage points: $99.9984 – $99.9924 = $0.006 ($99.9984 − $99.9924)/99.9924 = 0.006% or an annualized yield of 0.078% (or 0.006% times 13 weeks to a year). This yield is considerably higher than what might be earned by simply purchasing a 13-week bill and holding it to maturity. In general, the yield curve is an information tool because brokers and other traders identify the most attractive securities for trading based on a favorable curve shift. Decisions to lengthen or shorten the maturities of investments are also influenced by expectations about the shape and position of the yield curve. For example, if you expect an economic slowdown in the near future (maybe in 1 or 2 years), you might want to shift your allocation of assets (such as equities) toward those sectors (industries) that are expected to fare better (i.e., the countercyclical or defensive companies). If you are also a consumer and ponder the purchase of a new car or a house (in this case, you are also an investor in real estate) and expect a slowdown in economic activity, you need to realize that you might lose some return in real estate but gain in the purchase (and financing) of your new car. Before concluding this discussion, we want to mention that there are more strategies based on the yield curve involving shifts in the curve. Such strategies (or yield curve strategies) involve positioning the bond portfolio to exploit expected changes in the shape of the Treasury yield curve. We will explore some of these strategies in the next chapter.

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CHAPTER SUMMARY In this chapter, we discussed the fundamentals of a bond and its valuation. We mentioned the features of a bond by type of issuer (government or private), characteristic (option and option-free), and other measures (such as risk). Then we presented the basic bond valuation formula and illustrated the inverse relationship between a bond’s price and its yield. We derived three fundamental insights about the price of a bond under three interest rate environments (unchanging, rising, and falling). We illustrated these analyses using graphs and examples. Next, we presented the basic measures of yield (current yield, yield to maturity, and yield to call) that an investor should be aware of in deciding which type of bond to

BOX 12.5 Factors that Affect the Shape of the Yield Curve and Their Implications Each of the factors below may change the slope, curvature, and level of the yield curve.

MONETARY POLICY A steep curve may be an indication of higher expectations of future increase in short-term rates, like the Fed funds rate.

FISCAL POLICY High and rising budget deficits steepen the yield curve, while falling budget deficits flatten it.

INFLATION (EXPECTATIONS) If inflation expectations are expected to increase in the long term, a steep curve may reflect such expectations relative to the short term. Investors may demand higher yields for long-term investments compared with short-term investments.

STAGE OF THE MACROECONOMY When the economy is in the early stages of an economic downturn, the curve tends to steepen, and when the economy is recovering, the curve becomes flatter. Also, changes in exports and imports or the current account deficit/surplus affect the yield curve through changes in interest rates.

DEMAND/SUPPLY OF TREASURIES Unexpected changes in the supply of and/or demand for Treasuries can affect the shape of the yield curve because the base interest rate changes.

THE US DOLLAR Stronger economic growth strengthens the dollar and pushes up interest rates, thus raising and steepening the yield curve. Sources: Federal Reserve Bank of San Francisco Economic Letter, June 2006; A. Garner, The yield curve and inflation expectations, Federal Reserve Bank of Kansas City, Economic Review, September/October 1987.

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purchase. Then we addressed the important question of what happens to a bond’s price (volatility) when interest rates change by presenting the concepts of the duration and convexity of a bond. We showed these measures using examples and graphs. Finally, we presented a section on the yield curve, which shows the relationship between a bond’s yield and maturity structure, and outlined the four competing theories on its shape (normal, inverted, or flat). We ended the section by showing how an investor can use the yield curve to profit from it in swapping bonds. In the next chapter, these insights will be useful for learning about and formulating bond portfolios and strategies.

APPLYING ECONOMIC ANALYSIS A BOND’S REINVESTMENT RISK We presented above the bond’s total return when the bond is held to maturity. There are two important questions an investor must answer: First, should I invest my funds in a bond or should I place my funds in a bank account? Second, what is the reinvestment risk? We will make some assumptions before we answer these questions. One, that the reinvestment of interest will be at the current interest rate, and two, that the dollar return is potential (promised), since the investor holds the bond to maturity. Just as we computed the bond’s total rate of return, we can also compute the bond’s total dollar return from the same three sources—that is, coupon interest, capital gain/loss, and reinvestment of interest income. For example, for a bond with a 10% coupon, 15 years to maturity, and making semiannual payments, the dollar return from each source is: Total coupon interest (payment, PMT): $50 every 6 months for (15 years), 30 periods = $1,500 Capital gain/loss: $1,000—current price (at 12%) of $862.35 = $137.65 Reinvestment income: assuming a reinvestment rate (r) of 12% annually (or 6% ⎡(1 + r)n − 1⎤ semiannually), we have coupon interest + interest on interest = PMT ⎢ ⎥ − n PMT = r ⎣ ⎦ ⎡( 1.06 )30 − 1⎤ 50 ⎢ ⎥ − 30(50) $2,452.90. Thus, the (potential) total dollar return from this bond ⎣ 0.06 ⎦ would be $1,500 + $137.65 + $2,452.90 = $4,090.55. In other words, an amount of $862.35 invested in that bond would generate an amount of $4,090.55 plus the initial investment amount of $862.35. If the investor had placed the initial funds of $862.35 in a savings account earning 6% semiannually for 15 years, he would have earned $862.35(1.06)30 = $4,953.60, which is exactly the same amount as the bond. So he should be indifferent between the two investments, ceteris paribus. What about the reinvestment rate risk? For the bond to yield 12%, it must produce $2,452.90 by reinvesting the coupon payments. Stated differently, in order to generate a yield to maturity of 12%, the bond must earn approximately 60% ($2,452.90/$4,090.55) from reinvesting the coupon interest (payments). Thus the risk the investor faces is that the reinvestment of coupon payments may be less than the yield to maturity, hence the reinvestment rate risk. If that rate is less than the yield to maturity because of interest rate declines, then the bank account option may be more appealing. Therefore the investor must do this comparative analysis before deciding which instrument to invest in.

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INTERNATIONAL FOCUS EUROZONE’S SOVEREIGN DEBT CRISIS In 2010, the eurozone plunged into a situation where several of its peripheral countries faced severe government debt crises. These countries were Portugal, Ireland, Greece, and Spain (hence, the colorful acronym PIGS). Greece came first when both the International Monetary Fund (IMF) and the European Central Bank (ECB) came up with a rescue plan of almost 110 billion euros. Greece’s debt burden approached 150% of its GDP and the severe austerity measures put in place were designed to reduce the country’s excessive spending and raise its revenues. Greece’s debt-to-GDP level in early 2012 stood at 160%. Ireland, facing similar debt burdens (almost 125% of its GDP), also requested a bailout program in 2010 from the ECB and IMF. Portugal, whose debt-to-GDP ratio reached 100%, is (in April 2011) near the end of discussions before accepting a bailout package, and Spain is on a similar path. In February 2012, it reached 110% and is expected to soar to 118% by 2013. The Spanish economy (with a debt-to-GDP ratio of 55%) is far bigger than any of the three economies above; thus the rescue rationale is different. The Spanish debt level as of February 2012 stood at 67% of its GDP. Specifically, most of Greece’s debt is owned by domestic banks. The Portuguese austerity plan failed to win approval from the country’s parliament (resulting in resignation of the country’s prime minister). The Irish debt crisis was created by the high leverage of its banking sector. By contrast, the Spanish economy, which is the fourth largest in the eurozone, is considered “too big to bail out.” Spain’s debt was recently downgraded by Moody’s. Recent discussions on the sovereign debt situation call for debt restructuring, a reduction of debt levels, or a prolonging of the debt repayment. In fact, in April 2102 private creditors have agreed to engage in approximately 53% debt reduction in Greece’s debt (the program is known as private sector involvement or PSI) and restructure (extend) the rest for many more years in the future. One reason is that these countries’ austerity programs are not generating the desired effects of curbing spending and raising revenues. The other reasons involve the viability (and stability) of the euro, as potential defections could spell trouble for the eurozone (let alone for those nations who abandon it). Capital markets might demand higher guarantees (translating to higher interest rates) for long-term loans from the remaining nations, which could tumble the value of the common currency. Sources: A question of maturity, The Economist, April 20, 2011; They are bust: admit it, The Economist, March 31, 2011.

LESSONS OF OUR TIMES In April 2011, for the first time, Standard & Poor’s warned of a possible downgrading of the US debt (Treasury securities) if the United States did not get its fiscal house in order. The company did not reduce the country’s AAA rating, however, but reported that it gave a negative outlook. S&P finally stood by its warning and downgraded the US debt to AA+ grade in August 5, 2011. The US debt currently stands at over $14 trillion and is expected to jump in the near future due to spending increases on entitlements, health care, and defense. What would be the implications of an actual downgrading of US debt? A downgrade would spike interest rates on Treasuries, raising the cost of borrowing throughout the economy. That

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is because Treasuries are considered benchmark rates upon which all other rates in the economy are based. Thus, higher interest rates could harm economic recovery. Second, an actual downgrade would have severe implications for the Chinese economy, because it is the largest holder of US debt abroad. Another consequence of a downgrade of Treasuries, according to some analysts, is that stocks could benefit from such a decline in demand from Treasuries (as bonds would be worth less if rates climbed). Of course, other analysts believe that a downgrade warning would help Treasuries because it would make them more attractive in the long run. Finally, an actual downgrade would also have implications for the risk-free security, the only one of its kind in the world, which might not attract investments from investors worldwide in times of financial turmoil and uncertainty. Sources: US warned on debt load, Wall Street Journal, April 19, 2011; US bond downgrade would help stocks, hurt bonds, Denver Post, April 19, 2011; How S&P’s warning could actually help US debt, Associated Press, April 25, 2011.

KEY CONCEPTS A fixed-income security is one that pays an even specified amount (cash flow) over a predetermined period. A bond is a promissory note (security) that obliges the issuer to make specific payments to its holder during a specified period. The indenture is the contract of the bond. Treasury inflation-protected securities are marketable securities whose principal is adjusted for changes in inflation. Eurobonds are bonds issued in one currency but sold in other markets at that currency. A sovereign bond is a bond issue by a national government but in a foreign currency. A call option is a provision that allows the issuer of the bond to buy back the bond at a predetermined price at some future time. A put option is an option that permits the bondholder to redeem (sell back) to the issuer a bond earlier than its maturity date. A convertibility option gives bondholders the option to convert their bonds into a specified number of shares of common stock of the same company at a certain future period. An exchangeable bond is one that allows the holder to exchange the bond into shares of stock of another company. A floating-rate bond makes variable interest payments; its coupon rate is tied to a market interest rate or reference rate. Default risk refers to the risk that companies may be unable to meet their contractual obligations.

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Refunding of a bond means the replacement of a current, high-coupon bond issue with (the issuance of) new, lower-coupon bonds. A junk bond is a special type of high-risk, high-yielding bond. Interest rate risk emerges because of the inverse relationship between a bond’s price and the interest rate. Reinvestment rate risk occurs when the investor reinvests the proceeds of the bond at different interest rate than the (implied) yield to maturity. A bond’s current yield is the ratio of the bond’s interest or coupon payment to the bond’s current price. The yield to maturity is a promised yield or a yield that the investor earns when he keeps the bond to maturity. The yield to put is the interest rate that makes the present value of cash flows to the put date plus the put price on the date equal to the bond’s price. The yield to call is the rate of return an investor earns if the bond is held until the call date given that the bond was called. Duration is defined as the approximate percentage change in the price of a bond for a 1% change in yield. Convexity is the measure of the curvature of the bond price-yield relationship or the second derivative of how the price of a bond varies with interest rates. A yield curve is a graph showing the relationship between yields to maturity of various securities and their corresponding maturities. The market expectations theory of the yield curve suggests that the shape of the yield curve depends on investor expectations about future interest rates. The liquidity preference theory of the yield curve suggests that investors will want a premium for holding longer investment instruments. The market segmentation theory of the yield curve contends that investors have preferred investment horizons, short- and long-term, depending upon the nature of their liabilities and investment objectives. The preferred habitat theory of the yield curve postulates that investors have habitats or preferred maturities in mind when investing.

QUESTIONS AND PROBLEMS 1. Assume a bond with the following data: a coupon rate of 6%, maturity of 10 years, making semiannual payments. a. Calculate the value of the bond 1 year after the bond was issued, assuming that market interest rates remained the same.

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b. Calculate the value of the bond 2 years after the bond was issued, assuming that market interest rates remained the same. c. Compute the rate of return of the bond during this 1-year holding period. 2. Assume a bond with the following data: a coupon rate of 8%, maturity of 10 years, making semiannual payments. a. Calculate the value of the bond 1 year later, assuming that market interest rates fall to 6%. b. Calculate the value of the bond 2 years after the bond was issued, assuming that market interest rates rise to 8%. c. Illustrate these results with a graph. 3. Assume the following information for an existing zero-coupon bond: a par value of $10,000, maturity of 3 years, with a required rate of return of 12%. How much should investors be willing to pay for the bond? 4. Is the price of a long-term bond more or less sensitive to a change in interest rates than the price of a short-term security? If so, why? 5. Analysts suggest that a major economic expansion will favorably affect the prices of fixed-rate bonds, because the credit risk of bonds will decline as corporations realize better performance. Do you agree with these analysts’ conclusion if this economic scenario materializes? Explain. 6. Assume a shift in the yield curve, steeper today than it was a couple of days ago. If a company issues new bonds today, would its bonds sell for higher or lower prices than if it had issued the bonds a couple of days ago? Explain. 7. Read the following statements, taken from various financial newspapers, and answer the question(s) below each statement: a. A UK bond auction struggled to attract investors on Thursday amid further signs of strains in the gilts market because of the record amount of debt taken on by the government to revive the economy. The poor auction helped trigger a sell-off in the secondary market, and yields on 10-year benchmark gilts jumped 24 basis points to 3.36 per cent. Increasing risk appetite also undermined government bonds. (D. Oakley, Financial Times, April 2, 2009) 1. What is the interpretation of the inability of the auction to attract investors? 2. Why did the yield on the 10-year benchmark gilt increase? 3. What is the meaning of the last sentence of the above passage? b. Treasuries fell across the board as investors cut bond holdings ahead of next week’s auctions after the government reported fewer job losses for March than forecast. (Wall Street Journal, April 5, 2009) Interpret this statement in terms of bond prices and yields. c. Just under half of corporate debt in America was rated as “speculative” (BB or below) at the end of last year, according to Standard & Poor’s, a rating agency. The share of junk-bond issuers in the corporate-bond market had risen from a low of 28% in 1992. Most of the increase in junk issuance was in the B category. The increase reflects the expansion of capital markets to embrace more marginal firms. (The Economist, Feb. 26, 2009)

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What is the interpretation of an increase in junk bond issuance and of the last sentence in this statement? 8. Consult the financial press in today’s paper and record the 13-week and 26-week Treasury bill yields and prices. See if you can make some money by “riding the yield curve.” 9. Answer the questions below. a. Why do holders of mortgage-backed securities (MBS) suffer more when interest rates in the economy fall, triggering mortgage refinancing? b. Why do MBS lose more value relative to a plain bond when interest rates fall? What is this effect called? c. Why and how does mortgage refinancing disrupt the duration of an MBS investor’s portfolio? d. What would investors of, say, pension funds that have future liabilities to fund do if refinancing took place? 10. Describe how bond convexity affects the price-yield relationship of a bond. What are some of the implications of bond convexity for an investor trying to choose among bonds? 11. Explain the actions that an issuer and/or a holder of a callable and/or putable bond would take if interest rates in the economy fell or rose enough for such actions to be taken profitably. 12. What would entice you to invest in the longer-term end of the market if you were comfortable investing in the short-term end of the market? Which theories explain such movements? 13. Consider a 7% coupon bond with 5 years to maturity trading currently at $100 and making annual payments. Find the bond’s prices for a 100 basis points increase and 100 basis points decrease in the yield. Obtain the bond’s duration and interpret the result. 14. If the required liquidity premium for a short-term investor is 2%, what must the expected short rate be if the forward rate is 5%?

NOTES 1. 2.

3. 4. 5. 6. 7. 8. 9. 10. 11.

European Central Bank, The Euro Bond Market Study, 2004. J. Y. Campbell, R. Shiller, and L. M. Viciera, Understanding inflation-indexed bond markets, working paper, available at http://kuznets.fas.harvard.edu/~campbell/papers/CampbellShillerViceira_20090503. pdf M. Fleckenstein, F. A. Longstaff, and H. Lustig, Why does the Treasury issue TIPS? The TIPS-Treasury bond puzzle, NBER Working Paper number 16358, September 2010. Sources: SIFMA, CNNMoney.com and investinginbonds.com. ibid. It is still possible for the investor to pay taxes (at all levels of government) on the imputed or not actually received interest that accrues each year. European Central Bank, The Eurobond Market Study, December 2004. Read again the Appendix in Chapter 3 on present/future value calculations. For those students who want to be more mathematically savvy, here are the mathematical expressions for PVIFA and PVIF: 1/r[1−1/(1+r)T] and 1/(1+r)T, respectively. You can also find expanded tables either on the Internet by doing a search in any finance textbook. You can also compute a bond’s price using EXCEL. The relevant EXCEL function is PRICE. By inserting the above values along with the frequency input of 1 (for yearly payments or 2 for semiannual payments), you can obtain the same number(s) above.

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13. 14. 15. 16.

17.

The easiest approach is to use EXCEL and its function of YIELD. Thus, for the example above, type in the cells 1/1/2,000 for settlement, 1/1/2,009 for maturity, 10% for rate, 112.47 for price, 100 for redemption, 1 for frequency (to denote yearly payments), and leave blank the basis input. Click OK to obtain 8%. As with YTM, you can compute the YTC using the same EXCEL function substituting price for the call price. F. Fabozzi, Bond Markets, Analysis and Strategies, 4th ed. (Englewood Cliffs, NJ: Prentice Hall,). Ibid. If you want to see the shapes of the US yield curve over time in a dynamic setting (that is, by changing daily dates), visit the US Department of the Treasury (treasury.gov) and select Resource Center from the main menu. Then select Data and Charts Center and click on View Historic Treasury Yield Curve Chart. Arturo Estrella and Mary R. Tubin, The yield curve as a leading indicator: some practical issues, Current Issues in Economics and Finance, Federal Reserve of New York, Vol. 12(5), August 2006.

13 BOND PORTFOLIO MANAGEMENT AND PERFORMANCE EVALUATION

CHAPTER OBJECTIVES After studying this chapter, you should be able to sUnderstand the investment management process and its steps sKnow the pros and cons of the two main investment approaches, passive and active sDistinguish among the various passive and active investment strategies sMeasure and evaluate a bond portfolio’s performance

INTRODUCTION In this chapter, we will employ some of the techniques discussed in the previous chapter to build and manage bond portfolios. Specifically, the insight on interest rate risk is very important for applying two basic bond portfolio strategies, passive and active. As discussed previously, when a portfolio manager adopts a passive approach to investing he or she takes the prices of assets (securities) as given (determined) by the market. The manager makes no attempt to beat the market by searching for additional information, instead trying tries to maintain a balance between risk and return of the portfolio’s holdings. By contrast, in pursuing an active investment strategy, the manager attempts to outsmart the market and realize superior returns by exploiting information. Active portfolio managers also engage in forecasting and timing of the market in order to identify those equity sectors that are expected to outperform or those bonds that are mispriced, formulating their strategies accordingly. Naturally, within the various active bond investment strategies, special cases are available to manage and/or protect a portfolio, such as immunization and other competing active strategies, such as matched-funding techniques. In the second part of this chapter, we will present some portfolio performance evaluation measures and illustrate attribution analysis. We will also recall what is required of a manager before attempting to derive suitable measures to evaluate his or her performance. After all, as is typically the case, clients hire professional managers to manage 415

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their portfolios and earn above-market returns; thus clients want to evaluate them to see if such a cost is justified. We conclude the chapter by looking at the implications of the efficient market hypothesis for bond portfolio management strategies. We begin with the various steps in the (general) investment management process.

OVERVIEW OF THE BOND INVSTMENT MANAGEMENT PROCESS Recall from Chapter 2 that the investment process comprises two main steps: asset allocation and security selection. In that chapter, we also discussed the investor’s investment philosophy and risk tolerance. Finally, we also listed the two investment approaches (top-down and bottom-up) and investment strategies (active and passive). In this section, we blend all these insights to derive the steps in constructing a simple bond (or an equity, for that matter) portfolio. Bonds are a good way to ensure that funds will be available in the future when needed, ceteris paribus. This is because typically bonds have fixed payments and a specific maturity date. Bonds can also help to define your investment goals, which can range from preserving capital to managing risks and liabilities. Several strategies are available to achieve one or more of these goals, ranging from the simple buy-and-hold strategy to complex, active investment strategies involving asset/liability management and contingent procedures. Irrespective of the strategy adopted, the investor must follow the following four steps in the investment management process: sIdentify the objectives and constraints as well as the appetite for risk sEstablish the investment policy statement guidelines sSelect an appropriate investment strategy sMonitor, evaluate, and adjust the bond portfolio We begin with the first step in building a bond portfolio: the identification of investor objectives and constraints. Identification of Investor Objectives and Constraints An investor’s objectives and constraints vary by type of investor: individual (retail) or institutional. As discussed in Chapter 1, individual investors typically have various investment objectives depending on age, preferences, and the like. Here we discuss these objectives within the context of constructing a bond portfolio. Some return objectives that all bond investors have are as follows: Capital Preservation. This involves protecting the capital (principal) and should be set according to the pace of inflation so as to maintain, at least, a constant purchasing power. Current Income. This objective is suitable for investors who want to have (and perhaps live on) current income from their invested capital base. Capital Growth. Here the capital base grows (appreciates), and this growth should be set above the rate of inflation. Naturally, for individual investors these objectives also depend upon their attitude toward risk; that is, whether they are conservative or aggressive investors, and the stage

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of their life, young or old. For institutional investors, these objectives vary by type of institution. For instance, a pension fund would seek to earn enough cash from its investments in order to satisfy specific future member pension obligations. A bank’s objective would be to generate a rate of return on invested funds (in marketable securities, for example) that is greater than the cost of obtaining these funds (from certificates of deposit, for instance). Before creating an investment policy statement (IPS), the investor must also carefully identify those of her constraints (limitations) that would prevent or limit her from earning a target rate of return. Some of these constraints (first discussed in Chapter 1) are as follows: Time Horizon. Investors have different investment horizons, which affect their willingness (and ability) to accept more or less risk. Such a constraint also develops because of a “conflict” between the investor’s age and her financial needs. For example, an investor nearing retirement may be unwilling to invest in risky securities. Liquidity Needs. Investors have different needs for liquidity, depending on their age and the types of investments. If investors have high needs for liquid assets, shorter-term bonds, which can easily and quickly be converted into cash, may be appropriate. Other Constraints. Other investment constraints that investors face are tax liabilities, regulatory issues, and legal situations. These may prevent them from realizing a target rate of return if not properly accounted for, and they must not be ignored. In general, these constraints are relevant for establishing not only the investment policy but also for choosing the appropriate investment strategy, as we will see below. Establishment of Investment Policy Once the investor has identified his investment objectives and constraints, then he should proceed with setting his investment policy guidelines. Recall that the investment policy statement (IPS) refers to a document between the investor and the investment manager stating the manner in which the investor’s funds are to be managed. A major part of this document is the portfolio’s asset allocation decision. This document also includes the objectives and constraints of both parties and lays out the procedures, investment philosophy, and other guidelines to be followed by both parties. When they are investing on behalf of the sponsor (institutional client), investment advisers are also confronted by additional constraints, such as limitations on where the funds will be invested—in a specific sector (industry), for example—or on which bond grade, such as investment-grade bonds, may be acceptable. In general, some clients may have limitations (also by state law) as to which securities to hold in their portfolios. For example, pension funds or insurance companies are not allowed to invest in high-risk securities. They should use options and futures only to protect asset values. Institutional investors are also required by law to prepare and make public financial reports periodically (following the generally accepted accounting principles, or GAAP). Although such a requirement is good for investors, in terms of transparency of activities, it may generate complications for the institution’s investment policy. For example, before the adoption of rule 115 of the US Financial Accounting Standards Board (see Box 13.1), financial reporting requirements were set to use valuations of assets based on costs and not market

418 s Debt Securities

values (that is, marking them to market). The financial troubles of 2007 and 2008, however, made FASB reconsider this rule and allowed for a more lenient reporting requirement for institutions (such as banks), as Box 13.1 suggests. Establishing investment policy next involves the asset allocation decision. Asset allocation refers to the fraction of the total investment budget allocated to various asset classes, such as bonds and stocks. The question of why the investor should allocate might be asked. The answer is simple: you need to diversify your assets so as to spread the various risks. In that way, when one asset performs poorly, another may compensate for the asset’s poor performance. In fact, many investment advisers cite asset allocation as the most important step in the whole investment process (and that is what we stressed in Chapter 2). Another, equally interesting question would be how much of your funds to allocate to bonds. The answer to this question largely depends upon your own personal objectives, constraints, and risk tolerance. In general, bonds carry less risk than stocks because bonds typically represent a promise to pay bondholders periodically and at maturity. Even in the event of the bond issuer going into bankruptcy, bondholders get paid first (before stockholders); thus this promise is generally kept. Also, not all bonds have the same risk. Corporate bonds are riskier than government bonds, for example. Finally, some bonds are tax-exempt, like municipal securities; thus including them in your bond portfolio would make sense if you were in a high income tax bracket. The final decision is yours based on your personal financial specifics. The financial crisis of 2008 and the recent European sovereign bond crisis brought about several changes in the way institutional investors like pension funds and insurance companies should manage their bond portfolios. Box 13.2 discusses how pension funds in the United Kingdom have changed their investment policies regarding bond portfolios, and the box Lessons of Our Times discusses several new trends shaping the European insurance industry.

BOX 13.1 Recent Developments in Marking-to-Market Rules FASB EASES MARK-TO-MARKET RULES In April 2, 2009, in the middle of the global financial crisis, the US Financial Accounting Standards Board (FASB) eased the fair-value accounting rule so as to permit companies (and financial institutions) to limit their losses by allowing them to apply significant judgment in gauging the market prices of some investments such as mortgage-backed securities. Proponents say that such a change would permit banks to limit their write-downs and increase their net income. The move was made in response to the concern that the marking-to-market practice is often flawed when the markets do not function, as during periods of severe financial crises. Thus leaving the fair-value accounting principle unchanged would unfairly punish financial companies and endanger, unnecessarily, the system’s stability. Although banks and business groups welcomed the change, certain investor groups opposed it, arguing that big banks would be able to hide the true value of their “toxic assets.” In addition, certain investment managers worried that the rule change would give managers room to manipulate the truth as recorded in financial statements. Sources: The Economist, Bloomberg, and Reuters.

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Selection of a Bond Portfolio Management Strategy Once the investor’s goals and constraints have been set, the next step in the investment management process is to choose an appropriate portfolio strategy. In general, two types of portfolio management strategies are available: active and passive. The selection of either one depends on several factors particular to both the investor and the financial adviser (manager). In considering the proper bond investment strategy to follow, the issue of diversification is important, since choosing bonds of different maturities and issuers also offers protection from other risks, such as interest rate risk. If you want to preserve your capital and earn interest, a simple passive investment strategy is appropriate. Moreover, you need not be concerned about bond value fluctuations during your investment time frame because you buy the bond and hold it to maturity. Examples of such bonds are US Treasuries, both notes and bonds. Besides bonds, you could also invest in certificates of deposit (CDs). If you create a system (or ladder, see below) of such CDs, you can access your money easily and earn a higher yield. Finally, interest-bearing (money market) bank accounts could qualify as places to preserve capital in view of their liquidity and market-determined return. If your objective is to maximize interest income, you should choose bonds with high coupon rates and perhaps longer-term bonds. Such bonds, however, carry higher risks because their prices are more prone to interest rate changes over time. Regardless, these fluctuations should not worry you if you are a long-term buy-and-hold investor. Alternatively, you could invest in high-yielding or “junk” bonds, but the risks are higher. Finally, if you invest so as to accumulate a certain sum for the near future (say to buy a house or to put your child through college), some bonds (like zero-coupon bonds) offer such possibilities as long as you do not sell them before maturity. Other factors— such as selecting between a taxable zero-coupon and a tax-exempt bond and whether to hold your investments in a taxable or a tax-deferred account—play a role in this case as well.

BOX 13.2 Passive Investment Strategy and Pension Funds in the United Kingdom PENSION FUNDS SWITCH TO PASSIVE MANAGEMENT For a period of 5 years, from 2003 to 2008, the total annual costs of managing a pension fund have increased by 50%. Pension schemes were paying for outperformance (or alpha) while getting average performance (or beta). Since then, pension funds shifted away from peer-group comparisons to “liability-driven” strategies. A liability-driven strategy is one that secures a series of cash flows to ensure the full funding of a future liability. Analysts believe that the switch to more passive management was due to passive products offered in response to overpriced active products. Analysts also believe that they are seeing more and more of active strategies disguised in passive structures. More and more pension funds are putting a smaller portion of their portfolios into active products while removing poor-performing active managers. In addition, passive management strategies are a convenient way to park funds while you look for an active manager to manage these funds. What you get is a cheap way of rebalancing your portfolio. Source: Financial Times (FT.com), May 4, 2008.

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In selecting active investment strategies, additional considerations need to be taken into account, such as market or manager expectations about future economic activity (including interest rates and other macromagnitudes) at home and abroad, which could influence the performance of the bond class. In an active investment strategy, the portfolio manager attempts to construct efficient portfolios that maximize expected return for a given level of risk. Naturally, in between these two “extreme” strategies, intermediate strategies involving both active and passive insights have been developed. One such bond strategy is enhanced indexing (which will be discussed shortly). In sum, the investor and portfolio manager must jointly decide which of these (and more) strategies are best for the situation; selection of the proper one will depend on their views about market efficiency and the nature of the investment (or liabilities) sought by the client (investor). As discussed in Chapter 9, if an investor believes in the efficiency of the markets (the efficient market hypothesis), she would select a passive bond portfolio management strategy, otherwise an active approach would be suitable. Finally, if the client has a specific liability claim in the future (as is mostly the case for institutional investors), a combination of both active and passive strategies may be appropriate. Such a strategy might be a structured portfolio strategy, as we will see later in the chapter. Monitoring and Evaluating Portfolio Performance Inspecting, revising, and adjusting the bond portfolio periodically is necessary, since the investment process is ongoing. You need to review your investments regularly to see if your bond portfolio matches your original investment plan and if it is still on the right path (and right), given your objectives, constraints, and preferences. In general, this step involves measuring and evaluating the performance of the portfolio against some preestablished benchmark portfolio. The client can also evaluate the performance of the investment manager, but this is not always a simple task. For example, just because the manager has managed to “beat” the benchmark portfolio, it does not mean that the objectives of the client’s investment portfolio have been met. If the extra performance of the bond portfolio was 1% above the benchmark but the client needed 1.5% to satisfy future fixed liability claims, the manager has failed to meet the client’s objectives. Alternatively, the benchmark portfolio may have been wrong for such a portfolio, or the client may have failed to establish the investment objectives and investment policy in the beginning. In general, several measures are available to evaluate the performance of a bond portfolio and a bond manager, as established by the CFA Institute’s Global Committee on Performance Standards (GIPS). GIPS standards are principles that provide investment firms with guidance on the evaluation and reporting of their investment results. Besides performance measurement and GIPS, the client can also evaluate the manager’s performance using the so-called performance attribution. Such analysis seeks to identify those factors (management decisions) that contributed to the performance of the bond portfolio and to generate their quantitative assessment. Stated differently, this procedure attempts to evaluate the manager’s added contribution to the (value of the) bond portfolio beyond what a passive investment strategy would achieve.

PASSIVE BOND INVESTMENT STRATEGIES In general, passive bond portfolio managers accept asset (bond) prices as fair and try to manage only the risk of their bond portfolios. That they do not engage in frequent

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portfolio changes does not mean that decisions are not made. In fact, as mentioned above, investors must continuously monitor their investments for the appropriate risk exposure and preferred duration. There are three main passive strategies: buy and hold, indexing, and immunization. Each of these has variations, however, as we will show shortly. We begin with the buy-and-hold investment strategy. Buy-and-Hold Portfolio Strategy This is the simplest form of investing in bonds because it involves merely purchasing bonds and holding them to maturity. If your goal is to preserve your capital and earn interest, this strategy is right for you, since you will receive interest payments regularly, and at the end of the lives of the bonds, you will get their face values. Obviously the amount you will receive at maturity will be higher or lower than the amount you paid for each of these bonds—that is, whether you paid more (i.e., premium) or less (i.e., discount) for them. Buy-and-hold investors must find those bonds that match their desired qualities in terms of credit risk, maturity, and coupon rate as well as important options (such as call or put options). Further, these investors look for such investment vehicles that match their investment horizon and reduce interest and reinvestment rate risks. For example, if a bond that you selected has a call option embedded in it, you took the risk that your principal would be returned to you prior to the (bond’s stated) maturity date. Thus if the bond is indeed called away, you would be forced to (re)invest your dollar proceeds in new bonds at lower yields. One common way for passive investors to control interest rate risk is to form a laddered portfolio. A laddered bond portfolio is one composed of bonds with different maturities invested in a ladder-style maturity horizon. The cash flows provide an even and steady stream annually and are paid to the bondholder at regular (or defined) intervals. For example, a laddered portfolio may be composed of 1-, 4-, 5-, 10-, and/or 15-year bonds. Table 13.1 illustrates a simple 8-year laddered $800,000 bond portfolio with a coupon of 8%. As you see, each year the investor receives both interest income and principal in a steady form. The investor can have a portfolio of bonds invested in each year, not just one bond. One last word about passive investment is warranted. Investors can be aggressive even in the buy-and-hold strategy in the sense that they actively seek those bonds that satisfy their requirements and, occasionally, consider timing issues in their investment decisions. The latter means that they incorporate expectations about future market rates and other factors in their bond purchases. Indexing Bond Strategies As the name implies, bond indexing means constructing a portfolio whose performance—that is, its risk/return characteristics—will match that of a bond index. A bond market index is simply broad-based bond indexes commonly used by institutional investors such as the J. P. Morgan Government Bond Index, Bank of America Merrill Lynch Table 13.1 Example of a Laddered Bond Portfolio Year Interest income Principal

1 $8,000 $100,000

2 $8,000

3 $8,000

$100,000 $100,000

4 $8,000

5 $8,000

6 $8,000

7 $8,000

8 $8,000

$100,000 $100,000 $100,000 $100,000 $100,000

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Broad U.S. Market Index, and the Barclays Aggregate U.S. Bond Index. These are marketvalue weighted indexes of total returns and include all types of bonds whose maturity dates are greater than 1 year. This strategy is more flexible than the buy-and-hold one, despite the fact that it has most of the same characteristics. Specifically, an indexed bond portfolio—like the buy-and-hold or the laddered bond strategies—does not involve the risks of interest rate forecasting or using general market expectations. For example, given that bonds in an indexed or a laddered portfolio are held around yield-curve changes, a shift in the yield curve, which may offer better risk/return characteristics, would not be exploited by such strategies. Pure Indexing Strategy There are two main variations of indexing, pure and enhanced. Applying the pure indexing strategy merely involves the purchase of all the bonds in the relevant index by their proportional weight in that index. We showed this strategy also in the case of a stock portfolio, which is more common. Two important factors have contributed to the popularity of this strategy in recent years. First, there is the poor record of active bond portfolio managers of outperforming the bond indexes. Empirical research has also supported this observation.1 Second, lower management fees have resulted in generating higher, and closer to the comparable index, returns. This strategy is simple in principle but difficult to implement for several reasons. First, what is that “benchmark index,” and does it truly represent the “optimal performance” that we want to replicate? Second, as we mentioned earlier, just because the bond portfolio manager matches the index’s return, it does not mean that he has met the client’s (sponsor’s) return requirements. Third, the bond market, as opposed to the equity market, has less frequent trading and contains more positions because investors generally buy bonds to hold for longer periods (than they do with equities) and thus do not trade frequently. Thus the manager must purchase the positions that compose the index. Since these are fewer, his task becomes much more challenging. Finally, restricting the manager to matching a particular index means that he is giving up on, potentially, more attractive opportunities in others bond sectors in the economy. In Chapter 8 we first alluded to the dangers of selecting a benchmark portfolio. In general, there are two types of benchmark portfolios: a normal portfolio and a market index. The normal portfolio, or a customized portfolio, is one constructed especially for a particular client and reflects the client’s long-term goals and preferences. Some argue that normal portfolios are more appropriate benchmarks than general market indexes because they also incorporate features such as the managers’ investment style and philosophy. The construction of such a benchmark portfolio is a difficult task because it requires defining the relevant fixed-income universe of assets to be included in the normal portfolio and determining the appropriate weights for these assets.2 The deviations between the performance of the indexed portfolio and the market index are referred to as tracking errors. The reasons for such errors are transaction costs in the construction of the indexed portfolio and the difference between the indexed portfolio’s composition and that of the market index. In addition, a recent study found that the biggest cause of a negative tracking error in corporate bond exchange-traded funds (ETFs) was portfolio turnover, because of the costs of selling and replacing assets.3 A trade-off between the two sources of the tracking error exists. If the manager purchases all the bonds in the market index according to their proportional representations in

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the index (known as full replication), the transaction costs incurred from their purchase will result in the first form of tracking error. Note that each of the above market indexes includes more than 5,000 bonds; thus purchasing all of them might be infeasible. Still, if the manager did purchase them, he would follow that index exactly. By contrast, if he did not purchase all the bonds but only a sample of them (known as partial replication), he would save on transaction costs but run the danger of not picking a representative sample of the issues in the market index. Thus a tracking error would occur because of the mismatch of the indexed portfolio, so constructed, and the market index. Thus the manager walks a fine line regarding tracking errors, and resolving this issue might be a daunting endeavor. Enhanced Indexing Strategy So far we have been discussing the pure indexing bond strategy. The enhanced indexing strategy attempts to do better than the pure indexing strategy by replicating the total return of the benchmark index and accounting for the management (and advisory) fees. In other words, enhanced indexing includes some active management because of the latitude the managers have (to deviate from the index) in trying to reduce transaction costs. For example, they may (be allowed to) buy some illiquid positions at significant discounts and then sell them (later) at a comfortable margin or engage in efficient taxmanagement strategies. Several general strategies are designed to implement (pure and enhanced) indexing, such as stratified sampling and the optimization approach. Briefly, the stratified sampling (or cellular approach) involves categorizing the various bonds into cells or subclasses, which would represent different characteristics such as coupon, maturity, market sector, and the like. The idea then is to select those bond issues in each cell that can be used as representing the entire cell. In that way, the characteristics of the constructed bond portfolio will match the characteristics of the general bond index. The optimization approach to bond indexing uses the cell breakdown characteristics but seeks to maximize an objective (such as portfolio yield) subject to some constraints (like over- or underweighting some bond sectors). This approach relies on the constrained optimization mathematical approach—that is, linear (or nonlinear) programming—the explanation of which is beyond the scope of this textbook. Immunization Strategy Bond portfolio immunization seeks to insulate a bond portfolio from the effects of interest rate changes on the value of the portfolio and to derive a specific rate of return during the specified investment horizon. Recall (from Chapter 12) that changes in interest rates affect the bond’s price (and value) in two ways: (1) the bond’s price changes inversely with the a change in the interest rate (yield), the interest rate risk, and (2) the value of the bond’s dollar proceeds when it is reinvested at a different interest rate, the reinvestment rate risk. Thus the objective of immunization is to cancel those two changes out, leaving the portfolio’s worth unchanged. Immunization takes advantage of the duration of bonds and matches their duration to the length of the investor’s planned investment horizon. In this case, any changes in interest rates will affect both the price and reinvestment at the same rate, keeping the bond portfolio’s rate of return the same. Thus maintaining an immunized portfolio

424 s Debt Securities

implies rebalancing the portfolio’s average duration whenever interest rates change so as to keep it in line with the investor’s desired holding period. For example, assume that you will need $30,000 about 5 years from now for some specific purpose. If you decide to invest in bonds, you would select those bonds and immunize your bond portfolio in such a way that the portfolio’s value would be exactly $30,000 regardless of interest rate changes. Thus you might purchase 5-year zero-coupon bonds for that amount or several coupon bonds each with a 5-year duration. Let us present a simple example to see how immunization works. This example is similar to a typical immunization strategy that insurance companies employ. Specifically, assume that an insurance company wants to have, guaranteed, an amount equal to $13,382 in 5 years so it can satisfy specific claims. The company, in essence, has issued a 5-year guaranteed investment contract (GIC) at a 6% coupon rate. If the company decides to fund this obligation with a $10,000 annual coupon bond at 6% with 5 years to maturity and selling at par, then, as long as interest rates remain the same, the company will have fully funded its future obligation. However, during the 5-year period, interest rates are sure to change, and such changes will change, up or down, the value of the bond. This means that the company will be faced with interest rate and reinvestment rate risks due to the uncertainty generated from changes in interest rates. How can the company insulate its portfolio from such uncertainty? One option would be for the company to buy a zero-coupon bond, because the duration of such a bond is exactly equal to its maturity date. In the case where such bonds are unavailable, as in cases of longer maturities, the company would have to find a bond whose duration matched its planned investment horizon (the 5 years), even though the bond itself might have a larger maturity date. In our case, the duration of a 6-year maturity bond can be used to fund this obligation. Thus the insurance company would be fully immunized against interest rate fluctuations because the assets and the liabilities of the fully funded plan have equal durations. Let us illustrate two scenarios of changes in interest rates along with no change in interest rates (scenario 3). All calculations are exhibited in Table 13.2. Scenario 1: Interest rate falls to 5%. In this case the total dollar proceeds for the 5 years (assuming annual payments) from the bond will be $13,410.50. Scenario 2: Interest rate rises to 7%. In this case the total dollar proceeds for the 5 years (assuming annual payments) from the bond will be $13,356.80. Scenario 3: Interest rate stays at 6%. In this case the total dollar proceeds for the 5 years (assuming annual payments) from the bond will be $13,382.20. As you see from the table, the accumulated (future) dollar value of the invested coupon income ($600) varies from year to year and from interest rate to interest rate. The (descending) exponents in the calculations of each future value denote the remaining years to maturity of the bond. As you observe, under scenario 1, the company is better off because it will have more funds to fund its future liability claim; but under scenario 2, the company will be a bit short of that goal. Thus, for an investment horizon equal to the bond portfolio’s horizon, the interest rate and reinvestment rate risks will not always

Bond Portfolio Management and Performance Evaluation s 425 Table 13.2 Example of a Bond Portfolio’s Immunization

Source of Dollar Proceeds

Scenario 1 Interest Rate Falls to 5%

Scenario 2 Interest Rate Rises to 7%

Scenario 3 Interest Rate Stays at 6%

1st year’s interest 2nd year’s interest 3rd year’s interest 4th year’s interest 5th year’s interest Sale of bond

600(1.05)4 = 729.3 600(1.05)3 = 694.5 600(1.05)2 = 661.5 600(1.05)1 = 630.0 600(1.05)0 = 600.0 10,600/1.05 = 10,095.2

600(1.07)4 = 786.4 600(1.07)3 = 735.0 600(1.07)2 = 686.9 600(1.07)1 = 642.0 600(1.07)0 = 600.0 10,600/1.07 = 9,906.5

600(1.06)4 = 757.4 600(1.06)3 = 714.6 600(1.06)2 = 674.1 600(1.06)1 = 636.0 600(1.06)0 = 600.0 10,600/1.06 =10,000

Total final proceeds

$13,410.5

$13,356.8

$13,382.2

exactly offset each other. Note that the sale price of the bond (at the fifth year) includes 1 year’s worth of coupon interest because the bond still has 1 more year left to maturity. Why does immunization often, but not always, work? It works because it balances the loss in the value of the bond with the higher value of the bond. In other words, when interest rates fall, the bond’s coupon interest income grows less than if the interest rates remained the same, but the simultaneous gain in the value of the bond offsets this loss. Similarly, when interest rates rise, the coupon interest income is reinvested at a higher rate (assuming that it stays the same thereafter) and this (more than) offsets the reduction in the value (price) of the bond. Thus the net effect would be an almost guarantee that the future obligation would be met. What is also needed is rebalancing of the portfolio, shifting assets from one maturity range to another (see the next section). What are some of the problems/criticisms of the classic immunization strategy? In some cases, a specific duration strategy may not be the best one to guarantee the future funds (as we saw above); perhaps a bond of greater duration may be needed (say a 7-year bond). Also, in cases of inflation, the future earned sum may not be enough to match the required liability, which may change as a result of inflationary pressures. In sum, although immunization appears simple, it is still challenging to apply because investment managers need to rebalance their portfolios frequently when interest rates (and durations) change. Rebalancing Rebalancing refers to the natural corrective action a portfolio manager can take to realign the portfolio’s current asset allocation with the target (original) asset allocation. In other words, because various investments within a portfolio produce different returns over time, the portfolio’s risk/return characteristics tend to drift from the target characteristics, which may be inconsistent with the client’s goals and preferences. Thus, rebalancing restores the original proportions of each asset (or asset class) within the portfolio to its original percentages. Here is a simple example of rebalancing. Assume that an investor has decided to allocate 30% of his $50,000 (or $15,000) into a bond fund and the rest (70% or $35,000) into a stock fund. A year later, the investor checks the value of the portfolio and realizes that bonds have increased by 5% (to $15,750) while stocks have decreased by 10% (to $31,500). The new value of his portfolio is now $47,250. Thus the current bond and stock allocations are 33.33% ($15,750/$47,250) and

426 s Debt Securities

66.67% ($31,500/$47,250), respectively, which are different from the original 30% and 70% allocations. The investor therefore decides to rebalance the portfolio to restore his target asset allocations. The investor can accomplish this by selling some of the bond fund to buy more of the stock fund. The investor calculates that he should have $14,175 (found by multiplying his target bond allocation of 30% by the new value of the portfolio, $47,250) and not $15,750. The difference (or excess funds in the bond fund) of $1,575 between the current and target allocations should be used to buy more of the stock fund. In this way, the original asset allocation is restored. What else, besides abiding by his goals and preferences given his constraints, does the investor achieve by rebalancing? He earns higher returns because he sells high (the bond fund) and buys low (the stock fund). Let us now illustrate how rebalancing can help immunize a bond portfolio. Assume that a pension fund has a liability of $100,000 to fund in 5 years. An alternative way to immunize this liability is to consider two bonds of different durations that could be purchased in order to match the liability’s duration: for example, bond A with a 7% coupon and 5 years to maturity and bond B with a 6% coupon and 8 years to maturity. The duration of the two bonds is 4.23 years and 6.0 years, respectively. To create a portfolio with a desired duration of 5 years, we need to know how many of (or how much money for) each bond to purchase (to spend). Denote wA and wB the weights for each bond category. By definition, wA + wB = 1. The following relationship then can be constructed: wA dA + wB dB = dL

(1)

where dA, dB are the durations of bonds A and B and dL is the liability . Setting Eq. 1 equal to the desired liability’s maturity, that is 5, and plugging in the rest of the numbers, we obtain wA(4.23) + (1– wA)(6.0) = 5 wA = 0.5650, or 56.5% and wB = 1– 0.5650 = 0.4350 or 43.5% which means that 56.5% of our budget must be used to purchase bonds A and 43.5% to purchase bonds B. If we assume that the yield to maturity of each bond is 6%, then the pension fund would need $74,725.82 [= $100,000 / (1.06)5] to purchase each bond, or $42,220.09 (= 0.565 × $74,725.82) for bond A and $32,505.73 for bond B. One year later, interest rates change or decline to be specific, from 6% to 5%. The new duration of the liability will be 4, so dL = 4. But the durations of the other two bonds will change as well. Now they are 3.53 and 5.48 years, respectively. Substituting these new values into Eq. 1, we get: wA(3.53) +(1– wA) (5.48) = 4 wA = 75.9% wB = 24.1% As you see, rebalancing must be done frequently in order to keep the portfolio’s duration matched to the liability’s duration.

Bond Portfolio Management and Performance Evaluation s 427

Box 13.3 How PIMCO Uses Rebalancing in Its Global Bond Investment Strategies In order to offer flexibility and tap potential opportunities occurring around the globe, PIMCO’s unconstrained bond strategy is not tied to some specific index. For example, opportunities across regions and sectors as well as in currencies can arise that can be exploited by this strategy. Furthermore, changing policies and economic developments around the globe can offer a less risky exposure to the portfolio relative to traditional benchmark-tied products. Thus the ability to invest more defensively yields the potential to generate positive returns even when the outlook for bonds worldwide is shifting. For example, changing situations in high-debt nations and exposures to interest rate risk necessitate a more active approach to investing in such bonds. As a result, global rebalancing is necessary. To make this global rebalancing useful, the currencies of debt-laden countries need to weaken (against those of surplus countries). In addition, the portfolio includes higher-quality sovereign debt like that of Germany and Australia. Therefore investors who are concerned with interest rate risk can view the unconstrained bond strategy as a good investment option. Source: PIMCO.

The downside of rebalancing is that it increases transaction costs as bonds are bought and sold. The manager walks a fine line between frequent rebalancing, which entails high transaction costs, and less frequent rebalancing, which may reduce transaction costs but increases the probability of deviating from the target. Thus, a compromise must be achieved between the two which, ultimately, depends on the client and the portfolio manager. Box 13.3 describes how the Pacific Investment Management Company (PIMCO) uses rebalancing to formulate its “unconstrained” bond portfolio strategy. Dedication Strategy We mentioned earlier that the bond portfolio manager might select a zero-coupon bond that matches the duration of his portfolio and not worry, once and for all, about interest rate risk. If such a bond existed, the manager would follow a cash-flow matching strategy, since the portfolio would be automatically immunized. In other words, the cash flow from the zero-coupon bond and the client’s future obligation would exactly offset each other. When such a strategy is applied on a multiperiod basis it is known as a dedication strategy, since the manager can either choose a zero-coupon or a coupon-paying bond to match a series of the client’s obligations. Some problems still remain with these two variations of immunization. For example, too many constraints may be placed on the selected bonds, such as sinking-fund provisions, call options, and credit quality. Overall, in view of these potential problems of immunization, some people consider this strategy and its variations as active, not passive. As we will see below, active strategies are available that either combine the strategy of immunization and its dedication strategy variant, known as the horizon matching technique, or actively manipulate a portfolio while enjoying the security provided by classic immunization, known as contingent immunization.

