Signs That Markets Are Coming Back 9781783509188, 9781783509317

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SIGNS THAT MARKETS ARE COMING BACK

RESEARCH IN FINANCE Series Editor: John W. Kensinger Recent Volumes: Volumes 6
25:

Edited by Andrew H. Chen

Volumes 26
29: Edited by John W. Kensinger

RESEARCH IN FINANCE VOLUME 30

SIGNS THAT MARKETS ARE COMING BACK EDITED BY

JOHN W. KENSINGER University of North Texas, Denton, TX, USA

United Kingdom
North America
Japan India
Malaysia
China

Emerald Group Publishing Limited Howard House, Wagon Lane, Bingley BD16 1WA, UK First edition 2014 Copyright r 2014 Emerald Group Publishing Limited Reprints and permission service Contact: [email protected] No part of this book may be reproduced, stored in a retrieval system, transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without either the prior written permission of the publisher or a licence permitting restricted copying issued in the UK by The Copyright Licensing Agency and in the USA by The Copyright Clearance Center. Any opinions expressed in the chapters are those of the authors. Whilst Emerald makes every effort to ensure the quality and accuracy of its content, Emerald makes no representation implied or otherwise, as to the chapters’ suitability and application and disclaims any warranties, express or implied, to their use. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN: 978-1-78350-931-7 ISSN: 0196-3821 (Series)

ISOQAR certified Management System, awarded to Emerald for adherence to Environmental standard ISO 14001:2004. Certificate Number 1985 ISO 14001

CONTENTS LIST OF CONTRIBUTORS

vii

INTRODUCTION

ix

EQUITY HEDGE FUND PERFORMANCE, CROSS-SECTIONAL RETURN DISPERSION, AND ACTIVE SHARE David M. Smith THE MARKET TIMING SKILLS OF LONG/SHORT EQUITY HEDGE FUND MANAGERS Xin Li and Hany A. Shawky EXTENDING THE REAL OPTIONS APPROACH BY INCLUDING INFORMATION OPTIONS Andrew H. Chen, James A. Conover and John W. Kensinger QUANTITATIVE AND COMPUTER SKILLS EMPLOYERS WANT VS. WHAT THE BUSINESS CURRICULUM CAN PROVIDE Mark Tengesdal and Adelaide Griffin

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53

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THE UNEASY CASE FOR REAL ESTATE INVESTMENTS C. Sherman Cheung and Peter Miu

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DIVIDEND IRRELEVANCE AND FIRM CONTROL Steven A. Dennis and William Steven Smith

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LIST OF CONTRIBUTORS Andrew H. Chen

Cox School of Business, Southern Methodist University, Dallas, TX, USA

C. Sherman Cheung

DeGroote School of Business, McMaster University, Hamilton, ON, Canada

James A. Conover

College of Business Administration, University of North Texas, Denton, TX, USA

Steven A. Dennis

Department of Finance, University of North Dakota, Grand Forks, ND, USA

Adelaide Griffin

School of Management, Texas Woman’s University, Denton, TX, USA [Retired]

John W. Kensinger

College of Business Administration, University of North Texas, Denton, TX, USA

Xin Li

Department of Economics, University at Albany, Albany, NY, USA

Peter Miu

DeGroote School of Business, McMaster University, Hamilton, ON, Canada

Hany A. Shawky

Department of Finance, University at Albany, Albany, NY, USA

David M. Smith

Department of Finance and Center for Institutional Investment Management, School of Business, University at Albany (SUNY), Albany, NY, USA

William Steven Smith Department of Finance, University of North Dakota, Grand Forks, ND, USA Mark Tengesdal

School of Management, Texas Woman’s University, Denton, TX, USA

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INTRODUCTION The current volume in the Research in Finance series features an international set of contributors. The overall theme of the volume is a timely topic: “Signs that Markets are Coming Back.” The lead chapter sets the theme by examining the performance of hedge funds in market environments that are conducive to active management versus environments that are not. The author reports that equity hedge funds achieve their strongest performance during periods of elevated dispersion. This lead chapter offers interesting insights into the performance of equity investments. The second chapter continues the theme by examining any market timing skills hedge fund managers might possess. The authors report evidence of significant market timing ability by fund managers around market crisis periods. Further, they find that a significant number of managers behave more conservatively when the market return is expected to be far above average and more aggressively when the market return is expected to be far below average. The authors also distinguish between these managers’ skills in short versus long situations. The third chapter offers new insights into real options by explicitly differentiating between options with information bundles as the underlying versus options that have physical assets as underlying assets. The authors link these information options to the value chain that enumerates the stages in the process of adding value through information processing activities (called the virtual value chain). With Information Options, the underlying assets are information assets and the rules governing exercise are based on the realities of the information realm (infosphere). Analysis of information options offers new tools for evaluating investments in research, mineral exploration, logistics, energy transmission, and other information operations. The fourth chapter opens many doors by explicitly considering the ability of business schools to develop the quantitative and computer skills that today’s employers seek. University business programs, they argue, do not serve their students’ educational needs because they teach only the topics favored by the faculty. There needs to be continuing exchange of .

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INTRODUCTION

information between industry and education. Among employers’ complaints the authors list that (a) young workers are not able to think and solve complex problems, and (b) young adults lack the working knowledge needed to use common business software (perhaps not surprising). Many of the shortcomings the authors identify are not surprising, but some will truly astonish the reader. The fifth chapter also offers surprises by examining the difficulties in finding sound investments in the current real estate markets. The authors report that there are two distinct states of the real estate market
the lowreturn state is characterized by its high volatility and its high correlations with stock market returns, while the high-return state is characterized by its low volatility and its low correlations with stock market returns. The authors find that any statistically significant improvement in risk-adjusted return for a diversified portfolio that includes real estate is very much limited to the bullish environment of the real estate market. The sixth chapter offers a careful examination of whether the founders of a firm can create an artificial (or “homemade” dividend) while they still hold majority interest. The authors employ traditional discounted valuation in order to show that the act of creating an artificial dividend may decrease the value of the firm because it can divert funds from investment to the consumption of perquisites. The authors show that only when there is complete trust between the firm’s founders and the other shareholders, the founders can create an artificial dividend without cost (perhaps a rare situation when arms-length market transactions are involved in the stock sale). John W. Kensinger Series Editor

EQUITY HEDGE FUND PERFORMANCE, CROSSSECTIONAL RETURN DISPERSION, AND ACTIVE SHARE David M. Smith ABSTRACT This study examines several aspects of active portfolio management by equity hedge funds between 1996 and 2013. Consistent with the idea that cross-sectional return dispersion is a proxy for the market’s available alpha, our results show that equity hedge funds achieve their strongest performance during periods of elevated dispersion. The performance advantage is robust to numerous risk adjustments. Portfolio managers may use the current month’s dispersion to plan the extent to which the following month’s investment approach will be active or passive. We also estimate the active share for equity hedge funds and find an average of 53%. We further document the average annual expense ratio for managing hedge funds’ active share to be about 7%. This figure is remarkably close to active expense ratios reported previously

Signs that Markets are Coming Back Research in Finance, Volume 30, 1
22 Copyright r 2014 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1108/S0196-382120140000030001

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for equity mutual funds, which may be interpreted as evidence of uniform pricing for active portfolio management services. Keywords: Hedge funds; equities; portfolio choice JEL classifications: G11; G12; G23

Hedge funds have become a key investment vehicle for pension funds, endowments, foundations, and high-net-worth individuals. Hedge funds are lightly regulated and can be managed with a great deal of investment flexibility. Among other advantages, they can freely leverage their portfolios using margin and efficiently take bearish positions through short sales. Hedge-fund investors expect portfolio managers to reliably generate positive alpha net of fees. This is a near impossibility for any portfolio manager who is a “closet indexer,” so hedge-fund managers with aspirations to longevity in the role are likely to be found at the active end of the passive
active continuum. One focus of this chapter is the degree to which equity-oriented hedge funds pursue strategies that deviate from benchmark indexes. Zummo (2012) notes that an equity fund managed by A.W. Jones was the first hedge fund in existence and he reports that on a raw-return basis, long/ short equity hedge funds outperformed all other traditional categories of hedge funds between 1995 and 2010. The TASS database indicates that at year-end 2012, 1,251 of the 7,210 hedge funds in existence were classified as long
short equity funds. This category represents almost 10% of the $1.020 trillion hedge-fund assets under management (AUM) reported by TASS as of that date. In the case of both number of hedge funds and AUM, long
short equity holds third place behind funds of funds and multi-strategy funds. For several decades, researchers have examined actively managed mutual funds and commented on their frequent tendency to mimic indexes. Related work has tested mutual funds’ effectiveness against passively managed index funds and the value of active management across the market cycle. Given the similarities in the types of securities held by equity hedge funds and mutual funds, it is notable that these questions have not yet been addressed for equity hedge funds. This chapter examines the relation between hedge-fund performance and the cross-sectional return dispersion of the U.S. equity market, which can be interpreted as a measure of alpha

Equity Hedge Fund Performance

3

potential for active portfolio managers. Using four models to measure excess return, we find performance to have a strong positive relation with cross-sectional return dispersion. We also analyze whether hedge funds manage their equity portfolios to be distinct from relevant indexes, as well as costs and benefits of their doing so. We document that the average active share for equity hedge-fund portfolios is 53%, and that the expense ratio for that active share averages about 7%. The active alpha is between 6% and 7%. The magnitude of the active expense ratio is strikingly similar to that found by Miller (2007) for mutual funds, which suggests some uniformity of pricing for active portfolio management services.

LITERATURE REVIEW Several clusters of studies motivate and inform the present research. Below we introduce selected literature concerning cross-sectional dispersion of returns, the active
passive investment debate, and estimation of portfolio active share.

Cross-Sectional Return Dispersion Cross-sectional variability in returns is an important feature of equity markets, particularly from a portfolio management and performance measurement perspective. DeSilva, Sapra, and Thorley (2001) find that cross-sectional variability in individual security returns within a market (which they term “dispersion”) is an important determinant of the return dispersion across managed portfolios. In a high-dispersion environment, portfolio returns will tend to differ greatly from each other and from the aggregate market return. Despite the differentiating effect of high dispersion, DeSilva et al. question whether the diversity in portfolio “alpha” during such periods is an accurate reflection of the diversity of investment management talent. They also show that in years of high dispersion, a greater fraction of funds will have returns above the “index-plus-active-cost” level. An example may be instructive. Assume that the average equity mutual fund charges an expense ratio of 1.5% to compete against an index that returns 10%. The consequent target return for active management will be 11.5%.

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Further assume that actively managed equity mutual fund returns are normally distributed and the cross-sectional standard deviation of fund returns is 5%. Under these assumptions, 38.2% of active managers (the area to the right under a normal curve) will earn a return above 11.5%. In an alternative scenario, a higher cross-sectional standard deviation of 15% combined with the previous assumptions results in 46% of active managers exceeding the 11.5% hurdle. The effect is due to the mechanics of dispersion rather than to any difference in the management-talent distribution between the first and second scenarios. Ankrim and Ding (2002) argue that when cross-sectional return dispersion is high such as at the end of the 1990s, differences in skill across managers are magnified. Thus, managers with slightly below-average stock picks are penalized disproportionately for those suboptimal weightings. Indeed, DeSilva et al. propose making an adjustment to portfolio results for periods of unusually high and low security-return dispersion (their proposal is to weight alphas by the inverse of dispersion). Yu and Sharaiha (2007) as well as Bouchey, Fjelstad, and Vadlamudi (2010) interpret cross-sectional stock return dispersion to reflect the current alpha potential in the equity market. Bouchey et al. point out that crosssectional dispersion may bear a relation to the Fundamental Law of Active Management proposed by Grinold (1989), in which the breadth of investment opportunities is a key input to the information-ratio performance metric. They suggest that cross-sectional dispersion may be thought of as a proxy for Grinold’s concept of “market breadth.” Yu and Sharaiha note that the worst type of environment for stock pickers is low time-series return dispersion in the presence of low cross-sectional return dispersion. In such environments, active portfolio managers have few opportunities to distinguish themselves. Yu and Sharaiha suggest that superior portfolio managers could employ techniques such as variance swaps to hedge against low dispersion, thus magnifying returns and achieving more separation from peers. Although this chapter is the first to study hedge funds in the context of cross-sectional dispersion, previous researchers have examined the relation between hedge-fund performance and other financial market conditions. Just one example is Carlson and Steinman (2008), who find a negative relation between hedge-fund failures and U.S. equity and bond market returns, as well as the time series of market volatility. This result is strongest for funds that pursue long-bias strategies. They also find that the hedge-fund failure rate increases with emerging-market returns and the value of the U.S. dollar.