428 s Debt Securities

ACTIVE BOND PORTFOLIO STRATEGIES In general, active bond portfolio strategies aim at exploiting the changes in those factors that are expected to affect the value and performance of a bond (or a portfolio of bonds). Two basic factors may yield profits from active bond management: expectations about future interest rates (and levels) and changes in yield spreads (and thus risk premiums) among and across bond sectors that would identify mispriced bond issues. The goal of active bond portfolio management is to maximize the portfolio’s total return over some investment horizon. In other words, such strategies seek to outperform the market and earn a higher return relative to a passive investment strategy. The basic premise of such strategies is to make bets on the future path of interest rates and capitalize on them. Naturally if such bets are to generate abnormal returns, they must be based on good (accurate) interest rate forecasts and a superior ability to interpret information. The problem is, however, that interest rate forecasts are seldom accurate. Moreover, for some information to be valuable (for the active portfolio manager), it must be different from the market’s consensus, since the latter is embedded in current prices. Let us now present the main active bond portfolio strategies. We begin with those strategies that require interest rate forecasts as inputs so as to adjust bond portfolios accordingly. These are interest rate anticipation (expectation), credit analysis, valuation analysis, yield curve (and spread) analysis, bond swaps, and horizon analysis. Then we proceed with other active management techniques, such as horizon matching and contingent immunization. Interest Rate–Anticipation Strategy Among this class of active bond investment strategies, the interest rate–anticipation strategy is perhaps the riskiest because it involves forecasts of future interest rates. The goal is to preserve capital by positioning the bond portfolio in such a manner that it loses as little as possible when higher interest rates are anticipated and gains as much as possible when interest rates are expected to fall. In other words, the manager can alter (adjust) the portfolio’s sensitivity to interest rate changes. In terms of duration, this strategy entails increasing the portfolio’s duration when interest rates are expected to fall and decreasing the portfolio’s duration when interest rates are expected to rise. In other words, a manager would hold long-term bonds in an expected falling interest rate environment and shorter-term bonds (including Treasury bills) in an expected rising interest rate environment. For example, the UBS (Canada) Bond Fund invests in various Canadian government debt obligations and certain highly marketable corporate debt issues. The fund’s average term to maturity and composition are constantly adjusted to reflect the expected future direction of changes in interest rates. The fund’s objective is to beat the SC Universe Bond Index, and it can enhance returns through interest rate anticipation and yield curve strategies among others. Another way to use the rate-anticipation strategy would be to buy zero-coupon bonds and/or high-quality bonds (AAA for example, or similar). This is because such bonds are more sensitive to interest rate changes than other bond issues and their volatility makes them suitable for betting on interest rate movements. Moreover, using noncallable bond issues could be an alternative because of their duration and convexity characteristics relative to straight bonds. Finally, the use of derivative, interest-sensitive securities such as options and futures can be employed to implement an interest rate–anticipation strategy using over-the-counter (OTC) securities at lower (transaction) cost.

Bond Portfolio Management and Performance Evaluation s 429

Credit Analysis Credit analysis entails the thorough examination of a bond issuer’s creditworthy status to identify potential default risks. This is accomplished via expected changes in the rating of the particular bond issue by the credit-rating agencies before this is actually announced to the public. This is so because upon announcement, the market will immediately adjust to the bond rating change and will yield no extra valuable (profitable) information. Rating changes occur because of both in-company (internal) events, such as fundamental magnitudes, and external conditions, like the economic situation. Sometimes internal issues can be resolved but external issues may be beyond the control of the particular bond issuer. Thus bond portfolio managers often conduct their own in-house credit analysis, which complement the credit analyses of the three major credit-rating agencies, in order to gain a better perspective of the bond issues. In general, downgradings of bond issues occur during bad economic times (recessions) and upgradings occur during good economic times (expansions). As an example, consider junk bonds. These high-yielding bonds have wide spreads over Treasuries or other high-quality bond issues because they carry higher default risk and are more sensitive to ratings during changing economic times. As a result, bond portfolio managers will have to scrutinize such bonds—that is, conduct a detailed credit analysis—to determine whether these bonds are likely to default during down economic times. Valuation Analysis Under the valuation analysis strategy, the bond portfolio manager seeks to identify mispriced issues for inclusion in or exclusion from the bond portfolio. Specifically, underpriced bonds would be included and overpriced bonds would be excluded. A bond can become over- or undervalued for various reasons, such as rating changes, interest rate changes, and factors that cause a bond’s expected yield to maturity to differ from the current yield to maturity. Obviously such valuation analysis requires continuous bond evaluations and perhaps trading (buying and selling). Stated differently, valuation analysis can be successful if a bond’s (or a bond portfolio’s) characteristics are well-understood and can contribute to the accurate estimation of the bond’s yield. Specifically, the bond portfolio manager needs first to determine the factors that influence the yield of the bond (using interest rate forecast and inspecting the shape and position of the yield curve) and see how these factors may be expected to change that yield. Thus, for example, if the expected yield (to maturity) is less than the current bond’s yield, this would be a signal to buy the bond. Such analysis is sensitive to unexpected events or events that were not part of the original bond valuation analysis for the determination of the bond’s intrinsic value and yield. Bond Swap Strategies A bond swap simply involves exchanging one bond for another—that is, sell one bond and simultaneously buy another with the same attributes. Bonds easily lend themselves to swapping because of the existence of several similar bond characteristics such as coupon, price, maturity, and credit quality. Bond swapping is also an excellent way to extend or shorten the maturity of the bonds in the portfolio. Sometimes the bond manager may swap a short-term bond for a long-term one or vice versa in order to tailor the return of the investment portfolio to the specific objectives of the client. What is the economic

430 s Debt Securities

rationale behind bond swaps? Investors sell a bond to buy another for various reasons, such as to exploit current interest rate (market) conditions (a bond substitution swap), lower their overall tax liability, enhance their portfolio’s total return (a yield swap), and boost their portfolio’s overall credit quality. What are some of the dangers of bond swapping activities? First, the danger exists that the new bond purchased may not really be a true substitute of the bond sold (in terms of attributes). Second, there is the possibility that the market (or the interest rate) may reverse its (expected) course, thus working against your bet. Third, if the swap period takes longer than anticipated, the actual yield may be less than the expected one. Let use explain two of the above swap activities so that you can understand their risks and opportunities. Substitution Swap A bond or substitution swap strategy is the riskiest of all because, as mentioned above, it involves forecasts of interest rates. If you think that the overall interest rate environment is expected to change, then engaging in a swap may help to protect your bond holdings. The technique assumes a temporary imbalance (as the strategy is short-term) between yield spreads in bond issues of similar quality (or perfect substitutes). A worked example of a substitution swap is shown in Table 13.3. In this example, we have a current bond that the manager thinks of exchanging for another bond (the substitute bond). The details of the current bond are 20-year, 10% coupon, priced at $1,000, to yield 10%; those of the substitute bond are 20-year, 10% coupon, priced at $958.85, to yield 10.5% with a similar credit rating. Assume a reinvestment rate of 10% and a work-out period (or the period of yield realignment) of 1 year. As the example shows, the manager can pick up some additional basis points with the substitution swap. The gain per invested dollar is higher if you swap once a year, and you earn an average yield of 45 basis points in yield to maturity each time you do the swap.

Table 13.3 Example of a Bond Substitution Swap Assumptions Current bond: 20-year, 10% coupon, priced at $1,000 to yield 10% Substitute bond: 20-year, 10% coupon, priced at $958.85 to yield 10.5% (and similar rating) Reinvestment rate: 10% annually Realignment period: 1 year Proceeds

Current Bond

Substitute Bond

1. Initial investment 2. Interest income 3. Interest on interest (for half year) 4. Face value (at 10%)

$1,000.00 100.00 5.00 $1,000.00

$958.85 100.00 5.00 $1,000.00

Total dollar proceeds (2 + 3 + 4) Overall gain (2 + 3) Gain per dollar invested [(2 + 3)/1]

$1,105.00 $105.00 10.5%

$1,105.00 $105.00 10.95%

Bond Portfolio Management and Performance Evaluation s 431

What are the potential dangers from such a strategy? First, the market rate may change during that work-out period and move adversely. Second, the temporary imbalance in the spreads may not actually be temporary but permanent. In this case, capital gains will be wiped out. Third, even if these imbalances are transitory, the actions of many managers to simultaneously swap bonds may cause the yield differentials to narrow or even disappear (and arrive at current levels), thus rendering many swaps unprofitable. Fourth, the candidate (for substitution) bond may not actually be a truly similar one to the one you intend to sell. That is, the perceived difference in the spread may be due to the issuer’s lower credit quality and not to (temporary) deviations in yields. Yield Swap In contrast to the substitution swap, in a yield swap strategy the manager may attempt to swap a low-coupon bond with a (comparable) high-coupon bond in order to realize an instant increase in yields (current and to maturity). A manager, however, would be careful to properly interpret the differences in yields (between low-coupon and high-coupon bonds) of different-quality bonds because the market sometimes creates opportunities for differences in the yields of bonds of equal credit ratings. In a yield swap, the manager can also improve the tax status (taxable or tax exempt) of the bond portfolio because longer-term bonds (including municipal securities) typically yield more than shorterterm securities. In that way, extending the average maturity of the portfolio can contribute to the increase in the overall portfolio’s yield. Let us work through an example of a yield swap to highlight the opportunities and the risks. The example is shown in Table 13.4. Here, we have a current, low-coupon bond that the manager thinks of exchanging for another, high-coupon bond (the substitute bond). The details of the current bond are 20-year, 10% coupon, priced at $958.85, to yield 10.5%; those of the substitute bond are 20-year, 12% coupon, priced at $1,000, to yield 12%, with a similar credit rating. Assume a reinvestment rate of 12%. As the example shows, the manager can pick up some additional basis points with the bond yield swap. The gain per invested dollar is higher if you swap for yield because you hold the

Table 13.4 Example of a Bond Yield Swap Assumptions Current bond: 20-year, 10% coupon, priced at $958.85 to yield 10.5% Substitute bond: 20-year, 12% coupon, priced at $1,000 to yield 12% (and similar rating) Reinvestment rate: 12% Proceeds

Current Bond

Substitute Bond

1. Initial investment 2. Interest income 3. Interest on interest (for half year) 4. Value at year end

$958.85 100.00 3.00 $958.85

$1,000.00 120.00 3.60 $1,000.00

Total dollar proceeds (2 + 3 + 4) Overall gain (2 + 3) Gain per dollar invested [(2 + 3)/1]

$1,061.85 103.00 0.107%

$1,123.60 123.60 0.123%

432 s Debt Securities yield positive butterfly parallel shifts

negative butterfly

maturity

Figure 13.1 Some yield curve shifts and shapes.

new bond to maturity. Moreover, this strategy is not as risky as the substitution swap because it does not involve interest rate speculation. Again, what are the risks of such strategy? One major risk, inherent in bond portfolios, is reinvestment risk. If the assumed reinvestment rate changes (i.e., declines in this case), then the total terminal value of the portfolio will be lower than expected. Second, and related to the above, if the candidate bond has a call feature, the call option is likely to be exercised in the event of an interest rate decline. Yield Curve Strategies The goal of a yield curve strategy is to earn excess returns on a bond portfolio by correctly anticipating Treasury yield curve movements. The importance of the Treasury yield curve was highlighted in the previous chapter; now we can use it to exploit shortterm yield changes under different interest rate environments. In the previous chapter, we already learned one yield curve strategy: riding the yield curve. In this section, we will learn three more strategies based on shifts of the yield curve. There are three types of shift in the yield curve: parallel, steepening, and flattening. A parallel shift is to an even change (up or down) in the yields of all maturities. A steepening of the yield curve indicates a high(er) yield differential between long- and short-term yields. Finally, a flattening of the yield curve means a narrowing of yields between the short- and the long-term ends of the maturity spectrum. Among these shifts, some twists and butterfly shifts may also occur (recall the Fed’s “operation twist,” which took place in September 2011). A twist in the yield curve means that the spread between short- and long-term rates becomes wider than it already was. Twists can be flattening (with the short-term end higher than the long-term end) or steepening (with the short-term end lower than the long-term end). A butterfly shift is a type of nonparallel yield curve shift and involves the peakedness or curvature of the yield curve. Butterfly shifts can either be positive, when the yield curve becomes humped downward (so that short- and longterm rates are higher than medium-term rates), or negative, when the hump in the curve makes medium-term yields higher than both short- and long-term yields. Figure 13.1 illustrates some of these shifts and shapes.

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So, how can an investor take advantage of these shifts and shapes of the yield curve for the benefit of his bond portfolio? An important element in such strategies is the sensitivity of the bonds’ prices of interest rate changes. This essentially means that the maturity spectrum of the bonds in the portfolio will have a significant impact on the portfolio’s total return. For example, the price of a 2-year bond will not be very sensitive to how the 2-year yield had changed, but the price of a 20-year bond will be very sensitive to how long-term yields have changed. In section under the Buy-and-Hold Portfolio Strategy heading, we saw the laddered bond portfolio strategy, which entails owning bonds of (approximately) equal maturity over the investment horizon. Two other variations of this strategy exist: a bullet and a barbell strategy. In a bullet strategy, all the bonds in the portfolio have the same (or very similar) maturity date—that is, they are concentrated on a single point on the yield curve. In a barbell strategy, the bonds are purchased so as to cover both ends of the maturity spectrum. For example, the bond portfolio would be constructed so it has bonds with 5-year and 20-year maturities. With every yield curve change (shift), these strategies will have different yield outcomes; but one cannot identify the optimal yield curve strategy. For example, when the yield curve flattens, the barbell strategy will outperform the bullet strategy; but when the yield curve steepens, the barbell strategy will beat the bullet strategy. Finally, when a parallel shift occurs in the yield curve, both of these two bond strategies may be profitable depending upon the magnitude (and direction—positive or negative) of the yield change. For example, take bond A, with a yield of 9% and maturity of 10 years, and bonds B and C, with maturities of 5 and 20 years, respectively, and yields to maturity of 7% and 9%, respectively. Form a barbell portfolio with bonds B and C with equal weights. The average yield of the barbell portfolio would be 8%. If yields increased by 25 basis points across the board (that is, in a parallel shift of the yield curve), the barbell portfolio’s average return (yield) would be 0.5 (7.250%) + 0.5 (9.250%) = 8.25% which is less than the yield of the bullet portfolio (of 9%). The same situation would occur when yields dropped by 25 basis points, as the average yield of the barbell portfolio would now be 0.5 (6.75%) + 0.5 (8.750%) = 7.75% If yields now evenly increase by 300 basis points, the barbell portfolio’s average yield would be 0.5 (10%) + 0.5 (12%) = 11% which is greater than the bullet portfolio’s yield. Thus, depending upon the magnitude and direction of the yield curve’s shift, one strategy may offer more profitable opportunities than another. Horizon Analysis This strategy also involves forecasts of interest rates and attempts to compute the total rate of return of a bond (portfolio) under predicted changes in interest rates. Specifically,

434 s Debt Securities

under horizon analysis the manager identifies a particular holding period (shorter than the total investment horizon) and computes the expected investment’s total rate of return resulting from the change in the interest rates (yields).4 Let us show this strategy with a simple example. Assume that the portfolio manager has a 2-year investment horizon. Currently, a 10year bond offers an 8% coupon rate and sells so it yields (to maturity) 7%. Assume that the portfolio manager predicts that this (8-year, at that time) bond will sell so it yields 6% and that the coupon income from the bond will have to be reinvested at 6%. What would be the (predicted) total return on the bond investment during the 2-year investment horizon? First, compute the bond’s current price, P0, as follows (assuming annual payments): P0 = $80 (PVIFA7%, 10) + $1,000 (PVIF7%, 10) = $80 (7.024) + $1,000 (0.508) = $1,070 Then forecast the bond’s price, Pf, 2 years later: Pf = $80 (PVIFA6%,8) + $1,000 (PVIF6%, 8) = $80 (6.210) + $1,000 (0.627) = $1,124 The coupon interest (income) will be reinvested at 6% (for 1 year) and thus will generate a total $164.80 for 2 years: Reinvested income proceeds = $80 (1.06) + $80 = $164.80 Thus the 2-year total return on the bond would be 20.45%, computed as follows: Total rate of return =

$164.8 + ($1,124 − $1,070) = 0.2045 or 20.45% $1,070

This return, when converted into an annualized return—(1.2045)1/2– 1 = 9.75%— results in a higher yield than the bond’s promised yield owing to a fall in interest rates. Of course the above yield value would depend on the accuracy of the interest rate forecast. Other Active Management Strategies Horizon Matching Technique The bond portfolio horizon matching technique is a mix of passive and active actions and combines elements of portfolio dedication and immunization. Specifically, the manager selects a particular portion of the holding period and constructs a portfolio that matches the liability stream during that period (horizon) and then tries to cover the future liabilities using duration matching strategies (that is, to immunize the portfolio). The end result with such a strategy is to earn, with certainty, an amount of the liability stream during the holding period and then enjoy the flexibility of using duration techniques to match the subsequent cash flows to the required liability. An important element of this strategy is the decision on a suitable horizon so as to balance the benefits and costs of the certainty enjoyed in the early years with the costs and benefits of duration matching techniques.

Bond Portfolio Management and Performance Evaluation s 435 Table 13.5 Active Bond Portfolio Strategies and Their Risk Levels Strategy

Risk Level

Interest rate anticipation Credit analysis Valuation analysis Bond swap strategies s 3UBSTITUTIONSWAP s 9IELDSWAP Yield curve Horizon analysis Horizon matching Contingent immunization

High Medium Medium Medium to high High Medium Medium High Medium Medium

Contingent Immunization Contingent immunization combines passive and active investment management actions relying on the safety net (cushion) of the classic immunization strategy. The idea is due to Leibowitz and Weinberger.5 Specifically, the manager has the flexibility of pursuing active management but reverting to a protection of the bond portfolio when necessary. For example, if a bond portfolio is currently worth $10 million at 10% rates, the manager can achieve a future value of the portfolio (for 2 years, let’s say), via immunization techniques, of $12 million. The manager can afford to risk some losses early in the investment horizon by first calculating the minimum value of the portfolio that would guarantee the terminal wealth and then actively manipulating the excess value. So the minimum value (or the present value) of the future sum of $11 million is $9.09 [$11/(1.10)2]. Thus, if the manager sees that the value of his portfolio is about to dip below that minimum value (the floor value), the trigger would prompt him to stop active management and immediately immunize the portfolio so that it would earn the required terminal wealth. The trigger point is the above present value formula or the amount that it generates (under different interest rate scenarios). Therefore, contingent upon the initiation of the trigger point, the immunization strategy will begin so as to guarantee the minimum required portfolio performance. Table 13.5 summarizes the above 8, depending on active bond portfolio strategies and classifies them according to their riskiness, ceteris paribus. So what is the preferred investment management approach, passive or active? The box titled Applying Economic Analysis lists the advantages and disadvantages of each approach and offers insights to guide the investor to the correct choice.

BOND PORTFOLIO PERFORMANCE MEASUREMENT AND EVALUATION In this section we present and discuss various metrics for measuring and evaluating a bond portfolio’s performance (some of which were first defined in Chapter 3). Performance measurement entails the examination of the return of a (bond) portfolio realized over some investment horizon, the evaluation period. Performance evaluation involves the investigation of the overall performance of the portfolio by determining whether or

436 s Debt Securities

not and how the manager added value to the portfolio. Apart from discussing the usual performance evaluation methods, we will present another method, called attribution analysis, for evaluating a portfolio’s total performance. Bond Portfolio Performance Measures We have seen several portfolio performance measures in previous chapters, three of which we summarize below (the holding period return, the arithmetic mean, and the geometric mean), and then we discuss the fourth one (the dollar-weighted rate of return). Holding period return =

ending price − beginning price + distributions × 100 beginning price

(2)

Recall that one of the problems with the holding-period return (HPR) is that this method includes no additions and/or withdrawals during the portfolio evaluation period. The remedy is to compute a subperiod return and then the annual return that would be consistent with the evaluation period. The arithmetic and the time-weighted or geometric means are two of the three ways to address the above problem. The Arithmetic Average Rate of Return Arithmetic mean = ∑X n

(3)

The Geometric Rate of Return Geometric mean = [(1 + r1) (1 + r2) ··· (1 + rn)]1/n – 1

(4)

Recall (from Chapter 3) that the geometric or time-weighted return ignores the period-by-period variation in the portfolio’s returns, meaning that it was designed to insulate a manager’s performance from investor actions (additions and/or withdrawals) during the investment period. Thus it depends on the length of time an addition or a withdrawal has been in or out of the portfolio. Let us illustrate the geometric mean using EXCEL functions. Assume the following subperiod rates of return for a fund: 20%, 10%, and 5%. The Excel function of geomean ( ), with the above numbers in the parentheses, would return a rate of return of 10%.6 The Dollar-Weighted Rate of Return The fourth methodology to calculate the average subperiod return is the dollar-weighted rate of return. The dollar-weighted rate of return is found by computing that interest rate that equates the present value of the cash flows (CFt) from the subperiods and the terminal value (Vt) of the portfolio to the current (or initial) market value (V0) of the portfolio. This method is also known as the internal rate of return (IRR). It is computed as follows: V0 =

CF1 CF2 CFt Vt + ++ + 2 t (1 + rd ) (1 + rd ) (1 + rd ) (1 + rd )t

where rd is the dollar-weighted return.

(5)

Bond Portfolio Management and Performance Evaluation s 437

What are the similarities and differences between the time- and dollar-weighted rates of return within the context of evaluating a portfolio (or fund) manager’s contribution (or performance)? The common element of the two types of return is that they will produce the same number if there are no additions to or withdrawals from the portfolio by the client over the evaluation period. The difference between the two measures is that the dollar-weighted one places more emphasis on investor contributions/withdrawals during the investment period. So if an investor adds more money to the portfolio, the dollarweighted measure will capture this addition by enhancing the portfolio’s return. In other words, whereas the time-weighted return focuses on managers, the dollar-weighted return centers on the investor’s actions. Thus comparing returns and performance between portfolio managers (who may initially start with investments in identical portfolios but one portfolio experiences changes during the evaluation horizon) may be difficult, which is our task under examination here. Here is how you can compute IIR using EXCEL. Assume the following cash flows (the first, negative number refers to the initial cash outflow): -1, 0.4, 0.5, 0.3. The Excel function of irr (), again with the above numbers in the parentheses, would yield a value of 10%. Bond Portfolio Performance Evaluation Before embarking on evaluating a bond portfolio’s performance, two things should be determined: what is required of a portfolio manager and how the evaluation exercise is set up. The latter means constructing a reference portfolio (known as the benchmark portfolio) against which the manager’s return is evaluated. In general, two major requirements of a professional (bond) portfolio manager exist: sThe ability to generate abnormal, risk-adjusted returns sThe ability to effectively diversify all firm-specific risk In terms of the first requirement, a bond portfolio manager would alter his portfolio’s duration when anticipating interest rate changes. This essentially means that the manager would have a superior market-timing ability relative to other managers in order to derive above-normal returns. Regarding the second requirement, the manager should be

Box 13.4 Benchmark Issues Constructing or using a specific bond benchmark against which to measure an active bond portfolio manager’s performance is a big challenge. Selecting the right benchmark is essential in determining the risk/return profile for actively managing a bond portfolio. There are literally hundreds of bond benchmarks in the marketplace; which one to choose depends on the client’s risk/return characteristics (such as cash flow requirements) as well as objectives and constraints. For instance, a client’s bond portfolio that requires high liquidity might use a 3-month Treasury

438 s Debt Securities

index as a benchmark rather than another issue containing fewer liquidity issues and/or exhibiting greater interest rate sensitivity. In addition, new benchmarks are constructed in response to demand by investors. For example, in 1992 J. P. Morgan created its Emerging Markets Bond Index to offer a benchmark for emerging market bond portfolios. In general there are a number of factors that play a role in deciding the appropriate benchmark for a bond portfolio, such as whether the benchmark includes all securities available for investment and whether the benchmark is priced often (daily). In addition, even if the benchmark is the proper one for a bond portfolio, does this portfolio contain all or a sample (say, 80%) of the benchmark’s securities? The point is that managers and clients alike must understand the issues involved in actively managing bond portfolios and that the world is a dynamic one, requiring constant monitoring and updating of the portfolio and the benchmark. In recent years there has been a shift toward “unconstrained” bond and “multisector” bond funds portfolios. The first category means that such portfolios are constructed with no reference to market capitalization weight benchmarks. Such an approach to managing bond portfolios would offer managers more flexibility to invest in securities (stocks as well) when they think are attractive compared to an indexing approach. We saw an example of this approach in Box 13.3. The second category implies that bond funds invest in various sectors of the bond market. For example, if 40% of the Barclays Aggregate Bond Index is made up of US Treasury securities, a multisector bond fund tied to that index must mimic that proportion. Finally, benchmarking issues arise with hedge funds when they use strategies like short sales or market-neutral portfolios.

able to completely eliminate any nonsystematic risk in the bond portfolio so as to closely correlate her diversified portfolio to that of the fully diversified market portfolio. The benchmark portfolio must have some desirable properties in order to be considered an effective and appropriate performance evaluation tool. We first considered these properties in Chapter 10. There are two types of benchmark portfolios: ready-made market indexes and normal portfolios. Because various techniques for evaluating a portfolio’s (and a manager’s) performance use a market portfolio, caution must be exercised in using the market portfolio to compare returns, because it may be inappropriate. Constructing the normal portfolio is challenging and usually requires the input of the client (plan sponsor) regarding the composition and weights of the assets. Moreover, the “market portfolio” may not really be the true market portfolio against which a constructed portfolio is measured. These issues refer to as the benchmark error. Clients often sit down with a manager not only to construct appropriate normal portfolios that are comparable to the benchmark portfolio but also to ensure that the manager will not select an index that he can easily beat. Finally, the normal portfolio must reflect the manager’s own style of investing in terms of which securities to include in the portfolio and in what proportions. These two elements define how the manager’s performance is evaluated at the end of the investment horizon. Box 13.4 discusses some of the benchmark issues that plague both portfolio managers and clients. Performance Attribution Analysis Performance attribution analysis attempts to determine whether a portfolio manager’s performance is due to his skill in exhibiting superior selection abilities (the selection effect) or to his superior market-timing abilities (the allocation effect). Thus the selection

Bond Portfolio Management and Performance Evaluation s 439 Table 13.6 Performance Attribution Analysis Panel A: Construction of Benchmark and Actual Portfolio and Excess Return (1) (2) (3) (4) Benchmark Portfolio Rate of Benchmark Weights Weights Return (%) Return (1 × 3) (%)

Asset Equities Bonds Cash

0.60 0.30 0.10

0.70 0.20 0.10

4.00 2.50 1.00

2.40 0.75 0.10

Benchmark portfolio total return:

3.25

Return of actual portfolio: Excess return of actual portfolio (actual – benchmark):

4.56% 1.31%

Panel B: Asset Allocation Effect (1) (2) (3) Benchmark Portfolio Difference Weights Weights in Weights (2 – 1) Equities Bonds Cash

0.60 0.30 0.10

0.70 0.20 0.10

0.10 –0.10 0.00

(4) Benchmark Return (%) 4.00 2.50 1.00

(5) Contribution (3 × 4) (%) 0.400 –0.250 0.000 0.125

Panel C: Security Selection Effect (1) Portfolio Weights Equities Bonds Cash

0.70 0.20 0.10

(2) Portfolio Return (%)

(3) Benchmark Return (%)

5.50 3.20 1.00

4.00 2.50 1.00

(4) Excess Performance (2 – 3) (%) 1.50 0.70 0.00

(5) Contribution (1 × 4) (%) 1.05 0.14 0.00 1.19

Box 13.5 Bond and Fixed-Income Exchange-Traded Funds A bond ETF is an ETF that invests exclusively in bonds. It trades daily and represents a passive investment vehicle. A fixed-income ETF is a special type of mutual fund that tracks the performance of a bond index and can be traded on major stock exchanges. Examples of such ETFs are Standard & Poor’s Depository Receipts (SPDRS, or spiders), iShares, and Diamonds (out of the DJIA Index). Again, the trick for the manager (and the client) of the bond ETF is to make sure that it closely tracks (or matches) the respective index. Some indexes contain thousands of

440 s Debt Securities

bonds, such as the Morningstar Core Bond Index, while others, like Barclay’s iShare Aggregate Bond Fund Index, include just a few dozens. Like stock ETFs, bond funds give investors low fees, transparency, and flexibility. Thus they represent a cheap alternative to bond mutual funds. A major criticism of bond ETFs focuses on taxation issues (since income is taxed just like income from a mutual fund) and management fees compared with a buy-and-hold strategy. In addition, managers of active bond portfolios who have a solid record of beating the market (or indexes) have the option or flexibility to use margin and derivatives on these securities compared with managing a bond ETF. Here are some examples on the performance of some bond ETFS relative to their benchmarks*: Power Shares Emerging Markets Sovereign Debt Portfolio: 10.73% in 1-yr vs. 11.73% by JP Morgan EMBI Global Bank of America Merrill Lynch Build America Bond: 6.75% in 1-yr vs. 3.90% by Barclays Capital US Aggregate The bottom line in selecting an active or a passive approach is that it depends on the investor. If you are an investor not looking for immediate or high income and are for the long haul, you should not invest in bond ETFs. *Source: Invesco PowerShares Capital Management LLC (on the web), 2011.

effect measures the impact of selecting securities that provide different returns from the benchmark and the allocation effect measures the impact of over- or underweighting particular assets (or asset classes) relative to the benchmark. For example, a positive/ negative allocation effect results from over- or underweighting assets that generate better returns than the benchmark portfolio. Thus performance attribution analysis is done by comparing the manager’s portfolio (excess) performance to the performance of the benchmark portfolio. In general, once the benchmark portfolio is constructed, the two effects described above can be computed as follows: Selection effect = sum of the weights of assets times differences between actual and benchmark portfolio return Allocation effect = sum of the differences in weights of assets between actual and benchmark portfolio times the benchmark portfolio return A simple example can help to show how the process works. Table 13.6 contains the hypothetical data for this example. The benchmark portfolio is composed of equities, bonds, and marketable securities (cash) in the following proportions: 60–30–10. The manager’s actual portfolio also includes the above assets but in different proportions (weights) to reflect his investment style: 70–20–10. In other words, the manager has actively managed the portfolio by reweighting two asset classes in hopes of earning a higher return (beating the benchmark portfolio’s return). The return on each asset class is given in panel A of the table and thus the benchmark portfolio’s total return can be computed, which is 3.25%. The actual portfolio’s return is 4.56%; therefore the excess return (actual minus benchmark return) is 1.31%. Since the actual portfolio earned a higher return than the benchmark portfolio, decomposing this excess return into the asset allocation and the security selection effects would be worthwhile. In that way, we can learn the contribution of each effect to the overall

Bond Portfolio Management and Performance Evaluation s 441

portfolio’s return. As panel B of the table shows, the contribution of the manager’s asset allocation decision (to reweight the three asset classes in his managed portfolio) generated an extra return of 0.125%. Thus in this case, despite losing some return from the bond asset class, the manager managed to earn a positive return owing to the excellent performance of the equity market. Panel C of Table 13.6 illustrates the remaining excess return of 1.19%, which is attributed to the manager’s security selection ability in each of the two asset classes. Thus the above illustration shows how one can measure a manager’s performance and his ability to time (predict) asset class movements so as to profitably exploit these movements. Box 13.5 illustrates how active bond portfolio managers are compared with passive ones using a newly created bond class, the bond exchange-traded fund (ETF).

BOND MARKET EFFICIENCY AND PORTFOLIO MANAGEMENT An important consideration of bond portfolio managers (or portfolio managers in general) is the proper role of debt securities as part of a well-diversified or pure bond portfolio. Specifically, in a typical equity-debt portfolio, how should the composition of each asset class be determined? That is, should one asset class dominate another? In an efficient market, the optimal combination should be a mix without one class being disproportional to the other. In other words, one asset class should not offer superior information opportunities so as to be overweighted in the portfolio relative to the other asset class. Regarding evidence on bond market efficiency, some studies suggest that it is difficult to predict interest rate movements in order to exploit them within a bond portfolio.7 Other studies examine the impact of bond ratings on bond yields and find a significant impact following the change.8 In the United States, bond markets are becoming increasingly transparent. The National Association of Securities Dealers (NASD) now requires dealers to report all overthe-counter bond transactions through its Trade Reporting and Compliance Engine (TRACE) reporting system, which became operational in 2002. In Europe, the Markets in Financial Instruments Directive (MiFiD) is also concerned with bond market transparency in the European financial services industry at the retail investment spectrum. Specifically, it wants to ensure that pre- and posttrade bond price transparency, which is already available to wholesale bond market participants, will also be available to retail investors by “improving the quantity and accessibility of price and liquidity information about liquid and highly rated bonds.”9 In general, what would be the implication of an efficient bond market on bond portfolio management? If we believe that the bond market is efficient, the returns of active bond portfolios should not differ from those of passive bond index portfolios. In other words, active bond managers should not be able to outperform the benchmark bond indexes. Also, the returns of an active bond portfolio should not differ from those in active stock portfolios. A study by Blake et al. (1993) found that (about 361) bond funds did not beat the relevant bond indexes and the amount of underperformance was about equal to the management expenses.10

CHAPTER SUMMARY This chapter examined the bond portfolio investment management process and bond portfolio performance evaluation. The investment management process comprises the

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following steps: identification of the investor’s goals, constraints, and appetite for risk; establishment of the investment policy; selection of an appropriate investment strategy; and the monitoring, evaluation, and adjustment of the bond portfolio. Next we discussed several methods to manage a bond portfolio depending on the specific approach used, passive or active. Passive bond portfolio management does not rely on active trading and/or forecasting of interest rates, but active bond management does. Examples of passive management strategies are the buy-and-hold and indexing strategies and various ways of immunizing a bond portfolio. The goal of an active bond portfolio manager is to outperform the market so as to realize above-average returns. Examples of active investment management strategies include interest rate anticipation, valuation analysis, yield curve analysis, horizon analysis, and contingent immunization. Between the two extreme strategies, others that combine features of passive and active strategies exist, such as contingent immunization and match-funding techniques. Finally, we also presented some portfolio performance evaluation measures such as the arithmetic mean, the geometric mean, and the dollar-weighted rate of return, and we illustrated attribution analysis so as to distinguish a manager’s luck from skill. We concluded the chapter with a look at the implications of the efficient market hypothesis on bond portfolio management strategies.

APPLYING ECONOMIC ANALYSIS ACTIVE OR PASSIVE INVESTMENT MANAGEMENT? Let’s summarize the advantages and disadvantages of passive and active investment management first. Then we will discuss each. Feature

Passive

Active

Returns below-market after fees Management fees Tax-efficient

Average, no above market, No protection in down markets Low Tax efficient

Diversification Market belief Decision and analysis to market shifts Management skills

Same as market index Efficient Index replication, no expert advice None required

Above- and below-market, Protection in down markets Fees high and variable Yes and no depending on manager philosophy Improved or changing Inefficient (at times) Expert analysis, ability to react

Investment horizon

Short, medium, and long

Ability to forecast economic/financial magnitudes required Short, medium, and long

The choice between passive and active management strategies really depends on the investor and his or her unique needs, such as tax status, investment planning horizon, risk tolerance, age,

Bond Portfolio Management and Performance Evaluation s 443

and the like. It is not always true that the investor should select one approach only. Using both approaches to a bond portfolio can offer better results and still be conformable to the investor’s risk-return profile. The investor should decide thoughtfully and carefully. For example, manager selection is a key issue in any active investment strategies, and the average investor may not know much about the manager who manages bonds or bond funds. Moreover, in leaning toward a passive approach, the investor should consider the impact of market volatility, which can impact absolute returns and performance significantly over time. In considering active investment management relative to passive, which requires no management, investors typically spend time and money to search for and identify a winner bond fund to invest in. But what is a “winner” bond fund? Recall that “past performance is not a guarantee of future performance”! Numerous studies have found that the average active manager has not been able to outperform the respective portfolio’s benchmark. For example, a study by the Wall Street Journal (August 22, 2009) showed that (passively managed) fixed-income index returns beat actively managed fund returns in 2010. So is it worth paying for active management if the managers cannot earn above-average returns? Finally, in considering a strategy, investors should be mindful of the real costs and risks of each approach, such as index volatility and performance during down markets, under passive and manager skill, and the role of luck and fees, among others, under active management. The abundance of active managers in the market means that it is a lucrative and profitable business and the average investor should not go for it blindly. The rise of ETFs counterbalances active strategies and offers attractive returns with lower risk. Thus the investor should carefully weigh all these pros and cons before making a decision.

INTERNATIONAL FOCUS BOND INVESTMENTS AND STRATEGIES IN AND OUT OF THE EMU A recent study asked whether the members of the European Monetary Union (EMU) invest more or less in their area relative to the rest of the world. In other words, is a typical European investor’s bond portfolio mostly composed of EMU bonds or not? How about non-EMU investors; do they prefer EMU bonds? Answers to such questions would reveal the role of the euro area within the global financial system. The study found that the euro area has had a profound impact on the composition of global bond portfolios. Cross-country bond investments (within the EMU) are significantly greater than among non-EMU countries—a phenomenon known as “euro area bias.” Factors that explain bond cross-investment flows include informational barriers, exchange rate stability, and the levels of trade linkages among and between countries. Thus the above-mentioned bias has a strong influence on the composition the international bond portfolios of Euro member countries. The recent (2010 to date) European sovereign debt crisis, which resulted in several European nations’ debt downgrades, prompted bond investors to rethink credit risk and adjust their bond portfolio strategies (allocations). The credit risk of the widely used benchmark index of European government bonds, the Boxx EUR Sovereign Index, has risen dramatically since these downgrades (below AAA) in September 2010. Countries whose debt was downgraded include Greece, Ireland, Portugal, and Spain (and recently that of Italy as well). Thus, in a typical international bond portfolio where government and corporate bonds are included, sharp changes in

444 s Debt Securities

credit risk necessitate allocation changes. One such move would be to replace such troubled debt with carefully selected bonds that would possess the same characteristics as those they replaced before the debt crisis erupted. For example, sovereign bonds of commodity exporting countries or more bonds from the core European countries would be included. Such a strategy would be optimal for those investors who wished to explore opportunities in the general universe of fixed-income assets. An alternative strategy would be to complement the existing sovereign bond portfolio with higher-quality bonds, such as German bunds, particularly Pfandbriefe (mortgagebacked bonds). In such a restructured portfolio, higher-yielding corporate bonds and other emerging markets bonds would exhibit lower volatility owing to greater diversification and enhanced return. Within each allocation, strategic and tactical asset allocation strategies would be more effectively employed in managing the new government bond portfolio (recall that strategic allocation means ensuring that the portfolio conforms to the risk/return characteristics of the investor while tactical allocation refers to stock-picking and/or market timing activities). Sources: Deutsche Bank Group, Diversifying Sovereign Bond Portfolios, November 2010; P. Lane, Global Bond Portfolios and EMU, European Central Bank Working Paper Series, No. 553, November 2005.

LESSONS OF OUR TIMES LESSONS FOR THE EUROPEAN INSURANCE INDUSTRY The recent global financial crisis, the European sovereign debt crisis, and the upcoming European regulations regarding fund reserves (so-called Solvency II) have forced the insurance industry to adapt to the new normal global economy by adjusting their bond portfolios. The new normal for insurance investors and general bond market participants includes the following trends in an effort to better evaluate the implications of fundamentals economic shifts: Broader bond market exposure in order to include more markets, such as Brazil, which may offer attractive opportunities More allocation to income-generating bond investments, such as real estate and infrastructure, and less allocation to equities (in order to conform to the Solvency II guidelines, to be implemented in January 2013, which call for more credit spread exposure) Placement of more emphasis on credit risk analysis and sovereign bonds transparency in light of the recent European sovereign debt crisis Enforcement of tighter risk-management functions across investment portfolios, with an emphasis on transparency, and a more efficient allocation of in-house and outsourced investment management functions (in response to systemic and regulatory changes) Implementation of changes with respect to financial reporting and disclosure policy requirements, which will surely alter their asset allocation strategies (both strategic and tactical) in preparation of the upcoming Solvency II requirement In general, the new way in which European insurance companies will be operating will entail better risk control, more liability-driven investments (just like the pension fund industry as we saw in Box 13.2), and broader global exposure. Source: The new normal in European asset management, PIMCO, May 2011.

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KEY CONCEPTS The investment process comprises asset allocation and security selection. The investment policy refers to a document between the investor and the investment manager containing the manner in which the investor’s funds are to be managed. Passive bond portfolio managers accept bond prices as fair and try to manage only the risk of their bond portfolios. The buy-and-hold strategy involves purchasing bonds and holding them to maturity. Bond indexing means constructing a portfolio whose performance will match that of a bond index. The pure indexing strategy involves the purchase of all the bonds in the relevant index by their proportional weight in that index. The normal portfolio or a customized portfolio is one constructed especially for a particular client. The deviation between the performance of the indexed portfolio and the market index is known as tracking error. The enhanced indexing strategy attempts to replicate the total return of the benchmark index and accounting for the management and advisory fees. The stratified sampling involves categorizing the various bonds into cells that would represent different characteristics like coupon, maturity, and market sector. The optimization approach to bond indexing uses the cell breakdown characteristics but seeks to maximize an objective subject to some constraints. Bond portfolio immunization seeks to insulate a bond portfolio from the effects of interest rate changes and to derive a specific rate of return during the specified investment horizon. Rebalancing refers to the changing of the composition of the bond portfolio to match to portfolio’s current investment characteristics to those of the target (original) characteristics. In a dedication strategy, the manager can either choose a zero-coupon or a couponpaying bond to match a series of the client’s obligations. Active bond portfolio strategies aim at exploiting the changes in those factors that are expected to affect the value and performance of a bond (or a portfolio of bonds). In the interest rate–anticipation strategy, the manager can alter the portfolio’s sensitivity to interest rate changes. Credit analysis entails the thorough examination of a bond issuer’s status in terms of creditworthyness to identify potential default risks. Valuation analysis entails the identification of mispriced issues for inclusion in or exclusion from the portfolio. A bond swap simply involves exchanging one bond for another, assuming same attributes.

446 s Debt Securities

A substitution swap may help to protect a bond portfolio’s holdings if the overall interest rate environment is expected to change. In a yield swap, the manager attempts to swap a low-coupon bond with a (comparable) high-coupon bond in order to realize an instant increase in yields. The goal of a yield curve strategy is to earn excess returns on a bond portfolio by correctly anticipating the movements of the Treasury yield. Horizon analysis involves forecasts of interest rates and attempts to compute the total rate of return of a bond (portfolio) under predicted changes in interest rates. The horizon-matching technique is a mix of passive and active actions and combines elements of portfolio dedication and immunization. Contingent immunization combines passive and active investment management actions relying on the safety net of the classic immunization strategy. Performance measurement involves an examination of the return of a (bond) portfolio realized over some investment horizon, the evaluation period. Performance evaluation involves an investigation of the overall performance of the portfolio by determining whether and how the manager added value to the portfolio. Performance attribution analysis attempts to determine whether a portfolio manager’s performance is due to skill or to his superior market-timing abilities.

QUESTIONS AND PROBLEMS 1. Explain the pros and cons of the buy-and-hold strategy. In other words, comment on the composition of securities and their characteristics in the portfolio, expenses, and interest rate environment. 2. What are some of the factors that could change yields among bonds? If you expect a spread to be (abnormally) high, would you trade to take advantage of such a high spread? What are some of the drawbacks of such a strategy? 3. If portfolio managers expect interest rates to change, which active strategy would they employ in managing their portfolios? What if they expected the yield curve to pivot (not shift)? 4. Describe how you can manage interest rate risk with a ladders and barbells. 5. Explain the difference between enhanced indexing and active investment management. 6. Read the passage below from the financial press and answer the following question: what types of active bond portfolio strategies is the company employing, and why? ABC Capital Management LLC considers increasing the allocation of corporate bonds in its fixed-income portfolio over the next 6 months. The manager plans to purchase AA or better grade corporates in the expectation of economic recovery, which should narrow spreads, and an upgrading of some credits. 7. You read in the financial press that some ETFs take the form of “core/satellite” investment management of a bond portfolio. For example, a “core” asset allocation, like an investment-grade bond composition, is implemented with bond ETFs, while managers are used for “satellite” investments for that portion of the

Bond Portfolio Management and Performance Evaluation s 447

8.

9. 10. 11. 12.

investor’s portfolio that seeks higher return (thus assuming higher risk). What type of strategy or strategies would that be? Passive, active, or both? Assume that a portfolio manager has a 3-year investment horizon. Currently a 10-year bond offers a 5% coupon rate and sells that so it yields (to maturity) 4%. Assume that the portfolio manager predicts that this (7-year, at that time) bond will sell so that it yields 4% and that the coupon income from the bond will have to be reinvested at 4%. What would be the (predicted) total return on the bond investment during the 3-year investment horizon? Explain what performance attribution analysis entails. Search the financial literature to find articles on bond market efficiency. Do you conclude that the bond market is efficient or not? Comment. Assume that you have invested 60% of your $30,000 in stocks and the rest in bonds. One year later you observe that your stocks rose by 5% while your bonds declined by 3%. How can you restore your original asset allocation? Consider three bonds: X, Y, and Z. Bond X has a yield of 8% and a maturity of 5 years; it can be held in one portfolio, called a bullet portfolio. Bonds Y and Z have 3 and 8 years to maturity and yields to maturity of 7% and 8%, respectively. Answer the questions below. a. Construct a barbell portfolio with bonds Y and Z, assuming equal weights. Compute the portfolio’s average yield. b. If yields increase by 50 basis points across all maturities, what would be the portfolio’s average rate of return? Compare the bullet and barbell portfolios’ yields after the yield change. Comment. c. If yields decrease by 50 basis points across all maturities, what would be the portfolio’s average rate of return? Compare the bullet and barbell portfolios’ yields after the yield change. Comment. d. Now assume an even 200-basis point increase in yields. Which portfolio would fare better?

NOTES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Christopher Blake, Edwin Elton, and Martin Gruber, The performance of bond mutual funds, Journal of Business, 56(3), 1993, pp. 371–403. Frank Fabozzi, Bond Markets, Analysis and Strategies, 4th ed. (Hoboken, NJ: Prentice Hall, 2000), p. 489. M. J. Patterson, The biggest cause of tracking error in corporate ETFs, March 4, 2011, SeekingAlpha.com Martin L. Leibowitz, Horizon analysis for managed bond portfolios, Journal of Portfolio Management, 1(3), 1975, pp. 23–43. Martin L. Leibowitz and Alfred Weinberger, Contingent immunization: Part I. Risk control procedures, Financial Analysts Journal, 38(6), November/December 1982, pp. 17–32. Note that as you directly type geomean in the function bar, do not forget to add the equal () sign before the word. Adrian W. Throop, Interest rate forecasts and market efficiency, Federal Reserve Bank of San Francisco Economic Review, Spring 1981, pp. 29–43. Steven Katz, The price adjustment process of bonds to ratings reclassifications: a test of bond market efficiency, Journal of Finance, 29(2), May 1974, pp. 551–559. International Capital Market Association, Bond Market Transparency Standard–amended, January 14, 2009. Christopher Blake, Edwin J. Elton, and Martin J. Gruber, The performance of bond mutual funds, Journal of Business, 56(3), 1993, pp. 371–403.

Part VI DERIVATIVE MARKETS AND INSTRUMENTS

The past decade witnessed unprecedented turbulence and high anxiety following scandalous events, the collapse of giant companies, the wiping out of major banks, and the financial crisis of 2008. For these events, the misuse of derivative products and strategies was mostly to blame. In fact, in 2003, derivatives were termed “financial weapons of mass destruction” by Warren Buffett! Welcome to the world of modern derivatives, where new and often hard-to-understand financial and commodity products are continuously devised and used. These products were used by financial institutions and retail traders on other financial institutions, companies, and even countries. Although these traders’ main goal was to hedge the risks they wanted to retain, they were also using derivative instruments to bet on companies failing and nations defaulting. Despite these distressful situations, derivatives can offer risk protection and control for a company if used wisely. In general, investors use derivatives to hedge risks, speculate on asset values and movements, and exploit arbitrage opportunities. A derivative product (instrument) is an agreement (or financial contract) between two parties to trade a financial asset or commodity at a fixed price on or before some prespecified date. The value of a derivative instrument is derived from an underlying asset, which is traded separately from the derivative. Derivatives are traded on organized exchanges and over the counter. Various types of derivatives include swaps, interest rates, economic events, weather, and other complex (synthetic) schemes, but the most commonly known ones are options and futures. We discuss the latter two in Chapters 14 and 15 and all the rest in Chapter 16.

449

14 OPTIONS MARKETS AND VALUATION

CHAPTER OBJECTIVES After studying this chapter, you should be able to sExplain how the options markets operate sDistinguish between a call and a put option sDescribe some options strategies sUse the binomial and the Black-Scholes option valuation models sEmploy stock options

INTRODUCTION This and the next chapter discuss the types of securities that “derive” their value from other assets (the so-called underlying assets), which are called derivative securities. The two main derivative securities are options and futures. We begin by presenting the market in which options (or option contracts) are traded and continue with some basic options strategies. We also include a section on some other optionlike securities. Next we explain how an option is valued by presenting the two basic option valuation models, the binomial and the Black-Scholes-Merton formulas. Finally, we devote a section to some simple strategies for trading/using options in an effort to practice risk management and hedging.

AN OVERVIEW OF THE OPTIONS MARKET In this section we will discuss the market for options, which comprises the concepts of the various kinds of options, the participants in the option market, the exchange(s) in which these trade, and the role of the options clearing corporation.

451

452 s Derivative Markets and Instruments

Basic Option Concepts Call and Put Option Concepts An option is a contract that gives the owner the right but not the obligation to buy or sell an asset at a specified price on or before a specified date. Options are depreciating assets with a limited life (ending at expiration date). Although an option is a security (like a stock or a bond), it is also a contract with strictly defined terms and conditions. Options and stocks have both similarities and differences. For example, options trade just like stocks, on an exchange, but they have expiration dates (unlike stocks) and do not represent ownership in a company (as stocks do). In general, with the introduction of options, investors have investment choices (beyond equities and debt securities, both government and corporate). A call option conveys the right to buy an asset at a specific price on or before a specific date. The specific price is known as the exercise or strike price. The specific date is the expiration date, which, for listed options in the United States, is the Saturday following the third Friday of the month. To obtain this right, the buyer of the option contract pays a premium (which is the price of the option). This represents the ability to exercise the option when it is profitable to do so. The seller or writer of the call option receives that premium from the buyer in order to give the buyer that option. Naturally this implies that the holder of the option is not obligated to exercise the option. Thus in this case the only cost would be the premium. We will see later when exercising an option contract would be profitable. For example, a June call option on Hewlett-Packard (HPQ) with an exercise price of $37.50 gives the right to the owner to buy HPQ shares for a price of $37.50 any time on or before the call option’s expiration in June. The premium for the purchase of this option is $0.91. A put option entitles its holder to sell an asset at a specific price on or before a specific date. For example, a June put option on HPQ with an exercise price of $30 gives its holder the right to sell HPQ shares to the put issuer (writer) at that price at any time on or before the expiration date (in June). In general, put options work like insurance policies, just like car insurance, by protecting your car’s (insured) value in case of an accident. If you have no accidents, then the cost to you is simply the premium you pay to the company for taking the risk of insuring your car. In general, call and put options allow investors to manage risk. It is also useful to think of a put option as a short sale, since the purchaser of the option seeks to profit from the underlying asset’s price decline. Some terminology on long and short positions is in order. If you bought the right to purchase and held a contract (say 100 shares of HPQ) in your brokerage account, we say that you are long on a call contract. Similarly, if you purchased the right to sell a contract and are holding that right in your account, we say that you are long on a put contract. A short position describes a position in options in which you have sold (written or created) a contract. Thus you (the writer of the option) get to keep the premium received from the sale. If you sold the right to buy 100 shares of stock to someone, we say that you are short on a call contract. Similarly, if you sold the right to sell 100 shares of stock, we say that you are short on a put contract. Obviously if one investor is long on an asset another is short on it, since every option contract has two sides. Table 14.1 shows the actual details of call and put options on Hewlett-Packard (HPQ) stock when its underlying price was $25.39 (on November 25, 2011). The quotations refer to the previous trading day. One contract calls for the purchase or sale of 100 shares; thus its cost would be 100 times the price shown. If the call or put options traded with

Options Markets and Valuation s 453 Table 14.1 Selected Call and Put Options on Hewlett-Packard Call

Put

Expiration

Strike

Last

Volume

Open Interest

Last

Volume

Open Interest

Dec. 16

$17.00 20.00 21.00 22.00 28.00

$9.50 7.10 5.70 4.10 0.30

10 74 2 13 74

10 151 21 83 7,119

$0.03 0.10 0.14 0.25 3.00

153 45 42 26 43

210 921 1,010 3,576 1,426

Source: Yahoo! Finance. Notes: As of November 25, 2011; underlying stock price: $25.39; price represents listed exchange price only and it may not match the composite closing price.

the given strike and maturity month, then the options’ price and volume of trading that day are recorded in the table. The “Open Interest” columns simply state the number of outstanding contracts on the specific date for the calls and the puts. A large value for open interest implies higher liquidity and market activity for the derivative because of many buyers and sellers. Two general kinds of options exist: American and European. An American option is one that can be exercised on or before its expiration date. A European option allows exercise of the option only at expiration. Because of this difference, American options are more flexible than their European counterparts and thus more valuable. Profits and Losses on Options In general call options typically increase in value when the value of the underlying asset increases. The underlying asset can be a stock, a bond, or an index. When the market price (value) of the asset to be purchased exceeds the strike price of the asset, the holder of the call option will exercise the option to make a profit. The gross profit will be the difference between the market value of the asset minus the strike price. The net profit will be the gross profit minus the option premium (or the price paid for the option). If the asset’s value does not rise above its strike price during the specific period, the call option is simply not exercised and is left to expire worthless. Let use look at this process with an example. Using the data in Table 14.1, the second call option strike price for HPQ is $20, while the underlying stock price is $25.39. At this point, exercising the call option to buy HPQ stock at $20 is unprofitable. Let us see why. If the call holder exercises the option (said to “call away” the stock), his gross and net profits would be Gross profit of call at expiration = stock price − strike price = $25.39−$20.00 = $5.39 Net profit of call at expiration = gross profit of call − option premium = $5.39−$5.70 = −$0.31 Whereas profits on call options increase with the underlying asset’s rise in value, profits on put options emerge as the value of the underlying asset decreases. A put will be exercised only if the strike price exceeds the price of the underlying asset (or when the market price of the asset to be purchased is less than the strike price of the asset). This

454 s Derivative Markets and Instruments

means that the put holder can deliver an asset at a lower market value than that of the strike price. Note that it is unnecessary to own the asset to exercise a put option. Let us show with an example how profits or losses are made with put options. Using the data in Table 14.1 again, consider the last put option on HPQ with the exercise price of $28 and selling for $3 (under the “Last” column of the “Put” heading). If the investor chooses to exercise the put option immediately (which is profitable), he would earn the following amount: Gross profit of put = strike price−stock price = $28.00−$25.39 = $2.61 But given that he paid $3 for this right to sell (the put option), in all likelihood he would wait until expiration to exercise the option, hoping that the stock price would fall further so as to earn a positive net profit (his current net profit would be negative [a loss]: $2.61−$3.00 = −$0.31). If the stock’s price fell, say, to $24, the investor’s gross profit would be more than enough to earn a net profit of $1 per contract. If he realized this amount over, say, a 45-day period, his holding-period return would be computed as follows: Holding-period rate of return = net profit /option premium = $1/$3 = 33.33% The strike or exercise price can help to determine whether the contract is in, out, or at the money. A call option is in the money when the exercise price is less than the stock’s market price and a put option is in the money when the reverse is true (as we saw above). That is because the call holder has the right to buy the stock at a lower price than its market price. In this sense, we say that the amount by which the call option is in the money at any point in time is known as its intrinsic value (as we also see further on). A variation of that is deep in the money, which means that the strike price is well (substantially; that is, more than the premium value) below/above the market price for the underlying asset for a call/put option. An option is out of the money when its exercise is not profitable (or it yields a negative payoff). For example, a call option is out of the money when the strike price is greater than the stock’s market price and a put option is out of the money when the reverse holds. Again, a variation of deep out of the money exists. Finally, an option is at the money when the exercise and stock prices are equal, thus yielding a zero payoff. By default, both out-of-the-money and at-the-money options have no intrinsic value, and their time value is the full option premium (we will see the time value concept again further on). How does this buy/sell process take place? When you, the option holder, exercise an option, a writer (seller) may be found who is short on the same type of option (that is, he took the position opposite to yours) and assigned (by the Options Clearing Corporation, to be explained below). This means that he will make good on his obligation (to sell). Thus, for a call assignment, call writers are required (obligated) to sell stock at the strike price to the call holder; for a put assignment, put writers are obligated to buy stock at the strike price from the put holder. In reality, however, most options are never exercised (about 60% of them); rather, their holders choose to take their profits by simply exiting (trading out of) the options.

Options Markets and Valuation s 455

Options Payoffs at Expiration Let us illustrate in some detail the above profit/loss situations with call and put options. We start with the call options. Denote the value of the stock at expiration date as ST and the strike or exercise price as X. The gross payoff to the call holder at expiration is generally expressed as follows: Payoff to call holder = ST −X 0

if ST > X if ST  X

(1)

Note that the payoff cannot be negative because the option will not be exercised if the stock price is less than or equal to the strike price. Thus it is said that the call option expires worthless. The net profit, however, can be equal to the price paid for the option and can be negative (a loss). Figure 14.1 shows the payoff and the net profit from a call option in the form of a graph. As we see from it, the payoff at expiration is depicted by the upward-sloping line above $50 (the strike price) and the net profit/loss by the dashed upward-sloping line below the horizontal axis. The cost of the option is $10 and is shown by the $10 value on the vertical axis. The call holder breaks even when the dashed line crosses the horizontal axis at $60 and makes a profit for any price above that. The call holder is one party and the call writer the other party in the transaction. The call writer incurs a loss when the call holder incurs a profit and vice versa. In general, the payoff to the call writer is expressed as Payoff to call writer

= −(ST − X) 0

if ST > X if ST  X

(2)

Note that the premium paid by the call holder to the call writer is a cost to the former but revenue (income) to the latter. By charging this premium, the call writer is willing to bear the risk of losing money if the stock price increases. The call writer’s payoff and profit/loss situations are illustrated graphically in Figure 14.2. As you notice, these graphs (lines) are the mirror images of the call holder’s lines. The break-even point is again $60, and the negative payoff at that time is just offset by the $10 premium received upon writing the option. In discussing put options, the payoff expression for a put holder is given by the following:

payoff

$20 $10

profit

0 cost of option

50

−$10

Figure 14.1 Payoff and profit/loss of a call option at expiration.

60

ST

456 s Derivative Markets and Instruments

$10 0 50

60 profit payoff

Figure 14.2 Payoff and profit/loss of a call writer at expiration.

Payoff to put holder = 0 X−ST

if ST  X if ST < X

(3)

Thus for the put holder to make a profit, the strike price must be more than the stock’s price (and, of course, greater than the premium paid for the right to sell the stock). In terms of the illustration of these situations, Figure 14.3 exhibits the payoff and profit/loss situations for the put option at expiration. If the stock price at expiration is above $50, then the put option is worthless and will not be exercised. However, at a price below $50, the put value increases (as the upward line suggests). Figure 14.4 illustrates a short put, which is nothing else but a sale of a put option. The maximal loss is unlimited in falling markets, but the maximal gain is limited to the premium received for selling the put option. The Market for Options Investors in options can trade in organized exchanges and over the counter (OTC). The OTC market is flexible in the sense that option contract details (such as strike price, maturity, and number of shares) can be tailored to the needs of the specific investor (trader). The downside of that, however, is that the cost is relatively higher. The bestknown organized options exchange for listed options is the Chicago Board Options Exchange (CBOE), which was opened in 1973 by members of the Chicago Board of Trade (CBOT).1 According to CBOE, it is the leader in the options industry with options on more than 1,332 stocks and 41 indices, over $25 billion in contract value traded on a typical day, over 1 million options contracts changing hands on a daily basis, and professional instructors teaching options trading to over 10,000 people per year.2 However, since 2003, the International Securities Exchange (ISE), based in New York, has become the largest electronic options market. The ISE operates the leading options exchange in the United States and offers options trading on over 2,000 underlying financial instruments (such as equity, ETFs, and foreign exchange). ISE is regulated by the Securities and Exchange Commission (SEC) and is a member-owner of the Options Clearing Corporation (see further on). In September 2007, the ISE was acquired by Eurex, one of the world’s leading derivatives exchanges. There are other regional but smaller exchanges for options in the United States, such as the American Exchange (AMEX), Philadelphia Stock Exchange (PHLX), and Pacific Stock Exchange (PSE). Daily trading volume is handled electronically at the CBOE, where professional traders screen bid and ask prices and

Options Markets and Valuation s 457

$50 payoff

profit 50

price of put

Figure 14.3 Payoff and profit/loss of a put option at expiration.

put premium 0 profit

50

stock price

payoff −$50

Figure 14.4 Payoff and profit/loss of a short put at expiration.

act upon a trade immediately (within seconds). If you buy an option at the CBOE, you can sell it to any other options exchange but not back to the CBOE. Many major stock exchanges include options (and futures) trading and are part of the world federation of exchanges (WFE), which is composed of exchanges and clearinghouses known as the International Options Market Association (IOMA). IOMA was founded in Amsterdam in 1983; in 2002 it broadened its trading scope to include options trading on futures and commodities. The London International Financial Futures Exchange (LIFFE) is another options and futures exchange. In January 2002, LIFFE merged with the NYSE to form the Euronext trading platform (along with the Amsterdam, Brussels, Paris, and Lisbon exchanges) and became known as the Euronext.liffe. We will also learn more about this exchange in the next chapter. Box 14.1 provides some information on the new options trading floor at the NYSE and its competition with other trading floors. What is the options trading process? Basically it starts when an investor contacts a broker who, in turn, relays the information to the CBOE for execution. There are three basic order types: market, limit, and spread. A market order is one to buy or sell options immediately at the best price currently available. For example, if you think that a stock will begin rising very soon, you should place a call option market order quickly at the best possible price. A limit order is one to buy or sell options at a specified price. Finally, a spread order instructs your broker to buy and sell two (or more) different options on the same asset at the same time. For example, you could simultaneously buy and sell a stock call so as to profit from the reverse movement of the underlying asset’s price. Such an order also qualifies as a trading strategy; we will explore it in some detail further on. The next step would be for a designated primary market maker (DPM) to ensure a fair

458 s Derivative Markets and Instruments

BOX 14.1 NYSE’s New Options Trading Floor On March 2, 2009, the NYSE Euronext unveiled its state-of-the-art NYSE Amex options trading floor housed at its historic building at 11 Wall Street. The NYSE Amex options trading community will benefit from the enhanced speed, order executions, and capacity improvements of the NYSE Arca technology. According to the NYSE’s senior vice president, “adding the expertise and customer-focused approach of the NYSE Amex options traders and staff gives NYSE Euronext a new, complementary self-regulatory organization as well as the unique ability to leverage our multi-asset exchange model to another important customer segment.” Customers will benefit from both NYSE options exchanges (the other one is the NYSE Arca options) because they are offered the choice and flexibility of price-time priority on NYSE Arca options or the traditional market-maker model. Source: NYSE Euronext.

and orderly market (much like a specialist in the organized exchanges) in options trading. Your order will be directed for execution to a floor broker, who acts on your behalf (via your broker) by giving you the best possible price. The Options Clearing Corporation The options market is overseen and regulated by the SEC and the exchanges have their own regulatory and surveillance mechanisms. CBOE staff continuously monitors trading activity throughout the options industry in an effort to protect the interests of the options trading public. The Options Clearing Corporation (OCC) is the only clearing agency for all listed options and is independent in the interest of avoiding conflicts among market participants. The OCC is registered with the SEC and the Commodities Futures Trading Commission (CFTC). The OCC effectively guarantees contract performance and eliminates credit (default) risk in options trading. This is because it places itself between option traders, thus becoming the buyer of the option from the writer and the seller of the option to the buyer. The OCC has also evolved into a clearinghouse for a multitude of products. Specifically, it clears options on stocks, indexes, foreign currencies, and interest rate composites, among others. The OCC has received a triple-A credit rating from the Standard & Poor’s rating agency consistently since 1993. The OCC (as well as the investors’ brokers) require option writers (the investors) to maintain funds in their accounts to guarantee that they can fulfill their contract obligations. As with equity short sales, when the posted margin falls below the minimal required margin, the option writer will receive a (broker) call to post additional collateral. By contrast, there is no need for the option holder to post margin because he will exercise the option when it is profitable to do so. Margin requirements also depend on whether the underlying asset (stock) is or is not held in the portfolio. For example, if the stock is owned, margin requirements are met by simply having the broker hold the stock; but if it is borrowed, the margin requirement is determined by the status of the option (in or out of the money, for instance). We also discuss margin with an example in Chapter 15.

Options Markets and Valuation s 459

Option Market Participants Participants in the options market include both retail and institutional investors along with the exchanges. The majority of trades through the CBOE, about 65% of them, are done for the retail investors. Institutional investors who use the options market to enhance their performance include: sMutual Funds. Use the options market to meet redemption issues and protect holdings sHedge Funds. Use options to enhance returns based on leverage and take market positions sEndowment Funds. Use options to generate cash and protect holdings sPension Funds. Employ options to maintain a conservative profile to satisfy future claims

Options Products CBOE offers various products for options traders’ investment needs. Some of them are: LEAPS, or Long-Term Anticipation Securities. These are long-term option contracts that permit investors to maintain positions for as long as 3 years. There are two types of LEAPS: equity and index. Equity LEAPS offer investors the opportunity to benefit from companies without owning their stock and protect stock investors against declines in underlying securities. Index LEAPS allow investors to trade the entire stock market (or sector)—for example, by taking a bullish or a bearish position on the market. Some indexes are the Dow Jones and the Standard & Poor’s (as well as its sectors). Interest Rate Options. These are European-style options on the yield of US Treasury securities. These options give the investor the opportunity to invest based on his perception of the direction of interest rates or yields (as we saw in the previous chapter). When such an option is purchased, the two traders (the call buyer and the put buyer) have the exact opposite expectations about future interest rate movements. For example, a call buyer expects a rise in interest rates, whereas a put buyer anticipates a decline. The call option buyer will benefit (by expiration only) if the interest rate rises well above the strike price to cover the premium paid for the call. The reverse is true for the put buyer. Futures Options. These give their holders the right to buy or sell a specified futures contract with a futures price as the strike price of the option. The option holder benefits from the difference between the current (market) futures price on the specific asset and the strike price of the option. Foreign Currency Options. Currency option contracts allow for the purchase or sale of a fixed amount of foreign currency in exchange for a specified amount of the domestic currency. For example, a currency call option permits the holder to buy the currency at a fixed exchange rate at a later date. Such contracts exist for major currencies such as the euro, the British pound, and the Japanese yen. Foreign currency options can be traded at both the OTC market and organized exchanges such as the Philadelphia Stock Exchange and the London International Financial Futures Exchange.

460 s Derivative Markets and Instruments

Securities with Options As explained in previous chapters, some securities have embedded options in their contracts (or indentures), which can be exercised or not by their holders. For example, bonds carry call (callable bonds) and put (putable bonds) options, convertibility and exchangeability options. Similarly stocks can have warrants attached to them, and many loans have collateral attached (backing them up). Let use take a closer look at these two types of securities: warrants and collateralized loan obligations. Warrants. A warrant is an option issued by a firm to buy shares of its stock. Warrants are traded much like a stock and thus traders need not go through the OCC. The fundamental difference between a call option and a warrant is that the exercise of the warrant requires that the firm issue new stock to meet its obligation(s). Thus, the total number of shares outstanding increases with a warrant but not with the call option. Corporations sometimes attach warrants to bonds that act as “sweeteners” to induce potential buyers and allow the issuing firm to pay lower rates (and dividends, when attached to stocks). Sometimes, warrants can be sold independently of the security and are said to be detachable. Warrants can be both call and put, covered (having some backing of another instrument) and index (using an index as the underlying asset). Warrants can also be naked— that is, without the accompanying security (usually a bond)—and can be traded on a stock exchange. These are issued by securities firms and financial institutions. Warrants can be used to protect the portfolio’s value should the value of the shares fall, and they benefit from low cost. Collateralized Loan Obligations. These, known as CLOs for short, are loan arrangements under which the lender requires some collateral to be put up by the borrower to back up the loan. In case of default, the lender has the right to seize the collateral (usually real property); in the case of a nonrecourse loan, the lender cannot claim anything beyond the pledged collateral. Thus under a CLO, the borrower has a call option that would be exercised only if the value of the collateral fell below the value of the loan. In other words, the borrower turns over the collateral to the lender with the option to repurchase it at the maturity of the loan. In other words, the lender has an implicit call option if the value of the loan happens to be less than the value of the collateral. One way to highlight this situation (and its dangers) is by citing the 2008 financial crisis, which originated with subprime loans (the “subprime mortgage crisis,” as it was called) that carried adjustable rates. When the rates increased (which pushed up mortgage rates) and the property values declined, many borrowers defaulted on their loans (for other reasons as well); thus the securities backed by these mortgages lost their value. The spread of such losses was unprecedented and led to the 2008 financial meltdown.

SOME OPTION TRADING STRATEGIES If you browse the CBOE’s website and click on “strategies,” you will be amazed at how many strategies using options on various assets (equities, LEAPS, indexes, interest rates, and so on) are outlined and explained. This means that you can use an almost limitless variety of combinations of calls and puts in structuring a particular strategy. In general when you buy a call option, you are bullish on the prospects of the asset, since you profit from an increase in the asset’s price. By contrast, when you buy a put option, you are bearish on the prospect’s asset, since you profit when the asset’s value declines. The

Options Markets and Valuation s 461

mirror images of these strategies are the call and put writers. That is, the call writer is a bullish investor, while the put writer is a bearish investor. Among the dozens of options strategies that exist, we will present only a few of the most popular equity option strategies. Covered Call An important consideration in writing calls is that the writer protects or covers herself by owning the underlying stocks rather than having to buy them when need arises (that is, having written a naked call). Specifically, a covered call involves writing a call option contract and simultaneously owning an equivalent number of shares of the underlying asset (stock). This strategy is also called buy-write. The covered call strategy is the simplest and most widely used one and protects the call seller when the call holder exercises the option. Thus the covered call limits the loss (which can be huge) from a short call when the stock price moves above the stock’s strike price. The payoff structure is illustrated below. Payoff

ST ≤ X

ST > X

Payoff of stock Payoff of call

ST −0

ST −(ST − X)

Total

ST

X

Figure 14.5 illustrates the covered call strategy. Profit will be realized when the price of the owned underlying stock is at or above the call option’s strike price (at expiration). The point at which the profit line crosses the horizontal axis is referred to as the breakeven point, defined as the difference between the stock purchase price and the premium received. In general a covered equity call should be used by an investor who wants to limit the upside gain/loss potentials on a specific asset. Essentially this means that the investor has a neutral view (up or down) and leaning toward being bullish of the asset’s prospects. Such investors are typically institutional investors who are interested in boosting their incomes by the collected premiums on these positions without much danger from changes in the asset’s value. Thus a covered call strategy is considered a conservative strategy because the investor enjoys a decrease in the risk of owning the asset. As an Profit

0

Loss

Figure 14.5 A covered call strategy’s profit line.

profit

strike price

stock price

462 s Derivative Markets and Instruments

example, consider an institutional investor who owns 100 shares of ABC stock that currently sell for $50. If the investor intends to sell those shares when the share price hits $60 (within the next 3 months, he expects), she can write a 3-month call with an exercise price of $60 at a price of, say, $2.50. Thus by writing this contract the investor picks up (an extra) income of $250 (100 shares × $2.50). Protective Put The protective put investment strategy involves purchasing a put option with the simultaneous holding of the underlying stock itself. Why would an investor do that? The reason is that he might be concerned with (short-term) downside risk and at the same time protecting some gains in his shares. Thus the investor enjoys the returns of the shares he holds while limiting downside loss should the stock’s price decline. Below is the payoff structure of a protective put strategy at expiration. Payoff

ST  X

ST > X

Payoff of stock Payoff of put

ST X − ST

ST 0

Total

X

ST

Figure 14.6 shows the profit line of a protective put. Potential maximal profit depends on the price increase of the underlying security (which, theoretically, can be unlimited). As with the covered call case, the point at which the profit/loss line intersects the horizontal axis is the break-even point, defined as the sum of the stock purchase price and the premium paid. Theoretically, the maximal loss would be equal to the stock’s strike price minus the sum of the stock purchase price and the premium received (if the stock price falls to zero). On the other hand, the potential profits may be huge if the stock price moves as anticipated. In general, the protective put investor is a bullish investor. Notice the analogy to a covered call shown in Figure 14.5. Regardless of what happens to the stock price, you are guaranteed a payoff equal to at least the put option’s strike price. That is because you have the right to sell the stock for the strike price should it fall below that value. For example, if the stock price currently goes for $50 (ST) and its strike price is $55 (X), the net value of your portfolio would be X−ST = $55−$50 = $5 at expiration. Let us see this under two scenarios: one when the stock price falls and the other when it rises. If the stock’s price falls below the strike price ($55), you still have the option to sell it at $55. By contrast, if the stock’s price rises above $55, say to $58, you do not exercise your put option but hold on to the stock, whose value is now $58. Thus either way you are a winner (taking into account the premium paid). Some Practical Issues We discussed the protective put strategy along the lines of option trading above as a way to protect (lock in) a stock’s minimum value. Such a strategy is also referred to as portfolio insurance as a means of limiting investment losses while achieving upside potential. One practical problem with this is that puts may not be available for portfolios unless

Options Markets and Valuation s 463 Profit

strike price

0

stock price

Loss

Figure 14.6 A protective put strategy’s profit line.

the investor’s portfolio is some type of market index on which such options exist. For example, if the investor has a well-diversified portfolio that closely correlates with the S&P 500 Index (the so-called SPX), that strategy is possible. As a simple example, consider a portfolio manager who is interested in protecting the value of his portfolio, consisting of US stocks that match the composition of the S&P 500, which currently trades at 1,162. Thus assume that the value of the portfolio to be hedged is $116,200,000. First we need to find the number of put option contracts to buy to implement our strategy. The general formula is as follows: Number of index puts needed = value of portfolio/(index level × contract multiplier) The index options (SPY) have a multiplier of $100; thus multiplying the SPX value (1,162) by the multiplier ($100) we obtain $116,200. Then divide the portfolio value ($116.2 million) by the index value of options ($116,200) to obtain the number of contracts needed: $116,200,000/$116,200 = 1,000 contracts. Assume that the premium for the SPX December put is $5 and the cost of purchasing 1,000 contracts is $500,000 (or $5 × 1,000 × $100). Table 14.2 records two possibilities (one up and one down) and their consequences for the values of the protected (hedged) and unprotected (unhedged) portfolios. Consequently a 10% increase/decrease in the SPX results in levels of 1,278 and 1,046, respectively. Note that the profit/loss for the hedged portfolio is found by taking the difference between the increase or decrease in the unhedged portfolio and the cost of the option. For instance, $127,800,000 minus $116,200,000 equals $11,600,000, which is the increase

Table 14.2 Profit/Loss Outcomes of Unhedged and Hedged Options Portfolios Market Up/Down +10% 0% −10%

SPX at Expiration 1278 1162 1046

Unhedged Portfolio

Profit/Loss on Options

Profit/Loss Hedged

Protected Portfolio

$127,800,000 $116,200,000 $104,600,000

($5,000,000) ($5,000,000) $11,100,000

$11,100,000 ($5,000,000) ($5,000,000)

$127,300,000 $111,200,000 $111,200,000

Note: Values in parentheses denote negative values.

464 s Derivative Markets and Instruments

in the unhedged portfolio’s value. Then, subtracting the cost of the put option ($500,000) gives us the value of $11,100,000 as the (net) profit for the hedged portfolio. The value of the protected portfolio (last column) is found by adding the profit (or loss) values to the unhedged portfolio’s value. So the value for the 10% increase is $116,200,000 + $11,100,000 = $127,300,000. A similar approach is applied for the 10% decrease in the index value. Thus if the investor is correct and the market pulls back, the investor’s portfolio will rise and offset the losses taken by the unhedged portfolio due to the put options. If the market rises, contrary to the investor’s expectations, his portfolio will still profit. In the worst-case scenario, where the market does not move at all, the portfolio’s loss will be the premium paid for the put option insurance. Another issue is that the investor’s investment horizon may not match with the expiration time of the put option. Some long-term index options such as LEAPS extend over several years, but others have much shorter maturities. An alternative would be to create what we call “synthetic” protective put strategies to match these time frames. For this, traders rely on the option’s hedge measure, which is the change in the change in the (protective put option) given a change in the underlying stock portfolio (we discuss this hedge measure later). However, the difficulty with this is that it shows only a static picture, whereas hedging must be continuously monitored and updated. This is called dynamic hedging (or delta hedging), which results from changing market conditions (often several times during a day). The net effect is that while you eliminate risk (by using a hedge between the option and its underlying asset), the portfolio loses some value owing to frequent transactions. Collar A collar strategy consists of the simultaneous purchase of a (protective) put option and the writing of a (covered) call while holding shares of the underlying security (stock, ETF, or index). Thus we may say that there are “bounds,” upper and lower, on the value of the portfolio. Equity collars are employed by investors who want to limit the downside risk at the “cost” of placing a cap on the profit potential. Such investors may have a large equity position but do not want to (or cannot) sell their holdings, yet they want to limit their downside risk. These investors are mostly market-neutral. The payoff from such a strategy is shown in Table 14.3. Let us illustrate with an example. You currently hold several blocks of shares, each selling for $50. A lower bound or protective put can be placed on the holdings’ value with an exercise price (X1) of, say, $40. You also write a call option with an exercise price (X2) of, say, $65. The cost of the put can, perhaps, be raised from the revenues of the call and thus have an offsetting (zero) net. Since the call option limits the upside profit even if the stock’s price rises above $65, the

Table 14.3 Payoffs from a Collar Strategy Payoff

ST < X1

X1 < ST < X2

ST > X2

Buy Put (X1) Write Call (X2) Stock

X1 − ST 0 ST

0 0 ST

0 −(ST − X2) ST

Total

X1

ST

X2

Options Markets and Valuation s 465 Profit

0

Loss

call strike price

stock price

put strike price

Figure 14.7 A collar strategy’s profit line.

investor will not enjoy this value appreciation (it is capped at $65). Thus, in terms of the Table 14.3 structure, the two collars would be the minimum $40 and the maximum $65. Figure 14.7 illustrates the collar strategy. Since the typical collar strategy offsets the call and put premiums, the call strike price should be higher than the put strike price. That is because the investor receives downside put protection at a smaller cost than the cost of the put alone. Sometimes, the put-call combination can result in net credit, which means that the investor would receive cash for establishing the position. If the underlying asset’s price falls between the put and call strike prices (at expiration), the investor will lose the entire (net) premium paid or keep the net cash credit he received in implementing the position (combination). Box 14.2 describes how the collar strategy can be used to hedge currency swings. Straddle If the investor expects a big move in a stock’s price within a few weeks (such as a major announcement by the company) but is unsure of the price’s direction (up or down), a straddle could be the appropriate strategy. A straddle is a mix of call and put options each

BOX 14.2 Using the Collar Strategy to Mitigate Exchange Rate Exposure Companies might use the collar strategy to bet, for example, that a particular currency’s weakness will continue. Here’s an example: Assume that a company has euros that it wants to exchange for dollars in the next 2 months and the euro is currently trading at $1.40. The company wishes to lock in its exchange rate within a tight range. In order to do this, it must establish two separate options. The first option, which the company buys from a bullish (on the euro) seller, permits it to sell its euros in return for dollars if the euro reaches $1.42. The other option, which it buys from a euro-bearish counterparty, lets it sell those euros at a rate of $1.38. Thus the company has a guarantee that its rate will fall within the desired range. As a result, it will not be hurt if the euros depreciate far more, and at the same time it can benefit if its euros appreciate much more. Thus the company has a narrow protection level but gives up the upside potential.

466 s Derivative Markets and Instruments

with the same strike price and expiration date. This strategy will be sufficient regardless of the move of the price because its value is maximized when the stock’s price jumps upward or downward significantly. This means that the investor pays attention to the asset’s volatility. Obviously the only thing that can reduce its value is for the stock price not to move. The payoff of the straddle is illustrated in Table 14.4. If the stock price is equal to the strike price, both the call and the put expire worthless. The investor loses the premium paid up front for these options. Let us show this with an example in Table 14.5 (values assumed at expiration). Thus as the stock price differs significantly from the $50 price, the profit becomes larger and larger. Notice that when the price declines, the cost is the call option premium; when the price increases, the cost will be the put premium (at expirations). The upside break-even point would be the strike price plus cost of the options (net debit), and the downside break-even point would be the strike price minus the net debit. Straddles can be long or short. A long straddle is when the investor buys a long call and a long put on the same stock in hopes of the market moves sufficiently up or down and cover the premiums paid. A short straddle is exactly the opposite; it is when the investor sells a short call and a short put on the same stock. Because the investor shorts the options relative to buying them, the short straddle strategy carries more risk than the long straddle. In general the straddle strategy is a market-neutral one in options trading. Married Put If you consider the purchase of a stock whose price has declined but expect it to go back up with the suspicion that it may go down, then you would employ the married put strategy. This is similar to a protective put strategy where the investor is bullish but wants to hedge so as to be protected on the downside. Thus the investor purchases the shares of stock and a put option on them at the same time. The investor realizes a profit when the

Table 14.4 Payoffs from a Straddle Strategy Payoff Payoff of Call − Payoff of Put Total

ST  X

ST > X

0 (X − ST)

ST − X 0

X − ST

ST − X

Table 14.5 Profit/Loss from a Straddle Strategy Buy one strike 50 call at $3.00; Buy one strike 50 put at $2.80; current stock price: $50 Stock (1)

Call Profit/Loss (2)

Put Profit/Loss (3)

Net Profit/Loss (4) = (2) + (3)

$60 $55 $50 $45 $40

$7.00 $2.00 −$3.00 −$3.00 −$3.00

−$2.80 −$2.80 −$2.80 $2.20 $7.20

$4.20 −$0.80 −$5.80 −$1.20 $4.20

Options Markets and Valuation s 467

stock price exceeds the stock’s purchase price minus the premium paid and a loss when the stock price is less than (or equal to) the strike price of the put plus the premium paid. As an example, consider the purchase of 100 shares of ABC stock at $50 and a 48 put option trading at $2 as a protection for the investment. The maximum loss occurs when the stock price is at or below $50 at expiration, which would be the difference in the prices plus the put premium (if shares are not sold). So, for example, even if the stock’s price goes to $40, the investor’s loss would be the (paper) loss of $2 plus the $2 put premium. On the upside, if the stock price rises to $60 then the maximum (paper) gain would be the $10 minus the put premium of $2 or $8. Finally, if the stock price does not move at all at expiration, the maximal loss would be the put premium paid. The breakeven point would be found by adding the cost of the share ($50), the cost of the premium ($2), and any commissions (ignored here). This implies that the stock price would have to be higher than $2 before a profit could be realized. Figure 14.8 illustrates the married put strategy. The investor’s (theoretically) maximal profit depends on the underlying asset’s price increases. At expiration, if the asset’s price is at the level originally paid for it, the investor’s loss would be only the premium paid. As with the protective put strategy, the break-even point, found at the point the profit line crosses the horizontal axis, is the sum of the purchased asset price and the premium paid. Spread Strategies A spread strategy involves establishing a position with two or more calls or two or more puts on the same asset (stock) with different strike prices and expiration dates. The two main spread strategies are bull call and bear put spreads. The bull call spread strategy entails the purchase of a call option on an underlying stock and the simultaneous writing of a call option on this asset with the same expiration date but at a higher strike price (hence the bull spread notion). The bear put spread strategy involves the purchase of a put option and the simultaneous writing of a put option on a particular stock with same expiration month but with a lower strike price. Investors employ the bull call/bear put strategy when they want to exploit modest advances/declines in the underlying stock’s price. Figure 14.9 illustrates the two spread strategies. The bull call strategy is considered a hedging strategy because the price paid for the call with the lower strike price is offset, in part, by the higher price received from the writing of the call with the higher strike price. This strategy becomes profitable with stock price increases. The maximal profit is realized when the stock price rises above the

Profit

0

stock price

strike price Loss

Figure 14.8 A married put strategy’s profit line.

468 s Derivative Markets and Instruments (a) Bull call

(b) Bear put

Profit

Profit

higher strike price

higher strike price

stock price

stock price

lower strike price

lower strike price

Loss

Loss

Figure 14.9 Spread strategies.

higher strike price. Similarly, the bear put strategy is also considered a hedging technique because the price paid for the put with the higher strike price is partially offset by the premium received from writing the put at the lower strike price (when both options expire). Obviously, this strategy tends to be profitable when the underlying stock’s price decreases and the maximum profit is achieved when the stock’s price falls below the lower strike price when both puts expire. Let us classify the above strategies into bullish, neutral, and bearish and comment on the investor’s attitude—that is, whether he is conservative or aggressive. Table 14.6 summarizes the above. Finally, it is worth mentioning again that other option strategies exist, some of which are similar to the basic ones we have presented—for example, the strangle strategy, which involves the simultaneous purchase/sale of an underlying asset’s call(s) and put(s), is similar to the straddle strategy above—while others can be used by floor traders in applying arbitrage strategies (which are beyond the scope of this textbook). Speculating with Options A speculator is one who takes risky bets on the direction of the value of a security. In other words, he does not care whether the security’s price soars or collapses, only that he makes the right bet on what will happen in the near future. For example, if a speculator thinks that IBM shares will appreciate substantially in the next few months and buys call options, he would be speculating on the direction and the timing of the share price. If his

Table 14.6 Options Strategies and Investor Attitudes Strategy

Bullish/Bearish Neutral

Investor Attitude

Long call Covered call Protective put Married put Bull call spread Long put Bear put spread Collar Straddle (long and short)

Bullish Bullish Bullish Bullish Bullish Bearish Bearish Neutral Neutral

Aggressive Conservative Conservative Conservative Conservative Aggressive Conservative Conservative Aggressive

Options Markets and Valuation s 469

expectation came true, he would sell them at the higher price, thereby making a profit. In purchasing a call or a put, the maximal loss the speculator would incur would be the premium he paid for the option if his expectations are not met. Obviously such bets are risky and the speculator would have to do his homework before engaging in such activities. This, effectively, means that speculation is not for everyone. Two other comments on speculation are warranted. First, speculation does not have to be undertaken for a short period of time. It can run over a long term, meaning 2 or 3 years into the future, for the conservative and patient investor. For instance, one can speculate using LEAPS, which have expiration dates 2 or 3 years into the future. Second, one of the greatest characteristic of speculating in options is their inherent leverage. Recall that leverage is achieved by borrowing money (from your broker) so as to invest a higher amount than your budget allows. However, although leverage can enhance your return handsomely if your bet is correct, it can also lead to large losses if you are wrong! Let’s look at an example using real stock and call options prices for IBM. The purchase of a January 2013 call option costs $55.85, its strike price is $120, and the stock currently (as of September 20, 2011) trades at $174.72. The call option costs a little more than the stock’s intrinsic value of $54.72 (found by the difference between the current stock price, $174.72 and the strike price, $120). The option price also implies a time value of $1 (found by taking the difference between the option price, $55.72, and the intrinsic value, $54.72). The time value refers to what could happen to the stock’s price over time (more on the intrinsic value and time value concepts in the section below). You can either buy 1,000 shares of IBM at a cost of $174,720 (1,000 shares times $174.72) or 10 call options (of 100 shares each) at a cost of $558.50. Thus a huge initial cost difference exists between the two strategies. If IBM’s stock price rises to $200 any time before or on expiration day in January 2013, your options would be worth $80 (the difference between the stock’s price, $200, and the strike price, $120). This corresponds to a rate of return of 43%, or [($80−$55.85) / ($55.85)] *100. By contrast, the rate of return from the stock purchase would be only 14.5%, or [($200−$174.72) / ($174.72)]*100. The message from this simple example is that leverage can pay off! With a little initial expense, you managed to earn a huge return. This return occurs only if your expectations are realized. However, beware of the dangers of leverage and speculation! At this point, reading the box titled Applying Economic Analysis will help you to see a more detailed picture of the costs and benefits of outright stock purchases and call options. Also, read the box titled Lessons of Our Times to find out more about the dangers of derivatives trading when bets go wrong. In addition, you will learn of the activities of some famous rogue traders who have brought down banks and lost billions of dollars for their employers. The relevant question is then: Why do excessive speculation and fraud still exist in huge international banks, resulting in multibillion-dollar losses?

OPTION VALUATION Thus far, we have presented the basics of options and discussed some strategies regarding them. Throughout our discussion, the prices of these derivative products were taken as given. In this section, we will show how to price some products and discuss the factors that affect those prices. To be fair, the valuation of options is very complex, and for that reason we will only present some basic notions and the two most important option valuation models. We begin with the fundamentals of option valuation models and continue

470 s Derivative Markets and Instruments

with their corresponding mathematical models, the binomial and Black-Scholes-Merton option valuation models. Fundamental Option Valuation Concepts We have discussed the two basic option concepts: the underlying asset’s price, ST, and the strike (or exercise) price, X. The difference (or relationship) between the two defines the gross profit or loss from the option on or before expiration. For example, if ST−X is negative (ST < X), the option might be out of the money before expiration, but this does not mean that the option is valueless! There is still a chance that things might turn around and make the option valued (the worst outcome would be a zero value for the option at expiration). This difference is known as the option’s intrinsic value, or the amount of money that can be realized by immediate exercise of profitable (or in the money) calls or puts. Stated differently, it is what the option is worth currently if exercised or by liquidating the acquired (futures) position at the current price of the (futures) contract. If the difference is negative (in the case of puts and calls), the stock’s intrinsic value is zero. Mathematically, we can state the intrinsic value as follows: Call option: max [(ST − X), 0] Put option: max [(X − ST), 0] For example, a call option on 100 shares of ABC stock struck at $50 can be exercised when the market price of the stock at expiration is $55, yielding the following profit for the call holder: 100 max ($55 − $50, 0) = $500 If, instead, the price of a share were $45 when the option is expired, it would make no sense for the call option holder to pay $50 for a share of stock when it is worth only $45 Thus, the option expires worthless and its market value would be 100 max ($45 − $50, 0) = 0 Options are wasting or depreciating assets, since their value erodes or decays with the passage of time into expiration. Time decay is the (nonlinear) change in the value of the option, which becomes cheaper if the underlying asset is not moving (or has not moved) in the expected direction. The value of the option over parity to the asset is known as the asset’s extrinsic value. Alternatively stated, the difference between the actual option call price and the intrinsic value is known as the time value of the option. In plain English, time value is the amount of money option holders/sellers are currently willing to pay/accept beyond any intrinsic value the option may have for the option’s rights. More formally, the time value is expressed as Time value = option price − intrinsic value earlier For option writers, the time value of money is a good thing even if the underlying asset’s value remains stationary. This is so because the option buyer loses (the premium) if the option is not exercised by expiration with that premium going to the option seller

Options Markets and Valuation s 471

(writer). Thus, as time goes by and the option is out of the money, time value works for the seller and against the buyer. If the underlying asset’s value does not change, the longer the time to expiration, the higher the option value (in terms of time value). Although the intrinsic value of the option remains the same irrespective of the time left to expiration, an option closer to expiration is worth less than one farther from expiration. This is because of the time value factor, which implies that an option date longer to expiration has more chances to be in the money than one that is about to expire, and thus it is more valuable (expensive). Consequently deep out-of-the-money options cost less and out-ofthe-money ones cost nothing (that is, they are all time value). Box 14.3 illustrates how the time value affects options values. To better see the relationships among these concepts, consider the summary exhibit below. Option Situation In the money (ITM) Out of the money (OOM) At the money (ATM)

Intrinsic Value Increases Zero Zero

Time Value Decreases as situation gets closer ITM Decreases as situation gets closer OOM At maximum when ATM

Another factor that is crucial for the time value of options (and their valuation) is volatility. Volatility is the fluctuation in the price of the underlying asset or a measure of risk of the asset. Higher volatility means higher price fluctuations in either direction. Obviously higher/lower volatility results in higher/lower (put and call) option premiums. An option’s time value is also dependent on the underlying asset’s volatility until expiration, since the higher the volatility, the higher the time value of the option. Finally, the last factor that affects options pricing and valuation is interest rates. In general, as interest rates increase, call and put values (prices) decrease. Recalling that you

BOX 14.3 Time Value and Options Value An important notion in options strategies is time decay. As the option approaches expiration, it decays at a very rapid pace. This means that options nearing expiration experience their time value as moving exponentially, suggesting that more money is lost if the direction of the market is not the one that places the option in the money. At expiration, all the option is worth is its intrinsic value (whether it is in the money or not). The options strategist must be aware of the changes in time decay so as to use them to their advantage with the purchase of long-term options or the sale of options. For example, using long-term options will reduce the impact of time decay (relative to short-term options, which many investors may be tempted to buy because they are the cheapest) and thus allow the investor to wait for the expected move in the underlying stock without worrying about the effect of time decay. By contrast, in selling options, the goal is for the option to expire worthless or to buy it back at a lower price for a profit. The option strategist should always sell shorter options with less than 50 days to expiration. Time decay works to the option strategist’s benefit on a short-term short option because it decreases the option’s value, thereby producing a profit for the short seller. Source: J. Neal, Forbes.com, May 19, 2008.

472 s Derivative Markets and Instruments Table 14.7 Factors Affecting the Values of Call and Put Options Factor

Factor Change

Call Option Value

Put Option Value

Stock price Strike price Time to expiration Volatility Interest rate Dividends

Increases Increases Increases Increases Increases Increases

Increases Decreases Increases Increases Increases Decreases

Decreases Increases Increases Increases Decreases Increases

buy a call when you do not want to (spend more money) to buy stock directly, you can see that higher interest rates would induce you to spend less (by buying an option), save more (by not buying stock directly), and earn more by investing the money left (saved). Thus as interest rates rise, the demand for calls and puts would rise too, putting an upward pressure on their prices. A less important factor is dividends, since as dividends increase, call/put prices would decrease/increase. For example, if dividends increase, the stock price will decline, resulting in lower/higher call/put prices. Because exchangetraded stock options have a short life (of less than a year) dividends payable during the life of the option contract can be predicted fairly accurately. Table 14.7 summarizes the six factors that influence the value (price) of a call and put option. Binomial Option Pricing Despite the fact that a thorough understanding of option valuation involves very complex mathematics, it is possible to illustrate the basic idea with a simple example. In general, all available valuation approaches (the binomial one presented herein and the Black-Scholes-Merton presented later) rely on the notion of a perfect hedge or a replicating portfolio. In other words, in principle, it is possible to create creating a risk-free portfolio by combining an option with its underlying asset. This ensures that there are no arbitrage opportunities. Let us now show the basic approach to binomial option pricing. Assume that you bought a share of stock at $50 and forecast that it will go up to $65 or down to $40 within the next year. Ignore any dividends. Suppose further that a call option on the stock has an exercise price of $55 with a time to expiration of 1 year. These situations are shown in the diagrams below. $65

10 [=max (0, 65 - 55)] C0

$50 $40

0 [=max (0, 65 - 55)] Call option

Stock price

In general, to find the up and down stock prices we employ the following formulas3: up = e t and

down = e− t = 1/up

where e is the log base and  is the volatility or standard deviation. Therefore for an up price, we multiply the current stock price by the up value, and for a down price, we multiply the current stock price by the down value. Notice that the down formula is the

Options Markets and Valuation s 473

reciprocal of the up formula. This diagram depicts a two-state stock price model. The issue here is to find the proper value for the call option, C0, today, given your estimates of the values (at expiration) of the stock price. At the heart of this analysis is the replicating or hedged portfolio, which must be constructed. Denote the number of call options required as H. Utilizing the possible values for the call option (10 and 0), we model the number of options by setting the two resulting expressions equal to each other: 65 + 10H

and

40 + 0H

so that

65 + 10H = 40 + 0H

and solving for H: Sup−Sdown $65−$40 H = __________ = ________ =−2.5 $0−$10 C0down−C0up What does this number (or the hedge ratio) mean? It has two meanings. First, that we need 2½ times as many call options in the hedged portfolio and, second, that call options must be sold in order to create the hedged portfolio (hence the negative sign). Thus the stock is held long and the call option short. The hedged portfolio is then expressed as (50−2.5 C0). Alternatively, the hedge ratio can be expressed as follows: H =

Cup − Cdown Sup − Sdown

(4)

where C represents the call option’s up or down values and S stands for the stock prices up or down. In this case, the value will be a fraction (not a whole number as in the above example). Next we need to recall that a riskless investment is typically free from arbitrage; thus it is priced so that it earns exactly the risk-free rate (at expiration). The investor has designed a riskless portfolio with a payout of $40, as shown below. This portfolio is perfectly hedged and is independent of the stock price prevailing at end. Stock value Minus 2½ call options Net payoff

$40 0 ––– $40

$65 25 ––– $40

In other words, we seek to find the value (price) of the call option (C0) that would enable the hedged portfolio to grow to the certain value of $40. This is done with the following expression: ($50−2.5 C0) (1 + Rf ) = $40 where Rf is the risk-free rate at time of expiration (1 year here). If we assume that the risk-free rate is 5% (proxied by the yield to maturity of a 1-year Treasury bill), we can compute the value of one call option by solving for C0:

474 s Derivative Markets and Instruments

C0 =

$50 − $40 /1.05 = $4.76 2.5

Thus, $4.76 would be the intrinsic (fundamental or fair) value of a 1-year call option on the underlying stock assuming that the above inputs (expected stock prices and interest rates) are correct. Alternatively stated, this value is the binomial value or the value of the option if it were held rather than exercised. Note that the $40 riskless portfolio has a present value of $38.095 (or $40/1.05). This value must be set equal to the difference between the stock held long ($50) and the calls held short (2.5C0), that is, $50−2.5C0 and resulting $11.905. Hence each call option should cost $4.76 (or $11.905/2.5). The above approach is the simplest one for a two-state situation. What if we want to expand to multistate periods, such as weeks or months? In this case we need to construct a more detailed decision or price tree, just like the one shown in Figure 14.10. Recall that C refers to the call options to be priced today and the various subscripts refer to the future time periods. For example, node C1 denotes the next period’s higher stock price, while node C11 denotes the second period’s higher price. Similarly, C2 denotes the next period’s lower price, and C22 indicates the second period’s lower price. Other nodes can be interpreted accordingly. The way we work on stock price trees is backwards. That is, in order to price C1, we use information from C11 and C12. Similarly, to price C2, we use information from C21 and C22. Finally, to price C0, we use information derived from C1 and C2. You realize that as the number of subperiods increases, the number of branches (with the possible stock prices) also increases. This results in an even more complex tree structure. Recognize also that as stock prices move higher and higher or lower and lower, they may be considered as extreme or rare events and have smaller probabilities. By contrast, the midrange values seem more likely relative to the more distant ones. The probability of each outcome is described by the binomial probability distribution; thus the model is known as the binomial model. As such, owing to the complexity of its structure, it requires computer modeling to be applied. The Black-Scholes-Merton Option Valuation Model The disadvantage of the binomial option valuation model mentioned above can be an advantage for the Black-Scholes-Merton (BSM) valuation approach or model, which is easier to apply. Other than that, both option valuation approaches are identical in

C11 C1 C

C12 C2 C22

Figure 14.10 A multistate price tree.

Options Markets and Valuation s 475

their basic assumptions. One additional assumption is the constancy of both the riskfree rate and the volatility of the stock price. The Black-Scholes (1973) and Merton (1973) valuation formula is for European-style options or for options that are exercised only at expiration.4 Box 14.4 shows the controversy of using one over the other option valuation model. Before deriving the formula, an intuitive interpretation of it may be instructive. The formula itself has two parts. The first part is derived by asking what the expected benefit of purchasing a unit of the actual (underlying) stock would be. By computing the change in the value (or the premium) of the call option, given the change in the stock price (in probabilistic terms), and multiplying it by the current stock price, we can find that part. The second part refers to the (expected) value (of the money) to purchase the call option. Recall that the option will be exercised when the stock price is above the strike price at expiration. Finding this probability and multiplying it by the strike price gives us the second part of the equation. Finally, the difference between the two parts yields the fair price of the call option. In symbols, the basic formula is given below. C0 = S0 e-δT N(d1) − X e-rT N(d2)

(5)

Box 14.4 Black-Scholes-Merton or Binomial Model? On March 31, 2004, the Financial Accounting Standards Board (FASB) announced proposals that would force US-listed companies to record the estimated value of employee stock options as an expense item in profit and loss statements based on the fair value on the grant date. However, controversy over how to estimate the ultimate cost of such awards arose, since the FASB expressed a preference for a valuation method (the lattice or the binomial model), which can require millions of individual computer calculations. Opponents argue that the fair value of stock options cannot be reliably measured for financial statements, especially using measures like the Black-Scholes-Merton method. The difficulty stems from trying to predict the present value of employee options, which depend on future share price movements but cannot be traded on any open market. The choice of a valuation model will depend on the important features of each arrangement and the data availability necessary to use the model. For example, the Black-Scholes-Merton formula assumes that options are exercised at the end of the option’s contractual term and that volatility, dividends, and risk-free interest rates remain constant over the contract’s term. In addition, the formula must be adjusted to take account employee share options characteristics and similar instruments that are not consistent with the model’s assumptions. By contrast, the binomial formula can be designed to account for certain characteristics of employee share options. Thus it would be more able to reflect such characteristics in the estimation of fair value. The FASB proposes allowing individual companies to continue choosing the approach that suits them best, but made it clear that larger issuers of stock options should switch to the binomial method. Sources: D. Roberts and A. Michaels, FT.com, April 1, 2004, and D. Casserly, Institutional Investor, April 2, 2004.