Equity Hedge Fund Performance

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The Active versus Passive Portfolio Management Decision Sharpe (1991) observes that in the aggregate, active management is a zero-sum game before fees, with managers who beat their performance benchmarks winning at the expense of others who trail their benchmarks. After fees, the aggregate active-management efforts of investors should equal the performance of the overall market less average fees. In fact, this should be the expected return for any investor who uses naive selection to choose active portfolio managers. Substantial evidence exists about the success of active portfolio management against passive, index tracking strategies. Although some studies uncover evidence of significant management talent, the annual SPIVA reports (authored by, for example, Dash, 2009; Soe, 2013) show for many years and across numerous markets that benchmark indexes typically outperform active mutual fund managers. The various SPIVA reports consistently show that the proportion of winning funds shrinks as the performance measurement period lengthens. In general, passive managers outperform active managers because fees, expenses, and trading costs related to active portfolio management are responsible for lowering the returns. French (2008) compares the costs of active and passive management between 1980 and 2006. He finds that the average annual incremental cost of active investing over passive has varied between 56 and 76 basis points, with the long-term average being 67 basis points per year. Despite results such as French’s, some investors argue that active management can provide significant advantages in some sectors of the market. One basis for this belief is that the less efficiently priced a market, the more potential there is for a manager to add value. Conventional wisdom holds that due to less-intensive analyst coverage, emerging-market and small-cap stocks are examples of sectors that active management can better exploit. This has contributed to the idea that portfolios should have passive exposure for “core” holdings combined with “satellite” holdings in sectors where pricing may be less efficient and active management can be practiced. Conventional wisdom notwithstanding, the SPIVA reports consistently show that small-cap active managers underperform indexes at least as frequently as large-cap managers. Sorensen, Miller, and Samak (1996) provide a framework for optimizing the decision of how much an institutional investor should commit to actively versus passively managed assets. Their conclusions are based on the amount of stock-picking skill is evidenced by active managers. The authors conclude that even if the active managers

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show significant skill, passive investing should remain an important part of the overall portfolio.

Active Share The focus on active share has intensified as investors have become aware that savings on fees is a performance-enhancement strategy. The calculation of active share helps investors understand how much their portfolio differs from the benchmark index, and whether they are receiving only beta exposure but paying fees normally associated with alpha generation. Miller (2007) and Cremers and Petajisto (2009) provide alternative approaches to measuring active share. Both papers show that the portfolios of putative active mutual fund managers often differ little from the components and weights of benchmark indexes, while other managers build portfolios that reflect a high degree of thought independence. Both papers show that managers in the former group not only hew closely to indexes, but their small active shares tend to achieve weak performance. On the other hand, portfolios with a low correlation relative to the index are interpreted as “active,” and over time these managers also tend to perform well even net of expenses. The two seminal papers on active share use different approaches. Miller’s approach requires only the R2 from a regression of a fund’s returns on those of an appropriate benchmark index. His approach takes account of the leverage employed by portfolio managers. Introducing the expense ratio of the actively managed fund and a representative index fund allows for estimation of the expense ratio for the portfolio’s active portion. Miller’s analysis finds that many large-cap equity mutual funds maintain active expense ratios of approximately 7%. Thus, he concludes that actively managed mutual funds may be thought of as one part index fund and one part hedge fund, with respect to investment strategy as well as their effective expense ratios. Cremers and Petajisto (2009) develop and apply an approach that compares the weight of each fund’s holdings to the weights of those securities in the fund’s benchmark index. This method has the potential to show with high specificity which active bets a fund manager is making and how large they are. One drawback is that if managers window-dress their portfolios shortly before holdings-disclosure dates, this can somewhat complicate a holdings-based analysis. Our chapter examines hedge funds, and we do not have the luxury of knowing their portfolio holdings, whether window-dressed or not. Thus,

Equity Hedge Fund Performance

7

we lack the necessary inputs to use the Cremers
Petajisto estimation method. However, the TASS files contain enough information to approximate hedge-fund active share, expense ratios, active expense ratios, alphas, and active alphas following Miller’s approach.

HYPOTHESIS In this chapter, we examine one principal hypothesis, which can be stated in alternative form as follows: H1. Hedge fund performance and active share are positively related to the market’s contemporaneous and lagged cross-sectional return dispersion. Hypothesis H1 stems from the observation that active portfolio managers distinguish themselves by deviating from the component weights of their benchmark indexes. In the extreme case where all stocks in an index generate similar returns, the portfolio manager’s attempts to achieve enlightened reweighting are fruitless. Only if the difference between returns of high- and low-performing stocks is meaningful, will the rewards from active weighting of portfolio components be valuable to investors. Thus, following Yu and Sharaiha (2007) and Bouchey et al. (2010), we view the contemporaneous cross-sectional stock return dispersion as a proxy for the amount of alpha potential available in the equity market. If active portfolio managers have skill, the risk-adjusted return during periods of high crosssectional dispersion should eclipse returns of the same funds during periods of low cross-sectional dispersion. To the extent that cross-sectional dispersion is persistent, we should observe the same relation between equity hedge-fund performance and lagged cross-sectional return dispersion. At times when return dispersion indicates high alpha potential in the equity markets, hedge-fund managers on average should adjust their portfolios to capture that alpha. Thus, we expect to observe lower correlations between hedge-fund returns and index returns when dispersion is high. Accordingly, we hypothesize a positive relation between active share and dispersion.

DATA AND EMPIRICAL TESTS The hedge-fund data used in this chapter are obtained from the Lipper/ TASS database. TASS contains both active (“live”) and “graveyard” funds

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that have stopped reporting for a variety of reasons. The graveyard was established in 1994 when TASS began reporting hedge fund exits. Our TASS initial sample downloaded from November 2013 includes 6,115 live and 13,110 graveyard funds. We identify a sample of hedge funds that focus on U.S. equity investments by imposing all of the following screens on the initial downloaded hedge-fund universe. To be included in the sample, a fund must: (1) indicate that it holds equities, through a “1” in the AE Equities field. (2) have a “0” in the fields for the following instruments: Convertibles, Fixed Income, Corporate Bonds, Emerging-Market Bonds, Government Bonds, Distressed Bonds, Sovereign Debt, High Yield Bonds, MortgageBacked Securities, Currencies, and Commodities (of various types). (3) not show evidence of emphasizing non-U.S. investments, through its name (e.g., “Japan Fund”) or through a “1” in the geographical-focus fields for various non-U.S. markets. (4) list a “0” in the field indicating a market-neutral investment approach. (5) have a minimum of 20 monthly return observations, in order to allow for reasonably robust regression parameter estimates. At the time that some hedge funds are added to the TASS database, the fund sponsor sometimes backfills the monthly return series for previous months. This creates a bias in that such added funds tend to be successful, while other, unobserved funds may have produced poor returns, but these funds are never added to TASS. Fung and Hsieh (2000) point out that backfilled returns are biased upward, which can lead to incorrect inferences. To avoid backfill bias, we use returns beginning at the later of the start date for the fund’s coverage in TASS and the start date for the fund to report returns to TASS. After application of the screens, the final sample consists of 459 hedge funds, of which 93 are from the live subsample and 366 are from the graveyard subsample. Table 1 shows that the average equity hedge fund is in our sample for 69 months, based on the number of monthly returns for each observation. Table 1. Funds’ Number of Months in Sample. Mean Median Mode (18 funds) Maximum (3 funds) Minimum (8 funds)

69 56 25 207 24

Note: This table shows the number of months of returns for equity hedge funds in the sample.

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Table 2.

Hedge Funds’ Reason for Inclusion in Graveyard Subsample.

Reason for Deletion Fund liquidated Unable to contact fund Fund no longer reporting Unknown Fund has merged into another entity Fund closed to new investment Program closed

Percent of Graveyard Sample (n = 366) 36% 29% 28% 3% 2% 1% 1%

Note: This table gives, for the 366 graveyard equity hedge funds in the sample, the reason TASS provides for deletion from the “live” subsample.

Three funds are in the sample for all 207 months. Table 2 contains reasons that TASS provides for classifying its equity-oriented funds in the “graveyard” subsample. The most common basis for such classification, given by 57% of funds, are the related reasons that TASS was unable to contact the fund or the fund stopped reporting to TASS. Fund liquidation is the reason that a further 36% of the funds landed in the graveyard file. We measure hedge-fund performance using four models: the capital asset pricing model, the three-factor model of Fama and French (1992), the four-factor model of Carhart (1997), and the seven-factor model of Fung and Hsieh (2001). We obtained factors for the first three models from Kenneth French’s web site, and factors for the seven-factor model from the web sites of David Hsieh and the Federal Reserve Bank of St. Louis (FRED). The first three models are commonly used for individual stocks and stock portfolios, while the Fung and Hsieh approach is designed to accommodate the investment categories and techniques common to the hedge-fund industry. Although we report results for all four models, we use alphas from only the Carhart model in subsequent tests because it contains the largest number of factors chosen specifically for equities. Russell Investments provided us with the cross-sectional return volatility data. The CrossVol™ index series was introduced in 2010 by Russell Investments and Parametric Portfolio Associates (as described by Russell Investments, 2011). CrossVol measures return dispersion for a well-defined universe of equity securities within a given time period. In general, high CrossVol is associated with return correlations near +1 and low CrossVol is associated with return correlations closer to 0. We use monthly CrossVol to characterize market conditions, particularly the degree to which portfolio managers can take actions to distinguish their performance from their

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peers’. Between July 1996 and September 2013, the average value for the monthly CrossVol index for the Russell 1000 component stocks was 8.44, and the median was 7.44. The highest value was 21.72 in February 2000, and the lowest value was 4.47 in June 2011. For our study, we define “high” and “low” dispersion environments using the 7.44 median CrossVol value as the breakpoint. CrossVol is available for a variety of national stock markets, equity styles, and capitalizations. Our study uses the monthly CrossVol for only the Russell large-cap 1000 index to classify market conditions. Russell calculates the CrossVol index value as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX σt = t ð1Þ wit ðrit − rmt Þ2 i=1

where wit is the beginning-of-month weight of stock i in the Russell 1000 market index, rit is the month’s return for stock i, and rmt is the month’s return for the Russell 1000 market index. Our analysis also involves the estimation of each hedge-fund portfolio’s active share. Estimation requires the R2 from regressing the fund’s monthly returns on the returns for an appropriate benchmark index. Unfortunately, we do not know the actual performance benchmark index for each fund, so we attempt as best we can to infer this information. We calculate each fund’s R2 relative to 27 Russell and Standard & Poors U.S. domestic equity indexes, ranging from all-cap to large-cap to micro-cap, and value to growth. We assume that each fund’s “functional benchmark” is the index that produces the highest R2. The maximum R2 values reflect the following distribution of style- and capitalization-related benchmarks. All-cap funds constitute 8% of the total, large-cap 11%, mid-cap 30%, small-cap 22%, and micro-cap 28%. Regarding style, 55% of highest-R2 indexes are growth, 15% are core, and 29% are value. Note that these reported style and cap distributions overlap, so before rounding the numbers sum to 200% Following Miller (2007), the weight of an equity hedge-fund portfolio’s active share (wA) is calculated according to Eq. (2): pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 − R2 Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi wA = ð2Þ R þ ð1 − R2 Þ

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where R2 is the coefficient of determination from a regression of the hedge fund’s monthly returns on the monthly returns to the benchmark index. Miller (2007) shows that the active expense ratio CA can be estimated using Eq. (3): RðCP þ CI Þ CA = CP þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 − R2 Þ

ð3Þ

where CP is the estimated expense ratio for the hedge fund and CI is the expense ratio for an investment in a passive fund. Index-fund expense ratios represent the cost of passive management and thus serve as proxies for the expense benefit of active management. The relevant passive vehicle is identified for each hedge fund as described above in the “R2” discussion. The alpha for a passive portfolio is assumed to be the negative of CI, the cost of indexing. The alpha for each portfolio’s active share (αA), from Miller’s paper, is: RðαP þ CI Þ αA = αP þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 − R2 Þ

ð4Þ

where αP is the Carhart four-factor alpha.

RESULTS Table 3 contains the monthly alphas for all 459 funds, estimated using various risk-factor models. The models used include the capital asset pricing model, the Fama
French three-factor model, the Carhart four-factor model, and the Fung and Hsieh seven-factor model. Table 3 gives that for equity-oriented hedge funds as a group, mean and median monthly performance figures are nonnegative in all cases, and in three instances skewness is positive as well. The mean monthly alpha estimates using the first three models are all statistically significant when evaluated at conventional levels. Table 4 reports equity hedge-fund performance according to the prevailing stock-return dispersion environment. As noted, we define a high(low-) dispersion month as one in which the CrossVol figure for the Russell 1000 index exceeds (is below) its median of 7.44. For Table 4, we examine only those 218 funds in our sample with at least 20 months of returns during both high- and low-dispersion periods. This allows us to conduct tests that evaluate paired means. The four models are unanimous in their results: t-tests of

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Table 3.