476 s Derivative Markets and Instruments

where d1 =

ln(S0 /X) + (r − δ + σ2 /2) T σ T

d2 = d1 −  T

(5a) (5b)

and where C0 = the current price of the call option S0 = the current stock price X = the strike price  = the dividend yield of the stock T = the time left to expiration N(d) = the (risk-adjusted) probability for d (area under the standard normal curve up to d) r = the risk-free interest rate  = standard deviation of rate of return of stock The corresponding formula for valuing a European put option is given below: P = X e −rT [1 − N(d2)] − S0 e-T [1 − N(d1)]

(6)

where P is the price of the put option. Let us illustrate the call option formula with an example. Assume the following information: S0 = $50 X = $45 r = 0.05 T = 0.50 (half a year)  = 0.50 Assume further that the stock has no dividends. First compute the d1 and d2 parts, as follows: d1 =

ln(50/45) + (0.05 − 0 + 0.5 2 /2) 0.50 = 0.5455 0.50 0.50 d2 = 0.5455−0.3536 = 0.1919

Options Markets and Valuation s 477

Now we need to find the probabilities N(d1) and N(d2) using the normal distribution. Thus N(0.5455) and N(0.1919) are 0.7072 and 0.5761, respectively.5 Finally, these two numbers must be used in Eq. 4 to obtain the fair value for the (European-style) call option. Notice that because there are no dividends, the S0e-δT term is equal to S0. Thus, we have: C0 = 50 (0.7072)−45 e-(0.05)(0.50) (0.5761) = 35.36−25.28 = $10.07 This is the fair price for this option based on the inputs above. Notice that we stressed the last part of the previous sentence in order to caution you on some of its inputs, particularly the volatility () one, because it is not directly observable and must be estimated. If this input value, ceteris paribus, is incorrect, the option price may not be the “fair” one (that is, it may be interpreted as under- or overvalued by some analysts). There are two types of volatility, statistical and implied. Statistical (or historical) volatility reflects what has happened in the past of an asset’s price movements or how volatile the asset was. Statistical volatility is also known as the standard deviation. This type of volatility helps investors determine the strike price that would be best for a particular strategy. Implied volatility is what is implied (for the future) by the movements of current market prices. Stated differently, implied volatility reflects the market’s current sentiment and is derived from the option’s last traded price.6 This type of volatility serves an input for option valuation models. In sum, historical volatility refers to the past and implied to the future; that is, it is forward-looking. How do investors use implied volatility? One way is simply to compare the stock’s actual standard deviation to its implied one. If the actual volatility exceeds the implied volatility, the stock is undervalued and investors could buy the stock. By contrast, if the actual volatility falls short of the implied one, investors conclude that the option’s current price is higher than its actual price and thus could sell the stock. Stated differently, the option would be considered expensive as investors do not believe that its standard deviation justifies the stock’s (high) current price. Perhaps investors can go long on (buy) the options with the lower implied volatility and go short (write) the options with higher implied volatility. An important implied volatility index is the CBOE’s volatility index (VIX), which is a key measure of the market’s short-term volatility expectations. This measure is based on the S&P 500 stock index option prices. Figure 14.11 shows both indexes since 1990 (VIX values are on the left axis and S&P 500 Index values on the right axis). The VIX was introduced in 1993, and in 2003 it underwent a major revision in methodology. A related index is the CBOE’s S&P 500 3-month volatility index (VXV). In 2004, CBOE also launched a futures volatility index (VX) traded on its all-electronic Chicago Futures Exchange (CFE). This index, derived from real-time S&P 500 Index option prices, reflects investors’ consensus view of expected market volatility in the next 30 days. Options on this VIX are multiples of $100 and have contract months of 2 near-term contract months plus 1 month on the February quarterly cycle. Early in 2006, the CBOE also introduced the options VIX, which was the first product to be traded from an options-approved securities account.

478 s Derivative Markets and Instruments 70

1800 1600

VIX S&P 500

60

1400

50 1200 40

1000

30

800 600

20 400 10

200

10

08

20 2/ 1/

06

20 2/ 1/

04

20 2/ 1/

02

20 2/ 1/

00

20 2/ 1/

98

20 2/ 1/

96

19 2/ 1/

94

19 2/ 1/

19 2/ 1/

2/

19

92

0

1/

1/

2/

19

90

0

Figure 14.11 The Volatility (VIX) and S&P 500 indexes.

How else can the investor profit from implied volatility using VIX? If the investor expects implied volatility to go up/down,s he can buy a call/put option on the VIX. Thus, when an investor “buys volatility,” she can implement (establish) a long straddle strategy (position) whereby the position becomes profitable as implied volatility increases. In essence, what implied volatility shows is an estimate of how much an underlying asset moves up or down. The higher the implied volatility, the more the asset is expected to move higher and thus the higher the probability that such a movement will be to the investor’s favor. This is known as the option’s vega and is discussed in the next section. Apart from viewing these indexes as gauges of market sentiment, investors also use them as risk-management or hedging tools. Assume that the Federal Reserve (Fed) is expected to keep rates steady at its next meeting (announcement) but there is a chance of either raising or lowering rates by some basis points. Volatility will increase before that meeting, but if the Fed keeps the rates steady, implied volatility will fall because of correct expectations and reduced future uncertainty. If the Fed surprises the market by lowering rates, implied volatility will again fall because market participants view this move as a bullish signal (boosting the market) and there is less uncertainty. In addition, because volatility rises during periods of crisis (see figure for the spikes upward in the VIX), sometimes investors refer to the VIX as a “fear indicator.” Finally, notice the path of the VIX over time, which clearly shows considerable variation (that is, it is time-varying). This stands in sharp contrast to the BSM assumption of constant volatility, suggesting that the model must be used with caution. Thankfully, however, there are several extensions to the model that allow for time-varying stock volatility.7 Read the box titled International Focus to learn why and when volatility is important to trade and which banks have constructed indexes similar to the VIX to trade implied volatility.

Options Markets and Valuation s 479

Using the Black-Scholes-Merton Formula Now that the BSM approach has been presented, let us see how we can use it further for hedging purposes. In other words, we need to compute the Greeks, or the partial derivatives of Eq. 4, with respect to some of its parameters. For example, we can take the partial derivative of the equation with respect to the stock price in order to measure how much the price of the option changes when the stock price changes by $1. This is known as the hedge ratio or delta of an option. If we measure the sensitivity of the option price to changes in stock prices, both measured in percentages, we compute the option’s elasticity. The hedge ratio for a call option is positive and for a put option negative. Below are the relevant equations. Delta =

∂C = N (d1) for a call option ∂S

and N(d1)−1 for a put option

(7a) (7b)

For example, if a call option has a delta of 0.40, it would mean that it can gain or lose value of 40% (or 40 shares of 100 shares) when its price moves by 1%. Stated differently, for every call option written, 0.40 shares would be needed to hedge the investor’s portfolio. Therefore if you write 10 options and hold 4 shares of stock (based on the hedge ratio of 0.40), every $10 increase in the underlying stock’s price will result in a $4 gain on the stockholdings (or a $4 loss on the 10 options written). The net value of the portfolio remains unchanged; that is, it is fully hedged. The investor holding both the options and the stock in the right proportion hedges the portfolio. Finally, if the delta of the call option is 0.40, the put option’s delta would be 0.40−1 = −0.60, as implied by the formulas above. Another useful Greek symbol is the vega. Vega measures the sensitivity of the option price to implied volatility (changes) of the underlying stock. Its formula is as follows: Vega =

∂C = S N(d1) T − t ∂σ

This measure is the same for both (long) calls and (long) puts and always positive because when volatility increases/decreases, the options’ value increases/decreases. For example, assume a call option’s price to be $3.50, its volatility 25%, and its vega 0.25. If volatility increases to 26%, the call price will rise to $3.70, and if the volatility falls to 24%, the call price will drop to $3.25. Vega can be important for traders who employ the straddle option. The final Greek measure is the theta. Theta measures how much the price (value) of the option changes with the passage of time. Recall that as the option approaches its expiration date, the option contract’s value becomes more certain. This is the time value of the option (or its extrinsic value), which was explained above. Because the value of the option erodes over time, theta will be a negative number. For example, a theta value of −0.10 means that for each 100-share contract, the contract loses $0.10 per day as it moves closer to its maturity date. Consequently the theoretical value of the option will be its value minus the theta value. So if the option’s price is $3.50, its price that day will

480 s Derivative Markets and Instruments

be $3.40. For the sake of completeness, the formulas for the call and put options are given below. θ=

θ=

SN (d1)σ ∂C = − r X e −r(T −t) N (d 2) for a call option ∂T 2 T − t

∂C SN (d1) σ = + r X e −r(T −t) N (−d 2 ) for a put option ∂T 2 T − t

Put-Call Parity Formula A relevant question is this: What is the relationship between the prices of a Europeanstyle call and a put option of the same underlying stock with the same expiration date that does not allow for arbitrage opportunities? If we design two portfolios with the same value at expiration, they must also have the same (present) value today, otherwise an arbitrage opportunity would emerge. One such portfolio would be the call option plus the (present value of) the strike price and another one with the matching put option and the (underlying) stock. This relationship between the call and put prices, under the assumptions above, is exactly the put-call parity relationship. The formula is as follows: C0 + pv(X) = P0 + S0  C0−P0 = S0 − pv(X)

(10)

where pv(X) is the present value of the borrowing position of the strike price, X, to be repaid at maturity and discounted at the risk-free rate and expressed as pv(X) = X e −rT. P0 is the price of the corresponding put. We can alternatively see this relationship by holding the portfolio with the stock itself, where the put resembles the protective put option strategy. Similarly, holding the call and investing the present value of the strike price is what is known as a fiduciary call. In other words, if the investor invests the amount equal to the present value of the strike price in a risk-free bearing account, at expiration the value of the account should be equal to the cost of exercising the option (if profitable). This is the fiduciary call. The relationship between the protective put and the fiduciary call is as follows: Protective put = fiduciary call  stock + put = cash + call Let us illustrate the put-call parity with a simple example. Assume the following information on a stock for a 6-month period:

Price: Strike price: Call price: Put price: Risk-free rate: Six-month period:

S0  $50 X  $45 C0  $8 P0  $3 r  5% T  0.50

Options Markets and Valuation s 481 Table 14.8 Investor’s Net Position from Put-Call Parity Position

Current Cash Flow

Buy Call

–$8

Sell Put Sell Stock Invest X (45e−(.05)(.5)) Net Position

Cash Flow at Expiration

+$3 +$50 −$43.89

ST < 45 0 $45 − ST ST −$45

ST  45 –(ST − 45) 0 ST −$45

$1.11

$0

$0

Using the above numbers, we apply each side of Eq. 10: 8−3 = 5

and

50−45 e- (0.05) (0.5) = 6.11

As we see, the two sides are not equal, which means that the relationship is violated and thus arbitrage opportunities currently exist. Specifically, you can buy the cheap(er) portfolio, here the call, invest the strike price (the left-hand side of the equation), and sell the relatively expensive portfolio (the stock and the put). In other words, you can buy a call and sell the put. Let us now analyze this arbitrage strategy and trace the net effect 6 months from now. Table 14.8 summarizes the investor’s positions, based on the above results, and the last two columns the cash flow at expiration, when the stock price is ST. As you see, the current (immediate) cash flow is $1.11, or exactly equal to the difference between the two sides of Eq. 10, reflecting the option’s mispricing. In other words, the $1.11 inflow is realized in a riskless fashion. However, in 6 months, various investor trades (buys/sells) would restore parity (equilibrium) and yield exactly zero net.

USING STOCK INDEX OPTIONS Options can be traded on indexes. Options can also be traded as exchange traded funds (ETFs), which, you will recall, are funds designed to replicate and mimic particular indexes and are traded on an exchange much like an individual stock. Thus, an ETF option gives the right to trade a specific ETF at a specific price on or before a specific date (the expiration date). A stock index option gives the investor the right to trade (buy or sell) a specific stock index at a specified price on a specified date. The basic difference between a stock index option and an option on ETF is that the values of the former change at the end of the day (with the closing of the market), whereas the values on ETFs vary throughout the trading hours. Institutional and retail investors take positions on indexes and/or on options on ETFs to hedge against adverse market movements. For example, portfolio managers purchase options on indexes when their portfolios highly correlate with the relevant market index and thus the movements of the index. A put option can be purchased on the stock index, so that when the market declines severely, the value of the put option will limit the portfolio’s decline. Even in the case of a market advance, when the put option simply expires, many portfolio managers defend their hedging choice for portfolio protection. In addition, several portfolio managers use stock index options as a means of engaging in dynamic hedging. For example, when managers expect favorable market movements,

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they purchase call options on the stock index, thereby magnifying the effects of the market situation (because they have increased their exposure to that event). Furthermore, portfolio managers employ dynamic hedging allocation when they sell call options on indexes that are expected to remain relatively stable during a particular period. This strategy simply generates some cash in periods of flat economic activity. A final use of index stock options within a dynamic strategy context is for altering the risk/return characteristics of portfolios rather than engaging in costly portfolio restructurings and rebalancings. Options are also available on stock index futures. Investors hedge their stock portfolios using such options to offset a loss on their stockholdings while maintaining some upside gains (potential). Some important stock index futures are the S&P 500, Dow Jones, and some international indexes such as the German DAX and the British FTSE. Each contract is worth $250. In general, if you want to use the S&P 500 stock index futures to hedge against market movements, you can sell such contracts to protect the value of your portfolio. Here is an example. Assume that the value of your portfolio is $10 million and the December 2011 S&P 500 contract was 1,157.70 (as of November 25, 2011, as reported in the Wall Street Journal). The actual S&P 500 Index was 1,162 (as of November 23, 2011). How can you protect the value of your stock portfolio against any further market swings (up or down)? The strategy is to sell S&P 500 Index futures contracts. You find the number of contracts to sell by dividing the value of your portfolio by the cost of a contract. The latter is found by multiplying the cost of a contract by the futures price: $250 × 1,157.70 = $289,425. Thus you will need to sell 34.5 contracts (or $10,000,000/289,425). Two scenarios are plausible at maturity: an upmarket or a downmarket. If the market (i.e., the value of the S&P 500 Index) goes up, say to 1,200, the total value of your portfolio is computed as follows: Value of portfolio = $10,000,000 (1,200/1,157.70) = $10,365,379.63 Loss on futures contracts = 34.5 ($250) (1,157.70 − 1,200) = −$364,837.50 Total net = $10,000,542 If the market goes down, say to 1,100, by analogy we have: Value of portfolio = 10,000,000 (1,100/1,157.70) = $9,501,598 Gain on futures contracts = 34.5 ($250) (1,157.70 −1, 100) = $497,662.50 Total net = $9,999,261 Thus your portfolio’s value remains unchanged regardless of the market’s movement. In general index options enable an investor to capitalize on an expected market move or to preserve (protect) his holdings from the underlying index’s movements. Index options offer investors diversification (gaining exposure to the general market or a market segment), leverage (by paying a small amount, the premium, the investor can realize larger gains from favorable movements in the underlying index), and predictable risk (since an option index investor cannot lose more than the premium paid). What are the similarities and differences between stock options and index options? The fundamental difference between the two instruments is the underlying asset. Index

Options Markets and Valuation s 483

options are based on baskets of stocks, whereas stock options are based on single stocks. Also, index option holders cannot exercise their options (for positions) in the underlying index, while holders of stock options have the right to trade shares of stock. In other words, index options are settled in cash. Some similarities between the two instruments are that equity options all represent 100 shares of stock, are American style, and expire on the third Friday of each month. Index options are not as standardized but all refer to the $100 multiple.

CHAPTER SUMMARY In this chapter the fundamentals of options and option pricing were presented. Specifically the two types of options, calls and puts, and their graphic illustrations with the gains and losses from trading, as well as their payoffs at expiration, were discussed. We next explored the market for options and the Chicago Board of Trade’s products (such as Long-Term Anticipation Securities, interest rate options, futures options, and collateralized loan obligations among others), its participants (such as mutual funds, hedge funds and other funds), and the important role of the Options Clearing Corporation. We also presented and explained some basic option trading strategies, such as covered calls and protective puts, among others, and illustrated them graphically and mathematically. Finally, we discussed how one can speculate with options, using real examples. In the second part of the chapter, we presented two ways to value an option, the binomial model and the Black-Scholes-Merton formula, and highlighted their advantages and disadvantages. We elaborated on the use of the BSM formula by presenting some of its important derivatives, such as delta and vega. We also presented an important parity, the call-put parity condition for options, and emphasized its property for arbitrage opportunities. Finally, we included a section on index options and gave an example of how an investor should use them.

APPLYING ECONOMIC ANALYSIS PURCHASING STOCKS OR OPTIONS? This is an interesting question given the relationship between the two kinds of investment strategies (derivative values depend on the values of the stock). Let us address this question with a simple example. Assume that you expect a bullish market and thus you ponder whether to purchase a stock directly or call options on it. Currently the stock price is $50 and the call option premium is $5. The option exercise price is also $50. Your two mutually exclusive portfolio choices (ignoring commissions, dividends, and future taxes) are: All stock: buy 100 shares at $50 at a cost of $5,000 Call options: buy five contracts involving 100 shares each or 500 call options each selling for $5 The table below shows you the two options and their payoffs at various stock prices.

484 s Derivative Markets and Instruments

Portfolio

Stock Price

All Stock Call Options Stock-Options ror Stocks ror Options

$45

$50

$55

$60

$65

$70

$4,500 0 $4,500 −10.0% −100%

$5,000 0 $5,000 0 −100%

$5,500 $2,500 $3,000 10.0% −50.0%

$6,000 $5,000 $1,000 20.0% 0.00%

$6,500 $7,500 −$1,000 30.0% 50.0%

$7,000 $10,000 −$3,000 40.0% 100%

The all-stock portfolio values are simply the 100 shares times the share prices. The call options portfolio values are derived by multiplying the 500 call options by the excess of the stock price over the exercise price. For example, when the stock price is $55, the excess of the stock price over the strike price is $5 times the 500 calls, giving us $2,500. Naturally the options portfolio is worthless at any price at or below $50. The third row of the table shows the dollar payoff of the two investment choices (stock portfolio minus the call options portfolio values); the last two rows show the rates of return (ror) of each strategy. For example, the rate of return of the stock portfolio when the stock’s price is $55 is 10% (5,500/5,000−1). As you see from all these values, the stock portfolio yields positive values up to a point, but the call options portfolio yields (much) higher values as the stock price increases. The disproportional rates of return are due to the use of leverage in using options, and, theoretically, can generate unlimited profits. In sum, the choice of a particular strategy depends on your expectations about the direction of the asset (stock), at the same time keeping in mind the financial risk of that strategy! In this case the financial risk is limited to the premium paid for the option.

INTERNATIONAL FOCUS GLOBAL CURRENCY OPTIONS VOLATILITY INDEXES Options exchanges around the world have profited from recent volatility spikes as equity trading became lethargic. The Chicago Board Options Exchange’s volatility index, the VIX, recorded the busiest month in March 2011 (seeing a rise in volumes of 17%), while the International Securities Exchange, the US options exchange owned by Deutsche Börse, reported a 3.7% per cent rise in average daily trading volume amid several event risks. For example, the Japanese nuclear disaster, the North African countries’ uprisings and wars, the worsening European sovereign debt crisis, and so on contributed to the presence of extreme trading environments. Thus traders hedged equity risk by trading volatility. Option volumes are back because fear and greed (speculation) drive the markets. Over the course of the financial crisis, investors have been looking for ways to protect their investments, and the options markets have been in the middle of this. Major investment banks have launched similar volatility indexes (like the VIX) on currencies, arguing that foreign exchange volatility can serve as a good indicator of risk in other assets during times of uncertainty and turmoil. Sometimes such risk is known as “tail risk” or risk that is unlikely but which, if it occurred, would be damaging. For example, Credit Suisse

Options Markets and Valuation s 485

(in London) has recently created the Credit Suisse Advanced Volatility Index, which may be particularly suited for insurance companies and hedge funds. That index has been designed to deliver positive returns during extreme events while not losing much during good times. BNP Paribas has also launched its trading FX volatility index to exploit the volatility risk premium (or the difference between the actual or historical volatility and implied or expected volatility). The downside is that the index does not work well during extreme events (such as the collapse of the dotcom companies) that do not spread to the foreign exchange (forex) markets. The index is targeted at sophisticated institutional investors who regard volatility as a separate asset class. Finally, J. P. Morgan Chase & Co. has recently unveiled its index of global foreign exchange volatility, which follows implied volatility on major and emerging markets currencies. Options on the euro against the dollar account for the largest weighting in the index with the dollar against the yen for the second largest weighting. Sources: N. Marmery, FX-Week, July 11, 2011. L. McCormick, Bloomberg/Business Week, March 25, 2011. J. Grant, H. Weitzman, and A. Gangahar, FT.com, April 2, 2009.

LESSONS OF OUR TIMES WHAT, IF ANYTHING, HAVE BIG BANKS LEARNED FROM ROGUE DERIVATIVES TRADERS? It seems that every year we hear about huge losses incurred by big international banks because of speculative activities by “rogue” traders within these banks. A rogue trader has many definitions; for example, “one who trades outside well-defined trading boundaries,” “one who plays double,” or even “one who breaches boundaries set by a government authority,” according to an article in the Financial Times. These traders speculate on financial instruments, notably using derivative products, in their relentless quest for the highest profit—typically short-term. If you do a simple Internet search on rogue traders, you will find that they have spanned at least three decades and that there are quite a few of them. Let us cite some of the most recent ones who were heavily featured in the press and media in general. Nick Leeson brought on the collapse of Barings Bank in September 1995 by investing in the Singapore International Monetary Exchange (as well as the NIKKEI exchange) using derivative securities. One of his trading strategies was to buy and sell call and put options on the NIKKEI betting that the Japanese equity market would rise in performance. A few errors here and there (and the opening of an independent account) as well as the Japanese earthquake in 1995 forced him to buy additional contracts to support the market. His exposure grew fourfold, and when his scheme collapsed, the bank was almost 20% exposed in these contracts. Barings Bank was acquired by the insurance company ING for ₤1. Toshihide Iguchi explained in a detailed letter to his boss in Daiwa Bank in 1995 how he had carried out a series of trading frauds by forging some 30,000 trading slips over 11 years of dealing in government bonds in New York. The trading scheme was simple: when his trades were losing money, he would generate slips of bond sales to make the transactions look legitimate. Daiwa bank left the United States later that year. Jerome Kerviel worked for France’s second-biggest bank, Société Générale, in 2008 at its derivatives trading desk. It was a mystery for the bank to find out how an employee working in

486 s Derivative Markets and Instruments

a low-trading derivatives position could have taken unauthorized positions totaling 50 billion, or double the bank’s capital. He was involved in the practice of arbitrage, buying portfolios of financial instruments (like European index futures) in one market while simultaneously selling a similar offsetting position with a different value in order to minimize risk. The problem was that the offsetting portfolio was fabricated, which amounted to an unhedged bet. Such bets were enormous, in the billions of dollars. Kweku Adoboli of UBS was responsible for the latest incident of rogue trading, which cost the bank $2 billion following unauthorized trades. The trader was a director of exchange-traded funds and the Delta One desk in charge of several important profit-making activities. For example, in index arbitrage, traders attempt to exploit slight differences in the prices of stock indexes and index futures. Unauthorized sales included the use of stock-related financial products and foreign exchange derivatives as well as the establishment of a mirror account using phantom positions in the above-mentioned securities. So have the big banks learned anything from all these incidents of unauthorized trading? Was it possible that these traders’ supervisors did not know of their trading activities? Or did they know about them and, when good times rolled, looked the other way but took action only when losses mounted up? What about compliance and regulation? Some of these traders seemed able to exploit the weaknesses in compliance systems because of the power their profits gave them. Moreover, were the banks’ internal control systems weak and/or inadequate? If so, why didn’t they try to improve them to avoid future disasters? For example, why did UBS fail to learn the lessons of the billion-dollar losses at Société Générale and Barings? It remains to be seen if other rogue traders pop up in the near future. Chances are that they will. Sources: B. Moshinski, UBS fails to learn from previous rogue trade cases, Business Day, Sept. 9, 2011. S. Pignal, Rogue traders who went off the rails, FT.com, January 24, 2009.

KEY CONCEPTS An option is a contract that gives the owner the right, but not the obligation, to buy or sell an asset at a specified price on or before a specified date. A call option conveys the right to buy an asset at a specific price on or before a specific date. A put option entitles its holder to sell an asset at a specific price on or before a specific date. An option is in the money when it yields a positive payoff for the option holder. An option is out of the money when its exercise is not profitable. An option is at the money when the exercise and the stock price are equal, thus yielding a zero payoff. The Options Clearing Corporation effectively guarantees contract performance and eliminates credit risk in options trading. Interest rate options give the investor the opportunity to invest based on her perception of the direction of interest rates or yields. Futures options give their holders the right to buy or sell a specified futures contract with a futures price as the strike price of the option.

Options Markets and Valuation s 487

Foreign currency options are currency option contracts that allow for the purchase or sale of a set amount of foreign currency in exchange for a specified amount of the domestic currency. A warrant is an option (a call option) issued by a firm to buy shares of its stock. A collateralized loan obligation is a loan arrangement under which the lender requires some collateral to be put up by the borrower to back up the loan. A covered call is the purchase of an asset and the simultaneous sale of a call option on that asset. A protective put strategy implies the purchase of the stock and the placement of a put option on it at the same time. An equity collar strategy consists of the simultaneous purchase of a put option and the writing of a call. A straddle is a mix of call and put options each with the same strike price and expiration date. A married put strategy is one where the investor purchases the shares of stock and at the same time a put option on them. A spread strategy involves establishing a position with two or more call or two or more put options on the same asset (stock) with different strike prices and expiration dates. An option’s intrinsic value is the payoff that can be realized by the immediate exercise of a profitable calls or puts. Time decay is the (nonlinear) change in the value of the option, which becomes cheaper if the underlying asset is not moving (or has not moved) in the expected direction. The value of the option over parity to the asset is known as the asset’s extrinsic value. Volatility is the fluctuation in the price of the underlying asset or a measure of risk of the asset. Implied volatility is the volatility that yields a theoretical value consistent with the option’s market value. The delta of an option is the partial derivative with respect to the stock price in order to measure how much the price of the option changes when the stock price changes by $1. Vega measures the sensitivity of the option price to implied volatility (changes) of the underlying stock. Theta measures how much the price (value) of the option changes with the passage of time. The relationship between the call and put prices is known as the put-call parity. Portfolio insurance is a means of limiting investment losses while achieving upside potential. Dynamic hedging (or delta hedging) results from changing market conditions. A stock index option gives the right to trade (buy or sell) a specific stock index at a specified price on a specified date.

488 s Derivative Markets and Instruments

An ETF option gives the right to trade a specific ETF at a specific price on or before a specific date (the expiration date).

QUESTIONS AND PROBLEMS 1. Read the passage below and answer the two questions that follow. Currently a Google employee holding an option with a strike price of $450, compared with the market price of $500, can realize only ________, by exercising the options, selling in the market, and pocketing the difference. But another investor should be prepared to pay more than $500 for the unvested option, depending on its life, to reflect the possibility that the stock will rise before the option expires. a. Regarding the first sentence: if the employee exercises the option, he or she will realize what? (That is, complete the sentence.) b. Regarding the second sentence: what does this mean for the option? 2. Read the passage below and answer the question that follows. Google hopes that the plan will “close the gap between the option value at grant and the employee’s perception of the value,” according to the company’s executive compensation manager. The gap is particularly stark in the case of “underwater” options, where the exercise price is above the market price. What do or don’t these options have? Intrinsic value and/or significant time value? 3. Assume the following real information on IBM calls and puts as of May 29, 2009 (from Yahoo! Finance). For example, the symbol IBMFA.X is the IBM 105.00 call for June 2009. The IBM price was $106.28, and these options were expiring on Friday, June 9, 2009. Answer the questions below the chart. Calls Symbol

Last

Chg

Bid

Ask

IBMFT.X IBMFA.X IBMFB.X IBMFC.X

6.90 3.10 0.85 0.15

1.20 0.70 0.25 0.03

6.90 3.10 0.80 0.10

7.10 3.20 0.85 0.15

Volume Open Interest 802 4,793 4,422 15,477 1,977 11,185 90 6,318

0.45 1.05 1.40 0.00

0.60 1.70 4.40 8.70

0.65 1.80 4.50 8.80

2,860 2,502 297 50

Strike Price 100.00 105.00 110.00 116.00

Puts IBMRT.X IBMRA.X IBMRB.X IBMRC.X a. b. c. d.

0.60 1.75 4.50 10.5

9,485 7,855 1,989 835

Which options are “in the money” and which are “out of the money”? What is the meaning of “volume” and “open interest”? Why do the call option prices decline while the put option prices increase? What are the “bid” and “ask” prices, and what does the difference between the two mean?

Options Markets and Valuation s 489

e. Define the following: the in-the-money call, the put options call, and put premiums. Hints: Call premium = option price−(stock price−strike price); use the last-column prices. f. What are the out-of-the-money call and put premiums? 4. Using the information in problem 3, compute the put-call parity equation for the IBMFA.X call and IBMRA.X put. Assume also that the current 3-month Treasurybill rate is 0.25%. Explain your result. Hint: Use 1/12 months or 0.0833 for T in the equation. 5. Compare the profit/loss situations between going long on (i.e., owning) a stock and having a covered call strategy under the three market scenarios below. a. Stock price increases (call is exercised and stock shares are sold at strike price) b. Stock price declines (call expires worthless and shares are owned) c. Stock price is unchanged (call expires worthless and shares are owned) 6. Assume that you want to profit from either movement of the market on a stock as long as the movement is high enough to cover your costs of entering these option contracts. Which strategy would you apply and when would you profit from it? 7. Assume that you purchased shares of ABC stock at $50 per share with the intention of selling them in 3 months. You consider applying the covered call-writing strategy to hedge (somewhat) your position in the stock. The exercise price is $55, the premium on the call option is $2.50, and the expiration date is in 3 months. What would be the profit/loss situation if the strategy is used based on the following possible stock prices (40, 45, 50, 55, 60, 65)? 8. Given the following data, determine if the put-call parity holds and explain your result. Price, $60; strike price, $55; call price, $5; put price, $4; risk-free rate, 2.5%; period, 6 months 9. Based on the information below, compute the Black-Scholes-Merton formula (assume a no-dividend paying stock): S0 = $70, X = $60, r = 0.025, T = 0.50 (half a year),  = 0.60. What is the call option’s fair value? 10. You are given the following information on a stock: two possible stock prices at year end, Sup = $100, Sdown = $80; exercise price, $90; call option values, Cup = $10, Cdown = $0. Compute the hedge ratio and interpret its meaning. 11. After you have read the box titled International Focus, answer the two questions below. What are the uses of options in various markets and why? Why does volatility boost option exchanges? 12. How do institutional and retail investors take positions on indexes and/or options on ETFs to hedge against adverse market movements?

NOTES 1. 2. 3. 4.

www.cboe.com Source: CBOE, The Options Institute. John C. Cox, Stephen A. Ross, and Mark Rubinstein, Option pricing: a simplified approach, Journal of Financial Economics, 7, 1979, pp. 229–263. Fisher Black and Myron Scholes, The pricing of options and corporate liabilities, Journal of Political Economy, 81(2), May-June 1973, pp. 637–654. Robert C. Merton, Theory of rational option pricing, Bell Journal of Economics and Management Science, 4(1), 1973, pp. 141–183.

490 s Derivative Markets and Instruments 5.

6. 7.

You can find these values in two ways: either look at the cumulative normal distribution tables (found in all statistics textbooks) or seek the NORMDIST function in EXCEL. When using the tables, you may need to interpolate (for accuracy). However, with the EXCEL function, just enter the exact number in the X box, then enter 0 for mean, 1 for standard deviation, and type “true” in the cumulative box. Hit “OK,” and you will get the above values. CBOE’s site (http://www.cboe.com/tradtool/ivolmain.aspx) offers a free service (calculator) for calculating the implied volatility of options. Eric Ghysels, Andrew Harvey, and Eric Renault, Stochastic volatility, in C. Rao and G. Maddala (eds.), Statistical Methods in Finance (Amsterdam: Elsevier Science, North-Holland Series in Statistics and Probability, 1996).

15 FUTURES MARKETS AND STRATEGIES

CHAPTER OBJECTIVES After studying this chapter, you should be able to sTell what a futures contract is and why it is used sUnderstand the functions and characteristics of the futures markets sRecognize and use the relationship between spot and futures prices sComprehend the uses of financial futures sExplain some basic futures trading strategies

INTRODUCTION In this chapter we will discuss the futures market, another derivatives market. Briefly, the futures market involves the trade (purchase or sale) of some underlying asset (security) at some predetermined price at some set future date. The underlying asset can be a physical commodity (such as corn or copper) or a financial instrument (like a foreign currency or a Treasury bond). Although the structure of the modern futures market is a fairly recent phenomenon, such markets have existed since ancient times, traced back to the Greeks and Romans. The original futures market traded agricultural products and commodities, but the contemporary market also trades financial instruments, including stock indices and swap agreements. In addition, dramatic advances in telecommunications and other changes in the flow of financial capital around the world have transformed the futures market and made it among the most efficient of all developed financial markets. In the chapter, we will also discuss the fundamentals of the futures contract and its difference from other contracts and provide some examples of these contracts. Next, we give an overview of the global futures market, highlight the role of the clearinghouse, present the concepts of margin, and finally discuss briefly the futures market’s two basic 491

492 s Derivative Markets and Instruments

functions. The fourth section involves the determination of futures and spot prices and discusses concepts like cost of carry and price discovery. Finally, we end the chapter by briefly presenting some financial futures contracts strategies.

THE FUTURES CONTRACT Briefly, a futures contract conveys the obligation to a trader to deliver or buy an asset (physical or financial) at a predetermined price at a specific future date. A futures contract is a standardized contract in terms of the type of asset, price, and delivery date. An example will further clarify this definition. Assume that you learned that a breeder’s highly prized Abyssinian cat in your town has just given birth to a litter of kittens. Being a sophisticated cat lover, you would immediately feel that you would like to own one, so you rush to the breeder’s house to see the litter for yourself. After you’ve verified the breed, you enter into a contract with the breeder for one kitten to be delivered to you within 5 weeks (when the kitten is old enough to leave its mother). You also agree to pay $300 upon delivery of the kitten. This example describes the fundamentals of a forward contract, an arrangement between two parties for the delivery of a commodity at an agreed-upon price at some specified future time. No money changes hands now; that will happen only at the (future) mutually agreed upon time. Also, since this is a well-defined contract, both parties are obligated to abide by it; thus both parties are protected from price fluctuations. What are the differences between a futures and a forward contract? A futures contract is a uniform contract, traded on an organized exchange, with standardized contract terms. Standardized terms include the amount of the commodity to be delivered, delivery months, delivery location or locations, and acceptable qualities or grades of the commodity. Standardization enhances liquidity by enabling large numbers of market participants to trade the same instrument. However, there is a tradeoff to standardization. Although liquidity makes the contract more useful for hedging, it also reduces the usefulness of a futures contract as a merchandising vehicle. By contrast, a forward contract is traded in the over-the-counter (OTC) market and typically arises in the foreign exchange market. Further, forward contracts, being private arrangements, carry default risk (known as counterparty risk), whereas futures contracts are executed through clearinghouses that guarantee the transactions. Finally, futures contracts call for daily settling (for profit or loss) of the contracts (known as marked-to-market), whereas forward contracts call for settlement at the end of the contract. In general, futures markets formalize forward contracts. Futures contracts were traditionally traded in an open outcry system, where traders and brokers, wearing colored jackets, shouted bids and offers in a trading pit. This is still the main venue for trading agricultural and other physical commodity futures. But for financial futures, market participants post their bids and asks in computerized (electronic) platforms. Finally, who are the main players (traders) in the futures market? There are three main players: hedgers, speculators, and arbitrageurs. A hedger is a trader who uses the futures market to protect himself from future adverse price movements in the underlying cash asset (commodity) he owns. A speculator, by contrast, is a trader who makes bets on future directions of the asset’s price, without actually owning the asset, in an effort to profit from price changes. Finally, an arbitrageur is a market participant who attempts to exploit price inefficiencies by simultaneously purchasing and selling the same asset in two different markets to realize a riskless profit. We’ll discuss each player’s strategies in detail toward the end of this chapter.

Futures Markets and Strategies s 493

Elements of Futures Contracts The agreed-upon price to be paid upon delivery of the asset at contract maturity is called the futures price. The buyer of the asset in a futures contract is said to have a long position (or going long), whereas the seller of the asset in that contract is said to have a short position (or going short). Thus going long commits the trader to purchasing the asset at contract maturity and going short commits the trader to delivering the asset at contract maturity. Technically, since no money changes hands at the inception of the futures contract, the acts of “buying” and “selling” are symbolic only. When the buyer and seller enter a futures contract, this generates one contract of trading volume. In such contracts, there will always be an equal number of long and short positions. The number of contracts outstanding (obligated) for delivery is called open interest. Typically traders do not act at contract maturity (that is, most contracts do not lead to delivery of assets) but close out their positions before that. In this case, the trader settles the contract by offset. Thus sellers may buy in and buyers sell out their positions at any time before delivery. If an offset trade does not take place before contract maturity, the traders must close the trade at delivery (contract maturity). We will explain these concepts through an example further on. How are profits or losses realized for long and short traders at contract maturity and what do these mean? Denote the actual price of the asset at the time of delivery as the spot price. Then, Profit to long (buyer) = spot price (at maturity) – initial futures price

(1a)

Profit to short (seller) = initial futures price – spot price (at maturity)

(1b)

What is the implication of the above relationships to the buyer and seller? As is evident, the futures contract is a zero-sum game, since the profits to one trader are exactly the losses to the other. In other words, for every long position there is an offsetting short position; thus, summing over all investors, the aggregate profits are zero. Recognize also, from Eq. 1a or 1b, that profit will be zero if the spot price at maturity is equal to the original futures price and that profit will rise and fall linearly with changes in the ultimate spot price. This means that the profit to the futures contract buyer can be negative if the initial futures price is higher than the actual market (spot) price. Later we will take up the relationship between spot and futures prices in some detail. Table 15.1 illustrates some futures contracts as reported in the Wall Street Journal. The Clearinghouse Recall that a futures contract is traded on an organized exchange and thus each transaction needs to be cleared by a clearinghouse associated with the exchange. The clearinghouse is a separate corporation or is related to the exchange, and its role is to facilitate trading. It is like the Options Clearing Corporation we learned about in the previous chapter. Specifically, the clearinghouse guarantees that all traders honor their obligations, and it does so by becoming a buyer/seller to each seller/buyer. In other words, the clearinghouse guarantees to each side of a trade that contracts will be fulfilled. As a consequence, it puts its reputation (credibility) on the line. Since the trading parties need not know one another or transact directly with each other, the clearinghouse makes the trades impersonal. If it fails to serve as a guarantor of trades, the futures market may be severely damaged.

494 s Derivative Markets and Instruments Table 15.1 Examples of Futures Contracts Metal & Petroleum Futures Gold (CMX) – Troy oz.; $ per Troy oz. Contract

May June Aug

Chg

Open Interest

Open

High

Low

Settle

1170.00 1168.00 1170.50

1181.30 1167.80 1183.30

1170.00 1167.80 1169.80

1180.00 1180.70 1183.10

11.70 11.90 11.90

802 332,178 41,430

86.15 88.36 89.68

0.98 1.11 1.17

352,922 198,581 84,342

366.23 375.25

5.75 6.25

26,000 526,567

117 − 300 117 − 000

119 − 020 118 − 030

27.0 29.0

700,363 3,909

10,955

10,960

1183.00 1179.50

1183.40 1178.80

−21.90 −21.90

307,612 7,450

Crude Oil, Light Sweet (NYM) – 1000 bbls.; $ per bbl. June July Aug

85.58 87.54 88.62

86.50 88.57 89.88

85.16 87.16 88.36

Agricultural Futures Corn (CBT) – 5000 bu.; cents per bu. May June

361.20 368.50

367.00 376.00

360.25 368.00

Interest Rate Futures Treasury Bonds (CBT) − $100,000; pts. 32nds of 100% June Sept

118 − 060 117 − 100

119 − 040 118 − 040

Index Futures DJ Industrial Average (CBT) – $10 x index June

1141

11,157

S&P 500 Index (CME) − $250x index June Sept

1205.50 1199.50

1207.80 1200.20

Sources: CBOT and the Wall Street Journal, Saturday, May 1, 2010.

However, the clearinghouse requires traders to post guarantees in the form of a letter of credit or cash against the possibility of default. Regardless, a failure of the clearinghouse is a remote possibility in view of the fact that these corporations are very well capitalized and large. Figure 15.1 below illustrates the function of the clearinghouse. Let us illustrate this important function of the clearinghouse with a simple example. Assume that Haris wants to purchase one contract (of 5,000 bushels) of corn that trades on the first day of May (2010) at $3.62 (see Table 15.1). He is buying this contract from Nick, the seller of corn. The value of the contract is $18,100. This is also the open interest of one contract. Haris is going long on the contract and Nick is going short on it. Why would Haris and Nick want to enter into such a contract? Simply because Haris thinks

Futures Markets and Strategies s 495

Buyer

Clearinghouse

Seller

Figure 15.1 The clearinghouse and its traders.

Table 15.2 Profit/Loss on a Futures Trade Price of Corn

Clearinghouse Action

Potential Profit/Loss

Stays at $3.62 Rises to $4.10 Falls to $3.00

Buy/deliver at $18,100 Buy: 5,000 × $4.10 = $20,500 Sell: 5,000 × $3.00 = $15,000

$18,100 − $18,100 = $0 $18,100 − $20,500 = -$2,400 $15,000 − $18,100 = -$3,100

that the price of corn in May could be higher than $3.62 and Nick thinks that the price of corn in May could be lower than $3.62. So, in such circumstances, both parties may face losses. The clearinghouse will now enter the picture and arrange for the delivery of corn to Haris and for the acceptance of delivery from Nick. Thus Haris and Nick will not deal directly with each other. What are the possible dangers for the clearinghouse in the event of refusals by either party for fulfill its obligations? Table 15.2 below shows the two scenarios and their respective implications for the clearinghouse should the price of corn changes in either direction. Assume that the price of corn rises to $4.10. What would happen if Nick refused to deliver the corn (to Haris)? The clearinghouse is in a bind to buy the 5,000 bushels of corn at the spot price, at a cost of $20,500, and deliver it to Haris. Thus the clearinghouse faces a loss of $2,400 as the difference between the selling price of $18,100 and the purchase price of $20,500. What if the price of the corn falls to $3 in May? In this case, Haris may refuse to make a payment because he will be paying more for a commodity that now has a lower value in the spot market. The clearinghouse is again faced with losses because there will be no delivery of corn to Haris. What will happen in this case is that the clearinghouse will sell the corn on the open market and receive $15,000. As a result, the max potential loss would be $3,100 (because some or all of the loss may be recovered from Haris). To fully understand the significance of futures trading based on the above example, we need to explain why such profit/loss situations arise, how each party settles a contract, and what the clearinghouse can do to avoid potential losses. We explain each of these issues in detail next. Settlement and Margin The daily movements of the price of a bushel of corn affect the potential profits and losses of the futures contract. Such daily computations of profits or losses on futures contracts are referred to as marking (the futures contract) to market. As we saw above, if the price rises after the contract is arranged, the holder of the short position (Nick) has lost $0.48 per bushel, or debited $2,400 [5,000 bushels × (–$0.48)], but the holder of the long position (Haris) has profited $0.48 per bushel (or credited $2,400). The opposite situation occurs when the price of corn per bushel falls. Such adjustments are made daily and most transactions are settled in cash in the cash market instead of making a physical

496 s Derivative Markets and Instruments Table 15.3 Changes in Margin Positions Period

Futures Price

Spot Price

Haris’s Position (Long Position)

Nick’s Position (Short Position)

Day 1

$3.62

$3.62

Initial margin: $3,620

Initial margin: $3,620

Day 2

$4.10

$3.62

Account change: +$2,400 Ending balance: $6,020 No margin call

Account change: −$2,400 Ending balance: $1,220 No Margin call

Day 3

$4.15

$3.62

Beginning balance: $6,020 Account change: +$250 Ending balance: $6,270 No margin cal

Beginning balance: $1,220 Account change: −$250 Ending balance: $970 Margin call: +$2,650

delivery of the commodity. That is, the actual commodity is traded (sold and bought) in the cash market. Many futures contracts actually result in a physical delivery of the actual commodity unless the contract is reversed before maturity. The prices in both the futures and cash markets move in a parallel fashion because, at the expiration of the futures contract, the prices must converge (into one price). This is known as the convergence property; if it does not hold, arbitrage opportunities will arise. How can the clearinghouse protect itself from sustained losses of either party on a futures contract? One important safeguard is the posting of margin. Recall that margin refers to the funds deposited at the trader’s account with her broker and serve as a cushion in the account’s undesirable fluctuations. These funds also serve the function of guaranteeing the fulfillment of the contract and are known as initial margin. When the value of the trader’s account falls below a certain (predetermined) level, the broker will ask the trader (known as a margin call) to deposit additional funds to the account. These funds represent the maintenance margin designed to bring the account back to its initial level (also referred to as the variation margin). Naturally, if the account is in gain, the trader is allowed to withdraw cash from it. Thus posting margin makes futures trading safer and the clearinghouse is protected. Let us illustrate the margin concepts using the above example. Assume the initial margin requirement to be $3,620 given a price of $3.62 per bushel (or 20% of the value of the contract, $18,100). Assume further that the maintenance margin the broker imposes is $1,200. Table 15.3 shows the adjustments to margin magnitudes when the spot prices change. If the price of a bushel of corn rises to $4.10, then Haris’s and Nick’s positions are both in profit. No margin call is initiated by the broker for either investor. Up to that price, there is no danger for Haris or Nick because their ending account balances ($6,020 and $1,220, respectively, found by adding up the initial margin and account change values) are above the maintenance margin of $1,200. However, when the price goes even higher, to $4.15, Nick’s (short) position is in the red and the broker will make a margin call, asking Nick to post more collateral ($2,620) in order to bring the account up to its original level (of $3,620). You understand that the broker will never wait until the last moment to request collateral; he will do so much earlier than that (or before the $4.15 price becomes the new spot price). In fact, if the short-position investor fails to make the payment, the broker is entitled to close the account to protect his own interests and stop the account from accumulating further losses. Finally, Haris can withdraw the excess funds ($2,650) from his account so that both traders’ accounts have a closing balance of $3,620.

Futures Markets and Strategies s 497

We can deduce two important insights from the above example. First, it is easy to see the relationship between the amount of the funds withdrawn from this account by Haris and those deposited into it by Nick. This means that one person’s gain is exactly the other person’s loss. Second, you understand the importance of marking to market (on a daily basis) of all positions in the trade. For that reason exchanges impose daily limits on the allowable swings in a commodity’s futures price. In that way, an orderly and continuous futures market is maintained for the benefit of all transacting parties. Reversing Trades Given that most futures contracts are closed out before maturity, we say that the trader who wants to close out the contract early does so by offset or by reversing the trade, as we saw above. Table 15.4 illustrates how the trader can reverse a trade. For example, if Haris sees that traders are willing to pay $3.90 per bushel of corn a week after he has set up a futures contract, he might want to reverse the trade. He assumes that the price will not go any higher than that for the May contract and thus he might want to sell a May contract to someone else, say Helen. He has to reenter the futures market and make a reversing trade. Thus, Haris has reversed his position in the May futures contract. What is the role of the clearinghouse in this situation? The clearinghouse will notice that Haris has an offsetting position in the contract for May corn and thus will cancel both positions. Haris’s gross profit will be $1,400 [or 5,000 × ($3.90 – $3.62)]. In essence, futures contracts are very frequently replaced by adjusting the margin (equity) in the investor’s account and by the difference in the prices (futures and spot). Minimal margin requirements can also be raised by the exchanges following volatile trading days. For example, margin requirements on the Chicago Board Options Exchange for contracts are based on the CBOE’s volatility index, the VIX (which we learned of in the previous chapter). The exchange calculates margin based on the level of market volatility; thus, if prices for VIX contracts increase for a couple of days, the margin requirement will also be raised. VIX futures contracts are typically used to construct complex bets (or hedges) on the swings of the stock market. Also, CME Group raised collateral requirements for trading gold, copper, and silver futures after a volatile week (the third week of September 2011).

AN OVERVIEW OF THE FUTURES MARKET The very first account on a futures contract was presented by Aristotle in his Politics. Box 15.1 illustrates how such contracts arose. In the United States, the first organized futures exchange was established and headquartered in Chicago between the farmlands and the more developed eastern region of the country. In 1848, the Chicago Board of Trade (CBOT) was created and trading was mostly in in forward contracts. Table 15.4 Reversing the Trade Period

Haris’s Action

Nick’s or Helen’s Action

May 1

Initial Position: buy 1 futures contract at $3.62 per bushel of corn Reverse Trade: sell 1 futures contract at $3.90 per bushel of corn

Nick: sell 1 futures contract at $3.62 per bushel of corn Helen: buy 1 futures contract at $3.90 per bushel of corn

May 7

498 s Derivative Markets and Instruments

Box 15.1 The First Futures Contract Thales, a Greek philosopher from Miletus, was the first person to develop a universally applicable financial instrument. Thales used his forecasting skills to predict that the olive harvest would be extremely good the next season. Being very confident in his prediction, he made agreements with local olive-press owners to deposit his money (i.e., he bought a futures contract) with them to guarantee him exclusive use of their olive presses when the new harvest was ready. He was also able to negotiate good prices for the future harvest because the olive-press owners also wanted to avoid the possibility of a poor yield. When the harvest came, the olive yield was exceptionally good, and this raised the demand for oil presses. Thales then sold his (futures) contracts on the olive presses and made a lot of money. Source: Aristotle’s Politics.

In 1898 the Chicago Butter and Egg Board was established as an informal way of trading eggs and butter. In 1917, prices rose sharply as the United States was preparing for World War I; thus many contracts were unfilled. Following this turmoil, the Chicago Mercantile Exchange (CME) was formed in 1919, and new rules for more organized trading in these commodities were instituted. In 1972, the CME established the International Monetary Market (IMM) to offer futures contracts in major currencies. During the 1970s, financial futures contracts (like interest rate swaps) were offered for the first time as a response to the financial upheaval during that decade (which saw unprecedented interest rate levels). In 1982, the CME offered futures contracts on the S&P 500 Index as a means of managing volatility and uncertainty in financial instruments. Today, the CME is referred to as the CME Group. Box 15.2 contains some information on the CME’s effort to institute financial reforms designed to further boost its profits. Economic Functions of the Futures Market Futures markets are said to have a social function because they cater to the needs of several people. Specifically, they provide information about the future price of commodities and offer protection to traders, whether these are investors (hedgers) or speculators. Let us briefly discuss each of these functions. Price Discovery Futures markets are highly competitive; thus people look to them to discover information about commodity prices based on today’s forces of demand and supply. By observing the established futures price of a commodity today, traders can estimate what its price would be at a certain point in the future. In the case of many physical commodities, such as agricultural products, cash market participants base spot and forward prices on the futures prices discovered in the competitive open auction market of a futures exchange. The forces of demand and supply continuously push the price into equilibrium; thus participants discover the intrinsic price of the commodity. Although the exact future price cannot be known with certainty now, the price quoted in the market today is a good estimate of that future price.

Futures Markets and Strategies s 499

Box 15.2 CME Group’s Financial Reform Efforts On April 15, 2010, the CME Group, the world’s leading and most diverse derivatives marketplace, announced the launch of trading and clearing services for four new European biofuel and eight new petroleum swap futures contracts. Trading would be available on the New York trading floor and clearing services through CME’s Clearport, a set of flexible clearing services open to over-the-counter market participants to substantially mitigate counterparty risk and provide neutral settlement prices across asset classes. On March 4, 2009, the CME Group signed a licensing agreement with Standard & Poor’s to clear swaps on the S&P GSCI Excess Return Index. The S&P GSCI is the most closely followed benchmark for investment performance in the commodity markets. Although reform creates ample opportunities, much depends on the shape of final legislation. CME’s executives remain cognizant of the possibility that new rules may drive some activity abroad or require the clearing of unsuitably illiquid swaps. At the same time CME faces threats to its core business from NYSE Liffe. ELX—which is backed by Goldman, J. P. Morgan, and others— has offered Treasury futures contracts since July and plans to launch a eurodollar futures contract in June. Perhaps most important, ELX and CME are fighting over whether traders may move positions between exchanges—a change that would pry open CME’s tight grip on the market. The opportunities for CME may be vast, but they are also there for its rivals. Sources: CME Group news releases and The Economist, April 29, 2010.