Monthly Alpha of U.S. Equity Hedge Funds.

CAPM Mean t-stat (mean ≠ 0) Median Standard deviation Skewness Kurtosis

Fama
French Carhart Fung and Hsieh Three-Factor Model Four-Factor Model Seven-Factor Model

0.20% 6.49*** 0.15% 0.67% 0.25 2.02

0.14% 4.46*** 0.12% 0.68% 0.52 3.44

0.14% 4.21*** 0.12% 0.69% 0.41 3.56

0.00% −0.12 0.02% 0.78% −0.45 2.25

This table reports equity hedge-fund performance between July 1996 and September 2013 by estimating alpha from the capital asset pricing model, the Fama
French three-factor model, the Carhart four-factor model, and the Fung and Hsieh seven-factor model. The number of hedge funds in each case is 459. *** indicate that a mean value is significantly different from zero at the 1% level for a onetailed test.

Table 4.

Monthly Alpha of U.S. Equity Hedge Funds by Cross-Sectional Dispersion. CAPM

CrossVol Mean t-stat (paired means) Median Standard deviation Skewness Kurtosis Observations

High

Low

0.50% 0.09% 6.35*** 0.44% 0.13% 0.88% 0.60% 0.41 −0.91 1.23 4.01 218 218

Fama
French Three-Factor Model High

Low

0.33% 0.06% 3.72*** 0.29% 0.09% 0.94% 0.62% 0.19 −0.95 1.44 3.79 218 218

Carhart Four-Factor Model High

Low

0.29% 0.06% 3.32*** 0.27% 0.09% 0.96% 0.62% 0.12 −0.97 2.16 3.89 218 218

Fung
Hsieh Seven-Factor Model High

Low

0.16% −0.01% 2.03*** 0.09% 0.01% 1.05% 0.66% 0.58 −0.96 2.88 5.01 218 218

This table provides equity hedge funds’ monthly alpha, estimated between July 1996 and September 2013 using the capital asset pricing model, the Fama
French three-factor model, the Carhart four-factor model, and the Fung and Hsieh seven-factor model. Using paired t-tests, we compare the sample means for 218 individual hedge funds in high and low cross-sectional return dispersion months. In defining “high” and “low” dispersion environments, the breakpoint is a monthly CrossVol index value of 7.44. *** indicate that a mean value is significantly different from zero at the 1% level for a one-tailed test.

paired means indicate that equity hedge-fund performance is significantly higher in high-dispersion periods than in low-dispersion periods. This confirms our hypothesis that equity hedge-fund managers are particularly successful in pursuing active strategies when available alpha is high, and less so

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when available alpha is low. This finding is also consistent with the results of Petajisto (2013) for actively managed U.S. domestic equity mutual funds.

Using Lagged CrossVol For any analysis of contemporaneous cross-sectional dispersion, a valid criticism is that investors cannot use the contemporaneous information to improve performance. As noted by Yu and Sharaiha (2007), investors with knowledge of alpha potential as indicated by cross-sectional dispersion could adjust their tactics. Given the much higher expenses associated with active management, one approach could be to seek superior performance net of expenses by switching opportunistically between active and passive over time. Ankrim and Ding (2002) conclude that cross-sectional dispersion exhibits intertemporal persistence. Accordingly, we repeat our preceding tests of paired means using a lagged value of CrossVol. Table 5 contains our results, which strongly indicate that lagged cross-sectional dispersion can be used to classify the alpha potential in the market during the current Table 5.

Monthly Alpha of U.S. Equity Hedge Funds by Lagged Cross-Sectional Dispersion. CAPM

Lagged CrossVol

High

Low

Mean t-stat (paired means) Median Standard deviation Skewness Kurtosis Observations

0.47 0.09 5.18*** 0.39 0.14 0.90 0.67 0.28 −0.69 1.23 2.80 211 211

Fama
French Three-Factor Model High

Low

0.35 0.04 4.08*** 0.36 0.09 0.94 0.66 0.16 −0.82 2.56 2.93 211 211

Carhart Four-Factor Model High

Low

0.32 0.00 4.59*** 0.34 0.06 0.92 0.66 0.27 −1.20 2.90 3.98 211 211

Fung
Hsieh Seven-Factor Model High

Low

0.21 −0.10 4.06*** 0.24 −0.02 0.92 0.76 −0.28 −1.86 2.60 9.04 211 211

This table provides equity hedge-fund monthly alpha, estimated between July 1996 and September 2013 using the capital asset pricing model, the Fama
French three-factor model, the Carhart four-factor model, and the Fung and Hsieh seven-factor model. The sample means are compared for 218 individual hedge funds in paired t-tests, between high and low lagged cross-sectional return dispersion months. In defining “high” and “low” dispersion environments, the breakpoint is a CrossVol index value for the month of 7.44. *** indicate that a mean value is significantly different from zero at the 1% level for a onetailed test.

14

DAVID M. SMITH

month. Indeed, the results in Table 5 are generally even stronger than those for contemporaneous CrossVol in Table 4. This stronger effect may come about from equity hedge-fund managers’ enhanced efforts to achieve differentiating results when they have foreknowledge of the market environment, although the low lagged-CrossVol periods show a diminution in performance at roughly the same magnitude that high lagged-CrossVol periods show performance enhancement.

Active Share We now focus on portfolio active share. Following Miller (2007), we estimate equity hedge funds’ active share, active expense ratio, and active alpha. Active share requires only each hedge fund’s R2 from regressing its returns on those of its benchmark index. Active expense ratio requires the aforementioned R2, each fund’s total expense ratio, and the expense ratio for a representative passive investment. Active alpha requires the R2, the passive expense ratio, and each fund’s overall alpha. Table 6 contains a list of the exchange-traded funds (ETFs) that we used to represent each equity hedge fund’s passive counterpart. We choose each hedge fund’s passive ETF based on the index that generates the highest R2 relative to that fund’s monthly returns. The annualized expense ratios for the ETFs range from five basis points for a large-cap core product that tracks the S&P 500 to 25 basis points for all-cap growth and value products that track the Russell 3000 growth and value indexes, respectively. Table 7 documents the active share of equity hedge funds, evaluated relative to the highest-R2 benchmark index. Growth is the most common style by far, as judged by the fact that growth-index returns generally correlate most highly with over half of the 459 equity hedge-funds’ returns. Value is second, followed by the core style. As for capitalization of holdings, the mid-cap sector returns load most strongly, followed by micro-cap and small-cap. These equity sectors comprise the group that many market participants consider to have the greatest native alpha potential due to inefficient pricing. This perspective is supported by the fact that smaller-cap stocks tend not to have a robust analyst following. The average active share across all funds is 53.22%. This ranges from 34.45% for large-cap funds to 60.64% for core funds. Untabulated results show 25 of the 459 equity hedge funds in our sample with active shares above 80%, 71 above 70%, and 136 above 60%. On the other hand, 24 hedge funds have active shares below 30%, 61 below 40%, and 188 below

15

Equity Hedge Fund Performance

Table 6.

Representative ETFs for Use in Estimating Active Expense Ratio. Representative ETF for Each Equity Style

Equity Style All-cap growth

Name

iShares Russell 3000 Growth Index ETF All-cap core Vanguard Russell 3000 Index ETF All-cap value iShares Russell 3000 Value Index ETF Large-cap growth Vanguard S&P 500 Growth Index ETF Large-cap core Vanguard S&P 500 Index ETF Large-cap value Vanguard S&P 500 Value Index ETF Mid-cap growth Vanguard S&P Mid-Cap 400 Growth Index ETF Mid-cap core Vanguard S&P Mid-Cap 400 Index ETF Mid-cap value Vanguard S&P Mid-Cap 400 Value Index ETF Small-cap and micro-cap growth Vanguard S&P Small-Cap 600 Growth Index ETF Small-cap and micro-cap core Vanguard S&P Small-Cap 600 Index ETF Small-cap and micro-cap value Vanguard S&P Small-Cap 600 Value Index ETF

Ticker

Expense Ratio

IWZ

0.25%

VTHR IWW VOOG VOO VOOV IVOG

0.15% 0.25% 0.15% 0.05% 0.15% 0.20%

IVOO

0.15%

IVOV

0.20%

VIOG

0.20%

VIOO

0.15%

VIOV

0.20%

This table lists, for various equity investment styles, the low-cost representative ETF used and its annualized expense ratio.

50%. Some equity hedge-fund managers have clearly maintained portfolios that are close to indexes, while others are either showing a high degree of independence, or we may not have used the appropriate index to generate the maximum R2 value. These results for equity hedge funds contrast with Miller’s (2007) in his analysis of 152 U.S. large-cap mutual funds. He finds active share weights of 15.55% for such funds, and 22.05% across the entire Morningstar universe of 4,754 funds. We find that very few hedge funds have active portfolio weights that are as low as those reported by Miller for mutual funds. The next column to the right in Table 7 contains our estimate of equity hedge funds’ annualized expense ratios, the average estimate being 3.59%. This is lower than French’s (2008) estimate for all hedge-fund categories of 4.26%. French’s sample period ends prior to the worst of the 2008 bear market in stocks. Our equity hedge funds’ expense-ratio estimates include

16

DAVID M. SMITH

Table 7. Estimates of Active Share, Active Expense Ratio, and Active Carhart Alpha for Equity-Oriented Hedge Funds. Style

R2

Active Share

Expense Ratio

Active Expense Active Monthly Observations Ratio Alpha Mean Median

All equity 45.30% 53.22% hedge funds

3.59%

7.35%

0.42%

0.39%

459

Value style Core style Growth style

37.75% 57.87% 60.64% 43.74% 45.02% 53.40%

3.67% 3.87% 3.45%

7.03% 9.06% 7.04%

0.26% 0.25% 0.55%

0.20% 0.40% 0.49%

135 71 253

All-cap Large-cap Mid-cap Small-cap Micro-cap

55.55% 34.45% 44.66% 44.65% 47.71%

3.68% 3.15% 3.48% 3.43% 3.98%

7.91% 5.87% 6.94% 6.98% 8.49%

0.29% 0.29% 0.44% 0.10% 0.74%

0.19% 0.19% 0.46% 0.09% 0.66%

39 51 138 103 128

47.18% 60.45% 53.52% 53.48% 51.64%

This table contains estimates of how much equity-oriented hedge funds produce returns that deviate from those of style-appropriate benchmark indexes. R2 is generated by regressing each equity hedge fund’s monthly returns on the monthly returns of 27 Russell and S&P indexes. For each fund, the maximum of these 27 R2 values is recorded and then serves as the basis for estimating the values in Table 7’s other columns. Next the table combines each fund’s active share with its overall annualized expense ratio to estimate an annualized expense ratio for just the active portion of the portfolio. Finally, using each fund’s monthly alpha estimated from the Carhart four-factor model, we list the mean and median monthly alpha from just the active share of the fund’s portfolio.

a fixed management fee reported by each fund, plus the product of each fund’s incentive fee and its average annual return. It is likely that our Table 7 somewhat overstates funds’ expenses because it does not include the effect of negative returns pulling funds’ values below a high water mark. But, not all funds in the sample have high water marks, and during most of the sample period hedge funds as a group experienced positive returns. Based on those expense estimates as well as the active shares, we estimate active expense ratios following Miller (2007). He finds, for a sample of large-cap U.S. domestic equity mutual funds, the average annualized active expense ratio is in excess of 7%. Our average figure for equity hedge funds is quite similar, the range being 6
9% across the style and cap spectrum. Finally, based on the alphas generated using Carhart’s four-factor model for equity portfolios, we find an average monthly active alpha for our sample funds of 0.42% (median is 0.39%). Our active alpha estimates

17

Equity Hedge Fund Performance

are higher for growth-oriented funds than for either value or core styles. Micro-cap funds had much higher mean and median alphas than did any of the other styles. Interestingly, alpha does not vary monotonically across the cap spectrum. Funds whose returns are correlated with mid-cap indexes stand out as particularly strong performers, while their small-cap counterparts have the lowest alpha of all (though still positive). Table 8 contains further results for active share, this time presented by cross-sectional return dispersion environment. We include only the 220 funds for which we have a 20-month history in both high- and lowdispersion environments, and again conduct t-tests of paired means. We find that with great consistency, high-dispersion environments are associated with lower levels of active share. It appears as if equity hedge-fund managers detect that they are operating in a low-dispersion period, and they ratchet up their active share (i.e., establish greater independence from an index, reflected in a lower R2 value). For all except large-cap and smallcap-oriented hedge funds, the active share is statistically higher during lowdispersion periods. We find an opposite result for the active expense ratio and active alpha. The ranking of average alpha is always in favor of the high-dispersion period, and with two exceptions the same can be said of the active expense ratio. In eight instances, the differences for individual style of cap sectors are statistically significant. For all equity hedge funds that have enough months of return data from both market environments (220 funds out of our sample of 459), the average annualized expense ratio remains around 6.5% regardless of market environment. However, monthly active alpha is an average of 28 basis points higher in highdispersion periods than in low-dispersion periods.