Risk Reduction Futures markets also serve to help investors, both individual and institutional, to spread (or shed) unwanted risk. For example, a trader can eliminate the risk of having to pay a higher price for a commodity (such as heating oil) in the future by presetting the price of a gallon of heating oil today for delivery later in the year. The opposite bet is made by the seller of heating oil who wants to avoid the risk of having to sell a gallon of heating oil at some time in the future for less than he would like to. Thus, the futures market helps each trader to reduce those risks by providing an efficient means of managing them, thus making society more efficient and competitive. Hedging A hedger is a trader who sells and buys futures contracts in an attempt to offset risky positions in the spot market. A key aspect of hedging with futures contracts is that the price (paid or received) for the underlying asset is secured. Hedgers take the exact opposite position from the one they already have. They also take these positions as a substitute for cash settlement transactions. Hedging simply reduces the risk of loss or the downside of a trade, but, at the same time, it limits the upside potential of higher gains. We will discuss some hedging strategies toward the end of this chapter. Speculating A speculator, unlike a hedger, is a trader who purposely enters the futures market in order to make a profit. Hence he willingly accepts the risk of price fluctuations. You might wonder how such behavior serves a social function, since speculation is similar to

500 s Derivative Markets and Instruments

gambling (as in a casino). The point is that futures markets do not encourage or do not exist to provide the opportunity to speculate but they nevertheless present opportunities for speculation. Moreover, a speculator in his quest for profit provides liquidity to the market—a very important characteristic of the futures market—and thus indirectly helps the market to function smoothly and efficiently (in normal situations). This means that enterprises will have an easy way of eliminating the risk of volatility and uncertainty in financial instruments and proceed with the effective application of their plans. More on speculation later on. Regulation of Futures Markets Futures markets are subject to regulations. In the United States, there are several regulatory authorities (including the Securities and Exchange Commission, the Federal Reserve Board, and several in-house agencies) for the futures markets, but the most relevant one

Box 15.3 Organization of the Commodity Futures and Trading Commission The Commodity Futures Trading Commission (CFTC) consists of the commissioners, the offices of the chairman, and the agency’s operating units. The five commissioners are appointed by the president of the United States to serve staggered 5-year terms. The offices of the chairman include the Office of External Affairs, which acts as the CFTC’s liaison with news media as well as educational and academic groups and other entities. It provides information about the CFTC and spearheads customer protection initiatives. The Office of International Affairs coordinates the CFTC’s global regulatory efforts and assists the commission in the formulation of international policy. The Office of the Inspector General performs audits of CFTC programs and operations and reviews legislation and regulations. The Office of the Secretariat coordinates preparation and dissemination of policy documents and responds to requests filed under the Freedom of Information Act. Finally, there is the Office of Equal Employment Opportunity. The CFTC monitors markets and market participants closely and, in addition to its headquarters in Washington, DC, it maintains offices in Chicago, Kansas City, and New York, where futures exchanges are located. The general counsel is the commission’s legal advisor, representing the commission in appellate litigation including bankruptcy proceedings involving futures industry professionals; the general counsel also advises the commission on the application and interpretation of the Commodity Exchange Act and other administrative statutes. The executive director formulates and implements the CFTC’s management and administrative functions and the agency’s budget. The Division of Clearing and Intermediary Oversight oversees the compliance activities of the futures industry’s self-regulatory organizations, which include the US commodity exchanges, National Futures Association, and derivatives clearing organizations. The Division of Market Oversight is responsible for fostering markets that accurately reflect the forces of supply and demand for the underlying commodities and are free of abusive trading activity; it also oversees trade execution facilities and performs market surveillance. The Division of Enforcement investigates and prosecutes alleged violations of the Commodity Exchange Act and commission regulations. Finally, the chief economist provides economic support and advice to the commission, conducts research on policy issues facing the agency, and provides education and training for commission staff. Source: www.CFTC.gov

Futures Markets and Strategies s 501

is the Commodity Futures Trading Commission (CFTC). The CFTC is an independent agency of the government that was created in 1974. Its mission is to protect traders and the public from fraudulent actions associated with the trading of financial futures and options. It also fosters a sound and competitive environment for the trading of such derivative products. The CFTC maintains offices in New York, Chicago, Kansas City, and Washington, DC, in an effort to closely monitor markets and participants. Box 15.3 details the agency’s responsibilities. In the United Kingdom, the relevant regulatory authority is the Financial Services Authority (FSA), which is also an independent agency charged with regulating the financial services industry. Some of its objectives include the promotion of efficiency of economic resources, the minimization of regulatory barriers in an effort to maintain competitiveness in the financial markets, and the facilitation of innovation within the context of regulation. In Japan, the Financial Services Agency is a government organization charged with the task of supervising the country’s financial sector and securing its stability and viability. In Australia, the Australian Securities and Investment Commission is the government regulatory body charged with enforcing and regulating the financial markets and its participants. What are some of the issues you should watch for when you are ready to trade in the futures market? Table 15.5 contains some useful information on brokers and where to

Table 15.5 Useful Information and Insights before Trading in the Futures Market Remember the Basics sConsider your financial goals, resources and how much you can afford to lose above and beyond your initial investment. sUnderstand commodity futures and option contracts and your obligations in entering into those contracts. sUnderstand your exposure to risk and other aspects of trading by thoroughly reviewing the risk disclosure documents your broker is required to give you. sAlways ask questions and gather information before you open an account. Check the Status of Your Broker sCheck Broker Registration Status and Background Information. sBefore you open an account, always check on the status of the company or individual you are considering. sResources available include: NFA’s Background Affiliation Status Information Center (BASIC) and CFTC disciplinary history. What Should I Watch Out For? sIf it sounds too good to be true, it probably is: promises of huge returns with limited risk are usually false. sDo your homework! Don’t be pressured to “act now.” sBeware when a salesperson tells you to borrow money to invest, and never agree to give money to someone you have never met. sWatch out for guarantees of profit or boasts about past performance. sReview the CFTC’s information on Fraud Awareness and Prevention.

502 s Derivative Markets and Instruments Understand Your Goals sYou should know how much you can potentially lose and see if you can afford it. sSet some limits on the duration of your investment and the amount of loss you are willing to incur. sAlways remember that losses can exceed your original deposit due to leverage effects. Understand Risk sAlways ask for risk disclosure documents and read them very carefully. sRemember that commodity prices are volatile because they react to a host of unpredictable factors. sDistinguish between options and futures strategies, and other strategies that reduce risk. Source: SEC.

obtain help. It also cautions you to have a good understanding of the basics, your goals, and the risks involved before you trade. This advice comes from the Securities and Exchange Commission. The box titled Lessons of Our Times discusses current issues regarding the concerns the global derivatives markets have as a result of the 2008 global financial crisis. Several new reforms are proposed, initiated by the G-20 and undertaken by the Financial Stability Board, for implementation in order to make the OTC global derivatives markets more transparent and consistent on a global scale. International Futures Exchanges In this section we present very briefly three of the world’s major futures exchanges: NYSE Euronext, the Japanese derivatives exchange, and the Australian derivatives exchange. NYSE Euronext, Inc., is a European-American for-profit corporation formed in 2007 from the merger of the NYSE Group, Inc., and Euronext. Euronext is a Paris-based European stock exchange with subsidiaries in Belgium, France, the Netherlands, Portugal, and the United Kingdom. The merger of these two exchange giants created the world’s first global financial products exchange. Regarding the trading of futures and options, the NYSE Liffe is the relevant exchange of the NYSE Euronext; it was launched in 2008 (we first encountered it in the previous chapter). Recall that Liffe stands for the London International Financial Futures and Options Exchange; it is based in London. In Europe, NYSE Liffe trades futures and options in the countries mentioned above, and the value of these derivatives exceeds €2 trillion per day. The NYSE Liffe is considered the world’s leading futures and options trading venue. It was originally launched with “time-tested products like gold and silver futures and options and since September 8, 2009, also offers new equity index futures.”1 In Japan, the relevant futures exchange is the Tokyo Financial Exchange (TFX), which was established in 1989 by the country’s Financial Trading Law. It was originally created as a membership organization, with capital provided by large multinational organizations. In 2004, the TFX was incorporated in an effort to strengthen corporate governance

Futures Markets and Strategies s 503

Box 15.4 The Financial Futures Association of Japan The Financial Futures Association of Japan (FFAJ) was established in August 1989 by the authority of the minister of finance pursuant to the 1988 Financial Futures Trading Law. The primary objectives of the FFAJ are to ensure the protection of investors and sound growth of the financial futures industry through the proper management of financial futures firms. FFAJ reinforced its function as a self-regulatory body to further enhance its services, with the consequence that the over-the-counter financial futures transactions with retail customers are counted as a financial futures business. In addition, registration of the members’ sales representatives and mediation services to settle disputes between members and investors have been added to the major services of FFAJ. As of August 2011, FFAJ had a total membership of 177 organizations. It is pursuing its mission as the only self-regulatory organization for financial instruments firms and registered financial institutions carrying out financial futures business by providing services in guidance on industry-wide self-regulation, settlement of claims and grievances, and mediation services to settle disputes, among other services. Source: FFAJ, online.

and provide greater market transparency. In 1998, the TFX and Euronext Liffe agreed to cooperate in order to develop a more efficient operation for the two markets. In 2007, the TFX was transformed into a more comprehensive exchange able to handle any type of financial product. The main tasks of the TFX are to secure a fair market that offers and handles securities and derivatives and to act as a clearinghouse for the derivatives traded at TFX’s financial instruments markets.2 Box 15.4 highlights the role of the Financial Futures Association of Japan. Finally, in Australia, the country’s main stock exchange, the Australian Securities Exchange (ASX), was established in 1861; it merged with the Sydney Futures Exchange in late 2006 to form the ASX Group. The ASX is a public company and trades its own shares on the exchange. It provides futures and options—on such products as commodities, interest rates, and currencies, among other financial products—on global actively trading markets. Today, the ASX Group is one of the world’s top 10 listed exchange groups as measured by market capitalization. The Commodity Futures Market The commodity futures market emerged as an organized forward markets (for corn and wheat) in the mid-1800s. The two key drivers for its evolution were the industrial revolution and agricultural modernization (which revolutionized traditional harvesting methods). The forward contracts evolved into more standardized forms, as found in today’s futures contracts traded on exchanges. The purpose of the commodity futures exchange is to provide an organized venue (marketplace) in which participants (consumers and producers) can buy and/or sell various commodities in an effort to hedge their commercial risks. The prices of commodities futures are determined solely by demand and supply conditions. Table 15.6 lists some important commodities along with their contract specifications for trade.

504 s Derivative Markets and Instruments Table 15.6 Some Commodity Futures and Their Characteristics Grains and Oilseeds

Symbol

Contract Size

Min Tick

Corn Wheat Soybeans Crude palm oil Soybean meal Soybean oil

OO OO/GLBX OO/GLBX GLBX OO/GLBX OO/GLBX

5,000 bushels 5,000 bushels 5,000 bushels 25 metric tons 100 short tons 60,000 lbs.

$0.0025 per b. $0.0025 per b. $0.0025 per b. $0.25 per m.t $0.10 per s.t. $0.0001 per lb.

OO/GLBX OO/GLBX OO/GLBX

40,000 lbs. 40,000 lbs. 50,000 lbs.

$0.00025 per lb. $0.00025 per lb. $0.00025 per lb.

OO/GLBX GLBX GLBX

200,000 lbs. 44,000 lbs. 20,000 times the USDA monthly weighted average price per lb.

$0.01 per cwt $0.00025 per lb. $0.00025 per lb.

Random length lumber

OO/GLBX

$0.10 per 1,000 bd. ft. $0.50 per m.t.

Wood pulp

GLBX

110,000 bd. ft. of random length 2x4s 20 metric tons times the FOEX indexes Ltd

OO/GBLX OO/GLBX OO/GLBX

100 troy ounces 25,000 lbs. 5,000 troy ounces

$0.10 per t.o. $0.0005 per lb. $0.005 per t.o.

GLBX GLBX GLBX

37,500 lbs. 10 metric tons 50,000 lbs.

$0.0005 per lb. $1.00 per t $0.0001 per lb

Livestock Live cattle Lean hogs Feeder cattle Dairy Class III milk Dry whey Cash-settled butter

Forestry

Metals Gold Copper Silver Softs (NYMEX) Coffee Cocoa Cotton

Source: CME Group. Notes: OO stands for open outcry; GLBX for CME Group

Commodity markets are inherently volatile owing to factors such as demand and supply, weather, speculation, and so on. The Dodd-Frank Act of July 2010 mandated that the CFTC establish aggregate position limits on all physical commodity derivatives positions across US futures exchanges to prevent excessive speculation. Moreover, the

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International Organization of Securities Commissions (IOSCO) Task Force on Commodity Futures Markets, authorized by the G-20 in 2008, was asked to develop further guidelines to improve the functioning of commodity futures markets in response to volatility in commodity (especially agricultural) prices.

FUTURES AND SPOT PRICES We mentioned above that as the delivery date (the maturity of the futures contract) approaches, the futures price converges to the spot price of the commodity. Thus at maturity, the spot price must be equal to the futures price. If this condition does not hold, arbitrage opportunities arise. Recall that arbitrage refers to a riskless strategy with no up-front investment costs. The profit for the trader will be equal to the difference between the spot and the futures price. After this arbitrage opportunity is exploited, the two prices will be the same. Thus spot and futures prices follow a very close course over time. The box titled Applying Economic Analysis explains, using an example, the economics behind such an opportunity. Spot Futures Parity The convergence between the two prices is known as the spot futures parity condition, which states that, theoretically, the spot and futures prices must be equal, otherwise arbitrage opportunities would arise. It is similar to the economic law of one price. The law of one price states that in an efficient market, identical goods must have the same price. The parity relationship implies that in addition to the equality between the two prices, the cost of money dividends and other costs must all be accounted for. Note that in an inefficient and less liquid market—where transaction costs, regulations, and restrictions exist—deviations from the parity condition may not always generate profitable arbitrage. The parity condition can be expressed algebraically as follows: F0 = S0 (1 + rf )T

(1)

where F0 is the futures (or forward) price, S0 is the spot price, rf the risk-free rate, and T is the time period. This parity is especially useful for trading in currency markets, commodities, and bond markets. Here is an example. Assume that corn sells for $20 a bushel in the market and the current risk-free rate is 2% (also assume one period). What does the parity imply about the futures price, F0? The futures price is equal to $20.40, or $20 (1 + 0.02)1. The risk-free rate may also be viewed as the cost of carry, a factor that includes storage costs, dividends, and foregone interest (the opportunity cost). In general the cost of carry or the cost of holding a position can be expressed as Cost of carry = cost of borrowing + storage costs − dividends − net opportunity cost Thus Eq. 1 can also be interpreted as buying futures (or forward), which is equivalent to buying now and storing or carrying the underlying asset. For most investments, the cost of carry includes the risk-free return that can be realized by investing in a safe asset minus the return from holding an equally risky alternative instrument. It might include storage costs if the asset involves a physical commodity like wheat or oil.

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Let us illustrate the above parity condition with an example. Assume that the spot price of an asset is $50 and the annual risk-free rate is 3%. Assume that the asset is not a dividend-paying stock and does not incur any storage costs. What is the asset’s forward price for delivery a year from now, F 10? What would the price be 6 months from now? Finally, if the asset paid a dividend yield of 1%, what would its futures price be a year from now? The cost of carry in the first two cases is 3%. Thus, F 10 = $50(1 + 0.03) = $51.50 F 0.50 = $50(1 + 0.03)0.5 = $50.74

price a year from now without dividends price 6 months from now

The cost of carry in the third case is 0.03 − 0.01 = 0.02. Thus, F 10 = $50(1 + 0.02) = $51.00

price a year from now with dividends

Now let us further explain the implications when the spot and futures prices are not equal. Let us generalize Eq. 1 above as follows: F0 = S0 e rf T

(2)

where rf is the risk-free rate and e is the number 2.71828. If F0 > S0 e rf T, arbitrageurs would buy the asset and short forward contracts on it. By contrast, if F0 < S0 e rf T, they can short the asset and enter a long forward contract on it. Thus, using the above numbers, we obtain F0 = $50 e1 × 0.03 = $51.50 which corresponds to the above theoretically correct value for the parity condition to hold. A concept related to the (in)equality between the spot and futures prices is the convenience yield. Sometimes traders feel that owning the physical commodity outright gives them better yields (benefits) that owning a futures contract. Economic forces of demand and supply would normally dictate the choice. For example, if a trader decides to hold high levels of inventory of an asset today, he might think that in future the asset will be in (relative) scarcity. Thus he expects the futures price of the asset to be higher in the future than it is currently. The opposite would occur if the current levels of inventory held by the trader were low and could not be replenished to meet future demand. Therefore the term convenience yield refers to the net benefit from holding the physical asset and not the derivative instrument. In other words, the convenience yield represents the market’s expectations about the availability of the asset in the future. For instance, if the asset’s inventory is in abundance today, the convenience yield will be low, and vice versa. Thus restating Eq. 2 to include the convenience yield, c, gives us F0 = S0 e (rf − c)T

(3)

If, further, the asset incurs significant percentage storage costs, u, Eq. 3 becomes F0 = S0 e (rf + u − c)T

(4)

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John Maynard Keynes argued that as the futures contract approaches maturity (the delivery date), it will tend to trade at a higher price relative to the one prevailing away from expiration. In other words, he believed that if hedgers hold short positions, the futures price of the asset would be below the (expected) spot price. This phenomenon is known as (normal) backwardation. In terms of Eq. 4, backwardation occurs when the (net) convenience yield, nc, or the difference between the convenience yield and the riskfree rate (rf ) exceeds the risk-free rate. By contrast, when the net convenience yield is less than the risk-free rate, the phenomenon is known as contango: If nc > rf, then S0 > F0 If nc < rf, then S0 < F0

normal backwardation contango

Here is an actual example for the crude oil market, which was in contango early in 2009. Oil prices were very low (approximately $36 a barrel) because the US economy was still in a recession. Traders, oil companies, and investors stored millions of barrels of crude oil in tankers (which they either owned or leased) and refined them while in storage. The goal was to resell the oil (and its products) at higher prices when the economy recovered. What is the economics behind the relationship between spot and futures (or forward) prices? Let us start with some introductory economic concepts. We saw above that futures or forward contracts can be arranged for commodities like wheat or oil and other assets like stocks and gold. Is there any difference between the various assets used in the futures markets? We distinguish between two general types of assets (as you also recall from your introductory macroeconomic course): consumption and investment assets. A consumption asset is one that is used for consumption and generates utility or satisfaction. Examples of such assets are oil and wheat. An investment asset, by contrast, is one that is held for investment purposes. Examples of investment assets are stocks and gold. An investment asset can also be used for investment purposes, as in the production process (say as inventory). Also, a trader must understand that interest rates are essential inputs in the valuation of futures or forward contracts. Interest rates change frequently (even daily); as a result, the value of such contracts changes accordingly (or may not even be the same). The trader must perform a good interest rate forecast in order to avoid potential losses on the contracts entered. For example, assume that the contract’s underlying asset is positively correlated with market interest rates. If interest rates are expected to increase, the long investor would make a gain (and also because the proceeds can be reinvested at a higher rate). Thus a good (and accurate) forecast of the future interest rates is a crucial part of the investor’s position on the contract. Basis Risk The basis is the difference (spread) between the futures and spot prices. Recall that at maturity, the two prices must be equal (i.e., per the convergence principle). Basis = futures price of contract – spot price of asset However, these two prices may differ substantially before maturity. Hence, if the contract is to be liquidated before maturity, the investor (hedger) faces basis risk because the futures price will be different from the spot price. Let us consider an example of how an investor profits or gains from a change in the basis. Assume that an investor holds 100 troy ounces of gold (the contract size) and is

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short one gold futures contract. The price of gold, as of the end of October 2011, was $1,700 an ounce and the futures price for December 2011 delivery was $1,712 an ounce. In this case, the basis is $12 (or $1,712 – $1,700). Assume that tomorrow gold’s spot price rises to $1,710 while the futures price increase to $1,724. In this case, the basis changes to $14. What would be the investor’s gains or losses? Remember, the investor is long on the asset and short on the futures contract. Loss from long position (per ounce) Gain from short on contract (per ounce)

= $1,710 – $1,700 = $10 = $1,724 – $1,712 = $12

So he loses $10 from holding the asset but gains $12 from being short on the gold contract. His net position is a gain of $2 per ounce. The gain occurred because the change in the futures price was greater than the change in the spot price. Such a strategy for an investor to be long on the asset and short on the contract is known as a short hedge (as we will see in the last section). In general, basis risk may also occur for reasons (factors) that are beyond the control of the hedger, and it can change after the futures contract is set up. Here are some other examples of basis risk. A portfolio of NYSE-listed securities (shares) is hedged by the purchase of put options on the NYSE but underperforms the index. A farmer, who has his farm in a remote location, uses futures to hedge the price of corn he expects to produce. However, rising transportation costs cause the price of corn he receives to fall even though the price of corn remains unchanged if delivered to the location specified in the contract.

FINANCIAL FUTURES CONTRACTS Futures contracts also exist on financial instruments such as equity or bond indexes, interest rates, and currencies. Such contracts are called financial futures contracts. All financial futures contracts expire quarterly (namely, in March, June, September, and December). Financial futures contracts are more flexible than traditional futures contracts because they offer investors the opportunity to cash settle for the value of the underlying asset index. Further, they help investors tailor their risk/return profile as a means to reduce their risk exposure. Let us discuss some of the most important financial future contracts. Some Financial Futures Contracts Stock Index Futures A stock index futures contract is one written on a stock index such as the S&P 500 equity index. The S&P 500 futures contract was first introduced in 1982 by the CME. Today, it is one of the most actively traded equity instrument in the US futures market. How can one trade this contract? The value of an S&P 500 futures contract is found by multiplying the cost of a futures contract, $500, by the futures price of the index, say, 1,200. Thus, it would be $600,000. Given that small investors could not invest in this contract because of its large value, the CME reduced the size of the contract to $250 for the S&P 500 and in 1998 introduced the E-mini S&P 500 futures contract, valued at $50. The E-mini quickly became very popular not only among smaller investors but also among hedge funds.

Futures Markets and Strategies s 509

There are several other stock index futures contracts: the Dow Jones Industrials, NASDAQ 100, Russell 2000, and several foreign indexes such as (France’s) CAC 40, (Japan’s) NIKKEI, and (Germany’s) DAX 30. Each index has a different contract size denominated in the respective country’s currency. In general, stock index futures can be used for investment and hedging. For example, hedging with such instruments could entail insuring against a portfolio of shares, while investing could involve exposure to the equity sector without actually owning the shares directly. The latter means creating a synthetic position in stocks. Such a strategy is preferred by investors also because of lower transaction costs and the fact that it is much easier to get exposure to the equity sector. Interest Rate Futures An interest rate futures contract is an obligation to buy or sell positions in Treasury bills, bonds, notes, or other interest rates (including foreign ones, such as eurodollars). The purpose of such contracts is to hedge against interest rate risk—that is, adverse price movements. The concern is well founded given the higher interest rate volatility in recent years in the global marketplace. For example, if interest rates rise, the market value of the contract at maturity is less than the original futures price, and thus the contract deliverer realizes a profit. Stated differently, being short in the interest rate futures contract results in a gain when interest rates rise and a loss when interest rates fall. The CME trades most of interest rate futures contracts. The Chicago Board of Trade handles longer-maturity futures contracts such as those on Treasury bonds. Table 15.7 contains some specifics on the 13-week Treasury bill futures.

Table 15.7 13-Week Treasury Bill Futures Underlying unit Price quote Tick size Contract months Last trading day

Final settlement

Trading hours (All times listed are central time) Ticker symbol Exchange rule Source: CME Group.

One 3-month (13-week) US Treasury bill having a face value at maturity of $100,000 100 minus the Treasury bill discount rate for the delivery method (e.g., a 5.25% rate equals 94.75) One-half of one basis point (0.005), or $12.50 per contract (minimum fluctuation) Three serial expirations plus four quarterly expirations in the March, June, September, and December quarterly cycle The business day of the 91-day US Treasury bill auction in the week of the third Wednesday of the delivery month. Trading in expiring contracts closes at 12:00 P.M. on the last trading day Expiring contracts are cash settled against the highest discount rate accepted in the U.S. Treasury Department’s 91-day U.S. Treasury bill auction in the week of the third Wednesday of the contract month OPEN OUTCRY MON–FRI: 7:20 A.M. –2:00 P.M. CME GLOBEX SUN–FRI: 5:00 P.M. – 4:00 P.M. OPEN OUTCRY TB CME GLOBEX GTB These contracts are listed with, and subject to, the rules and regulations of CME

510 s Derivative Markets and Instruments

Box 15.4 Interest Rate Futures in the NYSE NYSE Liffe announced the launch dates for US Treasury and eurodollar futures products to coincide with the launch of New York Portfolio Clearing, the innovative new clearing joint venture with the Depository Trust & Clearing Corporation. NYSE Liffe will begin trading eurodollar futures on March 21, 2011, and will launch 2-, 5-, and 10-year US Treasury futures along with US Bond and Ultra Bond futures products on March 28, 2011, subject to regulatory filings. These products will be cleared through NYPC, which has received all the required approvals from the Commodity Futures Trading Commission and the Securities and Exchange Commission. Interest rate futures traded on NYSE Liffe will benefit from the powerful capital efficiencies of NYPC’s “one-pot” margining, which, for the first time ever, will assess margin across fixedincome securities, repos, and interest rate futures to more accurately capture the actual risk of a clearing member’s portfolio. Moreover, all US Treasury futures traded on NYSE Liffe will benefit from an innovative, streamlined delivery process allowing for the seamless netting of futures and cash securities. These innovations provide unique benefits to global futures market participants by reducing the cost, complexity, and risk inherent in the traditional trading and clearing model. The long-awaited move depends on securing regulatory approval for a new clearing venture that would allow traders to set futures and cash positions. Dealers have risen up at the pricing power they think CME’s dominance of the market affords, but Chicago’s exchanges have successfully seen off competitors, including a twin assault from two European exchanges. Sources: D. Cameron and J. Bunge, CME Group, and WSJ.com, April 6, 2010.

In the last section of the chapter we discuss some specific interest-rate futures strategies, such as short and long hedges, index arbitrage, and speculation. Box 15.4 presents the launching of interest rate futures in the NYSE. Currency Futures A currency (or foreign exchange) futures contract is a contract that specifies a set amount of a particular currency to be exchanged at a specific time. For example, the buyer of such a contract locks in the exchange rate to be paid for a foreign currency on the settlement date. If the buyer were a Greek investor, he would buy a currency futures contract to lock in the number of euros required to purchase a specific amount of some foreign currency. Traders use this market either to hedge their foreign currency positions if they are investors or to capitalize on expectations of exchange rate movements if they are speculators. Currency futures (or foreign exchange futures) are traded on the CME’s GLOBEX system (its electronic system, which matches buy and sell orders for each contract). Typically currency futures are quoted in dollars per unit of foreign currency. Currency futures were first created in 1972 at the CME as a response to the collapse of the fixed exchange-rate system. The International Monetary Market (IMM) was created around that time also to facilitate the traders’ access to the interbank exchange markets. On August 9, 2011, the CME Foreign Exchange (FX) reached a record high in single-day volume with 311,684 Australian dollar futures and options contracts. With

Futures Markets and Strategies s 511

over $100 billion in daily FX liquidity, CME FX is the largest regulated FX marketplace in the world. Currency futures contracts have different characteristics. For example, contracts specify where and when a contract is to be traded, the amount of price change (because such contracts are highly leveraged, a small change in price may result in large profits or losses), the number of units traded, the date of the contract’s expiration, and the rules that govern the transaction (such as margin requirements). You can buy or sell your contract at any time before expiration but you can close it out only on the expiration date. Here is an example of how to trade such a contract and how to determine its dollar value. One futures contract is for 12,500 euros (known as an E-micro EUR/USD futures contract, as quoted at the CME). At the price of $1.2892, the value of the contract would be $16,115. If the price of the euro currency future changes to $1.2895 (or by 3 ticks, where one tick of movement is $0.001), the value of the contract would increase to $16,118.75—that is, it would generate a profit of $3.75 for the contract holder. If the value of the contract declined over time, the buyer would be asked to post additional margin (the so-called maintenance margin). What is the economics behind trading foreign exchange futures? Traders closely watch various economic indicators, such as the gross domestic product (GDP), balance of trade among countries, and fiscal and monetary policies that affect interest rates and the like. Money in- and outflows along with a nation’s trade imbalance reflect a currency’s demand and supply and thus its price against another currency. Therefore futures traders observe if a nation has deficits or surpluses; that is, they look to see if all the above factors affect the value of the contract following changes (fluctuations) in the value of the currencies—changes that could result in a profit or a loss in their positions. Table 15.8 lists some of the major tradable financial futures instruments, but the list is not exhaustive because new financial products are constantly being created and some of the existing ones are illiquid and difficult to trade. ICE stands for Intercontinental Exchange; it operates leading exchanges, trading platforms, and clearinghouses for agricultural, currency, energy, and equity index markets. ICE operates three futures exchanges: ICE Futures Europe, which hosts trading in half of the world’s crude and refined oil

Table 15.8 Some Tradable Financial Futures Products Stock Index Futures

Exchange

DJIA DJIA, mini NASDAQ 100 E-mini NASDAQ 100 Nikkei 225 Russell 1000 Index mini S&P 500 S&P 500 E-mini

CBOT/CME Group CBOT/CME Group CME Group CME Group CME Group ICE CME Group CME Group

Interest Rate Futures Eurodollar Euroyen 13-week T-bills

CME Group CME Group CME Group

512 s Derivative Markets and Instruments

Stock Index Futures

Exchange

30-day federal funds US 30-, 10-, 5-, and 2-year T-bond and T-note

CBOT/CME Group CBOT/CME Group

Currency Futures Australian Dollar Brazilian Real British Pound Canadian Dollar Euro

CME Group CME Group CME Group CME Group CME Group

Other Products Volatility Index (VIX) DJIA Volatility Index Futures NASDAQ 100 Volatility Index Futures

CBOE Futures Exchange CBOE Futures Exchange CBOE Futures Exchange

products; ICE Futures US; and ICE Futures Canada, which list agricultural, currency, and index futures and options markets. ICE also provides trade execution and processing and clearing services for OTC energy and credit derivatives markets. The two such clearinghouses are ICE Clear Europe, which is based in London, and ICE Clear US, for the US market. Some Useful Information on Financial Futures S&P Futures versus Fair Value We hear daily in the news that the S&P futures are positive or the S&P futures are negative, and always before the opening of the exchanges. What do such statements mean? They simply foretell how the markets will open for the trading day, higher or lower, respectively. Such statements are accompanied by a number of points, say 10, which, in the case of a positive prediction, means that the equity market (such as the S&P 500 in this instance) is expected to open 10 points higher. It does not mean that the market will continue trading higher during the day! It may even close negative. What such statements intend to do, in general, is give an indication of how the market will (or is expected to) open and nothing else after that. Here is an actual example. Before the opening of the stock market on Thursday, December 1, 2011, in the United States, stock index futures pointed to a weaker open on Wall Street. Specifically, futures for the S&P 500 was forecast to open 0.5% lower, futures for the DJIA to open 0.4% lower, and futures for the NASDAQ 100 to open 0.2% lower. Some of the reasons were that the US Labor Department was expected to release claims for jobless benefits, the Institute of Supply Management was expected to release its November manufacturing index, the US Commerce Department was due to release October’s construction spending, the Fed was scheduled to release weekly money stock and debt measures affecting the reserves of banks, European stocks were down during that day (recall that the US markets open later because of the 5- or 6-hour difference between Europe and the United States), and a host of other factors, both in the United States (such as projected company news releases) and around the world (such as European and

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Asian countries’ financial actions). Naturally economists and traders were pessimistic on the above news and predicted a lower opening in the US equity market on Thursday. Further, investors often compare the futures number with the fair value of the stock index (recall that we first explained the fair value concept in Box 9.1 of Chapter 9). This arises because the theoretical cost of buying all 500 stocks in the S&P 500 Index differs from the cost of purchasing the S&P futures contract. The latter has no cost beyond its face value. Obviously one reason for the difference is the cost of borrowing, or opportunity cost, to purchase the index. Another reason is the fact that holders of futures contracts do not receive dividends or earnings, as the outright index holders do. Interested readers can visit the Yahoo! Finance or CNNMoney websites, for example, to follow the futures trends before the opening of each trading day. How and why do investors compute the fair value? If the fair value is higher than the S&P futures before the market’s opening, then the market will open lower. The opposite is true for a positive difference between the two values. Continuing with our actual example above, on Thursday, November 1, 2011, the S&P 500 futures level was 1,244.70, while the index’s fair value was 1,246.05 (for a difference of −1.35).3 Obviously, these values kept changing as the opening time approached, but they were unlikely to reverse direction. Thus calculating the fair value (price) relationship between the two magnitudes is an everyday task. This is usually done at the end of the trading day up to the preopening of the next trading day. Below is the formula that traders use to compute the fair value-futures price relationship: F = S [1+ r (t/360] – d

(5)

where F is the futures price, S is the spot price, r is the short-term interest rate, d is the dividend rate, and t the number of days from now until the futures contract date. Here is an example. Assume that the September S&P 500 futures price was 1,165 points, while the S&P 500 cash (spot) index was 1,160 points. The interest rate is 3% and the dividends to expiration of futures are 2.5 points (converted to S&P 500 points).4 The remaining days to expiration of the futures contract is 75. The fair value of futures is then: F = 1,160 [1 + 0.03 (75/360)] –2.5 = 1,164.75 The difference between the futures price and the fair value (or the amount of futures over- or under -pricing) is 1,164.75 – 1,165 = –25 points. Leverage Another important element in futures markets is leverage. Leverage refers to owing a large cash commodity account with relatively small capital (cash) amount. This means that the value of the contracts is higher than the initial amount you put into it (i.e., margin is small relative to full position). As a result, even small changes in prices would multiply gains or losses more than if the investor had held the assets outright (as we mentioned earlier). Let us show this with a simple example. Assume that you buy an index futures contract with a deposit (margin) of $5,000 while the index value is 1,200. The value of your contract is $300,000 (or $250 per contract × 1,200 index value). Note that every time the index price rises by 1 point, you gain $250. Assume that the index rises by 5% or 60 points. Your gross gain in this case

514 s Derivative Markets and Instruments

is $15,000 or, in terms of return, 200%; that is, ($15,000 – $5,000)/$5,000. By contrast, if the index declined by 5% or 60 points, your gross dollar loss would be $15,000, but your return would be a negative 400%; that is, (–$15,000 – $5,000)/ $5,000. So you see that although leverage magnifies gains, it more than magnifies losses! That is why many professionals call leverage a “double-edged sword.” Recall that we first encountered this notion in Chapter 2, when we discussed margin purchases.

FUTURES TRADING STRATEGIES In this section we briefly present some basic futures trading strategies relevant to hedgers, speculators, and arbitrageurs. We begin with hedging. Hedging We know that hedging refers to taking opposite positions at the same time (that is, both long and short) in order to reduce risk. Hedging is like purchasing insurance. A perfect hedge is one that completely eliminates risk. Such hedges are rare, however. Let us explain the two types of hedges, a short and a long hedge, with a simple example. Assume no daily settlements. Suppose that the investor knows that he will gain $1,000 for every 1-cent increase in the price of a commodity and will lose $1,000 for every 1-cent decrease in the price of the commodity. The investor can hedge the loss by entering a futures contract with the position opposite to the one he is exposed to. That is, the position should generate a loss for every 1-cent increase in the price of the commodity and a gain for every 1-cent decrease in the price of that commodity (during the same assumed period). Thus if the commodity’s price declines, the gain in the futures position would offset the loss on the investor’s portfolio. The opposite is true for a price decline. Such a hedge is known as a short hedge. So a short hedge greatly reduces the risk in the long position. A short hedge involves a (short) sell of the futures. By contrast, if the investor had taken a long position in the futures (contract), that is, if he had bought the contract, he would be taking a position known as a long hedge. This means that the investor does not hold any financial instrument but hedges with futures. An assumption is that the investor expects to be part of the cash market in the future and wants right now to lock in current prices for future payment. In the above crude examples, the hedgers were able to accurately time the initiation and ending of the process (of buying and selling the commodity). Recall from an earlier discussion that the price of the commodity (to be hedged) may not be exactly the same as the commodity underlying the futures contract or that the two prices may fluctuate during the period before delivery. We called this basis risk. The basis must be zero at the delivery (maturity) date of the contract. The implication of the basis risk is that investors cannot completely eliminate that risk despite hedging. What is the verdict on hedging? Some contend that a company need not hedge because shareholders naturally hedge themselves by holding well-diversified portfolios. On the other hand, some companies feel that they should hedge because they have no knowledge of forecasting economic magnitudes that could affect their production or inventory levels. By contrast, some companies feel that hedging is not necessary because intense competitive pressures create fair asset prices. Whatever the arguments are, to hedge or not to hedge will remain an empirical issue.

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Speculating A speculator, unlike a hedger, is one who tries to take a position in the market in an effort to earn a profit. In other words, a speculator is a person who takes both short and long positions in the futures market without intending to make/take delivery but betting on the direction of the price in the future. Below is an example using spreads. A spread, in this context, involves the simultaneous buying and selling of a futures contract. The objective is to profit from an expected change in the prices of the two contracts. Assume that the July futures price of corn is $3.78 per bushel and the September price is $3.84 per bushel. The difference (spread) is 6 cents. You expect the price difference to widen in the future (over the next few months). If you think you will be vindicated, you can sell the July contract and buy the September contract (sell the “cheapest” and buy the “dearest”). Now assume that you are indeed right (thanks to your superior forecasting skills and economic analysis) and you see that the July futures contract price increased to $3.81 while that of the September contract rose to $3.89. The difference in this case is 8 cents per bushel. You can now liquidate your position (both contracts at the same time) and translate your gain into a dollar amount: $100 (or 5,000 bushels × $0.02). Table 15.9 summarizes the activities of the trade. What is the function of speculators in the futures market? Many comments, both bad and good, have been made about them. One view is that speculators perform a social function by absorbing the excesses (of demand and/or of supply) of the market created by hedging activities. They do so by assuming the risk that hedgers want to shed. So, their role is considered favorable and essential for the smooth operation of the futures market (by providing liquidity to the market). By contrast, others believe that such activities destabilize the market and make it more volatile than otherwise. Whatever the view, the verdict on speculation is still unresolved. Program Trading and Index Arbitrage Program trading refers to the electronic trading of a large portfolio of securities (traded at the NYSE) and their corresponding futures and options. The NYSE defines such trading of stocks (typically 15 or more) as one involving a value in excess of $1 million. Such a means of trading securities is based on purely noneconomic reasons or on the relative price differences. No economic fundamentals like company earnings and growth or interest rates play a part in such trading activities. Box 15.5 highlights some dangers of program trading. The rapid growth of program trading is due to three factors: first and foremost, dramatic advances in technology, which have allowed the speedier execution of trades via Table 15.9 An Example of Speculation Contract July

September Gain / (Loss) Net Gain (Loss)

Activities Sell July Corn $3.78 bushel Buy July Corn $3.81 bushel ($0.03) bushel

Spread Buy September Corn $3.84 bushel Sell September Corn $3.89 bushel $0.05 bushel

$0.02 bushel

6 cents 8 cents 2 cents

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Box 15.5 Program Trading Issues Program trading or high-frequency trading has again rekindled the rant of investors in the aftermath of the “mini” or “flash” market crash in May 6, 2010. That day the DJIA was down by 1,000 points but quickly recovered. The SEC/CFTC report on that day concluded that the market was so fragmented and fragile that when a single large institutional investor (such as a mutual fund) placed a sell order (of the E-mini S&P 500 contract), the effect was accentuated by high-frequency trading, resulting in sharp price declines. Recall that program trading was blamed for the October 19, 1987, global stock market crash (known as black Monday). The DJIA plunged by 508 points, or by more than 22%, and the S&P 500 fell by more than 20%. Studies found three leading causes for the crash. One was program trading, as massive sell orders from large institutional investment firms were rapidly and automatically executed by computers. Such orders were based on external market trends and strategies, including portfolio insurance and arbitrage. Another possible cause was the lack of interplay (synchronicity) between the stock and derivatives markets (per the Brady Commission, which was appointed to investigate the cause or causes of the crash). Finally, the lack of liquidity in the market, which arose because sellers outstripped buyers, may have caused a significant drop in the prices of several stocks. Despite these three alternative explanations for the market crash of October 1987, most of the blame was placed on program trading.

computers at the lowest possible cost; second, the recognition that diversifying across stocks reduces risk: and third, the increasing sophistication of institutional investors in their trading activities and thus their need to be part of equity investments much more than before. Program trading gives rise to several other investment (or trading) activities, such as portfolio insurance (which we discussed in the previous chapter) and index arbitrage. We discuss the latter next. Index arbitrage refers to the investment strategy that seeks to exploit mispricing between the theoretical and the actual values of indexes such as the S&P 500. The simultaneous buying of the stock index and selling of the underlying stocks (cash product) in that index in an attempt to capture the temporary difference in the two index prices (the basis) is an example of index arbitrage. For example, if the S&P 500 futures price is higher than the index’s price, investors can sell short the futures contract and buy (go long on) the stocks in the index. In other words, index arbitrageurs sell the expensive product— the futures—and buy the cheap product—the stocks. The net effect of such a strategy is to equalize the futures price and the theoretical price (fair value) of the product. Here is an example of index arbitrage. You observe today that the value of an equity index is $100 and the cost of borrowing 3%. Assuming no-arbitrage conditions, the (noarbitrage) futures price of the index should be $103 (or $100 × 1.03). You expect the value of the index to advance by 10% next year, to $113.30. Suppose that today you also observe the value of the index’s futures price to be $110. You consider this to be a perfect opportunity to capitalize on this discrepancy and capture an arbitrage (or riskless) profit by going short in the futures market today and long in the spot market. Thus you borrow the $100 at 3% interest, buy the index, and simultaneously go short in the futures market, locking in the sale of the index for $110 a year from now. A year later, you “deliver” the index for $110, take the proceeds to repay the loan of $103, and pocket the difference

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of $7 (or $110 – $103). This amount is your future value of the arbitrage profit. Alternatively, converting the values into present values, the present value of the (future) profit is $6.796 (or $7/1.03), which is the same amount as the difference between the present value of the futures index $106.796 (or $110/1.03) and the spot price of the index, $100. In general, if the market is expected to go up, which means that the futures price is higher than the index value, index arbitrageurs would buy the stocks in the spot market (in the short term) and sell the futures contract (price). The net effect would be to balance out the two prices (and markets). If investors are there for the long run, they might do the opposite: that is, if the market is expected to advance, buy the futures contract and sell the spot prices. Using Currency Futures Traders can use currency futures contracts for both hedging and speculation. Hedging means limiting exposure to foreign exchange risk, as we saw earlier. The hedger locks in the exchange rate to be applied in the future when he receives a certain amount of foreign currency and wishes to convert it in his home currency. For example, a US investor expects to receive €1 million in 6 months. The current exchange rate implied for 6 months is $1.2643/€. He can lock in this rate for use in the future, and thus he is guaranteed that exchange rate when he converts the €1 million into dollars. Speculation in currency futures means attempting to profit from expected changes (rises or falls) in the exchange rate. For instance, if a speculator expects the euro to appreciate in the future, he will buy a futures contract that locks in the price he will pay for euros in the future. At settlement, he can buy the foreign currency (at the specified exchange rate) and then sell these euros in the spot market. In this way he would make a profit. Arbitrage Trading Arbitrageurs will buy and at the same time sell similar securities in order to exploit temporary mismatches in price. In its simplest form, the trader buys the asset when it trades at a lower price and immediately sells it in the market in which it trades at a slightly higher price. Thus a riskless profit (after commissions) is made. However, in fairly efficient markets, price differentials are so small that arbitrage strategies do not guarantee profits because of the very low profit margins. Sometimes such trading is impractical or not feasible because of the large asset quantities one must trade to obtain some profit. Another often-quoted form of arbitrage (or speculation, if you will) is risk arbitrage, where traders seek to trade under- or overvalued securities when they clearly expect things to turn around in the near future. Such arbitrage activities often take place before a merger between two companies, permitting the arbitrageur to profit from the merger—owing to an increase in the stock price of the acquired firm, of which he owns shares—if it goes through (we saw this strategy as pairs trading in Chapter 5). There are other forms of arbitrage, such as statistical arbitrage (mispricing of assets based on the expected value of these assets) and convertible arbitrage (involving the purchase of convertible securities and at the same time shorting the issuer’s stock), which are mostly used by hedge funds, but their further discussion is beyond the scope of this textbook.

CHAPTER SUMMARY In this chapter we discussed the futures markets and offered some strategies for arbitrageurs, hedgers, and speculators. We discussed the futures contract and its basic elements and illustrated how one profits or loses from being long (buyer) or short (seller) to the

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market. Next, we explained the role of the clearinghouse in the futures market and some of the risks involved. We also showed how a trader settles the position and how he reverses a trade should he want to cash out (close) his position before maturity. The next section discussed the economic functions of the futures market by elaborating briefly on each one of them. We also presented the regulatory statutes in the futures market, looked at some international foreign futures exchanges, and concluded with a look at the commodity futures markets. Then we dealt with the mathematical relationships between spot and futures prices, highlighted the implications of deviations between spot and futures prices, and concluded with some other issues, like basis risk. The previous discussion contained some examples of financial futures contracts, as opposed to commodity futures contracts, like stock index futures, interest-rate futures, and currency futures. We presented each of them with simple examples and underscored the implications for the trader. We then presented some issues surrounding financial futures trading, such as what a fair value is and how it can be calculated, and the impact of leverage. Finally, we examined some basic futures trading strategies from the perspectives of hedgers, arbitrageurs, and speculators along with some insights on index arbitrage and program trading.

APPLYING ECONOMIC ANALYSIS Consider the arbitrage opportunity that arises when the spot price and the futures price are not equal during the delivery period. Let us use some numbers to understand the economic rationale behind such actions. Assume that an investor observes the current (spot) price of an asset to be $50. Call that price S0. The forward price for that same asset is $52. Call that price FT. Assume further that you have an opportunity cost (for your funds) of 3%. That is, you can borrow or lend at 5%. Do you spot an arbitrage opportunity? If so, how would you exploit it (presumably at a profit)? Here are the three simple steps: sBorrow $50 to buy the asset. sBuy the asset for $50. sSell a futures contract for $52. In this transaction, you are incurring a cost (for your funds) of $1.50 (or $50 × 0.03) and a benefit of $2 (or 52 – $50). Thus you net a profit of $0.50 per unit or contract (or $52 – $51.5). In the opposite situation, where the forward price is less than the spot price, say $48, you should have sold the stock (if you owned it, or sell it short) for $50 and enter a forward contract to buy it back for $48 within the determined period. Thus you would earn interest on the proceeds from this investment equal to $1.50; that is, you would be $3.50 better off [or $1.50 + ($50 – $48)] than if you had held the asset in your portfolio for the same time period. One final illustration is in order. Knowing the spot price of the asset and your opportunity cost, can you predict the asset’s forward price, say, in the next year? In this case, it would be $51.50 or the spot price times the opportunity cost of funds (plus the original investment). So now you know that with any deviations from this parity, arbitrage opportunities would arise to equalize the two prices.

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INTERNATIONAL FOCUS THE CME GROUP’S PUSH INTO GLOBAL MARKETS The Chicago Mercantile Exchange (CME) Group announced (in April 2010) an agreement with Alberta’s Net Energy Canadian Daily Index to trade swaps for heavy crude oil. This partnership is another one on top of the group’s recent agreements with Japan’s Nikkei 225 futures and India’s National Stock Exchange. In 2011, the Asia-Pacific region became a focus for the CME after May’s launch of European clearing operations for energy derivatives. The CME Group’s international business accounts for 15% of its volume of trade. The CME Group is stepping up its moves into international foreign exchange markets with a revamp of its futures contracts based on the Chinese currency, the renminbi. The contracts are an indication of the CME’s deepening moves into Asia. While mergers proposed by rival exchanges such as the London Stock Exchange and Singapore Exchange (SGX) run into protectionist sentiment and regulatory hurdles, the CME has focused on expanding its business naturally. Renminbi futures contracts will be quoted in interbank terms to reflect the number of renminbi per dollar and will launch in August 22, 2011. The contracts will be cleared through the CME’s operations in Chicago, but a spokesman of the exchange said it had yet to make a decision on whether to build a separate clearinghouse in Asia (either in Singapore or Hong Kong). However, the CME is weighing the cost of opening another clearinghouse against a series of initiatives that either do not promise a return for several years or may not deliver a return at all. It also faces competition for clearing from the SGX, which will start to clear the nondeliverable forwards of emerging Asian currencies. Sources: CME Group, FT.com, and Reuters.

LESSONS OF OUR TIMES OTC DERIVATIVES MARKET REFORM In September 2009, the G-20 asked the Financial Stability Board (FSB) to evaluate implementation regularly and determine “whether it is sufficient to improve the transparency in the derivatives markets, mitigate systemic risk, and protect against market abuse.” This came in response to the 2008 global financial crisis, which exposed weaknesses in the structure of the OTC derivatives markets. The crisis proved that the potential for systemic risks (contagion) due to the close linkages between market participants and the limited transparency of counterparty relations is very real. The report by the FSB included 21 recommendations that focus on standardization, central clearing, exchange or electronic platform trading, and reporting of OTC derivatives transactions to trade authorities. These recommendations are summarized below. 1.

2.

Standardization: The fraction of the market that is standardized should be expanded so as to facilitate the central clearing and trading on organized platforms and thus improve market transparency and ease systemic risk. Central clearing: Specifying the elements in determining whether a derivative contract is standardized and thus suitable for clearing is more important than ever for practicing rigorous risk management as well as for the supervision and regulation of central counterparties themselves.

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3.

4.

Exchange or electronic trading: All standardized derivatives contracts should be traded on organized exchanges or electronic trading platforms. Moreover, increased public price and volume transparency for all derivatives transactions should be furthered. Reporting to trade repositories: Authorities must have a global view of the OTC derivatives market so as to effectively carry out their mandates. The trade repository must also have comprehensive, uniform, and reliable data in order to facilitate aggregation on a global scale.

The objective of the report is to minimize the potential for regulatory arbitrage (regulatory arbitrage refers to financial engineering tactics to avoid or circumvent unfavorable regulation, or taking advantage of regulatory differences between two or more markets). In view of the global nature of and the continuous innovations in the OTC derivatives markets, ongoing international coordination and monitoring are needed. The FSB OTC derivatives task force will continue to monitor the implementation of the above recommendations and submit an initial progress report to the FSB by March 31, 2011. Source: Implementing OTC derivatives markets reform, Bank of International Settlements, Financial Stability Board, October 25, 2010.

KEY CONCEPTS The futures market involves the purchase or sale of some underlying asset at some predetermined price at some set future date. A futures contract is a standardized forward contract in terms of the type of asset, price, and delivery date. A forward contract is an arrangement between two parties for the delivery of a commodity at an agreed-upon price at some specified future time. A hedger is one who tries to reduce the risk from potential futures price movements. A speculator is one who explicitly makes a bet on the future direction of the market in an effort to make a profit. An arbitrageur is one who tries to offset his positions in order to lock in some profit. The buyer of the asset in a futures contract is said to have a long position, whereas the seller of the asset in that contract is said to have a short position. Daily computations of profits or losses on the futures contracts are referred to as marking to market the futures contract. The convergence property refers to a situation in which prices in both the futures and cash markets move in a parallel fashion because, at the expiration of the futures contract, the prices must converge (into one price). The spot-futures parity condition states that theoretically, the spot and the futures prices must be equal. The cost of carry refers to a factor that includes storage costs, dividends, and foregone interest.

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When the futures price of the asset would be below the (expected) spot price, the phenomenon is known as (normal) backwardation. When the net convenience yield is less than the risk-free rate, the phenomenon is known as contango. The basis is the difference (spread) between the spot and the futures prices. Financial futures contracts are deals involving financial instruments like equity or bond indexes, interest rates, and currencies. A stock index futures contract is one written on a stock index like the S&P 500 equity index. An interest rate futures contract is an obligation to buy or sell positions in Treasury bills, bonds, notes, or other interest rates. A currency (or foreign-exchange) futures contract is a contract that specifies a set amount of a particular currency to be exchanged at a specific time frame. Leverage refers to owing a large cash commodity account with a relatively small amount of capital (cash). Program trading refers to the electronic trading of a large portfolio of securities (at the NYSE) and their corresponding futures and options. Index arbitrage refers to the investment strategy that seeks to exploit mispricing between the theoretical and the actual values of indexes such as the S&P 500.

QUESTIONS AND PROBLEMS 1. Give an intuitive explanation of why spot and futures prices must be equal. What would be the implications if they were not? 2. The passage below is from the financial press. The Commodity Futures Trading Commission has recently (2010) voted to approve futures based on cinema box-office receipts. The reasoning behind their approval was that a film’s domestic box-office receipts qualify as a commodity. By contrast, the US Senate has put a ban on such trading in its latest effort of financial reform and regulation. The Senate considers this as another gambling platform. The box-office futures prohibition is a response to recent efforts to create exchanges that would allow studios and speculators to hedge or wager on the risks of Hollywood releases. Moreover, some feared that manipulation by movie executives and cinema chain owners could tarnish the movie market. a. Why do you think there is opposition to the creation of a futures market for movies? b. Can you find any benefits to trading in such futures? 3. Assume that H wishes to purchase one contract of corn from N, a seller of corn. He buys a contract (of 5,000 bushels), which trades on the first day of June at $3.68. The value of the contract is $18,400. H is long on the contract and N is short on it. What are the possible dangers (losses) for the clearinghouse in the

522 s Derivative Markets and Instruments

4. 5.

6. 7. 8.

9.

10. 11.

event of refusals by either party to fulfill his obligations? Assume that the price of corn per bushel goes up to $4 and then falls to $3.10. How can the clearinghouse protect itself from sustained losses of either party on a futures contract? Assume that the spot price of an asset is $40 and the annual risk-free rate is 2%. Assume that the asset is not a dividend-paying stock and does not incur any storage costs. What is the asset’s forward price for delivery a year from now, F 10? What would be the price 6 months from now? Finally, if the asset paid a dividend yield of 1%, what would be its futures price a year from now? The cost of carry in the first two cases is 3%. Following the above problem, what would be the implications if the spot and futures prices were not equal? Which factors determine the price of financial futures contracts? What is the impact of the opportunity cost? The passage below is from the financial press: “Oil rose for a second day in New York on speculation that European governments will resolve their sovereign debt crisis, moderating the region’s slowdown and demands for raw materials.” What would be the impact on oil futures? Currently (as of the third quarter of 2011), there are renewed concerns that the United States and Europe will plunge into a second slowdown, which would reduce the demand for industrial metals (such as copper). What impact would that have on copper futures? World oil prices (and futures both in Europe and New York) soared, mirroring the performance of global equities and a somewhat weaker US dollar. Can you explain this inverse relationship between oil prices and the US dollar? Assume that the September futures price of wheat is $2.50 per bushel and the December price is $2.55. You expect the positive price differential to widen in the next few months.

a. What would you do if you turned out to be right? b. Assume that the September contract rose to $2.52 and that of December to $2.59. What would this new situation do to your futures position? 12. Below are several pieces of news regarding the commodity and financial futures markets. After reading them, answer the questions that follow. On Thursday, December 1, 2011, the US Energy Department’s Energy Information Administration announced that natural gas in storage (or the nation’s supplies) shrank. Crude oil prices flirted with $100 per barrel during the last few days of November 2011. They ended up higher for November 30, 2011. On Wednesday, November 30, 2011, the world’s five major central banks (the Fed, European Central Bank, and Banks of Canada, Japan, and Switzerland) announced a coordinated action to seriously tackle the European sovereign debt crisis. Weakness in the equity market, bearish global demand/supply fundamentals, and sluggish export demand for wheat were reported during the month of November 2011. a. What impact did that have on natural gas futures prices?

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b. What impact did that have on gasoline futures prices? c. What impact did the announcement have on financial and commodity futures? d. What impact did these factors have on wheat futures prices?

NOTES 1. 2. 3. 4.

www.nyse.com www.tfx.co.jp/en/about_tfx/index_shtml As of 8:53 a.m. using the CNNMoney site. To convert the dividends into points, you do the following: obtain the S&P 500 dividend yield, here 1.0345%, and multiply it by the S&P 500 spot index value, here 1,160. Obtain the value of 12 points. Then multiply these points by the days to expiration year adjustment (75/360) to obtain the final dividend conversion into points, or 2.5 points.

16 OTHER TOPICS IN INVESTMENTS

CHAPTER OBJECTIVES After studying this chapter, you should be able to sExplain and use two important international parities and strategies sUnderstand what credit derivatives are and their various types sDescribe some important alternative investment assets

INTRODUCTION This chapter briefly presents some interesting topics, often less discussed in typical textbooks, that an investor should know about forming a well-diversified portfolio. These topics include credit derivatives and alternative investments, which stand in contrast to the traditional investments we covered in the previous chapters. We begin with two important international interest rate parities (covered and uncovered) and present some simple foreign-exchange investment strategies. Next we discuss at some length the various types of credit derivatives, specifically credit default swaps, as well as other important, frequently used swaps, highlighting their roles in today’s globalized economy. We then continue by presenting and discussing the alternative investment asset class, which has risen in importance over the last decade. Specifically, we explore some important alternative investments such as real estate, hedge funds, infrastructure, private equity, and other tangible alternative investments. Finally, we dedicate a section to “putting it all together,” which should serve as an overview of what you have learned thus far. Hopefully, since you have become aware of the risks, costs, and benefits of investing, you will be able to proceed with caution and wisdom.

INTERNATIONAL PARITIES AND SOME STRATEGIES In this section, we discuss some fundamental concepts that underlie the international interest rate parities. We also present a couple of currency strategies (exploiting rate or price differentials) known as carry trades.

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Useful Concepts The exchange rate is the rate at which one currency is exchanged for another. A decline in a currency’s value relative to another currency is a depreciation of the currency (and an appreciation of the other currency). For example, when the euro depreciates against the US dollar, it means that the dollar strengthens relative to the euro. This is so because you will need more euros to buy $1. When an investor holds foreign assets denominated in foreign currencies, the investor is subject to exchange rate risk. Exchange rate risk is the possibility that the asset’s value will decline owing to a change in the exchange rate. What are some of the economic effects of a weak or a strong currency for the domestic economy? In general, a weak currency can boost exports, create more jobs, and depress imports because goods are cheaper for sale overseas. Thus it reduces unemployment. However, this can lead to higher inflation at home because of the rising incomes from higher exports and because domestic producers find it opportune to raise their prices. By contrast, a strong currency can boost imports, as consumers now have more purchasing power, but it can also lead to higher unemployment at home. The latter happens because exports are not stimulated, since the strong currency makes exports more expensive. On the other had, inflation remains subdued as domestic producers hesitate to raise prices. What are the various factors that can affect exchange rates? The list is long, but we can simply bundle them into economic and noneconomic factors. For example, inflation rates, interest rates, income levels, political factors, and expectations are some of these factors. For example, when a country’s inflation rate rises, say that of the United Kingdom, relative to that of another country, say that of the United States, the British pound depreciates. When United Kingdom’s interest rates rise relative to those of the United States, the pound appreciates (because investors find more attractive returns in the United Kingtom than in the United States). Finally, when the income levels of US residents rise relative to those in the United Kingdom, the dollar appreciates. Interest Rate Parity Let us begin with an example. Assume that you have to choose between two default-free investment alternatives for your $1: invest it at home for a year or invest it abroad for a year. For the latter option, you must buy the foreign currency (since you hold only your own, domestic currency), invest the resulting amount of foreign currency, and then sell that investment forward in exchange for the domestic currency amount (since you will need to convert the foreign currency to your own). In symbols, the return expression from the domestic investment would be (1 + rd)

(1)

where rd is the domestic interest rate. For the foreign investment, the return expression would be as follows: [(1 + rf ) f1]/e0

(2)

where rf is the foreign interest rate, f1 is the end-of-period forward rate, and e0 is the (spot) exchange rate. So what this equation says is that $1 converted into the foreign currency will generate so many foreign currency units when invested at the foreign interest rate and so may dollars when the proceeds are sold forward (today).

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Setting Eqs. 1 and 2 equal to each other, we obtain (1 + rd) = (1 + rf ) (f1/e0)

(3)

f 1 + rd = 1 1 + rf e0

(3a)

or, by rearranging it,

Thus, the interest rate parity (IRP) is an arbitrage condition stating that the future dollar proceeds from investing in two equivalent (and risk-free) investments must be the same. Alternatively stated, IRP holds that hedged returns from investing in different currencies should be the same regardless of the level of interest rates. The two versions of IRP are covered interest rate parity and uncovered interest rate parity. In simple terms, covered interest rate parity (CIP) requires that any discrepancies between the expected exchange rate and the spot rate in the next period should be hedged (i.e., covered) by a forward contract. Why does one care about CIP? If it does not hold, it would suggest that markets are inefficient and that traders do not exploit profitable opportunities; thus there are still capital controls in place across countries that increase trading costs.1 The uncovered interest rate parity (UIP) requires that interest rate differentials be offset by an expected depreciation/appreciation of the currency. If this parity does not hold, profit opportunities arise. Does UIP hold in reality? Empirical evidence has shown that it does not always hold and that it depends on the currency pair used. Also, it can hold over longer horizons but not over short ones.2 Carry Trade A carry trade is a round-trip transaction whereby an investor buys a currency with a low interest rate and sells (exchanges) it for a currency with high interest rate, thus profiting on the spread. Stated differently, the investor borrows a given amount in a currency with a low interest rate (known as the funding currency), exchanges the funds into a currency with a high interest rate (known as the target currency), and lends (invests) the resulting amount in that currency. Thus the strategy is applied by investors in foreign exchange markets to exploit interest rate differentials across nations. One traditional currency that fueled carry trades for more than a decade was the Japanese yen. Since the mid-1990s, the Bank of Japan has maintained very low interest rates, enabling investors to borrow yen to fund riskier activities elsewhere, particularly in the United States and emerging markets. Recently, however, the US dollar became the world’s funding currency in light of the extremely low interest rates in the United States. International investors short the US dollar to buy (or to leverage) risky, high-yielding assets around the globe. What is the economics of carry trades? Recall that UIP states that interest rate differentials between two countries are expected to close when the high-interest-rate currency depreciates against the low-interest-rate currency. When the depreciation takes place, investors who used carry trades will notice that their return is zero. In other words, the investors’ return from investing in the high-interest-rate currency is worth at least as much as the cost of borrowing in the low-interest-rate currency. That’s economic theory. Reality, however, is different. Traders do make profits in carry trades because, on average, the currency in the low-interest-rate country tends to depreciate rather than appreciate

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and the currency in the high-interest-rate country tends to appreciate (owing to excess demand for it) rather than depreciate. Hence investors make profits from this anomaly (known in the international financial literature as the forward premium puzzle), capitalizing on the spread (or differential) and the appreciation of the high-interest-rate currency. However, trader beware! Just because this seems straightforward and simple, keep in mind that currencies are highly volatile, interest rates change on a daily basis, and currencies correlate with each other. These factors, along with other, unpredictable ones, make carry trades difficult to predict, and they can turn against you. As another example, market traders attribute the collapse of profitable carry trades in the late 2000s to the rapid appreciation of the Japanese yen. Understand that as a currency appreciates, there is pressure to cover debts in that currency (by converting other assets into that currency); this affects the (borrowing) costs and can cause a carry trade to turn negative. Box 16.1 highlights some episodes of failed carry trades. International Arbitrage International arbitrage ensures that foreign exchange market prices are aligned. For example, if exchange rates for a given currency vary among financial institutions that provide foreign exchange, foreign exchange traders will buy the currency from the institution that offers a low quote and simultaneously sell it to the bank with the higher quote. There are two common types of international arbitrage: locational and triangular. We briefly explain each below. Locational arbitrage is simply the exploitation of spot price discrepancies on an exchange rate at two different locations, as explained above. If such arbitrage opportunities exist and a trader engages in such purchases/sales of the foreign exchange in question, the financial institution whose quote is lower than another institution’s will begin raising (its ask) prices in response to strong demand. At the same time, the financial institution that offered a higher quote will lower its (bid) prices in response to excess supply of the currency in question. Thus, within a very short period of time, the two prices will be equalized, providing no more arbitrage or riskless profit opportunities to these traders.

Box 16.1 Episodes of Failed Carry Trades In 2009, in the middle of the recession, the prices (values) of US risky assets increased sharply, and some said that the increases were not due to the fundamentals. So what could explain such a rise in asset prices? One popular explanation was the carry trades that emerged due to very low interest rates in the United States during that period. With near zero interest rates, the US currency became the funding currency for purchases of assets both in the United States and around the world. This also meant that investors were borrowing—effectively at negative interest rates—as the decline in the US dollar led to massive capital gains on short dollar positions. Such massive carry trades were also fueled by the perceived reduction in the riskiness of assets because the Fed kept buying up “toxic assets” (via its quantitative easing policies). But those days are gone because the US dollar will begin stabilizing soon and the reversal will force traders to

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cover their shorts. In addition, the US economy has started growing, still modestly, which means that higher interest rate expectations are on the horizon. In fact, the strategy lost 2.5% in 2010 as the dollar appreciated. Remember the yen situation! Remember also the lesson from a failed Icelandic Krona carry trade. In 2009, the Icelandic Krona was one of the sought after currencies (along with the Australian and New Zealand dollar). Iceland had a nominal interest rate of about 18% and was particularly attractive for carry trades. However, in 2009 Iceland’s economy (and the banking sector) collapsed, leading to the crash of the Krona. As a result, massive carry traders were wiped out. Sources: N. Roubini, Mother of all carry trades faces inevitable bust, Nov. 1, 2009, FT.com. A. Zendrian, Stay cautious with carry trades, Aug. 27, 2009, Forbes.com.

Triangular arbitrage opportunities emerge when the cross-rate quote of two currencies does not match the two currencies’ corresponding exchange rates. A cross-exchange rate is the ratio of each currency’s value against the US dollar so as to derive the value of one currency against the other. For example, if the spot rate for the euro is US $1.35 and for the Canadian dollar US $1, then the cross-exchange rate would be for the Canadian $1 to equal 0.74 euros (computed as $1/$1.35). If, at a particular point in time, the quoted cross rate is 0.75 euros per Canadian dollar, a trader would benefit by spending US dollars to buy Canadian dollars, then using them to buy euros, and finally, using the euros to buy US dollars. To make this train of events more concrete, assume that the trader has $1,000 that he uses to buy 1,000 Canadian dollars (found by dividing the $1,000 by $1). He then converts these funds into 750 euros (computed as $1,000 times 0.75). Finally, he converts the euros into US dollars as follows: 750 euros times 1.35, which equals $1,012.50. This amounts to a quick (gross) profit of $12.50. This is how triangular arbitrage is practiced. Obviously, such transactions are instantaneous and do not always guarantee profits. In fact, mostly financial institutions that deal in foreign currencies engage in such activities, and because of their active trading there are typically (or should be) no discrepancies in cross-exchange rate quotes.

CREDIT DERIVATIVES What are credit derivatives? Credit derivatives are financial instruments designed to shift and/or manage credit risk among participants such as financial institutions, firms, and other investors. Since this is a derivative instrument, its value derives from the credit performance of underlying companies, sovereign entities, or other financial claims. Credit derivatives allow financial institutions to limit credit exposure while keeping assets (like loan sales) on their balance sheets. Thus credit derivatives are confidential transactions that the customer need not be privy to, thereby freeing management from customer relationships and focusing it on risk-management decisions. J. P. Morgan Chase & Co. (then J. P. Morgan) was the pioneer in the creation and early use of credit derivatives, which spanned more than two decades.

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The Market for Credit Derivatives Credit derivatives grew rapidly in the latter part of 1990s in response to demand by financial institutions, which wanted to hedge against or diversify credit risks. Prior to that, banks considered shedding or hedging credit risk infeasible. Thus financial institutions mainly relied on traditional forwards, options, letters of credit, and other securitized products. Over time, low-cost credit derivatives were created so as to trade illiquid risk just like other risks in response to (global) competitive pressures, rising insolvency cases (such as WorldCom and Enron), and regulatory changes (i.e., Basel accords on bank capital requirements). As a result, banks were forced to actively manage their credit portfolios and become innovative. Thus complex and contingent-type credit derivatives have spawned underlying risks like default, catastrophe, earthquake, pollution, weather, and electricity beyond the traditional ones, such as interest rate, currency, equity, and commodity markets. So why did this investment class grow so spectacularly? Because of the unique ability of credit derivatives to isolate credit risk from interest rate risk and to transfer such risk. For example, credit risk is isolated via credit derivatives, interest rate risk through interest rate swaps, and exchange rate risk via foreign exchange derivatives. Moreover, credit derivatives offer disciplined pricing decisions, which allows financial institutions to make valuations more objectively. Thus credit derivatives have opened up new avenues of distribution for the credit risks of bank loans and other instruments into the general capital markets. Even prior to the 2008 financial crisis, credit derivatives, particularly credit default swaps (to be explained below), enabled banks, hedge funds, and asset managers to take positions in default risk. The market for derivatives and its subcategories continues to thrive and expand. According to the Bank for International Settlements, the latest size of the global overthe-counter derivatives exceeded $601 trillion. Table 16.1 illustrates the growth of that market on a yearly basis from 2008 to 2010. As you see from the table, the highest chunk of the market takes interest rate contracts, with over $465 trillion as of December 2010, followed by foreign exchange contracts, with over $57 trillion as of December 2010, and by credit default swaps, with about $30 trillion for the same period. It is important to note that the rising trend of the credit default swaps, before the crisis of 2008, came to a halt contrary to other risk categories, like foreign exchange and interest rate contracts, whose trend continued upward. More information on derivatives can be found at the International Swap and Derivatives Association’s (ISDA) website. There are several important and regularly traded types of credit derivatives. Among them are credit default swaps, total return swaps, asset swaps, and collateralized debt obligations. We explain each very briefly below. Credit Default Swap How do credit derivatives work? The majority of credit derivatives take the form of credit default swaps (CDSs). A credit default swap is nothing else but a bilateral contractual agreement (financial contract) to transfer the default risk of one (or more) reference entities from one party, the “protection buyer,” to another, the “protection seller.” Who are typical protection buyers and sellers? According the British Bankers Association (BBA), buyers and sellers of protection include banks, insurance companies, investment companies (such as hedge and pension funds), and corporate entities. The four largest US credit default swaps counterparties (as of 2006) were J. P. Morgan Chase, Citigroup,

530 s Derivative Markets and Instruments Table 16.1 Amounts Outstanding of OTC Derivatives (in billions of US dollars) Risk category

Foreign-exchange contracts Interest-rate contracts Equity-linked contracts Commodity contracts Credit default swaps Unallocated Total contracts

Notional amounts outstanding

Gross market values

Dec 2008

Dec 2010

Dec 2008

Dec 2009

Dec 2010

50,042 432,657 6,471 4,427 41,883 62,667 598,147

57, 798 465,260 5,635 2,922 29,898 39,536 601,048

4,084 20,087 1,112 955 5,116 3,927 35,201

2,070 14,020 708 545 1,801 2,398 21,542

2,482 14,608 648 526 1,351 1,532 21,148

Source: BIS

Bank of America, and Goldman Sachs.3 Of all these banks, J. P. Morgan holds most of CDSs, the notional value outstanding of which was approximately $76 trillion as of June 30, 2006, according to the US Office of the Comptroller of the Currency. In Europe, Deutsche Bank, UBS, and Barclays are the dominant ones. Figure 16.1 illustrates the process of a CDS. The protection buyer pays a (periodic) fee (xx basis point per annum) to the protection seller during the term of the agreement. If the entity in question, the reference entity (or the issuer of the debt instrument), on which protection is written, declares bankruptcy or moratorium (in case of a sovereign country), fails to make payments when due, or repudiates its debt, the protection seller is obligated to compensate the protection buyer for the loss. All the above occurrences are referred to as credit events. Note that the reference party is not part of this contract. The default or contingent payment can be a cash settlement scheme designed to reflect the loss incurred by creditors of the reference entity. The payment is typically calculated as a reduction in the price of the obligation below face value at some designated point in time. The face or par value of the amount of credit protection bought or sold is commonly referred to as the notional amount of the reference entity debt. The premium for a credit default swap is commonly known as a CDS spread and is quoted as an annual percentage in basis points of the notional amount (or a prespecified face value). A basis point on a contract protecting $10 million of debt from default for 5 years would be equivalent to $1,000 per year. Protection buyers actually pay the spread on a quarterly basis on the 20th of March, June, September, and December. If, however, the distressed entity or asset’s spread becomes large, the investor is required to pay the premium up front (at the beginning of the trade). In essence, what happens in a CDS is that the protection buyer takes a short position in the credit risk of the reference entity, effectively relieving the buyer from the risk of (exposure to) default, while the protection seller takes on a long position in the credit risk of the reference entity, which effectively is the same as the default risk if the seller lent to the reference entity directly. Thus credit derivatives allow banks to take a short credit position to hedge their exposure to credit losses without the explicit consent of the reference entity. This also alleviates bank-customer relationship problems (for the bank) without jeopardizing client relationships.

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Reference entity

xx basis point per annum Protection buyer

Protection seller default (contingent) payment

Figure 16.1 A credit default swap.

Another benefit of CDS is that it allows investors to benefit (i.e., speculate) on a negative credit market or entity opinion. For example, if an investor believes that the market has overestimated a reference entity’s prospects for growth, she can buy protection now in anticipation of the reference entity’s future deterioration. If the investor’s expectations are correct, she can close out her transaction at a profit by selling protection on the entity. It has been argued that such activities add liquidity to the market and facilitate the quality of price discovery.4 Despite the fact that CDS transfer risk, improve price discovery, add liquidity to the market, and enable financial institutions to hedge credit risks more effectively, they can potentially destabilize the market. One reason given is that the shifting of credit risk is done the other way around—that is, risk goes from those institutions best suited to manage it (like banks) to other entities that cannot manage it (like hedge funds).5 A recent example is that of the subprime crisis of 2008, in which CDS were written to bet against massive mortgage defaults. This led to the global financial meltdown, with prime examples being the near collapse (before being taken over by the federal government) of American International Group (AIG, an insurance company) and the collapse of Lehman Brothers.6 Within the CDS class, there are other subcategories like loan-only credit default swaps (LCDS), basket swaps, and CDS indexes. For example, an LCDS contract is designed to trace the credit of secured loans used in private equity buyouts. These are highly leveraged or junk-grade loans. When a company defaults, its secured bondholders get paid first, and if there is anything left after that, it accrues to the unsecured debtholders. This represents a new way of investing by hedge and other funds in a company’s capital. In the simplest case of a basket CDS, when a reference obligation (among several included in the basket) defaults, there is an immediate payout and a termination of the swap (sometimes this is known as first-to-default basket swap). Finally, in a CDS index, the credit risk of a basket of reference entities is transferred between the buyer and seller of protection. In general, the recent financial crisis has raised more questions about the use of CDS; that is why both the European Union and the US government have launched inquiries into these banks’ use of such derivatives. Box 16.2 lays out the reasons for such investigations. The box titled International Focus describes the use of CDS on European sovereign debt. Total Return Swap A total return swap (TRS) is an agreement between two parties to transfer the total return from a financial asset or reference obligation (or the particular debt issue for which credit protection is sought) from the total return payer to the total return receiver. Unlike a

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credit default swap, a TRS transfers the credit risk (along with market risk) from one party to another. Thus, a portfolio manager can use a TRS to increase exposure to a reference obligation, in contrast to a CDS, which is used to hedge a credit exposure. Banks and other financial institutions use TRSs to manage their credit risk exposure and also as a repo instrument for funding purposes. The generic TRS works as follows (see Figure 16.2). The total return payments from the payer include the interest payments on the underlying loan (the reference obligation), any appreciation/depreciation in the market value of the asset, and fees minus any default losses. In return, the total return receiver will pay the London Interbank Offered Rate (LIBOR)-based return plus a (negotiated) spread, which is independent of the reference obligation’s performance. In essence, the economic effect is that the total return receiver benefits as if it owned the underlying obligation. The spread can be a function of the credit rating of the swap counterparty, any profit margins, and any capital charges tied with the TRS. Common total return receivers are hedge funds and commercial banks that seek a more favorable exposure to the reference obligation compared with an outright purchase of the obligation. The bank or dealer hopes, on the other hand, to generate extra cash by charging a spread over the LIBOR (or market returns) it receives from lending and receiving a guarantee against depreciation of the assets. A TRS can be structured using any type of asset such as stocks, indexes, corporate bonds, mortgages, property, and so forth.

Box 16.2 The European Union and the United States Begin Probes into the Use of Credit Default Swaps In late April, 2011, the European Union’s antitrust regulators announced that they planned to launch investigations into the roles of the world’s largest banks—notably Goldman Sachs, Barclays, J. P. Morgan Chase, and Deutsche Bank—in the market for derivatives. Specifically, officials plan to examine whether these banks violated competition rules by abusive behavior and lack of transparency. The European Commission intends specifically to look at the credit default swap (CDS) niche of credit derivatives involving sovereign debt. Several of these banks that dealt in CDS, including the ones mentioned above, have had relationships with (or are shareholders in) Markit, a London-based organization that provides information on the market for CDS. In addition, several of the banks involved have a financial relationship with the Intercontinental Exchange, a public company that owns ICE Clear Europe and ICE Clear US, involved in the clearing of transactions. Critics charge that the banks that dealt with ICE created anticompetitive rules and practices so that other competitors, like Bloomberg and ThomsonReuters, would be blocked from doing business there. The US Justice Department began its own investigation of Markit in the summer of 2009 and expanded its efforts to look at clearing practices between companies like ICE and the banks. European regulators could fine banks involved in such antitrust and cartel practices for up to 10% of their global annual sales. Sources: T. Mucha, Europe launches investigation over derivatives, GlobalPost, April 29, 2011. L. Story and J. Kanter, Europe investigating banks over derivatives, New York Times, April 29, 2011.

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Reference obligation Cash flow

Total return (interest+appreciation+fees-losses)

Total return payer

Total return receiver LIBOR + spread

Figure 16.2 A total return swap.

What is better, entering a TRS or owning the reference obligation directly? A TRS allows the investor to pay a fee to the total return payer in exchange for receiving the total return on the reference obligation instead of financing the purchase himself. Also, a total return receiver can benefit from greater diversification of assets rather than resorting to the cash market. Finally, the investor can swap the total return for floating payments if these are desired. Thus a TRS has more advantages than simply owning the reference obligation and transacting in the cash market, perhaps several times, in order to achieve more efficient diversification of assets. Asset Swap An asset swap is a combination of an interestrate swap and a bond (or a note). So, the party that owns the bond (the protection buyer) enters into an interest rate swap agreement with the bank (which sold him the bond, the protection seller) to exchange fixed payments with variable ones. Thus he pays fixed and receives variable (floating) payments. Figure 16.3 shows the process. Effectively the asset swap alters the cash flow characteristics of a bond, enabling investors to hedge interest rate risk and construct portfolios with more suitable (for them) cash flow features. Given that the bond’s coupon rate is (typically) larger than the prevailing swap rate for that maturity, the floating rate part of the swap (the LIBOR reference rate) is increased by a spread, which reflects the difference between the bond’s coupon and the prevailing interest rate swap at the trade date. In essence, the spread over LIBOR is a measure of the credit risk in the cash flow of the underlying bond. Here’s an example of a simple asset swap. Assume that an investor purchases a $10 million 5.75% par value 5-year bond of a BBrated company. The bond’s coupon payments are semiannual. The investor simultaneously enters into a 5-year interest-rate swap with a bank where he is the investor, making fixed semiannual payments. The swap rate is 5% and the investor receives a 6-month LIBOR of 0.75%. In fact, the spread is the price of the asset swap. Table 16.2 illustrates the process. Thus, irrespective of whether interest rates change and assuming that the company does not default, the investor receives 75 basis points over LIBOR. Hence it is said that the investor has created a synthetic floating rate bond, which is, essentially, the objective of an asset swap. Collateralized Debt Obligation A collateralized debt obligation (CDO) is a security backed by one or more types of debt obligations such as bank loans, corporate or sovereign bonds, and mortgage-backed

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Bond coupons

price paid Coupons on bond Buyer

Seller LIBOR + spread

Figure 16.3 An asset swap.

Table 16.2 Example of an Asset Swap Rate received from company’s bond minus Payment rate to bank on swap plus Payment rate from bank on swap ----------------------------------------------------equals Net received by investor

5.75% 5.00% Six-month LIBOR -----------------0.75% + six-month LIBOR

securities. CDOs have various subcategories depending on the type of debt obligation. For example, if the underlying asset of a debt obligation is composed of bank loans, it is called a collateralized loan obligation. If the debt obligation is backed by corporate and/ or emerging market bonds, it is called a collateralized bond obligation. These securities are packaged and held by a special-purpose vehicle (SPV), which is a subsidiary organization designed to issue notes that entitle derivatives owners to payments even if the parent company defaults (or goes bankrupt). SPVs serve as counterparty for swaps and other derivative products with a legal status. CDOs became very popular in the late 1990s or early 2000s; by 2008 their value exceeded $500 billion. One important recent SPV is the European Financial Stability Facility (EFSF), which was created in May 2010. EFSF is an off-balance sheet of the European Central Bank which places CDOs to raise funds and finance deficit European nations to avert further fiscal (sovereign debt) crises in the eurozone. CDOs carry various tranches (components) such as senior (secured) and subordinate (unsecured) ones. Each tranche carries a rating with the senior one having at least an A-grade rating and the subordinate ones ranging from B to BBB. If a subordinate tranche is equity-linked, there is no credit rating on it. Payments (in the form of interest and principal repayments) from the underlying assets (debt obligations) accrue first to the senior tranche, and any residual cash flow goes toward the subordinate tranches. Some tranches receive fixed (typically the senior ones) and others (subordinate ones) floating rates. Obviously the ability to make payments to the tranches depends on the performance of the underlying assets. For example, in a mortgage-backed CDO, the ability to make scheduled payments to the investors depends on the ability of homeowners to pay their mortgages in full and on time. That would be possible, in general, during good economic conditions. If economic conditions worsen, several mortgage defaults will translate into losses for the subordinate (i.e., riskier) tranches (and perhaps some senior ones). As economic conditions deteriorate, the risk premiums on tranches increase

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(for example, during the financial crisis of 2008, they reached 5%, from close to zero a few years earlier). A subcategory of CDOs is a synthetic CDO. Synthetic CDOs comprise baskets of derivatives rather than actual debt and are backed by a pool of CDS. Lehman Brothers was at the forefront of these new financial instruments around 2005. Like a CDO, a synthetic CDO has tranches, the riskiest of which are equity (or first-loss) tranches. This is so because if the companies in the pool underlying the instruments default, these tranches will bear an immediate loss. Because these tranches were not rated, Lehman Brothers (and other banks later) managed to rate them so that funds, like pension and mutual funds, could buy them as a new way of earning higher yields and circumventing investment regulatory constraints. In the summer of 2006, Lehman Brothers struck a !100 million deal on synthetic equity CDOs that Moody’s rated A3.7 Additional deals ensued and demand was strong, especially from subprime companies. Late in September 2011, an SEC report on the role of the nation’s credit-rating agencies during the subprime financial crisis of 2008 found several flaws in the ratings of 10 such agencies (including the three major ones). Specifically, the SEC charged that these agencies did not address the conflicts of interest that arose, among other concerns, when they rated asset-backed securities.8 Box 16.3 highlights the explosive growth of credit derivatives and their acronyms, which gave rise to the term alphabet soup.

Box 16.3 The Credit Derivatives’ Alphabet Soup THE ABCS OF DERIVATIVES The 2000s were a decade during which many derivative products were invented by major investment banks such as J. P. Morgan, Lehman Brothers, Goldman Sachs, and so on. Fixedincome participants began speaking in a code on these derivative products that the average person could not understand. Here we present some of the most-used acronyms with a brief explanation attached to each. ABS (asset-backed security): securities backed by assets like credit-card loans, auto loans, home-equity loans, student loans, etc. ABX (asset-backed index): the index on which ABS are based ABCP (asset-backed commercial paper): short-term debt comprising consumer loans CDS (credit-default swaps): see text CDX (credit-default index): index on which CDS are based CDO (collateralized debt obligations): see text CDO2 (CDO squared): a pool of CDO tranches backed by CDOs CMO (collateralized mortgage obligations): bond classes that redirect the cash flows of passthrough securities, like mortgage securities within a pool MBS (mortgage-backed securities): securities that are backed by mortgages CMBS (commercial MBS): an MBS backed by commercial mortgages CMBX (CMBS index): an index (basket) of credit default swaps on ABS and CMBS RMBS (residential MBS): an MBS backed by residential mortgages

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SCDO (synthetic CDO): see text LCDO (loan-only CDO): syndicated secured loan CDS LCDS (loan-only CDS): see text Many blame the proliferation of complex and hard-to-understand derivative products for the financial crisis of 2008 and, lately, the European sovereign debt crisis, mainly through the use of credit default swaps.

ALTERNATIVE INVESTMENTS What Are Alternative Investments? An alternative investment is one that has different risk/return characteristics from a traditional investment, like a stock or bond. For example, it might be uncommon, relatively illiquid, rarely traded, and tangible or intangible. Moreover, it can have the potential for a higher return, can be less or negatively correlated with traditional investment instruments, and require longer-term investment horizons. Some examples of intangible alternative investments are real estate, private equity, hedge funds, and infrastructure. Some examples of tangible investments are art, wine, and classic cars. Figure 16.4 shows the alternative investment asset classes. Such investments gained momentum and popularity in the 2000s, when equity and bond markets around the world declined or offered low yields. These developments led investors to search for alternative investment vehicles in an effort to earn higher yields and achieve greater portfolio diversification. In addition, alternative investments tend to do well when inflation rises or when stock market volatility is rising. Alternative investment funds can also employ options, futures, and other derivatives to reduce their exposure to the market’s fluctuations and can sell stocks short. Finally, some funds also use arbitrage strategies to bet on price discrepancies between investments. Thus many analysts argue that alternative investments should be part of a well-diversified portfolio. However, the risks are varied and, on top of the ones already mentioned, many such investments are not publicly traded (i.e., on exchanges) or are not regulated at all. What’s more, many of the firms themselves are not registered with the SEC in order to avoid regulation and scrutiny. Potential investors can obtain more information on such investments by visiting the websites of the Alternative Investment Management Association (AIMA) and the Chartered Alternative Investment Analyst (CAIA). Box 16.4 discusses the long-short and market-neutral alternative funds strategies that have some dominance in the industry (mainly practiced by hedge funds).

Alternative Investments

Real Estate

Private Equity

Figure 16.4 Alternative investment asset classes.

Hedge Funds

Infrastructure

Other

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Box 16.4 Long-Short and Market-Neutral Alternative Funds Long-short alternative investment funds bet for and against stocks and thus are designed to limit downside risk when the stock market plummets. Over the last 3 years, their performance has been disappointing, since they fell by an annualized rate of 1.17% while the S&P 500 gained an annualized rate of 0.02%. In general, such funds should be able to give you better returns in periods of stock market declines. More recently, despite the stock market’s gain of 8.1%, for a period of 6 months in 2011, long-short funds gained a mere 1.25%. Some analysts point out that such funds are not designed to beat the market; rather, they are meant to deliver returns with less volatility. A similar category of such funds is the market-neutral funds, which are set up to generate positive returns regardless of the market’s ups and downs. These funds also delivered disappointing results (or 0.11% on an annualized basis) over the past 3 years, barely beating the S&P 500 (which delivered 0.02%). Compare these returns to the 3-m Treasury bill returns over the same (3-year) period, which produced annualized returns of 0.26%. Analysts cite this poor performance to factors like high expenses (which average 2.11% for the long-short and 1.79% for the market-neutral funds) and bad market timing moves. Source: Ann Tergesen, Do “alternative” funds deliver? Wall Street Journal (weekend edition), Sept. 24–25, 2011.

Let us now briefly present some important alternative investment classes—notably real estate investment trusts, hedge funds, private equity, and some tangible ones. We begin with real estate investment trusts. Real Estate Investment Trusts Recall from Chapter 6 that a real estate investment trust (REIT) is a corporation that owns and manages real estate and reduces corporate income taxes. Income taxes are satisfied as long as the trust distributes at least 90% of its income to the investors and that income (dividends) is taxed as ordinary income. In that sense, REITs resemble mutual funds. REITs, which were created by Congress in 1960, rose in importance dramatically and are now considered an important alternative investment class. In 2001, Standard & Poor’s took notice of such industry growth and included REITs in the S&P 500 Index. REITs pay out dividends to investors on a relatively consistent basis (and when other stocks have not) and have a lower correlation with equity and debt securities. In general, REITs deliver income and long-term growth, high dividend yields, and good share price appreciations. According to Ibbotson Associates, REITs offer an attractive risk/return profile and may enhance return or lower risk when they are included in a diversified portfolio.9 What are some of the risks of investing in REITs? First, it is important to keep in mind that real estate investments are lagging (indicators), which means that they trail economic activity. So when the economy rebounds, REITs will start growing as well. REITs are not low-risk investments despite their recent rally in 2009–2010 (see also Figure 6.5 in Chapter 6), during which they posted an impressive increase of about 90%. In 2007 and 2008, REITs lost approximately one-third of their value. Also keep

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in mind that REIT share valuations are different from those of a typical stock because they resemble mutual funds (and compute net operating cash flows); they need to pay out at least 90% of their income to shareholders. Since REITs must pay dividends, they may dip into reserves or borrow when cash flow is not present. Alternatively, they may choose to pay dividends in the form of stocks—a practice that does not enjoy approval from shareholders.10 Finally, since REITs can also be nontraded (meaning that they are not exchange-listed and traded) and are sold through financial advisors, you should be aware that they charge hefty fees and may be difficult to resell. Recently FINRA launched investigations of some of the firms that marketed such REITs because of misrepresentation of the risks and benefits from nontraded REITs.11 In general, prospective investors should read each REIT’s prospectus carefully to understand how the REIT operates. Hedge Funds We first defined a hedge fund in Chapter 6, so we will not discuss it at length here. We will simply say a few words on the issues of transparency and the so-called hedge fund puzzle. In general, the hedge fund industry is not regulated; therefore little and/or incomplete reporting takes place. Obviously investors are concerned with the lack of transparency in hedge funds, and this can pave the way for conflicts between investors and managers. Moreover, the recent interest displayed by institutional investors, not just individual wealthy investors, in hedge funds may raise the stakes for hedge fund disclosure. However, to date there has not been a consensus on a standard and amount (as well as the quality) of voluntary reporting. A recent paper by Goltz and Schroeder (2010), based on a survey of the European hedge fund industry, found that inadequate disclosure information, inappropriate use of risk and return measurement metrics, and lack of information on risks and valuation frameworks were the norm in the industry.12 How can you find out more about a hedge fund? Potential investors should perform due diligence. Due diligence simply means doing background research before entering a transaction (or a contract). For example, investors can request a due diligence form known as the Alternative Investment Management Association (AIMA) form (or questionnaire) from the hedge fund in question. This form contains a list of questions for managers to answer, such as what the manager’s (and his or her team’s) experience in managing funds is as well as information regarding fees, references, and other important data. Investors can also find out about the fund’s background from the SEC’s Investment Advisor Public Disclosure website or from the FINRA’s BrokerCheck database. Finally, interested investors can ask for copies of the fund’s recent audits, visit Morningstar’s website, or search other financial information sources (such as the Wall Street Journal, Bloomberg, and ThomsonReuters). Why have hedge funds historically performed better than the aggregate market and often on a consistent basis? Financial theory suggests that no investor (or investment strategy) should earn excess (abnormal) returns consistently. Why were hedge funds able to capitalize arbitrage opportunities, which, in theory, should not exist or should disappear very fast? It turns out that their strategy is based on momentum trading. Recall from Chapter 9 that momentum trading refers to the tendency of poorly performing and well-performing stocks in one period to continue their “anomalous” behavior in the next period. Thus momentum can cause persistence in the assets’ relative returns. Bond

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and Johnson (2010) have examined that strategy and concluded that when coupled with market timing ability (signals), it has produced a stream of positive returns (over the last 10 years) and beaten the market both in absolute returns and risk.13 Thus it can be concluded that hedge funds aggressively exploit market inefficiencies. Private Equity Private equity firms are privately held companies (partnerships) that primarily make specific investments in other, usually troubled companies. For example, a private equity firm may pay cash to acquire a public company and take it private. In other words, such funds seek an equity stake (or partial ownership) in companies. Private equity firms do not hold acquired firms forever. Once they restore the profitability of such firms, they (re) sell them to other (public) investors for a profit. The majority of private equity firms are private, and thus they are not required to abide by the Sarbanes-Oxley Act and the SEC disclosure requirements. In addition, such firms frequently take a major role in managing a company they have invested in and share their technical know-how not only of financial areas but also engineering, manufacturing, and the Internet. What are the reasons for the explosive growth of private equity funds? First, the makeup of such funds is now more diversified in the sense that such partnerships are no longer confined to the participation of wealthy individuals but professional managers (on behalf of institutional investors) can now be part of such structures. Second, because of their large pools, such funds are able to achieve greater portfolio diversification and realize superior returns given that their correlation with traditional financial assets is low. Some well-known private equity firms in the United States are the Blackstone Group; Kohlberg, Kravis and Roberts (KRR);and the Carlyle Group. In the United Kingdom, CVC Capital Partners and Barclays Private Equity are prominent. Private equity firms were involved in a frenzied rally for leveraged buyout deals in 2007 but remained lackluster in the first half of 2011. They have extended their operations outside the United States and the United Kingdom, most notably to Uganda, Malaysia, and Chile.14 Impressive private equity deal volumes also took place in China and Indonesia and continued to thrive in Africa, and the Middle East.15 Box 16.5 highlights the private equity and hedge funds deals in Brazil. Venture capital is a specialized type of private equity firm that buys stakes in startup companies in need of financing. Venture capital is a high-risk/high-reward venture, just like private equity funds. Venture capital also has long-term investment planning horizons because young companies require time to become established and profitable in the market. As a result, such investments are illiquid during the first phases of a company’s operations. Lately such capital has increased its stakes in enterprise companies, which provide software and Internet services to business customers in an effort to exploit technological and cultural gaps between established companies and start-ups. Infrastructure Funds Infrastructure is also an important alternative investment class; it is an amalgamation of assets in various sectors such as toll roads and bridges, air- and seaports, power distribution, dams, and so on. Thus infrastructure funds comprise heterogeneous assets, with each asset having its own risk/return characteristics. Various institutional investors like pension funds find this asset class attractive because they expect a steady cash flow over

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Box 16.5 Private Equity and Hedge Funds Deals in Brazil A flurry of private equity and hedge fund deals has taken place in Brazil lately. US firms like Blackstone private equity bought a 40% stake in Patria Investimentos, and J. P. Morgan Chase’s Highbridge hedge fund bought stakes in Gavea Investimentos (both Brazilian funds). Brazil is currently a hot spot for such deals because the country is growing fast. Being the largest emerging country with a well-established democratic system and a growing stock exchange (the BOVESPA, which ranks fourth among the world’s exchanges in market value), Brazil has restored confidence in foreign investments and now offers incentives to attract such investments. Investors in Brazil (like pension funds) are now (since 2009) free to place their funds in alternative investments, and such funds now account for 22% of investments in private equity and venture capital. In general, private equity and hedge funds have posted impressive rates of return over the past 3 years owing to a business-conducive environment, low interest rates, and a reduction in foreign investment tax. Sources: This year’s hot market for private equity firms and hedge-fund managers, Feb. 27, 2011, The Economist (from the print edition). Hot market investment in Brazil, Obelisk International, March 4, 2011.

long periods of time. This alternative asset class has also benefited from the willingness of foreign governments to allow foreign financing of their domestic infrastructure projects. How do governments pay for such projects? Some ways are through user fees (a pay-as-you-go system), implicit taxation like taxes on gasoline, and/or explicit taxation such as property or income taxes and bond issuances. What are the risks and benefits of investing in infrastructure projects around the world? Some risks and costs include inability to do business in a particular country either because of corruption or political instability, high initial capital expenditures, and extensive regulation. Some benefits include a long and steady cash flow, long-duration assets, and improved portfolio diversification. Infrastructure investments resemble real estate, utilities, and fixed-income products in that they invest in long-duration projects with predictable cash flows. According to a recent study, infrastructure returns were, on average, 18.3% from 2000 to 2007, while those of public utilities were around 13.3% during the same period.16 The financial crisis of 2008 shifted the interest of equity capital and infrastructure away from developing economies like the Philippines to emerging markets like Thailand and China, where higher rates of development (growth) existed. For example, high corruption in the Philippines and poor institutional support of projects and markets contributed to a decline in the financing of infrastructure projects by foreigners, while such financing increased in other, neighboring countries in Southeast Asia.17As another example of the importance of infrastructure projects, consider the huge inroads in African nations such as Egypt, leveraging the Nile for transportation; in Sudan, leasing land for growing crops and transporting them by cargo rail; and in Uganda, modernizing and operating an important railway.18

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Other Alternative Investments Some other unusual categories of alternative investments include tangibles such as wine, art, classic cars, antiques, memorabilia, and stamps. For most of these categories certain rules apply that an investor should bear in mind. For example, the laws of demand and supply are still valid. If there is a limited quantity of the item, its price will certainly go up with increased demand. Supply will never increase; rather, it will decrease over time. Also, prices of specialty items may not decrease when the economy is in a recession. For example, the price of a rare painting by a famous painter may never decrease because of a slowdown in the economy or deflation. Third, some items take time to mature and do not appreciate fast. Take, for instance, fine wine. Fine wine appreciates in value the longer it is kept in the cellar. You should also decide where your investment would be: in the purchase and storage of fine wines or in vineyard development. For purely informational purposes, a lot (vineyard) in Bordeaux would cost you £388,000 (or US $609,160 at the GBP/USD 1.570 exchange rate).19 What about fine art? Investing in fine art takes the form of buying (bidding for) a famous item at auction, holding it for a while, and then “flipping” it for a profit as its value appreciates. But simply doing this is not the only way to invest in fine art. Dedicated fine art funds now exist, and there are investment advisers who can help you with your limited experience in this alternative investment area. Such funds are structured like private equity funds, where investors contribute to the fund (paying a 2% annual management fee and 20% performance fee) and wait to see their returns (typically after several years).20 Some risks involved in such investments are the difficulty of valuing art works, the fact that there is no government regulation of the market, that art works are relatively illiquid, and that this type of investing requires a huge upfront outlay. Do classic (vintage) cars, sports souvenirs, and stamps offer good deals to investors? Classic cars enjoyed a boom in the 1980s, crashed in the 1990s, but rebounded a bit in the 2000s. Prices of classic cars have been rising steadily over the last few years. The typical price appreciation is about 5% per year, investors say.21 But classic cars can be very expensive to keep up (proper maintenance and storage), and insurance costs can be high, which may exceed any gains in price appreciation. Rare stamps can be enjoyed in a private collection or used as alternative investments. Rare stamps have been appreciating steadily by 11% per annum over the last 40 years.22 Lately stamps have been realizing high prices for collectors (appreciation about 10% annually on average), and demand has been rising.23 In addition, private stamp collectors can travel the world exhibiting their collections and earning serious money. However, as in the case of cars, storage and insurance costs can be high, which may eclipse any gains in value. Thus the investor needs to be careful before investing in such items and must decide whether this activity is for pure enjoyment or for profit. Box 16.6 highlights some thoughts on the future of the alternative investments industry.

Box 16.6 The Future of Alternative Investments The alternative investments industry has constantly been evolving from its origins in the 1990s to the present. During the previous decade, however, the transformations were more

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drastic in that the mix of investors in alternative investments, and particularly in hedge and private equity funds, has been altered from the few wealthy partners to more institutional and other sophisticated investors. Thus these new investors will impact the industry in a profound way in the areas of transparency, control, investment strategies, and due diligence. Among the forces that can transform the industry, none are more important than transparency and liquidity. This quest has generated new product structures in hedge funds, such as managed accounts and onshore regulated products. Managers of such funds are now required to make adjustments to the new environment by reviewing and revising internal control systems and procedures. A survey by KPMG, a tax audit and advisory firm in the United States, showed that most managers and investors oppose upcoming regulation because they fear that it will make their industry less competitive and also increase costs. Despite their opposition, financial regulation and supervision, taking place globally, are on their way, and these agents must learn and adapt to deal with such changes. For example, in the United States, the so-called Volcker rule (which proposes a ban on proprietary trading by banks) is very likely to affect the alternative investments industry. In addition, very recent regulation, put forth by the Federal Deposit Insurance Corporation, sets new standards on the potential acquisition of failed banks by private equity firms. On the other side of the Atlantic, the Alternative Investment Fund Managers Directive, which requires that hedge funds and private equity funds be under the supervision of a European Union regulatory body, is on its way for implementation (after a vote by the European Parliament in November 2010). Sources: The future of alternative investments, 2010, KPMG.com. R. Coll, R. Conner, J. Hare, D. Krohn, and M. Reed, Private equity investments in financial institutions: evolving standards and regulatory guidance, Journal of Private Equity, 13(4), Fall 2010, pp. 51–57.

Finally, the box titled Applying Economic Analysis illustrates the pros and cons of investing in traditional versus alternative investments as well as in both asset classes, and the box titled Lessons of Our Times highlights the dangers and consequences of including alternative investment classes in university endowment funds as seen during the 2008 global financial crisis.