Robustness One potential criticism of this study pertains to the rather unique long
short nature of equity hedge-fund portfolios. Although a positive R2 value for an equity mutual fund almost certainly reflects a positive return correlation, for long
short equity hedge funds, a high R2 can mask a negative correlation. In fact, of the 459 funds in our sample, 42 have negative return correlations with their “highest-R2” benchmark. These negative correlations are certainly due to the net-short positions maintained by these funds. To determine whether these funds drove our results, we remove them and recompute the active weights. The 417 funds with positive correlations have

45.44%

All cap t-stat (paired means) Large-cap t-stat (paired means) Mid-cap t-stat (paired means) Small-cap t-stat (paired means) Micro-cap t-stat (paired means) 1.20

3.23***

6.79% −1.26 5.66% 0.80 7.54% 0.60

6.16%

5.76%

7.23%

5.32%

7.25%

5.40%

4.50%

0.59%

0.35%

0.79%

0.82%

1.88%

0.70%

0.88

2.61***

0.21

1.35*

1.49*

1.37*

1.79**

1.95**

6.72%

1.07%

0.56%

0.72%

6.55% −0.59

6.17%

5.96%

6.45%

High

1.80**

2.65**

0.74

Low

0.55%

0.13%

0.57%

0.26%

0.67%

0.42%

0.62%

0.39%

0.44%

Low

Active Monthly Alpha

0.36

6.44%

6.83%

6.61%

High

Active Annualized Expense Ratio

59

49

76

20

16

132

32

56

220

Observations

This table contains estimates of how much equity-oriented hedge funds generate returns that deviate from those of style-appropriate benchmark indexes. Next the table combines each fund’s active share with its overall annualized expense ratio to estimate an expense ratio for just the active portion of the portfolio. Finally, using each fund’s monthly alpha estimated from the Carhart four-factor model, we list the mean alpha from just the active share of the fund’s portfolio. The sample means are presented for high and low cross-sectional return dispersion months. In defining “high” and “low” dispersion environments, the breakpoint is a CrossVol index value for the month of 7.44. For equity hedge funds, we present t-tests that evaluate means for the same fund in high versus low cross-sectional dispersion environments. ** and *** indicate that a mean value is significantly different from zero at the 5% and 1% levels, respectively, for a one-tailed test.

50.00%

53.64%

51.69%

55.87%

61.14% −3.02*** 43.00% 47.28% −1.53* 52.26% 57.82% −5.42***

62.22% −6.25*** 57.62% −0.52 58.92% −4.51*** 55.47% −1.11 54.66% −2.91***

54.95%

Value style t-stat (paired means) Core style t-stat (paired means) Growth style t-stat (paired means)

57.13% −6.15***

Low

51.60%

High

Active Share

Active Share, Active Expense Ratio, and Active Carhart Alpha for Equity-Oriented Hedge Funds, by CrossVol Level.

All equity hedge funds t-stat (paired means)

CrossVol

Style

Table 8.

19

Equity Hedge Fund Performance

an average active-share weight of 52.81%, almost identical to the 53.22%, we obtain for the whole sample. A second potential criticism is that the results may be driven by extreme values. To address this concern, we repeat all tests after winsorizing our monthly hedge-fund returns at the 1% and 99% levels (the respective returns are −16.31% and +17.42%). The study’s results remain qualitatively unchanged for both portfolio active share and relative performance in different cross-sectional dispersion regimes. As a third check, we let the hedge funds’ responses to TASS dictate the benchmark index we use in each case. For example, if a hedge fund has a “1” in the small-cap and value fields and a “0” in the other style-related fields, we use as a benchmark the Russell 2000 Value or S&P 600 Value indexes, whichever yields the higher R2. If fields spanning the capitalization or value spectra contain “1,” we use an all-cap or core index, respectively. In cases where funds did not respond, we use an all-cap core index (Russell 3000 or S&P 1500). Using these indexes, on average, our R2 values are lower and active share estimates are higher. However, our study’s conclusions remain unchanged.

Caveats Our sample selection process was hindered by data limitations. Hedge funds in TASS respond in binary fashion concerning their usage of various securities, sectors, and techniques. Consequently, users of these data cannot discern the hedge funds’ intensity of usage, whether a hedge fund’s response applies to the current period only, or indeed whether the response was truthful. Our “active-share” results are certainly affected by noise arising from responses that are imprecise or inaccurate for any of the foregoing reasons. A second concern pertains to whether our results can be implemented by investors. We classify the market’s cross-sectional dispersion condition according to the July 1996
September 2013 median CrossVol of 7.44. However, due to the ex-post nature of this classification, investors could not have known with certainty over most of those 17 years which market regime they were currently experiencing. That said, the cumulative median value stabilizes greatly by the middle of the sample period. After 2005, the cumulative median does not deviate from the whole-sample median by more than 0.99.

20

DAVID M. SMITH

A third concern relates to benchmark choice. As noted by Sharpe (1991), to produce an appropriate performance comparison, each manager’s benchmark portfolio should be identifiable prior to the start of the performance measurement period. We do not know the chosen benchmarks for hedge funds in our sample. Consequently, in estimating active share, active expense ratio, and active alpha, we infer benchmarks based on the ex-post return behavior of the equity hedge-fund portfolios. If we knew the actual benchmarks, our active share figures as reported in Tables 7 and 8 would likely be higher.

CONCLUSIONS This chapter examines the performance of actively managed equity-oriented hedge funds, conditional on the cross-sectional stock market return dispersion environment. Cross-sectional return dispersion can be interpreted as the alpha potential in the market. For the large-cap U.S. market, the monthly cross-sectional standard deviation of returns tends to range between 4% and 22%, with 7.44% the long-term median. Russell Investments calculates cross-sectional dispersion indexes that it has branded CrossVol™. We classify months according to their U.S. large-cap CrossVol values relative to the long-term median value. We use four models to estimate alpha for each equity hedge fund: the capital asset pricing model, the Fama
French three-factor model, the Carhart four-factor model, and the Fung and Hsieh seven-factor model. The results across the four models are highly consistent. On average, equity hedge funds have generated positive alpha during the sample period between 1996 and 2013. Consistent with the past findings on mutual funds, we find that hedge-fund performance is strongly related to the return-dispersion environment. High-dispersion periods are associated with significantly higher alpha estimated using all four pricing models, which confirms our hypothesis that equity hedge-fund managers tend to exploit opportunities to use active management and distinguish their performance from that of peers. If equity hedge-fund portfolio managers and investors are aware of the dispersion environment in which they are operating, they may be able to adapt their tactics and time their active versus passive approaches. We repeat our tests using lagged values for CrossVol and obtain even stronger results: during months immediately following above-median CrossVol levels, equity hedge-fund managers produce significantly higher performance than during

Equity Hedge Fund Performance

21

below-median periods. Thus, when alpha available in the market is higher, equity hedge-fund managers have the greatest success. A final part of this study involves estimating the active share of equity hedge-fund portfolios. Using the approach of Miller (2007), we find average active share to be 53%, which is more than twice the level reported in Miller’s own analysis of equity mutual funds. Surprisingly, active share is higher during low dispersion periods, which is contrary to our hypothesis. Perhaps equity hedge-fund managers sense when market conditions are not promoting alpha generation, and they may intensify their efforts during those times to differentiate their portfolios from the benchmark. We find that the active alpha generated across virtually all equity investment styles is significantly higher during high-dispersion periods. Thus, equity hedge-fund managers can distinguish their performance during high-dispersion periods. The higher active alpha does not, however, have a consistent effect on expense ratios paid by fund investors. We find average active expense ratios of about 7%, which is remarkably similar to the value that Miller reports for equity mutual funds. Despite hedge funds’ reputation for being unusually high-cost investment vehicles, our result suggests that the pricing of true-active portfolio management services may be more uniform than previously thought.

ACKNOWLEDGMENTS Thanks to Russell Investments, Kenneth French, David Hsieh, and the Federal Reserve Bank of St. Louis for providing data (the latter three through their web sites), to Michael Biagi for work on a pilot study that inspired this chapter, and to Bruce Geller and Ying Wang for helpful comments.

REFERENCES Ankrim, E. M., & Ding, Z. (2002). Cross-sectional volatility and return dispersion. Financial Analysts Journal, 58, 67
73. Bouchey, P., Fjelstad, M., & Vadlamudi, H. (2010). Measuring alpha potential in the market. Russell Research. Carlson, M., & Steinman, J. (2008). Market conditions and hedge fund survival. Washington, DC: Finance and Economics Discussion Series, Divisions of Research & Statistics and Monetary Affairs, Federal Reserve Board.

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Cremers, M., & Petajisto, A. (2009). How active is your fund manager? A new measure that predicts performance. Review of Financial Studies, 22, 3329
3365. Dash, S. (2009). S&P indices versus active funds (SPIVA®) scorecard, year-end 2008. S&P Dow Jones Indices. de Silva, H., Sapra, S., & Thorley, S. (2001). Return dispersion and active management. Financial Analysts Journal, 57, 29
42. Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns. Journal of Finance, 47, 427
465. French, K. R. (2008). Presidential address: The cost of active investing. Journal of Finance, 63, 1537
1573. Fung, W., & Hsieh, D. A. (2000). Performance characteristics of hedge funds and commodity funds: Natural versus spurious biases. Journal of Financial and Quantitative Analysis, 35, 291
307. Fung, W., & Hsieh, D. A. (2001). The risk in hedge fund strategies: Theory and evidence from trend followers. Review of Financial Studies, 14, 313
341. Grinold, R. (1989). The fundamental law of active management. Journal of Portfolio Management, 15, 30
37. Miller, R. M. (2007). Measuring the true cost of active management by mutual funds. Journal of Investment Management, 5, 29
49. Petajisto, A. (2013). Active share and mutual fund performance. Financial Analysts Journal, 69, 73
93. Russell Investments. (2011). Russell and Parametric launch joint index series that tracks crosssectional volatility. Press Release. Web. November 25. http://www.russell.com/us/news/ press-release.aspx?link=press-releases/2010/PR20101018.htm Sharpe, W. F. (1991). The arithmetic of active management. Financial Analysts Journal, 47, 7
9. Soe, A. (2013). S&P indices versus active funds (SPIVA®) scorecard, year-end 2012. S&P Dow Jones Indices. Sorensen, E., Miller, K., & Samak, V. (1996). Allocating between active and passive management. Financial Analysts Journal, 56, 18
31. Yu, W., & Sharaiha, Y. M. (2007). Alpha budgeting: Cross-sectional dispersion decomposed. Journal of Asset Management, 8, 58
72. Zummo, P. (2012). Hedge funds and funds of hedge funds. In D. M. Smith & H. A. Shawky (Eds.), Institutional money management: An inside look at strategies, players, and practices. Hoboken, NJ: Wiley.

THE MARKET TIMING SKILLS OF LONG/SHORT EQUITY HEDGE FUND MANAGERS Xin Li and Hany A. Shawky ABSTRACT Good market timing skills can be an important factor contributing to hedge funds’ outperformance. In this chapter, we use a unique semiparametric panel data model capable of providing consistent short period estimates of the return correlations with three market factors for a sample of Long/Short equity hedge funds. We find evidence of significant market timing ability by fund managers around market crisis periods. Studying the behavior of individual fund managers, we show that at the 10% significance level, 17.12% of funds exhibit good linear timing skills and 21.32% of funds possess some level of good nonlinear market timing skills. Further, we find that market timing strategies of hedge funds are different in good and bad markets, and that a significant number of managers behave more conservatively when the market return is expected to be far above average and more aggressively when the market return is

Signs that Markets are Coming Back Research in Finance, Volume 30, 23
51 Copyright r 2014 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1108/S0196-382120140000030006

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XIN LI AND HANY A. SHAWKY

expected to be far below average. We find that good market timers are also likely to possess good stock selection skills. Keywords: Hedge fund; market timing; nonlinearity; crisis; attrition JEL classifications: G11; G23; C34; C58

INTRODUCTION The recent financial crisis has once again focused our attention on the performance of hedge funds during periods of market turmoil. If hedge fund managers are viewed as sophisticated investors and fall in the category of informed traders, we expect them to outperform even during market downturns (see Brunnermeier & Nagel, 2004, for hedge fund performance during the technology bubble). However, are hedge fund managers able to forecast market trends and adjust their investment strategies accordingly? In this chapter, we first examine whether hedge fund managers are in general able to time the market, and more importantly, in the second part of the chapter we study individual manager’s behavior and discover that it is their nonlinear market timing ability that is more likely to generate the outperformance. We use a semiparametric panel model to examine the return correlations with the Fama and French (1993) market factors for a sample of Long/ Short equity hedge funds during three recent market crises (the LTCM debacle in the fall of 1998, the quant crisis in August 2007, and the financial crisis of 2008). We find evidence of significant market timing ability by fund managers around periods of crisis.1 Examining individual manager’s behavior, our results show that at the 10% significance level, at least 17.12% of funds exhibit good linear timing skills and at least 21.32% of funds possess good nonlinear market timing skills. Further, we find that there are a significant number of funds that successfully time the market, both linearly and nonlinearly, and that their market timing strategies are different during good and bad markets. Interestingly, we find that good market timers are also likely to have good stock selection skills. Studies on the market timing skills of portfolio managers are quite important because they not only allow us to evaluate the presence of market timing strategies but also enable us to more accurately evaluate the performance of these managers. For traditional performance measures,

The Market Timing Skills of Long/Short Equity Hedge Fund Managers

25

such as the Jensen measure (Jensen, 1968), if we ignore the manager’s market timing behavior, we obtain a biased measurement of risk.2 Treynor and Mazuy (1966) were the first to examine the issue of market timing using a sample of mutual fund managers. They developed a model where the manager’s response to the market is to change the portfolio beta as a linear function of the market signal. They concluded that they could not empirically detect any significant market timing skills for mutual fund managers. Ferson and Schadt (1996) model mutual funds’ time-varying conditional beta as a linear function of market factors and find similar results. On the other hand, Bollen and Busse (2001) proposed that using higher frequency data may change the results and they did find some evidence of market timing skills by mutual fund managers using daily return data. Since the early 1990s, multifactor models have become more of the standard approach to asset pricing. With the development of the Fama and French (1993) three-factor model to describe stock returns and the Fung and Hsieh (2004) seven-factor model, researchers use multifactor models to examine the correlation between hedge fund risk characteristics and the market.3 Recognizing that the betas in these models may not be static over time, many studies began exploring the mechanisms by which betas change as a result of changes in hedge funds’ asset allocations. Chen and Liang (2007) used multifactor models to examine whether hedge funds could time the equity market in terms of both market returns and market volatility.4 Their work provides some evidence of market timing skills for hedge fund managers. On the other hand, Fung, Xu, and Yau (2002) and Hayes (2012) found no significant market timing ability for hedge fund managers. The relative scarcity of studies on the market timing abilities of hedge fund managers is likely due to the lack of high-frequency hedge fund data. One contribution of this chapter is the use of a panel data structure that permits estimating betas for short time periods. Having established the ability of some Long/Short equity hedge fund managers to time the market, we extend our analysis to nonlinear market timing for two main reasons. First, linear market timing presumes that fund managers behave as risk-neutral agents trying to maximize their expected return. We should point out that this is true for perfect market timers because they do not worry about variance. Their only goal is to maximize return because they believe they can completely back out (cover their positions) in a timely manner before the market declines or collapses. However, in the real world, managers are not perfect market timers either because they do not have perfect foresight or because they cannot unwind their positions quickly enough due to liquidity reasons. As a result, rational

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XIN LI AND HANY A. SHAWKY

managers cannot ignore risk in their investment strategy and thus do not act as perfect (linear) market timers.5 The second reason for suspecting the presence of nonlinear market timing is largely empirical. If hedge fund managers do not change their investment strategies during market crisis from their strategies during normal market conditions, the beta changes would only be linearly correlated with market returns but would not be significantly correlated with market crisis indicators. However, in a recent paper, Cao, Chen, Liang, and Lo (2013) showed that market beta changes are linearly correlated with market liquidity indicators and find that hedge fund managers have significant market timing skills with respect to market liquidity. Since these market liquidity indicators are more informative in predicting market crisis than other normal market indicators, their finding provides support for suspecting that hedge fund managers are timing the market differently during market crisis than during normal times. The rest of the chapter is organized as follows. The second section describes the data sources and examines the sample characteristics. The third section presents the semiparametric model and describes its advantage in estimating betas for short time periods, and it also describes the motivation and empirical procedures used to estimate individual fund manager’s nonlinear market timing skills. The fourth section provides our empirical results. The fifth section presents some estimates of the relationship between market timing skills and fund performance. The sixth section concludes the chapter.

DATA AND PRELIMINARY ANALYSIS Hedge Fund Data The data on hedge funds we use is from the Lipper TASS database. After 1994, the TASS database is regarded as survivor-bias free since it includes both live and dead funds. We remove the data before 1994 to eliminate survivorship bias. The sample period includes data from January 1994 to January 2011. For our individual fund level analysis, we screen the sample to include only funds with 48 or more monthly return observations. Following Sun, Wang, and Zheng (2012), we also remove the first 18 monthly return observations to control for potential backfill bias.6 As indicated by Brown and Goetzmann (2003), there are large differences in the risk and return characteristics among the different categories

The Market Timing Skills of Long/Short Equity Hedge Fund Managers

27

of hedge funds. Since our primary focus is on managers’ ability to time the equity market, we focus our attention on a relatively homogeneous sample of Long/Short equity funds. Fung and Hsieh (2011) point out that Long/ Short equity funds are the oldest known category of hedge funds dating back to 1949 and as Table 1 indicates, they are the largest category in terms of both the number of funds and total assets under management. They also have very similar descriptive statistics (mean rate of return, Sharpe ratio, percentile distribution of rates of return) as the “all equity funds” category.7 During the period of our study (1994.1
2011.1), the Long/Short category was composed of 1949 funds out of the total 3304 equity funds. In addition to the commonly discussed biases present in hedge fund databases, another data problem brought up by Aggarwal and Jorion (2010) is the issue of duplicated funds. Under the same master feeder, there are usually several funds declaring to have different legal structures (Ltd. or LP.), different sources (onshore or offshore), different currencies (USD, CHF, or EUR), or different strategies. If they are heterogeneous individual funds (distinguishable) with separate managers or separate strategies, they should have heterogeneous returns. However, we find that some funds in our sample have nearly identical historical returns, that is, higher than 98% correlation. To avoid double counting, we remove the duplicates and only keep the oldest fund in the same “identical” fund family. In the following sections, we use the reduced sample for our analysis. The size of the reduced dataset shrinks to 1571 funds. Table 1 provides descriptive statistics for both the raw data and the reduced sample after removing duplicate funds and one clear outlier.

Risk Factor Estimates Since our focus is on Long/Short equity funds, we use the three Fama
French risk factors instead of the seven Fung
Hsieh risk factors. Table 2 presents the descriptive statistics for the Fama
French factors estimated over the entire period, January 1994
January 2011. The highest excess market return is 11.04% (April, 2009) and the lowest is −18.55% (October, 2008; second lowest came at −16.20% on August, 1998). We also note that the lowest two returns for the market factor (RMRF) occur in crisis periods, one in 1998 during the LTCM crisis and the other in 2008 during the financial crisis. Moreover, we find that the magnitude and the direction of the return for the market premium factor is a reasonable indicator for market crisis and booms, which we utilize later in the individual

3,304 165 1,949 467 37 286 400

Raw data All equity Funds Convertible arbitrage Long/Short equity Event driven Dedicated short bias Equity market neutral Emerging markets

0.86 0.58 0.92 0.79 0.18 0.55 1.07

0.86 0.59 0.90 0.83 0.19 0.58 1.08

Mean (%)

−0.12 −0.19 −0.11 −0.05 −0.97 −0.05 −0.15

−0.12 −0.24 −0.10 −0.00 −0.97 −0.09 −0.15

5th (%)

0.42 0.39 0.47 0.48 −0.05 0.21 0.51

0.46 0.34 0.50 0.55 −0.04 0.21 0.53

25th (%)

0.76 0.58 0.81 0.73 0.32 0.44 0.95

0.79 0.58 0.84 0.76 0.33 0.47 0.97

Median (%)

1.13 0.79 1.17 1.02 0.43 0.78 1.55

1.17 0.82 1.23 1.05 0.45 0.81 1.56

75th (%)

Average Monthly Returns

2.06 0.36 2.06 1.73 0.94 1.34 2.75

2.13 1.44 2.15 1.83 0.94 1.40 2.73

95th (%)

48.72 −0.73 40.46 0.45 −1.26 9.24 0.53

1.65 −0.26 0.67 1.08 −1.34 8.86 0.47

Skewness

2647.09 7.42 1734.79 18.14 5.49 126.53 6.11

20.39 5.23 7.26 18.04 5.66 111.85 6.46

Kurtosis

0.17 0.23 0.16 0.25 −0.00 0.13 0.15

0.17 0.25 0.16 0.26 −0.00 0.13 0.16

Sharpe Ratio

In this table, we report the total counts and cross-sectional summary statistics of average monthly returns and Sharpe ratio for equity hedge funds by strategy during the period of January 1994 to January 2011. The data source is the Lipper TASS hedge fund database. The sample includes both dead and live funds. “Raw data” figures are the statistics generated from the original TASS data (on funds with 48 or more monthly returns data observations) and we clean the raw data to delete the funds with “duplicated” performance records and input errors. We have summarized the new sample named “Reduced sample” in the table.

2,697 135 1,571 382 36 232 341

Number of Funds

Descriptive Sample Statistics for Hedge Fund Strategies from January 1994 to January 2011.

Reduced Sample All equity funds Convertible arbitrage Long/Short equity Event driven Dedicated short bias Equity market neutral Emerging markets

Strategy

Table 1.

28 XIN LI AND HANY A. SHAWKY

29

The Market Timing Skills of Long/Short Equity Hedge Fund Managers

Table 2. Factor RMRFa SMBb HMLc

Descriptive Sample Statistics for Fama
French Three factors. Mean (%)

Median (%)

Skewness

Kurtosis

Standard Deviation

0.52 0.23 0.28

1.30 −0.06 0.34

−0.80 0.83 −0.01

4.22 10.52 5.51

4.70 3.66 3.49

This table provides summary statistics of monthly returns for Fama
French three factors (RMRF, SMB, and HML) during the period of January 1994 to January 2011. a RMRF: Value-weighted return of all CRSP firms incorporated in the U.S. and listed on the NYSE, AMEX, or NASDAQ. b SMB: The average return on small portfolios minus the average return on big portfolios. c HML: The average return on value portfolios minus the average return on growth portfolios.

Table 3.

Correlation Table for Fama
French Three Factors.

Correlation

RMRFa

SMBb

HMLc

RMRFa SMBb HMLc

1.0000 0.2310 −0.2428

1.0000 −0.3709

1.0000

This table provides a correlation matrix of the Fama
French three factors (RMRF, SMB, and HML) during the period of January 1994 to January 2011. a RMRF: Value-weighted return of all CRSP firms incorporated in the U.S. and listed on the NYSE, AMEX, or NASDAQ. b SMB: The average return on small portfolios minus the average return on big portfolios. c HML: The average return on value portfolios minus the average return on growth portfolios.

regression approach. Table 3 reports the correlation coefficients among the three factors. It is significant to note that during this sample period, the correlation between the SMB factor and the market factor is positive and significant, while the correlation between the HML factor and the market is significant but negative.