PUTTING IT ALL TOGETHER So now that you have read this textbook up to this point, are you ready to begin investing? You believe that you understand many of the concepts and strategies that have been presented and thus feel that you are ready to take that first step. Keep in mind that investing is not a get-rich-quick scheme. It requires serious effort because it is about your real money. And make sure that you “know thyself ”!24 Do you know what purpose your investments will serve? Do you want to accumulate funds to make an important purchase, for retirement, for emergency times, or simply to preserve your capital? Obviously being a young person just starting a career, you need not worry about the of these. In general the younger you are, the longer your investment horizon and the more aggressive you should be as an investor. Then ask yourself what type of person you are. Are you an enthusiast, a thrill seeker, a conservative and calm person, or do you fall somewhere in between? In other words, are you a person who likes to do some research before doing something (rather than blindly trusting a friend or an investment adviser), or do you simply jump to the first opportunity that presents itself?

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The answers you give to these questions should tell you a lot about your risk tolerance or degree of risk aversion. Keep in mind that every investor is unique and every investment (or security) does not have the same meaning for everyone. Starting investing early, you have all the time in the world to weather the ups and downs in the markets, assume more risk, sort out market contradictions or inconsistencies (like which investment strategy is better, whether to go with mutual or index funds or hire a portfolio manager, and so on). And, of course, you will learn to know yourself better in the process. Then consider the limitations (constraints) you might face in the process of investing. For example, how much money do you have available to invest? Are you single or married, and do you have kids? Are you currently making a high income, which could put you in a high income tax bracket, or is your income a moderate one? In view of your list of objectives and constraints, the next step would be to decide which investments (securities) are appropriate for you given your investment philosophy and style. We have presented a whole lot of investment instruments, traditional and alternative alike, among which you can take your pick. Then you must decide how to allocate your funds among those you have identified and in what proportions, or you might simply start picking assets that you think would give you a better risk/return outcome in forming your investment portfolio. Recall that we called these the top-down and the bottomup approaches to investing, respectively. Figure 16.5 shows examples of aggressive and conservative portfolios. Once you have settled on the approach, are you going to invest passively, say, in a mutual or index fund, or are you going to have a portfolio manager actively manage your account (in the expectation of higher return but with higher risk)? Remember that the choice of strategy depends on your view of (the degree of) market efficiency. If you are a firm believer in market efficiency, you will probably go with passive investment strategies; but if you think that markets often behave inefficiently, the active investment strategy is likely to be your choice. Keep in mind some important facts before you make your investment decisions. Stocks have historically outperformed any other asset, returning a bit over 9%, followed by Treasury bonds, which yielded just 5% (recall that we saw these figures in Chapter 3). Inflation has historically averaged about 3.5%, and this reduces your nominal returns. Choose your financial adviser very carefully and always do your homework before saying

(a) Aggressive Portfolio Cash 5%

(b) Conservative Portfolio Cash 10%

Bonds 20%

Stocks 75%

Figure 16.5 Aggressive versus conservative investment portfolios.

Bonds 45%

Stocks 45%

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yes or no to offers. Always ask around and/or read comments and advice from reputable sources like the SEC or FINRA. Do not be swayed by articles on the Internet or in the press about “successful investment strategies,” “winning tips for stock-picking,” and the like. Make sure that you remember at all times that “if it sounds too good to be true, it probably is,” “past returns are no guarantee of futures returns.” Don’t be persuaded by the idea that “because everyone is buying the asset, I should too,” You should not. If you still want to learn more, the SEC’s site http://investor.gov is an excellent source of more detailed information. Finally, once you have constructed your portfolio, you should monitor or modify it periodically to ensure that it still conforms to your goals and constraints. If you decide on passive investment strategies, you will not have to worry about them often. Still, from time to time, you should evaluate your portfolio to see if it is consistent with your objectives and constraints. By contrast, if you go with active investment strategies, you would need to monitor it much more closely and frequently, revise or rebalance it whenever necessary, evaluate it, and change your investment strategies if necessary. Thus as you see, investing is an ongoing, dynamic process that should not be taken lightly. By now you have ample knowledge about the workings of the market and its participants and should always keep a keen eye on your investments and agents. Hopefully you can both enjoy this activity and be handsomely rewarded by it!

CHAPTER SUMMARY We discussed several interesting concepts in this chapter, ranging from international interest rate parities to credit derivatives and alternative investments. Regarding the international parities, we presented the two most important ones—namely the covered interest rate parity and the uncovered interest rate parity. We also presented some simple arbitrage strategies—namely the locational triangular arbitrage as well as the carry trade strategy. Next we discussed in detail the various types of credit derivatives and their role in a globalized financial market. Specifically, we presented credit-default swaps, asset swaps, total return swaps, and collateralized debt obligations and highlighted their risks and benefits. Next, we explored the alternative investment asset class, which has grown substantially over the last decade, and emphasized the pros and cons of these assets. We presented such alternative investments as real estate investment trusts, hedge funds, private equity and venture capital infrastructure funds, as well as some other tangible alternative investments like wine, classic cars, and stamps. Finally, we dedicated a section to “putting it all together,” which serves as an overview of what you have learned thus far in investments.

APPLYING ECONOMIC ANALYSIS TRADITIONAL OR ALTERNATIVE INVESTMENTS? There are several important differences between the traditional and alternative investments asset classes. They are the following: Valuation: With traditional investments like stocks and bonds, the investor can estimate (determine) their prices, which are based on current market prices; but it may be hard to determine the market value of alternative investments.

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Investment Horizon: Traditional investments have various investment horizons (short, medium, and long term) depending on the investor’s objectives and constraints. With alternative investments the typical investment horizon is long term because of lockout periods, lack of selling opportunities, and illiquidity. Liquidity: Traditional investments can be highly or relatively illiquid, depending on the asset, whereas most alternative investments are illiquid because of the absence of market standardization and the nature of the investments (recall private equity and/or venture capital), which are long-term. Risk/Return Profile: Traditional investments have varying risk/return characteristics because they are often traded in the market, because they are liquid, and because market values can be obtained at any point in time. By contrast, alternative investments use different investment approaches, have all of the differences mentioned above, are less transparent, and are not regulated. As a result, they have different risk/return profiles. Transparency/Regulation: traditional investments are, for the most part, transparent, regulated and disclose important information, whereas alternative investments are not transparent (information and strategies are proprietary), not regulated, and are not required to publish information for the general public. In addition, traditional and alternative investments have low correlations. Finally, traditional investments are closely tied to the state of the economy and may present higher risks, but alternative investments are relatively insulated from (immune to) the economy and/or market swings. Costs: Traditional investments may cost a bit or very little (if you deal with index funds), while alternative investments can assess hefty fees upon joining the fund as well as big management fees. Diversification Potential: following the above, adding alternative investments to a traditional investment portfolio should leave expected return the same but reduce risk (point A’ from A on the graph below) or increase expected return at the same level of risk (point A’’ from A on graph). The graph shows the original and the new efficient frontier. So what is the conclusion? You guessed it! It must be you who decides which asset class or classes to invest in. Perhaps you should invest in both asset classes. But before you take any action, you must clearly understand your objectives and constraints. Efficient Frontier expected return

traditional + alternative investments A’’ A’

A traditional investments

0

risk

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INTERNATIONAL FOCUS CREDIT DEFAULT SWAPS AND THE EUROPEAN SOVEREIGN DEBT CRISIS Over the last few years, several European nations—notably Greece, Ireland, Portugal, Spain, and lately Italy and France—have sparked fears of default on their debt. As of 2010, debt-toGDP ratios for these nations ranged from about 145% for Greece to 120% for Italy, to 95% for Portugal and Ireland, and to 65% for Spain. A year later, there is further deterioration in these nations’ finances, and markets speak of imminent default by Greece. A recent article by Bloomberg suggests that there is a 98% chance (as of September 23, 2011) that Greece will default on its debts within the next 5 years. As a result, credit-default swaps rose to unprecedented levels, or about $0.60, to insure $100 of Greece’s debt. Credit default swaps on Portugal rose to new highs to 1,224 basis points or to $1.22 million per year for 5 years’ worth of protection on $10 million in bonds for a buyer of such protection. Similar jumps in these derivatives occurred for Italy and France, according to the CME. Specifically, for Italy they were to 510 basis points (recall that 1 basis point is 1/100 of 1%) and for France at 197 basis points. Thus, sellers of Italian and French CDS would demand $510,000 and $197,000 per year, respectively, to insure $10 million in bonds. A basis point on a credit-default swap protecting !10 million of debt from default for 5 years is equivalent to !1,000 a year. Swaps pay the buyer face value in exchange for the underlying securities or the cash equivalent should a borrower fail to adhere to its debt agreements. Markit, the London-based financial data provider on CDS, estimates that just over $5 billion is tied up in such contracts, which will pay out of Greece defaults with a gross exposure of about $79 billion, along with other guarantees tied to Greece, according to the Bank of International Settlements. What would be the impact of a possible default in Europe on US financial markets? According to Ben Bernanke, it would be severe, because it would affect the global financial markets via increases in credit spreads and reduced stock prices. The general fear is that a default by a Eurozone member would spark a breakup of the euro and shake up the global financial markets (contagion). Also, a Greek default would mean drastic reductions in lending by banks, which hold a large chunk of that debt, and reduction in asset values for pension and mutual funds, which also hold some of that debt. The beneficiaries would be the holders of CDS, but even they may be in a situation where they may not collect. This means that CDS are tied to specific types of defaults, and the recent talk of “partial debt restructuring” on the Greek debt may not qualify as default, as in the case of the deterioration of a reference entity’s creditworthiness. Sources: A. Moses, Greece has 98% chance of default on Euro-region sovereign woes, Bloomberg, Sept. 23, 2011; M. Farrell, Europe default risk signal flashing red, CNNMoney, Sept. 16, 2011; L. Story, Derivatives cloud the possible fallout from a Greek default, New York Times, June 22, 2011.

LESSONS OF OUR TIMES UNIVERSITY ENDOWMENTS AND ALTERNATIVE INVESTMENTS Traditionally, university endowments invested in transparent, liquid, and relatively safe instruments such as bonds, money market instruments, and publicly traded equities. Over the past 20 years or so, however, endowment funds have embraced a new paradigm of investing, modeled on those of Harvard and Yale universities, whose portfolios have included illiquid and

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riskier asset classes. For example, such new investment instruments, the alternative investments, comprise private equity and venture capital, hedge funds, and other tangible assets like oil, gas, and timber. By employing speculative trading tactics via derivatives and leverage and taking on higher risk, endowment funds not only declined in value and returns but also magnified certain types of risks in the global financial market. Since alternative investments are, for the most part, illiquid, some university endowment managers were forced to sell into declining markets to get rid of these investments; thus added to market volatility. Yale’s endowment fell the most, by 24.6% during the 2008 financial crisis and Harvard’s endowment portfolio declined by 20%, while Boston University’s and Brandeis University’s funds fell by 22% and Dartmouth’s by 23%. Many critics of endowments’ aggressive adoption of alternative investments have argued that such funds fell “victim” of Wall Street’s charm and that this seriously undermined endowment stewardship. Such investments were expected to generate enviable long-term returns despite their exposure to high risk. In fact, over the long term, they have managed to deliver significant wealth to their respective institutions. But when the crisis hit, they were all seriously affected. Now many universities—like the University of Virginia, Harvard, and Duke University—are trying to dump stakes in their private equity holdings and venture capital. Diversifying beyond traditional investments is still desirable but not a panacea for investors of high net worth, especially endowment funds. Even if these funds were managed by the brightest managers in the country, returns during times of crisis will be less and the risks higher. Thus the new endowment model of investing has failed to manage volatility and deliver good returns during all times to its owners. Sources: Christopher Holt, University endowments share blame for financial crisis, seekingalpha.com, June 9, 2010. Educational Endowments and the Financial Crisis: Social Costs and Systemic Risks in the Shadow Banking System, Center for Social Philanthropy, Tellus Institute, Mass., 2010, http://www.tellus.org/publications/files/endowmentcrisis.pdf. Some university endowments tied to alternative investments suffering, Philanthropy News Digest, foundationcenter.org, Dec. 1, 2008.

KEY CONCEPTS Interest rate parity is an arbitrage condition stating that the future dollar proceeds from investing in two equivalent (and risk-free) investments must be the same. Covered interest rate parity requires that any discrepancies between the expected exchange rate and the spot rate in the next period be hedged (i.e., covered) by a forward contract. Uncovered interest rate parity requires that interest rate differentials be offset by an expected depreciation/appreciation of the currency. Carry trade is a roundtrip transaction whereby an investor buys a currency with a low interest rate and sells (exchanges) it for a currency with a high interest rate, thus profiting on the spread. International arbitrage ensures that foreign exchange market prices are aligned. Locational arbitrage is simply the exploitation of spot price discrepancies on an exchange rate at two different locations.

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Triangular arbitrage opportunities emerge when the cross-rate quote of two currencies does not match the two currencies’ corresponding exchange rates. Credit derivatives are financial instruments designed to shift and/or manage credit risk among participants such as financial institutions, firms, and other investors. A credit default swap is a bilateral contractual agreement (financial contract) to transfer the default risk of one (or more) reference entities from the protection buyer to the protection seller. The premium for a credit default swap is commonly known as a CDS spread. A total return swap is an agreement between two parties to transfer the total return from a financial asset or reference obligation from the total return payer to the total return receiver. An asset swap is a combination of an interest rate swap and a bond (or a note). A collateralized debt obligation is a security backed by one or more types of debt obligations such as bank loans, corporate or sovereign bonds, and mortgage-backed securities. Synthetic collateralized debt obligations (CDOs) comprise baskets of derivatives rather than actual debt and are backed by a pool of credit default swaps. An alternative investment is one that has different risk/return characteristics from a traditional investment like a stock or a bond. Due diligence means doing background research before entering a transaction. Private equity firms are privately held companies (partnerships) that primarily make specific investments in other, usually troubled companies. A venture capital company is a specialized type of a private equity firm that buys stakes in start-up companies that are in need of financing. Infrastructure comprises an amalgamation of assets in various sectors such as toll roads and bridges, air- and seaports, power distribution, dams, and so on.

QUESTIONS AND PROBLEMS 1. What is the difference between a covered and an uncovered interest parity? 2. What is carry trade and what are the risks of such an investment strategy? 3. Assume that the euro/US dollar exchange rate is currently $1.40 and the British pound/US dollar exchange rate is $1.55. a. What is the cross-exchange rate? b. If you find the cross-exchange rate to be 1.109, can you make profits by applying triangular arbitrage? Show your calculations. Assume that you invest $10,000. 4. What are credit default swaps and what are their benefits? 5. Assume that you purchase a $100 million 7.65% par value 5-year bond of a BBBrated company and simultaneously enter into a 5-year interest-rate swap with

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your bank. You agree to make fixed semiannual payments. If the swap rate is 7%, what is your benefit for entering the swap? 6. We read lately in the financial press that some mining companies will begin paying dividends in gold or silver and not cash. Some companies exchanged US dollars into metal in order to mint 1 troy ounce of gold and silver coins. Besides, some hedge funds have already allowed investors to denominate holdings in gold and exchange-traded funds backed by physical gold. Although investors like the idea of receiving gold coins as dividends instead of cash (like dollars or euros), some critics say that this is a dangerous trend. a. Do you think that metal is now becoming an alternative investment vehicle? b. Why do critics raise concerns about this practice? Hint: Think of the answer in terms of the demand for currencies like the US dollar and the euro. c. Can you think of any logistical problems that might arise in paying dividends in gold rather than in currency? 7. In the United States and many economies around the world, highways, bridges, schools, and hospitals, to name a few, are in bad shape and in need to urgent, significant repairs. How will governments be able to pay for such infrastructure repairs and/or improvements? What are some of the potential risks for infrastructure service providers? 8. Suppose a friend of yours who is already in the investments area approached you and suggested that you invest in cultivable land in other parts of the world. Do you think this would be a good idea as an alternative investment? Hint: Think of the answer in terms of population growth. 9. In 1997, the first weather derivative was created in the United States. Weather derivatives are simply financial instruments used to control unanticipated (adverse) weather conditions (such as hurricanes, unusual temperatures, and severe snowfalls). One problem with such financial products is that they are difficult to price because the underlying asset, the weather, is intangible and nontradable. Now answer the questions below. (For more details on weather derivatives, you may visit CME Group’s website, www.cmegroup.org.) a. Who would buy a weather derivative and why? b. How can an investor benefit from such instruments? c. How important is an accurate weather forecast?25 10. REITs are listed and traded on exchanges and also nontraded. What could be some of the risks of investing in nontraded REITs? 11. Why would it not be a bad idea to start thinking about starting your own microbrewery (to brew your own beer and sell it for profit) when you have other traditional investments? Hint: Think of the relationship between traditional and alternative investments.

NOTES 1. 2. 3.

Daniel L. Thornton, Tests of covered interest rate parity, Federal Reserve Bank of St. Louis, July/August 1989. James R. Lothian and Liuren Wu, Uncovered interest rate parity over the past two centuries, Journal of International Money and Finance, 30(2), April 2011, pp. 448–473. B. Protess, Banks increase their holdings in derivatives, New York Times, Sept. 23, 2011.

550 s Derivative Markets and Instruments 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

18. 19. 20. 21. 22. 23. 24.

25.

International Monetary Fund, Global Stability Report, 2006. D. Mengle, Credit derivatives: an overview, Federal Reserve Bank of Atlanta Economic Review, fourth quarter 2007, p. 17. H. Sender, Greenlight founder calls for CDS ban, Financial Times, Nov. 9, 2007. P. Davies, Synthetic CDO equity investments, July 31, 2006, FT.com SEC report cites flaws at credit rating agencies, Yahoo!Finance, Oct. 2, 2011. The REIT Story, REIT.com, Feb. 2011. Jeffery R. Kosnett, Growing risk in REITs, March 5, 2010, Kiplinger.com Terry Pristin, A closer, and skeptical, look at nontraded REITS, New York Times, July 19, 2011. F. Goltz and D. Schroeder, Hedge fund transparency: where do we stand? Journal of Alternative Investments, 12(4), Spring 2010, pp. 20–37. S. Bond and L. Johnson, Alternative asset pricing: momentum and the hedge fund puzzle, Journal of Alternative Investments, 13(1), Summer 2010, pp. 55–71. B. Protess, Think globally, deal locally, New York Times, Sept. 28, 2011. Ibid. Alternative Investments in Perspective, RREEF Research, A Member of the Deutsche Bank Group, September 2007. Rommel C. Gavieta, The global financial crisis, vulture funds, and Chinese official development assistance: impact on Philippine infrastructure development, Journal of Structured Finance, 16(2), Summer 2010, pp. 62–76. M. Kassem and A. Shahine, Leveraging the Nile, Bloomberg Markets, December. 2010, pp. 112–118. C. A. Taylor and M. King, Investing in a vineyard? Beware grapes of wrath, The Guardian, April 23, 2011. Christine Senior, The art of alternative investment, October 2010, FTMandate.com Elan Weisz, Driving a tough bargain in the vintage car market, Oct. 20, 2010, CNBC.com Jack Shamash, Stamps do not always deliver top investment returns, August 6, 2010, Guardian.co.uk Barbara Kollmeyer, From stamps to betting on life spans, June 18, 2009. Marketwatch.com The “know thyself ” maxim comes from ancient Greek, meaning “know yourself,” or do not think that you know everything or are better than others. It was inscribed on the entrance of the Apollo Temple in Delphi, Greece. Sean D. Campbell and Francis X. Diebold, Weather forecasting for weather derivatives, Journal of the American Statistical Association, 100(469), March 2005, pp. 6–16.

APPENDIX

551

1%

0.990 0.980 0.971 0.961 0.951 0.942 0.933 0.923 0.914 0.905 0.896 0.887 0.879 0.870 0.861 0.853 0.844 0.836 0.828 0.820 0.780 0.742 0.706 0.672 0.608

Period

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 50

0.980 0.961 0.942 0.924 0.906 0.888 0.871 0.853 0.837 0.820 0.804 0.788 0.773 0.758 0.743 0.728 0.714 0.700 0.686 0.673 0.610 0.552 0.500 0.453 0.372

2%

0.971 0.943 0.915 0.888 0.863 0.837 0.813 0.789 0.766 0.744 0.722 0.701 0.681 0.661 0.642 0.623 0.605 0.587 0.570 0.554 0.478 0.412 0.355 0.307 0.228

3% 0.962 0.925 0.889 0.855 0.822 0.790 0.760 0.731 0.703 0.676 0.650 0.625 0.601 0.577 0.555 0.534 0.513 0.494 0.475 0.456 0.375 0.308 0.253 0.208 0.141

4% 0.952 0.907 0.864 0.823 0.784 0.746 0.711 0.677 0.645 0.614 0.585 0.557 0.530 0.505 0.481 0.458 0.436 0.416 0.396 0.377 0.295 0.231 0.181 0.142 0.087

5% 0.943 0.890 0.840 0.792 0.747 0.705 0.665 0.627 0.592 0.558 0.527 0.497 0.469 0.442 0.417 0.394 0.371 0.350 0.331 0.312 0.233 0.174 0.130 0.097 0.054

6% 0.935 0.873 0.816 0.763 0.713 0.666 0.623 0.582 0.544 0.508 0.475 0.444 0.415 0.388 0.362 0.339 0.317 0.296 0.277 0.258 0.184 0.131 0.094 0.067 0.034

7%

Present Value Interest Factor of $1 (lump sum) per Period at i% for n Periods, PVIF(i,n)

0.926 0.857 0.794 0.735 0.681 0.630 0.583 0.540 0.500 0.463 0.429 0.397 0.368 0.340 0.315 0.292 0.270 0.250 0.232 0.215 0.146 0.099 0.068 0.046 0.021

8% 0.917 0.842 0.772 0.708 0.650 0.596 0.547 0.502 0.460 0.422 0.388 0.356 0.326 0.299 0.275 0.252 0.231 0.212 0.194 0.178 0.116 0.075 0.049 0.032 0.013

9% 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467 0.424 0.386 0.350 0.319 0.290 0.263 0.239 0.218 0.198 0.180 0.164 0.149 0.092 0.057 0.036 0.022 0.009

10% 0.901 0.812 0.731 0.659 0.593 0.535 0.482 0.434 0.391 0.352 0.317 0.286 0.258 0.232 0.209 0.188 0.170 0.153 0.138 0.124 0.074 0.044 0.026 0.015 0.005

11% 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322 0.287 0.257 0.229 0.205 0.183 0.163 0.146 0.130 0.116 0.104 0.059 0.033 0.019 0.011 0.003

12% 0.885 0.783 0.693 0.613 0.543 0.480 0.425 0.376 0.333 0.295 0.261 0.231 0.204 0.181 0.160 0.141 0.125 0.111 0.098 0.087 0.047 0.026 0.014 0.008 0.002

13%

0.877 0.769 0.675 0.592 0.519 0.456 0.400 0.351 0.308 0.270 0.237 0.208 0.182 0.160 0.140 0.123 0.108 0.095 0.083 0.073 0.038 0.020 0.010 0.005 0.001

14%

0.870 0.756 0.658 0.572 0.497 0.432 0.376 0.327 0.284 0.247 0.215 0.187 0.163 0.141 0.123 0.107 0.093 0.081 0.070 0.061 0.030 0.015 0.008 0.004 0.001

15%

1%

0.990 1.970 2.941 3.902 4.853 5.795 6.728 7.652 8.566 9.471 10.368 11.255 12.134 13.004 13.865 14.718 15.562 16.398 17.226 18.046 22.023 25.808 29.409 32.835 39.196

Period

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 50

0.980 1.942 2.884 3.808 4.713 5.601 6.472 7.325 8.162 8.983 9.787 10.575 11.348 12.106 12.849 13.578 14.292 14.992 15.678 16.351 19.523 22.396 24.999 27.355 31.424

2%

0.971 1.913 2.829 3.717 4.580 5.417 6.230 7.020 7.786 8.530 9.253 9.954 10.635 11.296 11.938 12.561 13.166 13.754 14.324 14.877 17.413 19.600 21.487 23.115 25.730

3% 0.962 1.886 2.775 3.630 4.452 5.242 6.002 6.733 7.435 8.111 8.760 9.385 9.986 10.563 11.118 11.652 12.166 12.659 13.134 13.590 15.622 17.292 18.665 19.793 21.482

4% 0.952 1.859 2.723 3.546 4.329 5.076 5.786 6.463 7.108 7.722 8.306 8.863 9.394 9.899 10.380 10.838 11.274 11.690 12.085 12.462 14.094 15.372 16.374 17.159 18.256

5% 0.943 1.833 2.673 3.465 4.212 4.917 5.582 6.210 6.802 7.360 7.887 8.384 8.853 9.295 9.712 10.106 10.477 10.828 11.158 11.470 12.783 13.765 14.498 15.046 15.762

6% 0.935 1.808 2.624 3.387 4.100 4.767 5.389 5.971 6.515 7.024 7.499 7.943 8.358 8.745 9.108 9.447 9.763 10.059 10.336 10.594 11.654 12.409 12.948 13.332 13.801

7%

Present Value Interest Factor of an (ordinary) Annuity of $1 per Period at i% for n Periods, PVIFA(i,n)

0.926 1.783 2.577 3.312 3.993 4.623 5.206 5.747 6.247 6.710 7.139 7.536 7.904 8.244 8.559 8.851 9.122 9.372 9.604 9.818 10.675 11.258 11.655 11.925 12.233

8% 0.917 1.759 2.531 3.240 3.890 4.486 5.033 5.535 5.995 6.418 6.805 7.161 7.487 7.786 8.061 8.313 8.544 8.756 8.950 9.129 9.823 10.274 10.567 10.757 10.962

9% 0.909 1.736 2.487 3.170 3.791 4.355 4.868 5.335 5.759 6.145 6.495 6.814 7.103 7.367 7.606 7.824 8.022 8.201 8.365 8.514 9.077 9.427 9.644 9.779 9.915

10% 0.901 1.713 2.444 3.102 3.696 4.231 4.712 5.146 5.537 5.889 6.207 6.492 6.750 6.982 7.191 7.379 7.549 7.702 7.839 7.963 8.422 8.694 8.855 8.951 9.042

11% 0.893 1.690 2.402 3.037 3.605 4.111 4.564 4.968 5.328 5.650 5.938 6.194 6.424 6.628 6.811 6.974 7.120 7.250 7.366 7.469 7.843 8.055 8.176 8.244 8.304

12% 0.885 1.668 2.361 2.974 3.517 3.998 4.423 4.799 5.132 5.426 5.687 5.918 6.122 6.302 6.462 6.604 6.729 6.840 6.938 7.025 7.330 7.496 7.586 7.634 7.675

13%

0.877 1.647 2.322 2.914 3.433 3.889 4.288 4.639 4.946 5.216 5.453 5.660 5.842 6.002 6.142 6.265 6.373 6.467 6.550 6.623 6.873 7.003 7.070 7.105 7.133

14%

0.870 1.626 2.283 2.855 3.352 3.784 4.160 4.487 4.772 5.019 5.234 5.421 5.583 5.724 5.847 5.954 6.047 6.128 6.198 6.259 6.464 6.566 6.617 6.642 6.661

15%

1%

1.010 1.020 1.030 1.041 1.051 1.062 1.072 1.083 1.094 1.105 1.116 1.127 1.138 1.149 1.161 1.173 1.184 1.196 1.208 1.220 1.282 1.348 1.417 1.489 1.645

Period

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 50

1.020 1.040 1.061 1.082 1.104 1.126 1.149 1.172 1.195 1.219 1.243 1.268 1.294 1.319 1.346 1.373 1.400 1.428 1.457 1.486 1.641 1.811 2.000 2.208 2.692

2%

1.030 1.061 1.093 1.126 1.159 1.194 1.230 1.267 1.305 1.344 1.384 1.426 1.469 1.513 1.558 1.605 1.653 1.702 1.754 1.806 2.094 2.427 2.814 3.262 4.384

3%

1.040 1.082 1.125 1.170 1.217 1.265 1.316 1.369 1.423 1.480 1.539 1.601 1.665 1.732 1.801 1.873 1.948 2.026 2.107 2.191 2.666 3.243 3.946 4.801 7.107

4% 1.050 1.103 1.158 1.216 1.276 1.340 1.407 1.477 1.551 1.629 1.710 1.796 1.886 1.980 2.079 2.183 2.292 2.407 2.527 2.653 3.386 4.322 5.516 7.040 11.467

5% 1.060 1.124 1.191 1.262 1.338 1.419 1.504 1.594 1.689 1.791 1.898 2.012 2.133 2.261 2.397 2.540 2.693 2.854 3.026 3.207 4.292 5.743 7.686 10.286 18.420

6%

Future Value Interest Factor of $1 per Period at i% for n Periods, FVIF(i,n)

1.070 1.145 1.225 1.311 1.403 1.501 1.606 1.718 1.838 1.967 2.105 2.252 2.410 2.579 2.759 2.952 3.159 3.380 3.617 3.870 5.427 7.612 10.677 14.974 29.457

7% 1.080 1.166 1.260 1.360 1.469 1.587 1.714 1.851 1.999 2.159 2.332 2.518 2.720 2.937 3.172 3.426 3.700 3.996 4.316 4.661 6.848 10.063 14.785 21.725 46.902

8% 1.090 1.188 1.295 1.412 1.539 1.677 1.828 1.993 2.172 2.367 2.580 2.813 3.066 3.342 3.642 3.970 4.328 4.717 5.142 5.604 8.623 13.268 20.414 31.409 74.358

9% 1.100 1.210 1.331 1.464 1.611 1.772 1.949 2.144 2.358 2.594 2.853 3.138 3.452 3.797 4.177 4.595 5.054 5.560 6.116 6.727 10.835 17.449 28.102 45.259 117.391

10% 1.110 1.232 1.368 1.518 1.685 1.870 2.076 2.305 2.558 2.839 3.152 3.498 3.883 4.310 4.785 5.311 5.895 6.544 7.263 8.062 13.585 22.892 38.575 65.001 184.565

11% 1.120 1.254 1.405 1.574 1.762 1.974 2.211 2.476 2.773 3.106 3.479 3.896 4.363 4.887 5.474 6.130 6.866 7.690 8.613 9.646 17.000 29.960 52.800 93.051 289.002

12% 1.130 1.277 1.443 1.630 1.842 2.082 2.353 2.658 3.004 3.395 3.836 4.335 4.898 5.535 6.254 7.067 7.986 9.024 10.197 11.523 21.231 39.116 72.069 132.782 450.736

13% 1.140 1.300 1.482 1.689 1.925 2.195 2.502 2.853 3.252 3.707 4.226 4.818 5.492 6.261 7.138 8.137 9.276 10.575 12.056 13.743 26.462 50.950 98.100 188.884 700.233

14%

1.150 1.323 1.521 1.749 2.011 2.313 2.660 3.059 3.518 4.046 4.652 5.350 6.153 7.076 8.137 9.358 10.761 12.375 14.232 16.367 32.919 66.212 133.176 267.864 1,083.657

15%

1%

1.000 2.010 3.030 4.060 5.101 6.152 7.214 8.286 9.369 10.462 11.567 12.683 13.809 14.947 16.097 17.258 18.430 19.615 20.811 22.019 28.243 34.785 41.660 48.886 64.463

Period

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 50

3%

4%

5%

6%

7%

1.000 1.000 1.000 1.000 1.000 1.000 2.020 2.030 2.040 2.050 2.060 2.070 3.060 3.091 3.122 3.153 3.184 3.215 4.122 4.184 4.246 4.310 4.375 4.440 5.204 5.309 5.416 5.526 5.637 5.751 6.308 6.468 6.633 6.802 6.975 7.153 7.434 7.662 7.898 8.142 8.394 8.654 8.583 8.892 9.214 9.549 9.897 10.260 9.755 10.159 10.583 11.027 11.491 11.978 10.950 11.464 12.006 12.578 13.181 13.816 12.169 12.808 13.486 14.207 14.972 15.784 13.412 14.192 15.026 15.917 16.870 17.888 14.680 15.618 16.627 17.713 18.882 20.141 15.974 17.086 18.292 19.599 21.015 22.550 17.293 18.599 20.024 21.579 23.276 25.129 18.639 20.157 21.825 23.657 25.673 27.888 20.012 21.762 23.698 25.840 28.213 30.840 21.412 23.414 25.645 28.132 30.906 33.999 22.841 25.117 27.671 30.539 33.760 37.379 24.297 26.870 29.778 33.066 36.786 40.995 32.030 36.459 41.646 47.727 54.865 63.249 40.568 47.575 56.085 66.439 79.058 94.461 49.994 60.462 73.652 90.320 111.43 138.24 60.402 75.401 95.026 120.80 154.76 199.64 84.579 112.80 152.67 209.35 290.34 406.53

2% 1.000 2.080 3.246 4.506 5.867 7.336 8.923 10.637 12.488 14.487 16.645 18.977 21.495 24.215 27.152 30.324 33.750 37.450 41.446 45.762 73.106 113.28 172.32 259.06 573.77

8%

Future Value Interest Factor of an Ordinary Annuity of $1 per Period at i% for n Periods, FVIFA(i,n) 10%

11%

12%

13%

14%

15%

1.000 1.000 1.000 1.000 1.000 1.000 1.000 2.090 2.100 2.110 2.120 2.130 2.140 2.150 3.278 3.310 3.342 3.374 3.407 3.440 3.473 4.573 4.641 4.710 4.779 4.850 4.921 4.993 5.985 6.105 6.228 6.353 6.480 6.610 6.742 7.523 7.716 7.913 8.115 8.323 8.536 8.754 9.200 9.487 9.783 10.089 10.405 10.730 11.067 11.028 11.436 11.859 12.300 12.757 13.233 13.727 13.021 13.579 14.164 14.776 15.416 16.085 16.786 15.193 15.937 16.722 17.549 18.420 19.337 20.304 17.560 18.531 19.561 20.655 21.814 23.045 24.349 20.141 21.384 22.713 24.133 25.650 27.271 29.002 22.953 24.523 26.212 28.029 29.985 32.089 34.352 26.019 27.975 30.095 32.393 34.883 37.581 40.505 29.361 31.772 34.405 37.280 40.417 43.842 47.580 33.003 35.950 39.190 42.753 46.672 50.980 55.717 36.974 40.545 44.501 48.884 53.739 59.118 65.075 41.301 45.599 50.396 55.750 61.725 68.394 75.836 46.018 51.159 56.939 63.440 70.749 78.969 88.212 51.160 57.275 64.203 72.052 80.947 91.025 102.44 84.701 98.347 114.41 133.33 155.62 181.87 212.79 136.31 164.49 199.02 241.33 293.20 356.79 434.75 215.71 271.02 341.59 431.66 546.68 693.57 881.17 337.88 442.59 581.83 767.09 1,013.7 1,342.0 1,779.1 815.08 1,163.9 1,668.8 2,400.0 3,459.5 4,994.5 7,217.7

9%

INDEX

AAL see asset allocation line ABCP see asset-backed commercial paper abnormal return 238, 277, 335 ABS see asset-backed security ABX see asset-backed index accounting profit 354 active investment strategies 37–9, 52, 197; for bond portfolio management 428–35, 445; bond swap strategies 429–32, 445; contingent immunization 435; credit analysis 429, 445; economic analysis 442–3; EMH implications 269–71; for equity portfolio management 308–10, 329; horizon analysis 433–4, 446; horizon-matching technique 427–8, 434, 446; individual investors 308–9; institutional investors 309–10; interest rate-anticipation strategy 428, 445; risk levels 434; substitution swap strategy 430–1; valuation analysis 429, 445; yield curve strategies 432–3, 446; yield swap strategy 431–2, 446 Adoboli, Kweku 485 ADRs see American Depository Receipts adverse selection 14, 24 after-tax returns 132 age 9–10, 24 agency bonds 133–4, 378 aggressive investors 34, 52 aggressive portfolio 543

AIG see American International Group AIMA see Alternative Investment Management Association Aker, George 14 Alcoa 96, 303, 306, 342 Allianz Capital Appreciation Fund 166 allocation 261; Buffet lessons 51; effect 438; hedging 482; qualitative asset 193; quantitative asset 193; see also asset allocation; capital allocation line allocationally efficient market 261 alpha-beta debate 250 alphabet soup 535–6 alpha coefficient 169 alpha of stock 245, 250, 251 Alternative Investment Management Association (AIMA) 536, 538 alternative investments 1, 170; classes 536; classic cars 541; defined 536, 548; economic analysis 544–5; fine art 541; future of 541–2; hedge funds 538–40; infrastructure 539–40, 548; long-short 537; market-neutral 537; private equity 539–40, 548; rare stamps 541; REIT 537–8; tangibles 541; university endowments 546–7; wine 541 AM see arithmetic mean American Bond Assurance Association (AMBAC) 385 557

558 s Index American Depository Receipts (ADRs) 105, 111 American International Group (AIG) 22, 531 American option 453 American Stock Exchange (AMEX) 45, 90; bonds trade 382; NASDAQ merger 93; as options exchange 456; trading structure 93 Ando, Albert 71 animal spirits 282, 288 announcement effects 276–8 annualize 58 annual percentage rate (APR) 60–1, 76 annual percentage yield (APY) 61 appreciation 137, 166, 525 APR see annual percentage rate APT see arbitrage pricing theory APY see annual percentage yield arbitrage 240–1, 251; economic analysis 518; index 308, 329, 516–17, 521; international 527, 547; locational 527, 547; regulatory 520; risk 517; trading 517; triangular 528, 548 arbitrage pricing theory (APT) 183; assumptions 242; CAPM compared to 243–4; EMH implications 271–2; investment decisions and 246–7; opportunities 241–2; overview 240; risk factors 242–3; summary 247 arbitrageur 492, 517, 520 Arca system 92, 458 Archilochus 32 Aristotle 497 arithmetic average rate of return 436 arithmetic mean (AM) 59–60, 76 Arthur Anderson accounting firm 16 ask price 46 assets 4–5; Buffet allocation lessons 51; Command Asset Programs 100; consumption 507; depreciating 470; derivative 137, 145; financial 4–5, 23; investment 4, 56, 263, 280, 340, 507; investment companies 158; liquid 11; real 4–5; risk-free 28, 52; single asset risk 64–8; toxic 418; underlying asset price 470; universe of publicly traded 233; see also capital asset pricing model; financial assets; investment environment; net asset value asset allocation 29, 214, 418; AAL 203; academics and 195; approaches 195–7; CAL 202–4, 214; CAL borrowing and lending opportunities

204–7; CML 206–7, 214; defined 193; examples 197–211; funds 163; global decisions 212–13; implementing 197; introduction 185, 192; in investment process 28–30, 52; practical problems 201–2; process 193–5; qualitative 193; quantitative 193; risk aversion and 207–9; SAA 194, 197, 214; summary 211; TAA 194, 197, 214 asset allocation line (AAL) 203 asset-backed commercial paper (ABCP) 535 asset-backed index (ABX) 535 asset-backed security (ABS) 134, 379, 535 asset/liability management 195, 214 asset management accounts 100 asset-only approach 195, 214 asset swap 533–4, 548 ASX see Australian Securities Exchange asymmetric information 14–15, 24 at the money 454, 486 attribution return 246 auction 90; markets 46, 53; TIPS 381 Australian Securities and Investment Commission 501 Australian Securities Exchange (ASX) 503 automatic trading mechanisms 102–4 BA see bankers’ acceptance Bachelier, Louis 281 back-end load 164 backwardation 507, 521 balanced funds 163 Baldwin, E. J. 42–3 banks 85; banking 18; capital and liquidity 109; central 288–9; discount method 119; EXIM 134; see also investment banker; investment banking; specific banks bankers’ acceptance (BA) 118, 122–3, 144 Bank of America 91, 530 Bank of International Settlements (BIS) 99, 374, 529 Bankruptcy Reform Act of 1978 134 barbell strategy 433 Barclays Capital 91, 530 bargain hunting 263 Basel Committee 87, 109, 529 basis point 396

Index s 559 basis risk 507–8, 521 basket CDS 531 Basu, Sanjoy 276 BBA see British Bankers Association bearer bonds 282 bearish trend 268 bear put 467 beat the market 287 beauty contest 282, 288 “Beginner’s Guide to Asset Allocation, Diversification, and Rebalancing” 29 behavioral finance 35, 52; argument 282, 291; behavior biases 283–5; human behavior models 285–6; implications for technical analysis 286–7; information processing biases 283; irrational decisions 284; overview 280–3; summary 288 behavior biases 283–5 benchmark error 438 benchmark portfolio 437–8 Berkshire Hathaway Inc. 32, 51, 302, 336 Bernanke, Ben 289, 546 Bernoulli, Daniel 73 best efforts 152, 178 best-fit alpha 169 beta coefficient 66, 235, 250, 251 BEY see bond-equivalent yield bid-ask price 93, 102 bid price 46, 93, 110, 377 binomial option pricing 472–5 BIS see Bank of International Settlements BlackRock 50 Black-Scholes-Merton valuation approach: advantages 474–5; controversy 475; formula 475–7; hedging uses 479–81; volatility and 477–8 Blake, Christopher 441 block houses 92 blocks 92, 110, 157, 172, 464 blue chip stocks 95 BM&F see Brazilian Mercantile and Futures Exchange Bogle, John 29, 32, 38, 177, 279, 310 bonds 162; agency 133–4, 378; AMBAC 385; AMEX trade 382; bearer 282; BEY 394; Brady 383; Bulldog 98, 130, 382; callable

395; catastrophe 384; collateralized bond obligation 534; convexity 399–401, 411; corporate 134–5, 382; default risk 384–5; defined 376, 410; determinants and covenants 385; domestic bonds 98; duration 395–9, 411; economic analysis 408; Eurobonds 98–9, 382, 410; exchange 92; exchangeable 384, 410; features 376, 383–4; floating-rate 384, 410; foreign 98, 130, 382; general obligation 132; global 382; global market 374–5; government 131–2, 376–8; government-related 378–82; indexing strategies 421–3, 445; introduction 373–4; inverse relationship between prices and yields 388–93; junk 385–6, 411, 419; Kangaroo or Matilda 98, 382; long-term 376; Matador 382; MBIA 385; medium-term 376; NYSE trade 382; perpetuities 397; pricing 386–95; ratings 134–5; reinvestment risk 408; revenue 132; Samurai 98, 130, 382; secured 134, 376; sovereign 383, 410; summary 407–8; types and characteristics 376–86; unsecured 376; valuation formulas 386–8; Yankee 98, 130, 382; yield curve 400–7, 411; yield measures 393–5; zero-coupon 131, 376, 382, 397 Bond, S. 538–9 bond-equivalent yield (BEY) 394 bond ETF 439–40 bond indexing strategies 421–3, 445 bond market: efficiency 441; index 421–2; international 98–9, 374–5; Japanese 374; U.S. 97–8, 375 bond portfolio management: active investment strategies 428–35, 445; bond market efficiency and 441; buy-and-hold strategy 421, 445; duration 398; in EMU 443–4; introduction 415–16; investor objectives and constraints 416–17; IPS 417–19, 445; laddered bond portfolio 421; overview of process 416–20; passive investment strategies for 420–8, 445; performance measurement and evaluation 420, 435–41, 446; strategy selection 419–20; summary 441–2 bond swap strategies 429–32, 445 book building 153, 178 book-to-market effect 278 book value 227–338, 337, 365

560 s Index book value of equity per share (BVPS) 298 borrowers 86, 204–7 Boston Stock Exchange 93 bottom-up investment strategy 35–6, 49, 52, 141–2 bounded rationality 282 BOVESPA 540 Brady, Nicholas 383 Brady bonds 383 Brazilian Mercantile and Futures Exchange (BM&F) 97 breakeven point 462 Brennan, Michael J. 43 Brinson, Gary 12, 194 British Bankers Association (BBA) 529 Brock, W. 278 brokerages 12, 90; services 99–100; Vanguard Brokerage Services 99, 164–7 brokered market 45–6, 53 brokers 12, 42, 90, 99–100, 110 broker’s call rate 42 bubbles 274–6, 288–9, 365 budget deficit 313 Buffett, Warren 32–3, 51, 272, 281, 302; buying and selling stocks 364; equity valuation and 336–7 bull call 467 Bulldog bonds 98, 130, 382 bullet strategy 433 bullish trend 268, 483 bundling 100, 110 bunds 383 Burmeister, Edwin 246 business cycle 318–22, 326–8, 330 business risk 70 butterfly shift 432 buy-and-hold strategy 38, 52, 304–5, 335–6; in bond portfolio management 421, 445 BVPS see book value of equity per share CAIA see Chartered Alternative Investment Analyst CAL see capital allocation line callable bond 395 call date 395

call options 6, 24, 137, 353, 383, 410; as basic concept 452–3; defined 486; formula 480 call price 395 capital allocation line (CAL) 202–4, 214, 232, 248; borrowing and lending opportunities 204–7; defined 250; Markowitz diversification approach and 227–30 capital appreciation 137 capital asset pricing model (CAPM) 183, 334, 346; alpha-beta debate 250; APT compared to 243–4; assumptions 233–6, 246; criticism 239; defined 251; deriving 236–9; EMH implications 271–2; financial crisis of 2008 and 240; investment decisions and 246–7; overview 232–3; summary 247; uses 239 capital charge 354 capital gain 56–7, 61, 74 capitalized sample 306 capital loss 56–7 capital market line (CML) 206–7, 214, 233 capital markets 18, 76; agency bonds 133–4, 378; characteristics 129–31; corporate bonds 134–5, 145; defined 144; derivative securities 6, 24, 137–8, 451, 485–6; equity securities 136–7; fixed-income securities 131–5, 144; government bonds 131–2, 376–8; introduction 115–16; investment strategies 141–2; munis 132–3, 144; summary 142; yields and spreads 135–6; see also money markets CAPM see capital asset pricing model captive finance companies 121 CAR see cumulative abnormal return carry trade 524, 526–8, 547 cash market 495 catastrophe bonds 384 CBOE see Chicago Board Options Exchange CBOT see Chicago Board of Trade CD see certificate of deposit CDO see collateralized debt obligation CDSs see credit default swaps CDS spread 530, 548 CEFA see Closed-End Funds Association central banks 288–9 certificate of deposit (CD) 117, 419

Index s 561 ceteris paribus 27–8, 50, 70, 239, 315; decreasing 354; higher yield 133; increasing 247; investments 408; outperforming 247; portfolio 322; risk 435; value 395 CFA see Chartered Financial Analyst Institute CFTC see Commodity Futures Trading Commission Charles Schwab 99 Chartered Alternative Investment Analyst (CAIA) 536 Chartered Financial Analyst Institute (CFA) 20, 420 chartism 265 chartists 265 Chicago Board of Trade (CBOT) 90, 509 Chicago Board Options Exchange (CBOE) 456–7, 477, 497–8 Chicago Butter and Egg Board 498 Chicago Mercantile Exchange (CME) 90, 267, 498, 509, 519 Chordia, Tarun 279 churning 101 CIP see covered interest rate parity circuit breakers 103, 111 Citigroup/Solomon Smith Barney 16, 529 classic cars 541 classified stock 300, 329 class shares 166–7 clearinghouse 493–5 clearing procedures 87, 99 CLIs see composite leading indicators CLOs see collateralized loan obligations Closed-End Funds Association (CEFA) 159 closed-end investment companies 159–61, 178 CMBS see commercial MBS CMBS index (CMBX) 535 CME see Chicago Mercantile Exchange CME Group 498–9 CML see capital market line CMO see collateralized mortgage obligations coefficient of variation (CV) 67, 77 cognitive heuristics 282 coincident indicators 322, 330 collateral 5, 385 collateralized bond obligation 534

collateralized debt obligation (CDO) 213, 534–6, 548 collateralized loan obligations (CLOs) 460, 487 collateralized mortgage obligations (CMO) 213, 379, 535 combined portfolios 197–201 COMEX see Commodity Exchange Command Asset Programs 100 Commentaries of the Imperial Academy of Science of St. Petersburg (Bernoulli) 73 commercial MBS (CMBS) 535 commercial paper (CP) 118, 121–2, 144 commission brokers 90 commissions 102 Commodity Exchange (COMEX) 90 Commodity Exchange Act 500 commodity futures market 503–5 Commodity Futures Trading Commission (CFTC) 107, 500, 501 common stockholder 5–6, 23 common stocks 5–6, 61, 95, 136–7; characteristics 298–302; defined 145, 328; dividends and splits 300–3; equity securities and 298–302; shareholder equity 298; shareholder rights 298–9; stock types 300; voting privileges 299–300 communism 88 competitive bidding 120, 131, 376–7 completion portfolios 310 composite leading indicators (CLIs) 327–8 conservative portfolio 543 consolidated tape 94 constant growth model 342–5, 366; see also Gordon model constraints 1, 9–11, 24, 416–17 Consumer Confidence Index 314 consumer price index (CPI) 355 consumption asset 507 contango 507, 521 contingent claims 6, 137 contingent deferred sales load 164 contingent immunization 435, 446 contrarian investors 287, 291 convenience yield 506–7 convergence property 496, 520

562 s Index conversion premium 383 conversion ratio 383 convertibility option 383, 410 convexity 399–401, 411 corporate bonds 134–5, 145, 382; see also senior securities corporate finance 19 corporate governance 17 corporation 298–9 correlation 219–20; covariance and 190–3, 214 correlation coefficient 192, 214 cost of carry 505, 521 country risk 70 coupon payments 131, 376 covariance 190–3, 214, 219–20 covenants 385 coverage ratios 385 covered call 461–2, 487 covered interest rate parity (CIP) 526, 547 cowboy capitalism 88 CP see commercial paper CPI see consumer price index credit analysis 429, 445 credit default swaps (CDSs) 213, 529–32, 535, 546, 548 credit derivatives: asset swap 533–4, 548; CDO 213, 534–6, 548; CDSs 213, 529–32, 535, 546, 548; defined 528, 548; market for 529; TRS 531–3, 548 credit enhancement 385 credit or default risk 70 creditors 15 credit risk 132 Credit Suisse 16, 153, 484 cumulative abnormal return (CAR) 277 cumulative dividends 302, 329 cumulative voting 299, 328 currency futures 510–12, 517, 521 currency swap 138 current yield (CY) 393, 411 custodial account 124 CV see coefficient of variation CY see current yield daily limits 497 day-of-the-week effect 273

day orders 47 day trading 362, 366 DCF see discounted cash flow DDM see dividend discount model dealer market 46, 53 dealer paper 122 dealers 93, 110 DeBondt, W. F. M. 276, 283 debt: CDO 213, 534–6, 548; Eurozone debt crisis 409, 534, 546; Greek debt crisis 143, 546; margin 42; U.S. 409–10 debt securities 6, 24, 89; see also fixed-income securities decimal pricing 46 dedication strategy 427, 445 deep in the money 454 deep out of the money 454 default risk 130, 384–5, 410 defensive investors 34, 52 deficits 313 de Grauwe, P. 88 delta 479, 487 demand loan 123 deposit and liability management strategy 139 Depository Trust and Clearing Corporation (DTCC) 99 depreciating assets 470 depreciation 470, 525 derivative asset 137, 145 derivative securities 6, 24, 137–8, 451, 485; see also contingent claims designated market makers (DMMs) 91 designated primary market maker (DPM) 457–8 detachable warrant 460 Deutsche Bank 530, 532 Deutsche Börse 92 direct investing 115–16, 144 directly placed paper 122 direct market 45, 53 dirty price 378 disbursed capital gains and losses 157 discounted cash flow (DCF) 342 discounts 159; brokers 12, 99–100, 110; DCF 342; OID 382; rates 317, 329; see also dividend discount model disposition effect 284