MOTIVATION AND ECONOMETRIC MODELS Semiparametric Panel Data Model The Trimmed Least Absolute Distance estimation methodology is used to test for the existence of market timing skills for hedge fund managers. We will apply this technique for three distinct market crisis data panels in order to

30

XIN LI AND HANY A. SHAWKY

trace the changes in hedge fund factor loadings around periods of market crisis.8 While the standard approach to examine hedge fund risk exposure is to utilize multifactor models using indexes, such as the HFR equally weighted indexes (see Agarwal & Naik, 2004), we utilize a panel data approach to overcome many of the weaknesses attributed to the index methodology. The first weakness with the index approach is the attrition and selectivity bias problem. As pointed out by Liang (2000), the attrition rate for hedge funds is fairly high. He finds that the attrition rates for TASS reported funds in 1996, 1997, and 1998 are as high as 13.36%, 10.85%, and 4.19% (only through July 1998), respectively. For our sample of Long/Short equity funds, the attrition rates in 1998, 2007, and 2008 are 4.64%, 14.97%, and 20.61%.9 The sample we use might come from a conditional distribution of the population. If we assume that these funds disappear from the TASS live database because their performance deteriorated seriously enough so that they die, then ignoring the attrition problem would cause a selectivity bias and an overestimate of the funds’ performance as a whole. To address this concern, we formulate our problem as follows: rit = αi þ βl Ft þ uit ( rit ; rit ≥ ct rit = unobserved; otherwise

ð1Þ

where rit is fund i’s observed monthly excess return over the one-month Treasury bill rate at time t, rit is the true value for the funds monthly excess return. rit will only be observed when the true return value exceeds some threshold, ct : ct is further simplified as a constant within each panel because each panel includes only one-year horizon.10 αi is the individual effect for fund i, which mainly captures a manager’s stock selection ability. Ft is a 3 × 1 vector of monthly excess return on the three risk factors, proxied by the Fama
French factors: RMRF, SMB, and HML for Long/Short equity funds. Coefficients βi is a 1 × 3 vector of factor loadings for fund i and uit is the error term. Eq. (1) is the standard truncated model setting. We should point out that a censored model is also appropriate if we report the fund’s return as zero after it disappears from the sample. Thus, the problem can now be formulated as follows: rit = αi þ βl Ft þ uit   r ; rit ≥ ct ð2Þ rit = it 0; otherwise

The Market Timing Skills of Long/Short Equity Hedge Fund Managers

31

If we use the equally weighted index method or simply truncate the data in the panel data analysis, we will wrongly treat the observed return as the true value and generate biased results. Fortunately, many established procedures such as the MLE and Heckman’s two-step estimation of the Tobit model are now available to solve this kind of truncation and censoring problems. We choose a newer procedure proposed by Honore´ (1992) which solves the selectivity bias and has some other desirable features that will be illustrated later in this section. The second weakness with the index approach is its inability to accommodate short time periods with the limited frequency of hedge fund data. If we want to compare the beta between two time periods, say one year, the OLS method implemented in the index approach will fail because of the lack of sufficient observations. Using panel data methods is an effective approach to overcome the data frequency problem by introducing thousands of individual observations. It is important to note that due to the incidental parameters problem, traditional panel data models (such as the Tobit model) that use the MLE method would be inconsistent when estimating short time periods with fixed individual effects. The first question to pose within our suggested model is whether the individual effect αi is a fixed or a random effect? The αi in our model is the manager’s stock selection ability. For αi to be a random effect, it should be uncorrelated with the independent variable Ft (the market factors). However, as pointed out by Kacperczyk, Nieuwerburgh, and Veldkamp (2011) and Fung, Hsieh, Naik, and Ramadorai (2008), managers’ stock selection skills are indeed influenced by market conditions. Thus, we include αi as a fixed individual effect instead of a random effect. While this makes our estimation consistent with the real world, it prevents us from using traditional panel data models with MLE estimation methods. Fortunately, the Honore´ (1992) semiparametric procedure can provide us with a consistent estimator for short periods and also for fixed individual effects through a trimming mechanism to re-censor the residuals to restore symmetry. Also, if we assume that for any pair of time (s < t), conditional on ðα; Xs ; Xt Þ; ɛ s and ɛt are independent, identically and continuously distributed, the trimmed data can difference away alpha, which removes the inconsistency generated by estimating thousands of fixed effect parameters in traditional parametric procedures. This trimmed least absolute deviations (LAD) estimation is consistent as long as our time period is longer than or equal to 2. Thus, this approach enables us to take advantage of the additional information available in the panel data as well as provides us with a consistent estimator to compare betas for short time periods.

32

XIN LI AND HANY A. SHAWKY

The trimmed LAD procedure we use in this chapter has other desirable characteristics. For example, compared with traditional MLE, it does not require parametric specification of error term distribution (such as a normal distribution), nor does it assume homoscedasticity across individuals. This is particularly important when using financial data where the disturbance term distribution may be heavy tailed and nonnormal. We should also point out that we assume that βi = β þ di and as a replacement of the moment condition in MLE, we assume medianðdi jXÞ = 0. By this setting, we estimate the median of the individual fund betas instead of the mean.

Estimating Nonlinearity in Individual Funds’ Market Timing Behavior Motivation Previous studies on hedge funds either find some evidence of linear market timing skills (see Agarwal & Naik, 2002; Fung & Hsieh, 2001) or fail to find such evidence (such as Fung et al., 2002; Hayes, 2012). Most of this work uses a hedge fund index approach and only examines the presence of linear market timing. However, we argue that nonlinear market timing is not only more consistent with rational risk-averse behavior but is also likely to be more consistent with hedge fund managers’ behavior. There are at least two compelling explanations for the possible existence of nonlinear market timing in the hedge fund industry. First, linearity of market timing depends on the correct forecast of the market by the fund manager. Even if the manager’s strategy aims at linearly adjusting beta with the movement of the market, the actual result we observe will deviate from their goal because they are likely to fail in correctly forecasting the market and thus their input in the model is incorrect. Second, even if we assume that their short-term forecast of the market is correct, the strategy does not necessarily have to be linear timing. As we pointed out earlier, if fund managers do not believe that they can enter and exit the market quickly enough, then it is rational to include the assets’ return variance in the model and not only expected returns. The optimal portfolio will be positively correlated with the mean
variance efficient portfolio.11 It is useful to consider how the mean
variance portfolio allocations might change as the market moves.12 To illustrate, assume we have a portfolio with large-cap stock, small-cap stock, and a risk free asset, with expected returns 10%, 16%, and 6%, respectively. The standard deviation of the returns on the large-cap stock and the small-cap stock are 15% and 25%, respectively, and the correlation between their returns is 0.1.

The Market Timing Skills of Long/Short Equity Hedge Fund Managers

33

The optimal weight for small-cap stock in the tangency portfolio is 0.50. Suppose now that the expected return on the small-cap stock increases to 18% and at the same time the correlation between the two risky assets increases to 0.9 (because of market turbulence). For perfect market timers, they will certainly increase the weight of the small-cap stock to capture the profit. However, for a “nonperfect” market timer who chooses the mean
variance efficient portfolio, the optimal weight for the small-cap stock in the tangency portfolio would decrease to −6.75 instead of increase (changing from buying to shorting). Note that such an opposite movement in portfolio weights with the market return suggests that linear market timing fails to explain the mean
variance efficient feature of a hedge fund portfolio. If the manager adjusted the portfolio according to a linear function, then the change would always be in the same direction as that of the market change.13 This feature of linear market timing is inconsistent with mean
variance analysis and thus we propose an econometric model that is capable of capturing nonlinear market timing skills of hedge fund managers. Econometric Model Specification We now examine how hedge fund managers might adjust their strategies to take advantage of market timing. Assuming that managers are able to take advantage of both linear and nonlinear market timing, we set out to estimate both the linear trend and the nonlinear changes in betas across time. To examine betas for our sample of Long/Short equity funds, the Fama
French three-factor model is most appropriate: rp;t þ 1 = αp þ Φp;t Xt þ 1 þ up;t þ 1

ð3Þ

where rp;t þ 1 is fund p’s monthly excess return calculated as the fund’s return minus the one-month U.S. Treasury bill rate. The factor 3 × 1 vector Xt þ 1 = ðRMRFt þ 1 ; SMBt þ 1 ; HMLt þ 1 Þ0 . RMRFt þ 1 (i.e., Rm;t þ 1 − Rf ;t þ 1 ), the excess return of the market is the value-weighted return on all NYSE, AMEX, and NASDAQ stocks minus the one-month U.S. Treasury bill rate. The other two factors are the average return on small stock portfolios minus that of big stock portfolios and average return of value portfolios minus average returns on growth portfolios. In the rest of the chapter, we also write RMRFt þ 1 as mt þ 1 . The coefficient vector Φp;t = ðγ p;t ; βp;t ; ηp;t Þ, where γ p;t is the factor loading of RMRFt þ 1 , βp;t is the factor loading of SMBt þ 1 , and ηp;t is the factor loading of HMLt þ 1 . The factor loadings are decided by the manager’s investment choice made one period ahead, so there is a time lag in the subscript of factor loadings.

34

XIN LI AND HANY A. SHAWKY

Instead of assuming static coefficients, we examine how managers adjust their betas according to the market. If managers have market timing ability, they will adjust their portfolios according to their forecast of the next period’s market return. Thus, the factor loadings should be a function of the conditional expectation of next period market excess return ðmt þ 1 Þ at time t. We also assume that the assets under management are liquid enough to be adjusted according to their desired strategies and that any transaction costs generated by such adjustments are negligible. We further assume that the forecast errors are unknown until the next period and that these errors are independently distributed with zero mean. Following Ferson and Schadt (1996), Busse (1999), and Cao et al. (2013), we demeaned the manager’s market signal as mt þ 1 − m for simplicity of interpreting the coefficients and since the constant term in the function already captures the m, our dynamic coefficients can be expressed as: γ p;t = Ef½φp;1 þ φp;2 ðmt þ 1 − mÞ þ φp;3 1fmt þ 1 > mg þ φp;4 ðmt þ 1 − mÞ2 þ φp;5 1fmt þ 1 > mg ðmt þ 1 − mÞ2 jIt g = φp;1 þ φp;2 ðmt þ 1 − mÞ þ φp;3 1fmt þ 1 > mg þ φp;4 ðmt þ 1 − mÞ2 þ φp;5 1fmt þ 1 > mg ðmt þ 1 − mÞ2 þ vp;t þ 1 βp;t = Ef½ψ p;1 þ ψ p;2 ðmt þ 1 − mÞ þ ψ p;3 1fmt þ 1 > mg þ ψ p;4 ðmt þ 1 − mÞ2 þ ψ p;5 1fmt þ 1 > mg ðmt þ 1 − mÞ2 jIt g = ψ p;1 þ ψ p;2 ðmt þ 1 − mÞ þ ψ p;3 1fmt þ 1 > mg þ ψ p;4 ðmt þ 1 − mÞ2 þ ψ p;5 1fmt þ 1 > mg ðmt þ 1 − mÞ2 þ up;t þ 1 ηp;t = Ef½μp;1 þ μp;2 ðmt þ 1 − mÞ þ μp;3 1fmt þ 1 > mg þ μp;4 ðmt þ 1 − mÞ2 þ μp;5 1fmt þ 1 > mg ðmt þ 1 − mÞ2 jIt g = μp;1 þ μp;2 ðmt þ 1 − mÞ þ μp;3 1fmt þ 1 > mg þ μp;4 ðmt þ 1 − mÞ2 þ μp;5 1fmt þ 1 > mg ðmt þ 1 − mÞ2 þ ωp;t þ 1

ð4Þ

where the dummy variable 1fmt þ 1 > mg equals 1 if the market excess return at time t is not less than the market average across time, and equals 0 otherwise. Table 4 presents a detailed description of all of the coefficients in our model. The coefficients φ2 ; φ4 ; φ5 ; ψ 2 ; ψ 4 ; ψ 5 and μ2 ; μ4 ; μ5 are essential to estimating a manager’s market timing skills. They measure how the market factor loadings change with the forecasted market conditions. The coefficients φ2 ; ψ 2 ; μ2 measure the linear change of a fund’s factor loadings with

The Market Timing Skills of Long/Short Equity Hedge Fund Managers

Table 4.

35

Description of the Coefficients in Individual Regression Model.

Coefficient

Dependent Variable

Description of the coefficient

φ1

m

Constant correlation with the market factor: RMRF

φ2

ðm − mÞm

Linear change of correlation with the market according to the excess market return forecast.

φ3

1fm > mg m

+(−)φ3: the fund’s correlation with the market will ↑(↓) by a fixed amount if the forecasted market return is higher than average

φ4

ðm − mÞ2 m

Funds’ relative aggressiveness in investing in RMRF factor when the excess market return is forecasted to be much lower than the average

φ5

1fm > mg ðm − mÞ2 m

φ4 + φ5: measurement of funds’ relative conservativeness in investing in RMRF factor when the excess market return is forecasted to be much higher than the average

ψ1

SMB

Constant correlation with the market factor: SMB

ψ2

ðm − mÞSMB

Linear change of correlation with the SMB factor according to the excess market return forecast

ψ3

1fm > mg SMB

Fixed amount change in the correlation with the SMB factor when the forecasted market return is higher than average

ψ4

ðm − mÞ2 SMB

Funds’ relative aggressiveness in investing in SMB factor when the excess market return is forecasted to be much lower than the average

ψ5

1fm > mg ðm − mÞ2 SMB ψ4 + ψ5: funds’ relative conservativeness in investing in SMB factor when the excess market return is forecasted to be much higher than the average

µ1

HML

Constant correlation with the market factor: HML

µ2

ðm − mÞHML

Linear change of correlation with the HML factor according to the excess market return forecast

µ3

1fm > mg HML

Fixed amount change in the correlation with the HML factor when the forecasted market return is higher than average

µ4

ðm − mÞ2 HML

Funds’ relative aggressiveness in investing in HML factor when the excess market return is forecasted to be much lower than the average

µ5

1fm > mg ðm − mÞ2 HML µ4 + µ5: funds’ relative conservativeness in investing in HML factor when the excess market return is forecasted to be much higher than the average

a

“m” is the excess market return, RMRF.

36

XIN LI AND HANY A. SHAWKY

the market’s excess return; the coefficients φ4 ; φ5 ; ψ 4 ; ψ 5 and μ4 ; μ5 measure the funds’ second-order market timing skills. The coefficients φ4 ; ψ 4 and μ4 denote the degree of a fund’s aggressiveness in seizing an opportunity or unwillingness for deep shorting position when the market return is far below average; while the coefficients φ4 þ φ5 ; ψ 4 þ ψ 5 , and μ4 þ μ5 measure the funds’ degree of cautiousness when the market return is far above average (aggressiveness and cautiousness are relative to a fund’s linear timing behavior). If the coefficients are statistically significant, then we conclude that the fund manager possess the corresponding market timing skill. It is useful to examine the coefficients of the RMRF, SMB, and the HML factors in detail. For the RMRF factor, φ2 measures the linear change of beta with the excess market return forecast, while φ4 and φ5 indicate how the fund will react when the excess market return is forecasted to be too far from the average. The dummy before the ðmt þ 1 − mÞ2 variable is introduced to capture the asymmetry in the funds’ reaction to the market. Positive coefficient φ2 and negative φ4 þ φ5 indicates the fund’s portfolio return ðrt þ 1 Þ correlation with the market return ðmt þ 1 Þ will generally increase when market return is higher. However, when the market return continues to rise to a level much higher than the average, the manager might think twice about continuing to increase their long positions in the market, causing the correlation to increase at a slower pace or even reverses its direction. Meanwhile, we note that a positive coefficient φ2 and positive φ4 are also regarded as good market timing skills. Positive φ2 means that when the market is declining, the fund manager will decrease the fund’s correlation with the market and even take a short market position. However, deep shorting in depressed markets is very risky and thus, it is reasonable to expect managers to be less exposed to short market positions than what is suggested by the positive φ2 . Next, we consider the coefficients of the SMB (Small minus Big) factor. A positive ψ means a relatively higher position in small stocks and a negative ψ means a relatively higher position in large-cap stocks. So, if ψ 2 is positive, it suggests that the manager is moving toward small-cap stocks when the market is expected to rise. When the fund becomes more concerned about the market, it is likely to slow down the pace of adding smallcap stocks or even selling some small-cap stocks, which is likely to result in negative ψ 5 þ ψ 4 . The coefficients μ’s for HML factor are similar. It is known that the value factor “HML” will have higher return during bear markets and lower return in bull markets. Thus, having a negative μ2 means that the fund can exploit the factor return premium to make more profit by going toward value stock in bear markets and against value stock

The Market Timing Skills of Long/Short Equity Hedge Fund Managers

37

in bull markets. However, if the market continues to rise and fears of a future market downturn increase, the market value of their holdings may decline because of investors’ expectation on possible hard times ahead. Keeping this in mind, the fund may be more willing to choose high B/M stock (value stocks) when the market situation is believed to deteriorate in the near future ðμ4 þ μ5 > 0Þ. Thus, we interpret negative μ2 , negative μ4 , and positive μ4 þ μ5 as good indicators of market timing skill. In order to estimate all the coefficients described above, we substitute the coefficients of Eq. (4) to the factor model in Eq. (3) and get the following reduced form: rp;t þ 1 = αp þ Γp;t ðXt þ 1 ⊗Yt þ 1 Þ þ ɛp;t þ 1

ð5Þ

where Γp;t = ðφ1 ; φ2 ; φ3 ; φ4 ; φ5 ; ψ 1 ; ψ 2 ; ψ 3 ; ψ 4 ; ψ 5 ; μ1 ; μ2 ; μ3 ; μ4 ; μ5 Þ Xt þ 1 = ðRMRFt þ 1 ; SMBt þ 1 ; HMLt þ 1 Þ0 Yt þ 1 = ð1; mt þ 1 − m; 1fmt þ 1 > mg ; ðmt þ 1 − mÞ2 ; 1fmt þ 1 − mg ðmt þ 1 − mÞ2 Þ where ɛ p;t þ 1 is a combination of the forecast error in Eq. (4) and error term in Eq. (3).

EMPIRICAL RESULTS Panel Data Model Results We use the panel data model to obtain the factor loadings from the Fama
French (1993) model at two different stages of the market: before the market crisis and during the market crisis. We examine how the factor loadings change across the two stages. In order to capture hedge funds’ market timing skills during the three recent market crises (the LTCM collapse, the quant crisis, and the 2008 financial meltdown), we run the model in three corresponding panels as described in Table 5. To test whether the funds’ behavior changed before the crisis and during the crisis, we partition each panel into two halves as shown in Fig. 1. Table 5 gives that the market factor loadings are quite different in the two periods in each of the three panels. This difference can be seen from the coefficients on the dummy variables reported in the second column. The coefficient of the market excess return factor RMRF decreases by 0.37

38

XIN LI AND HANY A. SHAWKY

Table 5.

Estimation of Risk Exposures during Normal and Crisis Market Periods.

Before During Before the LTCMb the LTCMa,c the Quant Crisisd 4.64% βRMRF

0.6839***

βSMB

0.2624***

βHML

0.1973***

−0.3708*** 0.1029 −0.4497***

During the Quant Crisisa,e 14.97%

0.2565***

−0.0354

0.0331

−0.3038***

0.1646***

0.3137***

Before the During the Financial Financial Meltdownf Meltdowna,g 20.61% 0.2773***

0.2058***

−0.1078*** −0.2865*** −0.5051***

0.3649***

***Significant coefficient at 1% significance level. This table presents coefficient estimates of the trimmed LAD semiparametric method to estimate the model: rit* = αi + β1i RMRFt + β2i SMBt + β3i HMLt + uit, where the observed rit* equals rit if rit* ≥ min {ct}, otherwise equals 0. Here the subscript i denotes individual hedge funds. We do not require a parametric specification on the distribution of the error term and we allow correlation between α and the factors. Assuming βi = β + di (j = 1, 2, 3) we need median (di|X) = 0. Our estimator is consistent for panels with short time periods and we carry out the estimation separately for each panel (comprised of funds in different time periods). Notice that the coefficients reported in the second column of each panel are the coefficients for the dummy variables (i.e., changes in level of betas) instead of the level themselves. a This coefficient is before the dummy variable showing the difference between the “during crisis” period and “before crisis” period. b January 1998
June 1998. c July 1998
December 1998. d November 2006
April 2007. e May 2007
October 2007. f January 2008
June 2008. g July 2008
December 2008.

in the second half of the first panel, which means that fund returns are less correlated with the market around the LTCM time period than the normal time period before the crisis. The factor loading of HML also decreases around the LTCM collapse which indicates that funds hold relatively fewer value stocks. However, the direction of the changes within the next two panels is different from that of the first panel. The coefficient of RMRF stays almost the same in the quant crisis period and significantly increases by 0.21 during the financial meltdown period. The coefficient of SMB decreases by 0.30 during the quant crisis and by 0.29 during the financial meltdown period, which suggests that during both crises, managers might have increased the relative weight of large-cap stocks in their portfolios. The coefficient of HML increases by 0.31 in the quant crisis panel and by

The Market Timing Skills of Long/Short Equity Hedge Fund Managers

39

0.36 in the financial meltdown panel, which suggests that funds are more focused on value stocks during both crises. It is interesting to note the reversal in the direction of these portfolio allocation changes. From Fig. 1, we note that the three crisis periods are actually at different stages of the market cycle, although our intention at first was to choose the panels to reflect changes in crises. In the first panel, the market is on its way to recover while in the third panel, the market has declined to a trough. For a good market timer with liquidity concern, it is reasonable to start selling out (decrease market correlation) of the market near the peak and behave more aggressively near the trough. This may explain why funds were more conservative in the second half of the LTCM panel but more aggressive in the later part of the financial meltdown panel. Market cumulative return according to Fama-French market factor 800 700

500 400

0

Panel B

100

Panel C

200

Panel A

300

1990m1 1990m7 1991m1 1991m7 1992m1 1992m7 1993m1 1993m7 1994m1 1994m7 1995m1 1995m7 1996m1 1996m7 1997m1 1997m7 1998m1 1998m7 1999m1 1999m7 2000m1 2000m7 2001m1 2001m7 2002m1 2002m7 2003m1 2003m7 2004m1 2004m7 2005m1 2005m7 2006m1 2006m7 2007m1 2007m7 2008m1 2008m7 2009m1 2009m7 2010m1 2010m7 2011m1 2011m7 2012m1

Market Return

600

Fig. 1. Cumulative Return across Time. This figure plots the cumulative market return from January 1990 to January 2012 (January 1990 level is normalized to 100). The market return is measured by Fama
French market factor which is the valueweighted return of all CRSP firms incorporated in the U.S. and listed on the NYSE, AMEX, or NASDAQ that meet certain criteria. The black vertical line partitions show the panels we choose for analysis in the section “Panel Data Model Results”: Panel A: January 1998
June 1998 (I: Before the LTCM), July 1998
December 1998 (II.LTCM) Panel B: November 2006
April 2007 (I: Before the quant crisis), May 2007
October 2007 (II: Quant crisis) Panel C: January 2008
June 2008 (I: Before the financial meltdown), July 2008
December 2008 (II: Financial meltdown).

40

XIN LI AND HANY A. SHAWKY

Individual Fund Level Nonlinear Market Timing Results In addition to the Fama and French (1993) three-factor model, we also use the Carhart (1997) four-factor model and the Fung and Hsieh (2004) twofactor model adapted to Long/Short equity funds. The estimates using these models are quite similar and thus we limit our discussion to the Fama
French model results. Table 6 contains regression estimates using Eq. (5) for individual funds and reports the White corrected standard errors. We calculate the proportion of funds whose p-value falls into the various significance levels as given in the table.14 Table 6 presents the cross-sectional distribution of the p-value of the market timing skill coefficients across all funds in the sample. At the 10% significance level, we find that 16.87% of funds have positive φ2 , 9.36% have positive ψ 2 , and 18.33% have negative μ2 , which are all evidence of good linear market timing skills. Managers with good linear market timing skills are able to capture more profit by holding assets that have higher (lower) correlation with the market during good (bad) markets. We also find that 19.67% of funds have positive φ4 , 11.01% have positive ψ 4 , and 21.64% have negative μ4 . These estimates demonstrate good nonlinear market timing skills when the market is bad. Meanwhile, 24.57% of the funds have negative φ4 þ φ5 , 10.31% have negative ψ 4 þ ψ 5 , and 17.25% have positive μ4 þ μ5 . This demonstrates that these funds are relatively more conservative (compared with linear timing) in good markets. The results so far indicate that a substantial portion of Long/Short equity hedge funds possess some level of good and statistically significant market timing skills. This ability to time the market is largely accomplished through adjusting their loadings on the RMRF and the HML factors. The impact of the SMB factor (ψ’s) loadings on market timing is inconclusive. The fraction of perverse nonlinear market timing is quite small for both the RMRF and the HML factors. The estimates show that there are some funds that time the SMB market factor counter to what is suggested by good nonlinear market timers. The “perverse” SMB market timing suggests that when the market is very good, funds will be more aggressive by holding even more small-cap stocks than is suggested by a linear market timing strategy. Using the most conservative approach to conduct a joint test, we find that there are at least 21.32% of funds that exhibit good nonlinear market timing skills, and there are at least 17.12% of funds that exhibit good linear timing skills.15,16 At the 10% significance level, only 9.48% of funds exhibit both linear and nonlinear market timing on the market premium factor

3.18 1.78 2.61 7.00 2.86 1.21 3.95 1.72 3.12 0.76 4.46 1.34

4.84 3.56 4.77 12.29 6.37 2.23 6.81 3.18 5.98 1.97 8.15 2.86

8.08 6.87 6.68 17.50 11.01 4.65 11.78 5.35 10.06 4.26 12.92 4.96

p-value < 0.05 13.43 12.35 10.88 24.57 18.46 8.78 20.75 10.31 18.33 7.64 21.64 9.36

p-value < 0.1 16.87 13.69 19.67 11.58 9.36 16.68 11.01 22.15 8.47 20.31 10.25 17.25

p-value < 0.1 10.12 7.77 11.78 7.07 4.96 10.63 6.43 14.13 4.46 12.60 4.58 10.50

p-value < 0.05 6.56 4.71 7.70 4.96 2.67 5.86 3.44 8.91 1.85 7.51 2.04 6.05

p-value < 0.025

Ha: coefficients > 0

Ha: coefficients < 0

p-value < 0.025

H0: coefficients ≤ 0

H0: coefficients ≥ 0

Percentage of the Funds

P-value Distribution for Market Timing Coefficients across Individual Funds.