Index s 563 distributions 56–7, 65–6, 157 diversifiable risk 69, 186 diversification 29, 106; covariance and correlation 190–3, 214; economic analysis 211–12; efficient 189–90, 214; fallacies 209–11; household 189; international 188–90; introduction 185; naive or random 186–8, 213; potential 545; principle 186, 213; summary 211; superfluous 188; time 209–11; types 186–92; see also Markowitz diversification approach dividends 6, 10, 57, 61, 74; common stock characteristics 300–3; content of 356–7; cumulative 302, 329; defined 329; economic analysis 363; ex-dividend date 300, 329; extra 300; liquidating 300; noncumulative 302; preferred stock characteristics 302; special 300; stock dividend 301–4 dividend discount model (DDM): constant growth model 342–5; defined 366; for equity valuation 340–52; IBM and 342; multistage growth model 345–6; S&P 500 and 342; using earnings instead of dividends 346–52 dividend irrelevance theory 350 dividend yield 10, 57, 61, 74 DJIA see Dow Jones Industrial Average DMMs see designated market makers Dodd-Frank Act 504 dogs of the Dow 362, 366 dollar-cost averaging 40–1, 53 dollar-weighted rate of return 436–7 domestic bonds 98 double-alpha, no beta strategy 246 Dow, Charles 265–6 Dow Jones Industrial Average (DJIA) 38, 102–3, 278, 516; blue chip stocks 95; components and statistics 96 down formula 472–3 downtrend 268 Dow theory 265–6, 290 DPM see designated primary market maker DTCC see Depository Trust and Clearing Corporation dual listing 93 due diligence 538, 548 duration: bond 395–9, 411; of bond portfolio 398; characteristics 398–9; computing 396;

defined 396; Macaulay 397; measure 396; principles 398; special cases 397–8 dynamic hedging 464, 487 EAR see effective annual rate earnings announcements 273 earnings before interest and taxes (EBIT) 352–3 earnings per share (EPS) 301, 350, 352 earnings yield 359 EAY see effective annual yield EBIT see earnings before interest and taxes ECNs see Electronic Communications Network economically efficient market 263 economic analysis 21–2; active investment strategies 442–3; alternative investments 544–5; arbitrage opportunity 518; bond’s reinvestment risk 408; diversification 211–12; dividends 363; education and 74–5; financial globalization 108; ICI 175–6; insider trading 142; in investment process 50; Keynes’s beauty contest 288; passive investment strategies 442– 3; Porter’s industry competitive strategy 325–6; positive 232; stocks or options purchase 483–4 economic environment: defining investments 3–4; financial intermediaries in 7–9; financial markets in 7–9; investment framework 3–9 economic function 85, 86 economic policies 314–18 economic profit (EP) 354–5, 366 economic theory 284, 350 economic value added (EVA) 354, 366 economies of scale 9, 167 EF see efficient frontier effective annual rate (EAR) 60–1, 76 effective annual yield (EAY) 61 efficiency 8; bond market 441; semistrong form market efficiency 264, 279, 290; strong form market efficiency 264, 279, 290; weak form market efficiency 264, 278, 290 efficient diversification 189–90, 214 efficient frontier (EF) 189–90, 230–2, 248, 250 efficient market hypothesis (EMH) 8, 280; active and passive investment strategy implications 269–71; allocationally efficient market 261; announcement effects 276–8; anomalies and tests 272–80; APT and CAPM implications

564 s Index 271–2; day-of-the-week effect 273; final verdict 279–80; financial crisis of 2008 and 272; forms of markets 263–4; fundamental analysis implications 266–9; introduction 261–2; investment manager implications 271; longhorizon returns 274–6; notion of 262–3; price/ earnings effect 276; return patterns 273–6; revisiting 281–2; short-horizon returns 274–6; size effect 276; summary 287–8; technical analysis implications 265–6; trading and investing implications 264–5 efficient tax management 167 EFSF see European Financial Stability Facility Eichengreen, B. 88 elasticity 138, 479 elasticity of demand 138 Electronic Communications Network (ECNs) 94 Electronic Municipal Market Access (EMMA) 378 EMH see efficient market hypothesis E-mini S&P 500 508 EMMA see Electronic Municipal Market Access EMU see European Monetary Union endowment funds 11, 459 enhanced cash management strategy 141 enhanced indexing 308, 329, 423, 445 Enron 17 EP see economic profit EPS see earnings per share equilibrium price of shares 47–9, 335 equity: account 44; benchmark 95; funds 162; private equity firms 539; ROE 347–52; shareholder 298; WEBS 105 equity collar strategy 464–5 equity portfolio management: active investment strategies 308–10, 329; international investing 310–12; passive investment strategy 304–8, 329 equity securities 5–6, 89, 136–7; buying and selling 359–63; common stock characteristics 298–302; introduction 297; preferred stock characteristics 302; stock market quotations 303–4; summary 325 equity valuation: book value 227–338; Buffet and 336–7; buying and selling equities 359–63;

content of dividends 356–7; DDM for 340–52; EP 354–5; free cash flows and 352–3; general measures 337–40; inflation and 355–6; information signals in 356–7; introduction 333; liquidation value 338–9; options valuation approach 353–4; PBV 338, 351; P/E ratio and 357–9; price/sales value 338; prices and returns 333–7; replacement value 339, 366; stock market 357–9; summary 363, 365 estimated return 277 ETF option 481, 487 ETFs see exchange-traded funds ethics: agency and 13–18; CFA code of 20; unethical behavior 16, 24 E*Trade 100 euro 105, 528 Eurobonds 98–9, 382, 410 Eurocurrency 118, 127–9 Euronext 92, 98, 105, 457, 502–3 European Bank of Reconstruction and Development 282 European Financial Stability Facility (EFSF) 534 European insurance industry 444 European Monetary Union (EMU) 443–4 European option 453 European primary market 150 Eurozone debt crisis 409, 534, 546; see also Greek debt crisis; Iceland financial crisis EVA see economic value added excess return 64, 76 exchangeable bond 384, 410 exchange rates 313–14; exposure 465; risk 105, 525 exchange-traded funds (ETFs) 93, 305, 422; defined 178; investment companies and 170–4; NAV and 173; stocks and 101 ex-dividend date 300, 329 exercise price see strike or exercise price EXIM see Export-Import Bank expectations 313; homogenous 233; market expectations theory 402–3, 411 expected returns 27, 51, 63–4, 71, 76; HPR 334; standard deviation of 187 expiration date 452 Export-Import Bank (EXIM) 134

Index s 565 ex post return 28 extra dividends 300 extrinsic value 470, 487 Facebook 300 face value 117, 119, 121, 131, 376, 380; see also par value factor bets 247 fads 275, 285 fair game 9, 72–3 fair market 91, 503 fair prices 87, 237, 261 fair value 266, 291, 364, 418, 512–13 fair-value accounting 364, 418 fair-value futures 512–13 Fama, Eugene 240, 278, 280, 281, 356 Fannie Mae 133–4, 162, 378–9 Farmer Mac 133–4 FASB see Financial Accounting Standards Board fat tails 66 FCEE see free cash flow to equity FCFF see free cash flow to the firm FDIC see Federal Deposit Insurance Corporation fear indicator 478 Fed see Federal Reserve Federal Deposit Insurance Corporation (FDIC) 4, 134, 210, 401, 542 federal funds 118, 124–6, 125 federally related enterprises 133, 378 Federal Open Market Committee (FOMC) 125 Federal Reserve (Fed) 10, 87, 88, 401; Regulation Q 129; Regulation T 41; trading requirements 107 Federation of European Securities Exchange (FESE) 97 fed funds rate 125, 144, 317 fed model 359 fed wire 125 Ferson, Wayne 246 FESE see Federation of European Securities Exchange FFAJ see Financial Futures Association of Japan Fidelity Investments 99, 164 fiduciary call 480 FIFO see first-in first-out

Financial Accounting Standards Board (FASB) 364, 418 financial assets 4–5, 23 financial crisis of 2008 8, 70, 418; CAPM and 240; causes and consequences 22; commercial papers during 122; EMH and 272; lessons of 23, 109; margin calls 104; Markowitz on 213; stock market performance 27; as subprime crisis 460; trust lacking 87 Financial Futures Association of Japan (FFAJ) 503 financial futures contracts: currency futures 510–12, 517, 521; defined 521; interest rate futures 509–10, 521; leverage 513–14, 521; S&P futures versus fair value 512–13; stock index futures 508–9, 521 Financial Industry Regulatory Authority (FINRA) 166, 544 financial intermediaries 7–9, 24 financial leverage 43, 53, 323, 330 financial markets 18, 110; circular flow of funds 86; in economic environment 7–9; investment risks 138–9; market timing 37; rising and falling 40; role of 7–8; see also global financial markets; trading markets financial risk 70 Financial Services Authority (FSA) 501 Financial Stability Board (FSB) 519 fine art 541 FINRA see Financial Industry Regulatory Authority firm 152–3 firm commitment 152, 178 firm-specific risk 69, 186 first-in first-out (FIFO) 337 first-to-default basket swap 531 fiscal policy 315, 329 Fisher, Irvin 62 Fisher equation 62, 355 fixed-income ETF 439–40 fixed-income securities 6, 131–5, 144, 373, 410 flat curve 400 flattening 432 flight to quality 132, 136 flight to safety 69, 75, 136

566 s Index floating-rate bond 384, 410 floor brokers 90 FOMC see Federal Open Market Committee Forbes 168 foreign bonds 98, 130, 382 foreign currency options 459, 486 foreign entities 7 foreign exchange risk 70 forward contract 492, 520 forward earnings yield 359 forward P/E ratio 357 forward price 518 fourth market 94 Fox, Justin 272 fractional shares 157 framing effect 283 Franklin Templeton 164 Freddie Mac 22, 133–4, 162, 378–9 free cash flow to equity (FCEE) 352–3, 366 free cash flow to the firm (FCFF) 352–3, 366 French, Kenneth 240, 278 frictionless market 233 front-end load 164 FSA see Financial Services Authority FSB see Financial Stability Board full replication 306, 423 full-service brokers 12, 99–100, 110 fundamental analysis 30, 52, 291; defined 329; EMH implications 266–9; industry analysis 322–5; introduction 297; investment strategies 39; macroeconomics 312–22; overview 311–12; summary 325; top-down 312 futures contract 492–7, 520 futures index 266, 290 futures market 6, 24; commodity 503–5; defined 491, 520; financial futures contracts 508– 14, 521; futures contract 492–7, 520; hedging in 514; introduction 491–2; overview 497–505; spot prices 493, 505–8, 518; summary 518, 520; trading 501–2; trading strategies 514–17 futures options 459, 486 futures price 493 GAAP see generally accepted accounting principles Garten, J. 88

GDP see gross domestic product Geithner, Timothy 379 generally accepted accounting principles (GAAP) 417 General Motors (GM) 8, 162, 186–7 general obligation bonds 132 geometric mean (GM) 59–60, 76 geometric rate of return 436 gilts 69, 383 Ginnie Mae 133–4, 378 GIPS see Global Committee on Performance Standards global bonds 382 Global Committee on Performance Standards (GIPS) 420 global financial markets: economic function 86; globalization and trends 104–5; global monetary authority 88; introduction 85–6; investing and returns 105–7; miscellaneous functions 88–9; pricing function 86–7; provision of services 87–8; regulatory structures in U.S. exchanges 107; securities exchanges 89–99; securities exchanges trading 99–104; summary 108 global funds 163 global IPOs 176–7 global monetary authority 88 GM see General Motors; geometric mean going long 493 going short 493–4 Goldman Sachs 90, 150, 342, 530, 532 go long 170 Goltz, F. 538 good bargains 30 good buys 36 good-till filled (GTF) 47 Google 155, 300 Gordon, Myron 343 Gordon model 343 go short 170 government 7, 85 government bonds 131–2, 376–8 government-related bonds 378–82 government-sponsored enterprises (GSEs) 133, 378 Graham, Benjamin 32–3, 35

Index s 567 Grantham, Jeremy 272, 288 Great Depression 27, 133 Great Recession 75 Greek debt crisis 143, 546 Greenspan, Alan 401 Grinblatt, Mark 168 gross domestic product (GDP) 313, 320 Groupon 154–5 growth funds 162, 174 Grullon, Gustavo 356–7 GSEs see government-sponsored enterprises GTF see good-till filled head and shoulders pattern 266 hedge 137, 145, 193, 472–3; long 514; radio 479; short 508, 514 hedged portfolio 472–3 hedge funds 87, 178, 459; alternative investments 538–40; investment companies 170–1 hedgehog bests fox 32 hedger 492, 499, 507–8, 520 hedging 6, 499; allocation 482; BlackScholes-Merton valuation approach for 479–81; dynamic 467, 487; in futures market 514 herding behavior 282 higher-than-average risk 235 high-frequency trading 516 highly marketable or highly liquid 116 high-speed trading 102 holding period return (HPR) 57–8, 63–6, 238; determining 74; expected 334 holding period yield (HPY) 61 homogenous expectations 233 horizon analysis 433–4, 446 horizon-matching technique 427–8, 434, 446 hostile takeover 299 hot stocks 360–3 households 7, 13, 22, 71, 86, 155 HPR see holding period return HPY see holding period yield Hudson, Robert S. 278 human behavior models 285–6 humped curve 400 Hybrid Market 92 hybrid security 6, 302, 329

IASB see International Accounting Standards Board IBM: balance sheet items 338; DDM and 342; equilibrium price example 47–9, 335; selected data 341, 358, 361; stock price 351, 469 ICE see Intercontinental Exchange ICE Futures Canada 512 ICE Futures Europe 511–12 ICE Futures US 512 Iceland financial crisis 143–4 ICI see Investment Company Institute IMF see International Monetary Fund IMM see International Monetary Market immunization strategy 423–5, 445 implementation lag 316 implied volatility 477 income funds 162 indenture 376, 383, 385, 394, 410, 460 index arbitrage 308, 329, 516–17, 521 index funds 163 indexing strategy 38, 207, 270, 291, 305–6; bond indexing strategies 421–3, 445; enhanced indexing 308, 329, 423, 445; pure indexing 422–3, 445 index portfolios 246–7 indirect investing 115–16, 148, 156 individual retirement account (IRA) 175 industry analysis 322–5 industry life-cycle 312, 323–5, 330 inflation 9, 313; equity valuation and 355–6; hedge 137; relative rates 107; risk 70, 138, 145; TAAPS and 379; TIPS and 379; see also Treasury Inflation Protected Securities inflation-adjusted return 62–3 information processing biases 283 informed decisions 1 infrastructure 539–40, 548 initial public offering (IPO) 149, 152–5, 298; defined 177; global 176–7 inputs of production risk 71 inside quotes 94, 102 insider trading 107, 142, 264, 279 Instinet 94 institutional investors 6–7, 24, 305–10 insurance principle 187, 209–10 Intercontinental Exchange (ICE) 90

568 s Index interest rate-anticipation strategy 428, 445 interest rate parity (IRP) 525–6, 547 interest rates 138, 313, 471–2; futures 509–10, 521; IRP 525–6, 547; margin 42; nominal 62–3, 76, 106, 316, 528; options 459, 486; relative 106–7; risk 70, 138, 145, 293, 411; UIP 526, 547 interest-rate swap 138 intermarket spreads 135 intermediaries 86, 90 internal rate of return (IRR) 436–7 Internal Revenue Service (IRS) 137 International Accounting Standards Board (IASB) 364 international arbitrage 527, 547 international diversification 188–90 International Monetary Fund (IMF) 22, 88, 130, 212, 409 International Monetary Market (IMM) 498, 510 international money markets 127, 144 International Options Market Association (IOMA) 457 International Organization of Securities Commissions (IOSCO) 505 International Securities Exchange (ISE) 456 International Swap and Derivatives Associations (ISDA) 529 in the money 454, 486 intraday return 273 intramarket spreads 135 intrinsic price 336–7 intrinsic value 266, 291, 336, 454, 470, 487 inverse floater 384 inverted curve 400 investments: ceteris paribus 408; defined 1, 3–4, 23; in global financial markets 105–7; investing dangers 328; why study 18–20; see also alternative investments investment assets 4, 56, 263, 280, 340, 507 investment banker 150–2, 178; see also underwriters investment banking: introduction 148; investment banker 150–2, 178; IPO in 152–5; primary market 148–9; shelf registration 150; summary 165 investment companies: assets 158; closed-end 159–61, 178; defined 156, 178; ETFs 170–4;

functions 157–8; hedge funds 170–1; introduction 148, 155–6; managed 158; open-end 161; REIT 169–70, 178, 537–8; summary 165; types of 158–69; unmanaged 158 Investment Company Act of 1940 156–7 Investment Company Institute (ICI) 155, 175–6 investment environment: investors in 6–7; overview 4–5; securities 5–6 investment framework: agency and ethical issues 13–18; economic environment 3–9; introduction 3; investment environment 4–9; investment information in 12–13; investment management process 11–12; investor objectives and constraints 9–11; summary 20–1 investment horizon 11, 24, 167, 464, 545 investment information: asymmetric 14–15, 24; in investment framework 12–13; sources 13 investment management process 11–12 investment managers 11–12, 271 investment opportunity set 227, 250 investment philosophies: Bogle 32; Buffett 32–3; Markowitz 31; personal 34–5; Samuelson 31 investment policies 10, 26–7, 161 investment policy statement (IPS) 11, 417–19, 445 investment process 1, 416, 445; asset allocation 28–30, 52; defined 51; economic analysis 50; introduction 26–7; risk-return trade-off 27–8; security selection 30–1, 52; summary 49–51 Investments & Pensions Europe 249 investment strategies: bottom-up 35–6, 49, 52, 141–2; capital markets 141–2; CML and 206–7; deposit and liability management strategy 139; dollar-cost averaging 40–1; enhanced cash management 141; fundamental analysis 39; margin purchase 41–4; market neutral 140–1; money markets 139–41; mutual funds 173–5; pairs trading 141; portfoliospecific 39; short sales 44–5; technical analysis 39; top-down 35–6, 49, 52, 141–2; see also active investment strategies; passive investment strategies investors: age 9–10, 24; aggressive 34, 52; contrarian 287, 291; defensive 34, 52;

Index s 569 individual 304–5, 308–9; institutional 6–7, 24, 305–10; intelligent 33, 69; in investment environment 6–7; long-run 35, 52; objectives and constraints 9–11, 416–17; preferences 10; psychology 38; retail 6–7, 24; risk-averse 9, 24; risk-loving 9, 24; risk-neutral 9, 24; short-run 34–5, 52; SPIC 17, 107, 111; utility 207, 214 Investors for the Long-Run (Siegel) 35 investor’s input 231 invoice price 378 IOMA see International Options Market Association IOSCO see International Organization of Securities Commissions IPO see initial public offering IPS see investment policy statement IRA see individual retirement account IRP see interest rate parity IRR see internal rate of return Irrational Exuberance (Shiller) 365 IRSI see Internal Revenue Service ISDA see International Swap and Derivatives Associations ISE see International Securities Exchange iShares 105, 171 Japanese bond market 374 Jensen, Michael C. 244–6, 251 Jensen measure 245–6, 251 Johnson, L. 538–9 joint-hypothesis problem 280 JP Morgan Chase 90, 150, 153, 484; CDSs 529–30, 532 junk bonds 385–6, 411, 419 Kahneman, Daniel 281, 283 Kamstra, Michael 359 Kangaroo or Matilda bonds 98, 382 Kerviel, Jerome 485 Keynes, John Maynard 71, 282, 288, 507 kurtosis 66 laddered bond portfolio 421 Ladefoged, Nils 249 lagging indicators 322 lags 316

large-cap stocks 162 last-in first out (LIFO) 337 law of diminishing marginal utility 72 law of one price 240, 505 LCDO see loan-only CDO LCDS see loan-only credit default swaps leading indicators 320–1, 330; see also composite leading indicators lead underwriter 151 LEAPS see Long-Term Anticipation Securities Leeson, Nick 485 Leggio, Karyl B. 43 Lehman Brothers 22, 125, 531 lending portfolio 204, 214 leptokurtic 66 LeSourd, Veronique 246 leverage 385, 513–14, 521 leveraged portfolios 227 leveraged position 205 leverage ratios 385 leveraging 43–4 LIBOR see London Interbank Offered Rate Lien, Donald 43 Life-Cycle Hypothesis 71 Li Feifei 43 LIFFE see London International Financial Futures and Options Exchange LIFO see last-in first out limit buy 46 limited liability 136, 298 limit order 46–7, 53, 457 limit-order book 46 Linter, John 356 Lipper Average 168 liquidating dividends 300 liquidation value 338–9, 365 liquidity 11, 24, 545; capital and 109; risk 70, 130 liquidity preference theory 403–4, 411 load 164, 178 loan-only CDO (LCDO) 536 loan-only credit default swaps (LCDS) 531, 536 locational arbitrage 527, 547 London Interbank Offered Rate (LIBOR) 118, 126–8, 532–4

570 s Index London International Financial Futures and Options Exchange (LIFFE) 105, 457, 502–3 London Stock Exchange (LSE) 96, 105, 109 long hedge 514 long-horizon returns 274–6 long position 493, 520 long-run investors 35, 52 long-short alternative investments 537 long-short strategy 140 long straddle 466 Long-Term Anticipation Securities (LEAPS) 459, 469 long-term bonds 376 Long-Term Capital Management (LTCM) 140, 171 loss aversion 285, 291 lower-than-average risk 235 low or no risk 116 LSE see London Stock Exchange LTCM see Long-Term Capital Management MA1 see 1-year moving average MA3 see 3-year moving average Macaulay, Frederick 396–7 Macaulay duration 397 macroeconomics: business cycle 318–22; economic policies 314–18; equilibriums 315; fundamental analysis 312–22; magnitude 313–14; overview 312–13; risk exposure 246; see also microeconomics Macy’s 162 Madoff, Bernard 17 maintenance margin 42, 44, 53, 496, 511 Malkiel, Burton 168, 281, 286, 359 managed investment companies 158 margin 41, 53, 495–7; debt 42; interest rate 42; purchase 41–4; variation 496 marginal impact 200, 214 margin calls 42–3, 53, 104 marketable securities 117 market anomaly 273, 291 market capitalization rate 337 market efficiency see efficient market hypothesis market equilibrium 183, 206, 232, 263 market expectations theory 402–3, 411 market-neutral alternative investments 537

market neutral strategy 140–1; see also long-short strategy market-on-close orders 47 market order 46, 53, 457 market portfolio 206, 233–4, 251 market risk 69, 138, 188 market risk premium 234 market segmentation theory 404, 411 Markets in Financial Instruments Directive (MiFiD) 441 “The Market for Lemons: Quality, Uncertainty, and the Market Mechanisms” 14 market timing 37, 52, 238, 251, 310 market-weighted index 95 marking to market 495, 520 Markowitz, Harry 31, 285; EF and 189–90, 230–2, 248, 250; on financial crisis of 2008 213; portfolio theory 183, 185, 200 Markowitz diversification approach: CAL and 227–30; EF in 230–2; introduction 221; optimal risky portfolio 227–30; risky portfolio review 222; summary 247; two-asset portfolio 222–7 married put strategy 466–7, 487 Marshall, P. S. 42–3 MAs see moving averages Matador bonds 382 Matilda bonds see Kangaroo or Matilda bonds maturity date 376 maturity risk 130 maximization of utility 190 May Day 100 MBIA see Municipal Bond Insurance Association MBS see mortgage-backed security mean reversion 202, 285, 291 mean variance criteria 230 mean-variance optimizers 233 medium-term bonds 376 memory bias 283 mental accounting 284 Merrill Lynch 22, 91, 150 Merton, R. 171 Michaely, Roni 357 microeconomics 71, 282 mid-cap companies 95

Index s 571 mid-cap stocks 162 MiFiD see Markets in Financial Instruments Directive Miller, Merton 350, 357 MMMFs see money market mutual funds Modigliani, Franco 71, 350, 357 momentum effect 274 monetary policy 316, 329 money left on the table 154 Money Magazine 168 money market mutual funds (MMMFs) 161 money markets 18, 76, 161; BA 118, 122–3, 144; characteristics 116–17; CP 118, 121–2, 144; defined 144; eurocurrency 118, 127–9; federal funds 118, 124–6; instruments and rates 118; international 127, 144; introduction 115–16; investment strategies 139–41; LIBOR 118, 126–8, 144; marketable securities 117; nonmarketable securities 117; repo 123–5, 144; summary 142; T bills 117–21, 144; yields and spread 129 Moody’s 135, 308, 535 moral hazard 14, 24 Morgan Stanley 153 Morgan Stanley Capital International (MSCI) 171 Morningstar 168–9 mortgage-backed security (MBS) 134, 379, 401, 535 moving averages (MAs) 266, 268–9, 291 moving average technique 266 MSCI see Morgan Stanley Capital International multistage growth model 345–6 Municipal Bond Insurance Association (MBIA) 385 municipal securities (munis) 132–3, 144 Municipal Securities Rulemaking Board 378 munis see municipal securities mutual funds 9, 13, 32, 161, 459; Bogle on 177; classification 164; class shares 166–7; defined 178; fee structure 163–8, 178; investment strategies 173–5; load 164, 178; NAV 165; no-load 164; operating expenses 165; passthrough status 167; performance 168–9; securities lending programs 175; theorem 231; turnover rate 168, 178; 12b-1 fees 165 Mutual Fund Sourcebook 163

Nai-Fu Chen 244 naive or random diversification 186–8, 213 naked call 461 NASD see National Association of Securities Dealers NASDAQ see National Association of Securities Dealers Automated Quotations NASDAQ Composite and 100 95 NASDAQ futures index 266 National Association of Securities Dealers (NASD) 17, 93, 441 National Association of Securities Dealers Automated Quotations (NASDAQ) 45, 93–4 National Bureau of Economic Research (NBER) 50 NAV see net asset value NBER see National Bureau of Economic Research neckline 266 negative skewness 66 negative weights 227 neglected-firm effect 278 net asset value (NAV) 157–9; defined 178; ETFs and 173; mutual funds 165 net capital gain 137 net operating profits after taxes (NOPAT) 354 New York Mercantile Exchange (NYMX) 90 New York Stock Exchange (NYSE) 41, 300; as auction market 46; bonds trade 382; chronology of events 90; interest rate futures 510; membership prices 91; one tick 46; options trading 457–8; prices of seats 91; publications 45; transaction steps 92–3 noise trader 247 noisy market hypothesis 271, 289–90 no-load funds 164 nominal interest rate 62–3, 76, 106, 316, 528 nominal rate of return 62, 76, 380 noncompetitive bidding 120, 131, 377 noncumulative dividends 302 nonmarketable securities 117, 144 nonnegotiable certificate of deposit 117 nonsystematic risk 186 NOPAT see net operating profits after taxes Nordstrom 162 normal curve 400

572 s Index normal distribution 65–6 normal portfolio 194, 309, 329, 422, 438, 445 normative economics 232 NYMX see New York Mercantile Exchange NYSE see New York Stock Exchange NYSE-listed transactions 100 OCC see Options Clearing Corporation OCF see operating cash flow odd-lot orders 47 Odean, T. 283 OECD see Organization for Economic Cooperation and Development offset 493, 497 OID see original issue discount OMOs see open-market operations 1-year moving average (MA1) 362 open-end investment companies 161 open interest 493–4 open-market operations (OMOs) 317, 329 open markets 125, 149, 317, 329 open outcry 492 operating cash flow (OCF) 352–3 operating leverage 323, 330 Oppenheimer Funds 164 opportunity cost 4, 23 optimization approach 423, 445 options 6, 24; American 453; AMEX for 456; binomial option pricing 472–5; CBOE for 456–7, 477, 497–8; convertibility 383, 410; defined 486; economic analysis 483–4; ETF 481, 487; European 453; foreign currency 459, 486; futures 459, 486; futures securities and 89; global volatility indexes 484; interest rate 459, 486; introduction 451; IOMA 457; LIFFE 105, 457, 502–3; market for 456–60; market participation 459; NYSE trading 457–8; OCC 458, 486; overview 451–60; products 459; profits and losses 453–6; purchase over stocks 483–4; securities 89, 460; speculating with 468–9; stock index 481–3, 487; summary 483, 486; trading strategies 460–9; see also call options; put options Options Clearing Corporation (OCC) 458, 486

option valuation 353–4, 469–81; binomial option pricing 472–5; Black-Scholes-Merton (BSM) valuation approach 474–81; fundamental concepts 470–2; overview 469–70 Organization for Economic Cooperation and Development (OECD) 322, 327–8 organized securities exchange 90, 110 original issue discount (OID) 382 OTC see over-the-counter OTC Bulletin Board (OTCBB) 93 OTC securities exchange 46, 92–5 out of the money 454, 486 overconfidence 283 overreaction hypothesis 275 oversubscribe 153, 178 over-the-counter (OTC) 46, 92–5, 110, 382, 492; derivatives market reform 519–20 Pacific Investment Management Company (PIMCO) 50, 427 Pacific Stock Exchange (PSE) 93, 456 paid-in-capital 298 painting the tape effect 275 pairs arbitrage trading 141 pairs trading strategy 141, 170, 517 parallel shift 432 parking 8 Parmalat 16 partial replication 423 par value 117, 298, 328, 376 passive approach 32, 234 passive investment strategies 37–9, 52, 197; for bond portfolio management 420–8, 445; dedication strategy 427, 445; defined 291; economic analysis 442–3; EMH implications 269–71; for equity portfolio management 304–8, 329; immunization strategy 423–5, 445; individual investors 304–5; institutional investors 305–8; pension funds and 419; rebalancing 425–7, 445 pass-through status 167 Paulos, John Allen 281 paying for order flow 101 payment in kind 172 payrolls and average pay 19

Index s 573 PBV see price/book value peak 318–19, 330 penny stocks 93 pension funds 249; passive investment strategy and 419; performance 459 P/E ratio see price/earnings ratio perfectly efficient market 263 perfectly hedged portfolio 140 performance: GIPS 420; mutual funds 168–9; pension funds 459; stock market 27; T bills outperforming stocks 75 performance attribution analysis 438–41, 446 performance evaluation 244–6, 435–41, 446 performance measurement 420, 435–41, 446 perpetuities 397 petrodollars 129 Philadelphia Stock Exchange (PHLX) 93, 456 PIMCO see Pacific Investment Management Company pink sheet stocks 93 planning horizon 233 PNP Paribas 484 policy portfolio 194 Politics (Aristotle) 497 Ponzi scheme 16–17 Porter, Michael 323–4 Porter’s industry competitive strategy 323–6 portfolios 10; aggressive 543; benchmark 437–8; ceteris paribus 322; combined 197–201; completion 310; conservative 543; defined 27, 51; expected standard deviation of returns 187; formation 18; hedged 472–3; holdings 56; index 246–7; lending 204, 214; leveraged 227; manager 11; marginal impact 200, 214; market 206, 233–4, 251; normal 194, 309, 329, 422, 438, 445; perfectly hedged 140; performance evaluation 244–6; policy 194; reference 437; replicating 472; risk 188; securities 188; speculative 71; two-asset 222–7, 254–6; well-diversified 241–2; zero-beta 246; see also bond portfolio management; equity portfolio management; risky portfolios portfolio insurance 462–3, 487 portfolio selection problem 183 portfolio-specific investment strategies 39

portfolio theory 31, 183, 185, 200; see also asset allocation; diversification Posen, A. 288 positive economic analysis 232 potential 495, 545 Prague Stock Exchange (PX) 97 precautionary motives 71, 77 preferences 10; see also liquidity preference theory preferencing 101 preferred habitat theory 404, 411 preferred stocks 6, 24, 137; characteristics 302; defined 145, 329; see also hybrid security premium 6, 159, 452; conversion 383; market risk 234; risk 64, 76, 129; security risk 235 presidential election cycle effect 278 price/book value (PBV) 338, 351, 365 price discovery 492, 498, 530–1 price/earnings ratio (P/E ratio) 95, 276, 283, 287, 289, 360; defined 366; equity valuation and 357–9; trading rules 361–2 price fixing 100 prices 276, 283, 287, 289; ask 46; bid 46, 93, 110, 377; bid-ask 93, 102; binomial option pricing 472–4; call 395; dirty 378; equilibrium price of shares 47–9, 335; in equity valuation 333–7; fair 87, 237, 261; forward 518; futures 493; impact 102, 110; intrinsic 336–7; invoice 378; law of one price 240; purchase 57; spot 493, 505–8, 518; strike or exercise 137, 452, 453, 468, 470; of time 207; underlying asset 470; yields and 388–93 price/sales value 338 price-weighted average 95 pricing function, global financial markets 86–7 primary investment market 110 primary market 110, 148–9, 150 primary securities dealers 149 primary securities market 4, 88–9, 98 primary trends 265 principal-agent conflict 15, 24 prisoners’ dilemma 286, 291 private equity firms 539–40, 548 private placement 149, 177, 298 professional conduct 20

574 s Index profitability ratios 385 program trading 92, 110, 515–16, 521; see also high-frequency trading promised yield 386, 394 prospectus 153, 178 protective covenants 385 protective put 462, 487 proxy 136; fight 299; voting 299, 329 prudent man law 10, 16 PSE see Pacific Stock Exchange Public Company Accounting Oversight Board 17 public offering see initial public offering Pukthuanthong-Le, Kutara 278 purchase price 57 purchasing power 62 pure indexing 422–3, 445 put-call parity 480–1, 487 put options 6, 24, 137, 353, 383, 410; as basic concept 452–3; defined 486; formula 480 PX see Prague Stock Exchange q ratio 365, 366 quadratic optimization 307–8 qualitative asset allocation 193 quantitative asset allocation 193 Qubes 171 random behavior 63 random diversification see naive or random diversification random walk 262, 281, 285, 290 rare stamps 541 rate of return (RoR) 106, 334, 436; arithmetic average 436; dollar-weighted 436–7; geometric 436; IRR 436–7 real assets 4–5, 23 real estate investment trust (REIT) 169–70, 178, 537–8 real estate mortgage investment conduits (REMICs) 389 real rate of return 61–3, 380 rebalancing 425–7, 445 recession 75, 320, 365 recognition lag 316 redeemable trust certificates 159

red herring 153 reference obligation 531 reference portfolio 437 reference rate 127 refunding 385, 411 regional exchanges 93 regression analysis 216–19 regret avoidance 285, 291 regulation 17, 41, 129, 545 Regulation Q 129 Regulation T 41 regulatory arbitrage 520 regulatory environment 10, 24 regulatory structures 107 Reinganum, Marc R. 276 reinvestment risk 138, 145, 393, 408, 411 REIT see real estate investment trust relative income levels 107 relative inflation rates 107 relative interest rates 106–7 relative returns (RR) 106 relative risk 232 relative strength index (RSI) 39 relevant riskiness 235 REMICs see real estate mortgage investment conduits replacement value 339, 366; see also q ratio replicating portfolio 472 repo see repurchase agreement Report on Socially Responsible Investing Trends 18 repurchase agreement (repo) 123–5, 144 required returns 68–9, 77 Reserve Primary Fund 76 reserve requirement 316–18, 329 residential MBS (RMBS) 535 residual claim 136 resistance level 266, 269, 290 resistance line 362, 366 retail investors 6–7, 24 retirement account 175 returns: abnormal 238, 277, 335; after-tax 132; AM 59–60; APR 60–1; attribution 246; CAR 277; defined 74; EAR 60–1; effects 275; EMH patterns 273–6; in equity valuation 333–7; estimated 277; excess return 64, 76; expected

Index s 575 27, 51, 63–4, 71, 76, 187, 334; global financial markets 105–7; GM 59–60; HPR 57–8, 63–6, 74; inflation-adjusted 62–3; intraday 273; introduction 56; long-horizon 274–6; measuring 56–7; nominal 61–2, 76; over multiple periods 58–60; real 61–3; required 68–9, 77; risk aversion and 69; risk-return profile 545; RoR 106; RR 106; short-horizon 274–6; summary 73–4; target 71; time-of-day 273; time-weighted average return 59; yield 61 return on equity (ROE) 347–52 revenue bonds 132 revenue stream 5 reversal effect 276 reverse dilution 301 reverse repo 124, 144 reverse requirement 317–18 reverse stock split 301, 329 reversing trades 497 riding the yield curve 406 risk 1; in active investment strategies 434; appetites 9; APT factors 242–3; arbitrage 517; basis 507–8, 521; bond reinvestment 408; business 70; ceteris paribus 435; country 70; credit 132; credit or default 70; default 130, 384–5, 410; defined 24, 64, 77; diversifiable 186; exchange rate 105, 525; financial 70; in financial markets 138–9; firm-specific 69, 186; foreign exchange 70; higher-than-average 235; inflation 70, 138, 145; inputs of production 71; interest rate 70, 138, 145, 293, 411; introduction 56; liquidity 70, 130; lower-than-average 235; low or no 116; macroeconomic exposure 246; market 69, 138, 188; maturity 130; measure 28; nonsystematic 186; portfolio 188; reinvestment 138, 145, 393, 408, 411; relative 232; single asset 64–8; sources of 69–71; stand-alone 65; summary 73–4; systematic or nondiversifiable 69; tail 484; tax 139, 145; tolerance 9, 543; total 69, 77, 186, 245, 256, 258, 310; transferring in global financial markets 87; unique 186; unsystematic or diversifiable 69 risk-adjusted basis 67–8 risk-adjusted ratings 169 risk-averse investors 9, 24

risk aversion 9, 24, 68, 196, 543; asset allocation and 207–9; returns and 69; utility and 71–3 risk-free assets 28, 52 risk-free instrument 140, 144 risk-free rate 118 risk-loving investor 9, 24 risk-neutral investor 9, 24 risk per unit of return 67–8 risk-pooling 209 risk premium 64, 76, 129 risk-return profile 545 risk-return trade-off 27–8, 51 risk tolerance 33–4, 196 risky portfolios 197–201, 222, 227–30 RMBS see residential MBS road show 153 ROE see return on equity rogue traders 485–6 Roll, Richard 244, 273 RoR see rate of return Ross, Stephen A. 240–1, 244; see also arbitrage pricing theory Roth IRA 175 round-lot orders 47 RR see relative returns RSI see relative strength index Russell 2000 and 3000 95, 162 SAA see strategic asset allocation St. Petersburg Paradox 73 saitori 97 Sallie Mae 133–4 sampling 305–6 Samuelson, Paul 31 Samurai bonds 98, 130, 382 Sarbanes-Oxley Act of 2002 17, 107 saving 4, 23 savings account 117 scale orders 47 SCDO see synthetic CDOs Schroeder, D. 538 Schwert, William 356 SCL see security characteristic line SEAQ see Stock Exchange Automated Quotations seasoned offering 149, 177

576 s Index SEC see Securities and Exchange Commission secondary investment market 110 secondary securities market 88–9, 98 secondary trends 265 sector rotation 37, 52, 309 secured bonds 134, 376 securities: ABS 134, 379, 535; classifications 5–6; debt 6, 24, 89; defined 5, 23; derivative 6, 24, 137–8, 451, 485; fixed-income 6, 131– 5, 144, 373, 410; hybrid 6, 302; in investment environment 5–6; LEAPS 459, 469; marketable 117; MBS 134, 379, 401, 535; munis 132–3, 144; mutual funds lending programs 175; nonmarketable 117, 144; options and futures 89; options with 460; organized 90; portfolio 188; securities exchanges and 89; selection in investment process 30–1, 52; senior 134; TIPS 120–1; see also equity securities Securities and Exchange Commission (SEC) 10, 337, 544; “Beginner’s Guide to Asset Allocation, Diversification, and Rebalancing” 29; Fair Disclosure regulation 17; insider trading defined 142; Municipal Securities Rulemaking Board 378; Ponzi scheme defined by 17; regulatory body 107; website 41, 44 securities exchanges 88; BM&F 97; brokerage services 99–100; clearing procedures 99; defined 110; international 95–8; international bond market 98–9, 374–5; LSE 96; primary securities market 88; PX 97; secondary securities market 88; securities and 89; trading costs 100–2; trading on 99–104, 110; TSE 97; U.S. bond market 97–8, 375; U.S. organized 90–3; U.S. OTC 93–5; U.S. stock market indexes 95, 113–14 Securities Industry Financial Markets Association (SIFMA) 386 Securities Investor Protection Corporation (SPIC) 17, 107, 111 securitization 134 security analysis 30, 35, 52 Security Analysis (Graham) 35 security characteristic line (SCL) 238

security market line (SML) 232–3, 236–7, 251, 334 security risk premium 235 security selection 309 selection effect 438 selectivity 238 semistrong form market efficiency 264, 279, 290 senior securities 134 sensitivity analysis 348 separation theorem 231, 250 SETS see Stock Exchange Electronic Trading Service settlement 495–7; see also Bank of International Settlements SGX see Singapore Exchange shareholders 15, 298–9 shares 47–9; BVPS 298; class 166–7; EPS 301, 350, 352; equilibrium price of 47–9, 335; fractional 157; iShares 105, 171; WEBS 105 Sharpe, William F. 168, 169, 204, 244–6, 251 Sharpe measure 169, 204, 244–6, 251 Shefrin, Hersh 284 shelf registration 150, 178, 298 Shiller, R. 276, 285, 362, 365 Sholes, M. 171 short hedge 508, 514 short-horizon returns 274–6 short-interest ratio 43–4, 53 short position 44, 493, 520 short-run investors 34–5, 52 short sales 41, 44–5, 53 short straddle 466 short-term notes 376 SIC see Standard Industry Classification sideways trend 269 Siegel, Jeremy 35, 271, 289–90 SIFMA see Securities Industry Financial Markets Association Singapore Exchange (SGX) 519 single-index market model 240, 256–9 size effect 276 small-cap companies 95 small-cap market 93, 95, 162 small-cap stocks 162 smart money 247

Index s 577 smart trader 247 SML see security market line social investing 17 socially responsible investing (SRI) 18 social responsibility 17–18, 24 soft dollars 101 Solvency II 444 sovereign bond 383, 410 S&P 500 see Standard & Poor’s 500 index SPDR see Standard & Poor’s Depository Receipt special dividends 300 specialists 90–2, 110 special-purpose vehicle (SPV) 534 speculating 499–500, 515 speculative motives 71, 77 speculator 35, 52, 492, 499–500, 520 S&P futures 512–13 SPIC see Securities Investor Protection Corporation spikes 129 splits 278, 300–3; see also stock split spot futures parity 505–7, 521 spot prices 493, 505–8, 518 spread order 457 spreads 102, 129, 457; capital markets 135–6; CDS 530, 548; defined 145; intermarket 135; intramarket 135; yield curve 405 spread strategies 467–8 SPV see special-purpose vehicle SRI see socially responsible investing stakeholders 13–14 stand-alone risk 65 Standard Industry Classification (SIC) 309 Standard & Poor’s 500 index (S&P 500) 27, 118, 135, 266, 305, 359; DDM and 342; equity benchmark 95, 307 Standard & Poor’s Depository Receipt (SPDR) 171 Statistical Abstract of the United States 19 statistical volatility 477 Statman, Meir 284 steepening 432 Stern Stewart & Co. 354 Stevens, Paul 175

stocks 93; alpha of 245, 250, 251; blue chip 95; buying and selling 360–3, 364; classified 300, 329; economic analysis 483–4; ETFs and 101; GM 186–7; hot 360–3; IBM 351, 469; largecap 162; mid-cap 162; purchase over options 483–4; small-cap 162; stock tables 94–5; T bills outperforming 75; in weak economic recovery 50; see also common stocks; preferred stocks stock dividend 301–4, 329 Stock Exchange Automated Quotations (SEAQ) 96 Stock Exchange Electronic Trading Service (SETS) 96 stock index futures 508–9, 521 stock index options 481–3, 487 stock market: equity valuation and 357–9; indexes 95, 113–14; performance 27; quotations 303–4 stock repurchases 301 Stocks for the Long Run (Siegel) 271 stock split 113, 278–9, 301–3, 329; announcement 278; reverse 301, 329 stop-buy orders 47 stop-loss orders 47 stop orders 47 straddle 465–6, 487 straight voting 299 strangle strategy 468 strategic asset allocation (SAA) 194, 197, 214 stratified sample 306, 423, 445 street name 44, 99 strike or exercise price 137, 452, 453, 468, 470 strong form market efficiency 264, 279, 290 stylized facts 66 subordinated debentures 134 substitution swap strategy 430–1, 446 Summers, L. H. 285 SuperDot 92 superfluous diversification 188 SuperMontage 94 support level 265, 290, 366 support line 362 Survey of Consumer Finances 200 swaps 138; asset 533–4, 548; bond strategies 429–32, 445; currency 138; first-to-default

578 s Index basket 531; interest-rate 138; ISDA 529; LCDS 531, 536; substitution strategy 430–1, 446; TRS 531–3, 548; yield strategy 431–2, 446; see also credit default swaps swing trading 362, 366 syndicate 151–2, 178 synthetic CDOs (SCDO) 535, 536, 548 systematic or nondiversifiable risk 69 T. Rowe Price 164 TAA see tactical asset allocation TAAPS see Treasury Automated Auction Processing System tactical asset allocation (TAA) 194, 197, 214 tail risk 484 take-effect lag 316 tangency 229, 250 target return 71 taxes 10, 24; after-tax returns 132; EBIT 352–3; efficient management 167; NOPAT 354; risk 139, 145 tax-exempt yields 133 Taylor, Mike 249 T bills see Treasury bills T bonds 131–2 TD AmeriTrade 100 technical analysis 30, 52, 290; advance/decline ratio 39; behavioral finance implications 286–7; EMH implications 265–6; investment strategies 39; RSI 39; TRIN 39 technical component 231 term repos 124 tertiary trends 265 TFX see Tokyo Financial Exchange Thaler, R. H. 276, 281, 283 Thales 498 there is no such thing as a free lunch (TINSTAAFL) 280 theta 479, 487 thinly trading 97 third market trades 94 Thomas, Lee R. 278 3-year moving average (MA3) 362 tick 511 tilts 308

time decay 470, 487 time diversification 209–11 time-of-day return 273 time value 78–81, 469, 471 time value of money (TMV) 78–81 time-weighted average return 59 TINSTAAFL see there is no such thing as a free lunch TIPS see Treasury Inflation Protected Securities Titman, Sheridan 168 TMV see time value of money T notes 131–2 Tobin, James 71, 231, 339, 365, 366 Tokyo Financial Exchange (TFX) 502–3 Tokyo Stock Exchange (TSE) 97 Tol, Ramon 249 top-down investment strategy 35–6, 49, 52, 141–2 Torous, Walter N. 43 Toshihide Iguchi 485 total book value 337, 365 total return swap (TRS) 531–3, 548 total risk 69, 77, 186, 256, 258, 310 toxic assets 418 TRACE see Trade Reporting and Compliance Engine tracking error 306–7, 422, 445 trade deficit 313 Trade Reporting and Compliance Engine (TRACE) 441 traders 39, 93, 492; noise 247; rogue 485–6; smart 247 traders’ index (TRIN) 39 trading costs 100–2 trading halts 102–3, 110 trading markets: auction market 46, 53; brokered market 45–6, 53; dealer market 46, 53; direct market 45, 53 trading on stock exchanges 99–104, 110 trading orders: limit orders 46–7, 53; market order 46, 53; odd-lot 47; round-lot 47; scale 47; stop orders 47 trading range 302 trailing P/E ratio 357 transactions motives 71, 77

Index s 579 transferring risk 87 transparency 545 Treasury Automated Auction Processing System (TAAPS) 149, 379 Treasury bills (T bills): auction results 119; data 377; defined 144; in money markets 117–21, 144; purchase mechanics 120–1; rates 117–18; stocks outperformed by 75; yield 119, 121; see also government bonds Treasury Direct 117, 131 Treasury Inflation Protected Securities (TIPS) 120–1, 138; auction dates 381; buying 381; defined 410; key facts 381; reasons for issuing 380–1; working of 380 trends 18, 104–5, 265, 268–9 Treynor, Jack L. 244–6, 251 Treynor measure 245–6, 251 triangular arbitrage 528, 548 TRIN see traders’ index trough 318–19, 330 TRS see total return swap truth in lending laws 61 TSE see Tokyo Stock Exchange turnover rate 168, 178 Tversky, Amos 281, 283 12b-1 fees 165 two-asset portfolios 222–7, 254–6 UBS 530 UIP see uncovered interest rate parity UIT see unit investment trust unbundling 100, 110 uncovered interest rate parity (UIP) 526, 547 underlying asset price 470 undervalue 336–7 underwriters 150–2 underwriting 152 unethical behavior 16, 24 unique risk 186 unit investment trust (UIT) 158–60, 178 universe of publicly traded assets 233 university endowments 546–7 unmanaged investment companies 158 unsecured bonds 376 unsystematic risk 69

uptrend 268–9 utility: defined 71–2, 77; investor’s 207, 214; law of diminishing marginal utility 72; risk aversion and 71–3; wealth and 72 utility theory 248 valuation analysis 429, 445, 544; formulas 386–8; see also Black-Scholes-Merton valuation approach; equity valuation; option valuation value-at-risk (VaR) 245, 251 value investing 32 Value Line Investment Survey (VLIS) 345, 348, 350 value/wealth principle 50 Vanguard Brokerage Services 99, 164–7 Vanguard Group of Investment Companies 29, 32 VaR see value-at-risk variation margin 496 vega 478–9, 487 venture capital 539, 548 VLIS see Value Line Investment Survey volatility 276, 291, 471; Black-Scholes-Merton valuation approach and 477–8; defined 487; global indexes 484; implied 477; statistical 477 Volcker, Paul 364 volume 493 voting: cumulative 299, 328; privileges 299–300; proxy 299, 329; straight 299 WACC see weighted average cost of capital Wall Street Journal 107, 168, 173, 275, 279, 303 Wang, L. 283 warrants 460, 487 WB see World Bank weak form market efficiency 264, 278, 290 WEBS see World Equity Benchmark Shares weekend effect 273 weighted average cost of capital (WACC) 353, 354–5 well-diversified portfolio 241–2 Wells Fargo 153 WFE see world federation of exchanges Williams-Sonoma 70 Wilmington Trust 100

580 s Index Wilshire 5000 95, 168, 305 window dressing 125 wine 541 winner’s curse 286 World Bank (WB) 130, 282 WorldCom 16 World Equity Benchmark Shares (WEBS) 105 world federation of exchanges (WFE) 457 wrap account 100, 110 writer 452, 471 Yahoo! Finance 173, 348, 350, 513 Yankee bonds 98, 130, 382 yields 57, 61; BEY 394; bond measures 393–5; capital markets 135–6; convenience 506–7; CY 393, 411; defined 76; earnings 359; forward earnings 359; money markets 129; prices and 388–93; promised 386, 394; returns 61; tax-exempt 133; T bills 119, 121; yield to

worst 395; YTC 395, 411; YTM 393–4, 411; YTP 394, 411; see also dividend yield yield curve: bonds 400–7, 411; factors affecting shape 407; riding 406; shape theories 401–4; significance 404–6; spread 405; strategy 406; yield curve strategy 432–3, 446 yield swap strategy 431–2, 446 yield to call (YTC) 395, 411 yield to maturity (YTM) 393–4, 411 yield to put (YTP) 394, 411 yield to worst 395 YTC see yield to call YTM see yield to maturity YTP see yield to put zero-beta portfolio 246 zero-coupon bonds 131, 376, 382, 397 zero-sum game 265, 493