3.25 2.29 4.58 3.12 1.40 2.74 2.10 5.09 0.76 3.69 1.15 2.36

p-value < 0.01

Excess return of the fund (rt + 1) is calculated as the monthly return of the fund minus the monthly return of the one-month Treasury bill rate (Rp,t + 1 − Rf,t + 1). mt + 1 is the RMRF factor, calculated as the value-weighted return on all NYSE, AMEX, and NASDAQ stocks minus the one-month U.S. Treasury bill rate. SMB and HML are the average return on small stock portfolios minus that of the big stock portfolios and the average return of value portfolios minus average returns on growth portfolios, respectively.

rp;t þ 1 = αp þ φp;1 mt þ 1 þ φp;2 ðmt þ 1 − mÞmt þ 1 þ φp;3 1fmt þ 1 > mg mt þ 1 þ φp;4 ðmt þ 1 − mÞ2 mt þ 1 þ φp;5 1fmt þ 1 > mg ðmt þ 1 − mÞ2 mt þ 1 þ ψ p;1 SMBt þ 1 þ ψ p;2 ðmt þ 1 − mÞSMBt þ 1 þ ψ p;3 1fmt þ 1 > mg SMBt þ 1 þ ψ s;4 ðmt þ 1 − mÞ2 SMBt þ 1 þ ψ p;5 1fmt þ 1 > mg ðmt þ 1 − mÞ2 SMBt þ 1 þ µp;1 HMLt þ 1 þ µp;2 ðmt þ 1 − mÞHMLt þ 1 þ µp;3 1fmt þ 1 > mg HMLt þ 1 þ µs;4 ðmt þ 1 − mÞ2 HMLt þ 1 þ µp;5 1fmt þ 1 > mg ðmt þ 1 − mÞ2 HMLt þ 1 þ ep;t þ 1

We run the following regression for each of the 1571 Long/Short equity funds and report the cross-sectional distribution of the p-value (For the φ4 + φ5, ψ4 + ψ5, and µ4 + µ5 coefficients, we use Wald test to calculate the p-value).

φ2 φ3 φ4 φ4 + φ5 ψ2 ψ3 ψ4 ψ 4 + ψ5 µ2 µ3 µ4 µ4 + µ5

p-value < 0.01

Table 6. The Market Timing Skills of Long/Short Equity Hedge Fund Managers 41

42

XIN LI AND HANY A. SHAWKY

RMRF. Interestingly, we find that none of the funds with good linear market timing skills (positive φ2 ) exhibit significant perverse nonlinear market timing skills (none of them have positive φ4 þ φ5 ). Also, when a fund’s return indicates good nonlinear timing skills, ðφ4 þ φ5 < 0Þ, the fund will not be identified as a bad linear market timer whose φ2 < 0. Due to this subtle characteristic in funds’ behavior, our identification of good market timers on market factor RMRF becomes easier and more compelling. We can conclude that a given fund is a good market timer because either it has good linear market timing skills or it has good nonlinear market timing skills. We do not have the abnormal case in which a fund manager is identified as a good linear market timer and is also identified as having bad nonlinear market timing skills, or vice versa. Actually, this rule applies to all three factors (RMRF, SMB, and HML). In summary, a hedge fund achieves good market timing skill on a certain factor if it has the desired linear timing or nonlinear market timing coefficient or both. Using a joint test with a conservative Bonferroni correction, we find there are at least 267 (17.00%) Long/Short equity funds with good market timing skill on the RMRF factor and 210 (13.37%) funds that have good market timing skill on HML factor. Similarly, perverse linear timing skills and bad nonlinear timing skills tend to be synchronous, but the perverse timing skills are much less significant than the good timing skills for the RMRF and the HML factors.17

ECONOMIC IMPLICATIONS OF MARKET TIMING Market Timing Skills and Fund’s Performance Having documented that some hedge funds possess significant market timing skills, it is natural to consider how market timing strategies contribute to a fund’s traditional alpha measure or other performance measures such as the mean rate of return. First, how will the performance of funds possessing good market timing skills compare to other hedge funds and is there a relation between good market timing and good stock selection abilities? Second, will the degree of market timing matter to a funds’ performance, and finally, will funds with higher sensitivity to the market generate higher returns? It is important to point out that for an ideal pattern of market timing, φ2 should be positive since traders will want the portfolio to be highly

The Market Timing Skills of Long/Short Equity Hedge Fund Managers

43

correlated with the market when they perceive a strong market and negatively correlated with the market when they perceive a weak market. This suggests that for good market timers, we should not observe the counter-market behavior in which there is a significant increase in beta as the market declines. The counter-market behavior produces similar returns as writing a put option strategy on the market index and simultaneously taking on extreme market risk (Agarwal & Naik, 2004; Goetzmann & Massa, 2001; Lo, 2001; Siegmann & Lucas, 2002). However, funds can indeed generate good profits by writing out of the market puts or being “Contrarian,” although it is not market timing profits by our definition. We do not expect good market timers to be the super profit generators compared to these aggressive put writers. To examine these performance issues, we conduct a simple percentile comparison test. We select the “good market timer” group and the “bad market timer” group from the sample of funds and list the percentiles of their performance (Sharpe ratio, three-factor alpha, and mean return) within each group. Table 7 gives that the good market timers generally outperform bad market timers by an annualized Sharpe ratio of 100bp.18 The results also indicate that market timing skill on the RMRF factor does play a positive role in extracting positive alpha for the funds. Measured by Jensen’s alpha, good market timers generally outperform bad market timers by an alpha of 150bp per year.19,20 The alpha outperformance of good market timers indicates that these managers are also likely to be superior stock pickers. It is significant to note that we did not find significant correlation between market timing coefficients and the individual fund performance measures. This suggests that while market timing does matter to a fund’s outperformance, it is not clear if the higher sensitivity to the factor loadings necessarily produces better performance. In other words, the optimal market timing strategy is not determined simply by setting the sensitivity parameters (such as φ2 ; φ4 ; φ5 ) as high as possible. The analysis on the HML factor generates similar results.

Market Timing and Liquidity Pressure Good nonlinear market timers are believed to bear less risk when the market is really bad. We investigate whether this strategy relieves a funds’ liquidity pressure. If hedge fund investors are risk averse, they will be concerned about the funds’ performance and its survival during bad markets.

0.174 0.440 0.633 0.907 3.359

20% 40% 60% 80% Maximum

0.257 0.469 0.675 0.945 3.359

Good market timers 0.156 0.366 0.570 0.831 2.488

Bad market timers 0.020 0.284 0.519 0.850 4.347

All Long/ Short fundsb 0.118 0.380 0.588 0.879 4.347

Good market timers 0.037 0.210 0.463 0.926 3.115

Bad market timers

“Three-Factor” Alpha

0.417 0.723 0.967 1.342 4.22

All Long/ Short funds 0.540 0.830 1.042 1.366 4.22

Good market timers

0.466 0.735 0.964 1.440 3.076

Bad market timers

Mean Monthly Rate of Return (%)

We separate the funds into good market timer group and bad market timer group, according to the performance of market timing coefficients on the RMRF factor(mt + 1). Good market timers are those funds with either significantly positive φ2 or significantly positive φ4 or significant negative φ4 + φ5, as given in Table 6. Bad market timers are funds with the opposite directions on the coefficients. For the whole sample and for each subgroup, we provide the quintile summary of the funds’ annualized Sharpeffi ratio, mean monthly rate of return, pffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi and the “three-factor” alpha. Annualized Sharpe ratio is calculated as 12EðRi − Rf Þ= VarðRi − Rf Þ. α is calculated from rt + 1 = αp + γp,t mt + 1 + βp,tSMBt + 1 + ηp,tHMLt + 1 + up,t + 1. a Truncated at 0.1% and 99.9% level. b All Long/Short funds are the reduced sample described in Table 1, containing 1571 Long/Short equity funds.

All Long/ Short fundsb

Annualize Sharpe Ratio

Percentile Summarya of Different Performance Mearsures for Market Timers on RMRF Factor.

Performance percentile

Table 7.

44 XIN LI AND HANY A. SHAWKY

45

The Market Timing Skills of Long/Short Equity Hedge Fund Managers

If a funds’ poor performance triggers these risk-averse investors to withdraw their assets, the negative net investment flow will generate added losses for the fund because of having to unwind some of their positions prematurely. Following Ding, Shawky, and Tian (2009), we estimate the investor-driven liquidity to measure fund flow, estimated using the following expression: ILt =

NIFt AUMt = − ð1 þ rt Þ AUMt AUMt − 1

where the ILt is the investor-driven liquidity at time t, NIFt is the net investment flows during period t, AUM is the asset under management, and rt is the fund’s rate of return during period t. Our results show that funds with good market timing skills generally have less investor-driven liquidity pressure than bad market timers during extreme market conditions. As given in Table 8, the maximum investordriven liquidity pressure encountered by good market timers is generally Table 8. Influence of Funds’ Market Timing Skills (on RMRF) on Investor-Driven Liquidity Pressure.a Average Liquidity Pressure (Mean ILt) (%)

Maximum Liquidity Pressure (Min ILt) (%)

Percentile

All Long/ Short fundsb

Good market timers

Bad market timers

All Long/ Short funds

Good market timers

Bad market timers

20% 40% 60% 80% Maximum pressure

−1.296 −0.912 −0.655 −0.290 5.367

−1.282 −0.970 −0.776 −0.385 2.904

−1.368 −0.821 −0.627 −0.302 1.295

−22.663 −14.941 −9.962 −6.540 −0.612

−22.846 −15.242 −9.739 −7.009 −0.612

−26.590 −19.333 −11.587 −6.745 −2.411

We separate funds into good market timers and bad market timers, according to their estimated market timing coefficients on the RMRF factor (mt + 1). Good market timers are funds with either significantly positive φ2 or significantly positive φ4 or significant negative φ4 + φ5, as given in Table 6. Bad market timers are funds with the opposite directions on the coefficients. For the whole sample and for each subgroup, we present the percentile summary of the funds’ average investor-driven liquidity pressure and the maximum investor-driven liquidity pressure. Investor-driven liquidity is calculated as ILt = AUMt/AUMt − 1− (1 + rt), AUM is the asset under management of the fund. a Truncated at 0.1% and 99.9% level. b “All Long/Short funds” are the funds that are in the reduced sample described in Table 1 and have monthly reported return and at least one nonzero reported asset. There are 1,344 such funds.

−0.4237*** 0.1868 −0.5155***

Leveraged funds 0.7229*** βRMRF βSMB 0.2261*** βHML 0.2007*** 0.2548*** −0.0012 0.1663***

0.2473*** 0.0513 0.1710*** −0.0296 −0.2629*** 0.3363***

−0.0286 −0.3380*** 0.2280***

During the Quant Crisisa,e

14.97%

Before the Quant Crisisd

0.2945*** −0.1593*** −0.5274***

0.2594*** −0.0687 −0.5320***

0.2111*** −0.2532*** 0.3947***

0.2060*** −0.3140*** 0.3663***

During the Financial Meltdowna,g

20.61%

Before the Financial Meltdownf

**Significant coefficient at 2% significance level. ***Significant coefficient at 1% significance level. In this table we reestimate the trimmed LAD semiparametric model for two subsamples, funds that reported using leverage, and funds that reported not using leverage: r*it = αi + β1i RMRFt + β2i SMBt + β3i HMLt + uit, where the observed rit equals r*it if rit ≥ min{ct}, otherwise equals 0. a This coefficient is before the dummy variable showing the difference between the “during crisis” period and “before crisis” period. b January 1998
June 1998. c July 1998
December 1998. d November 2006
April 2007. e May 2007
October 2007. f January 2008
June 2008. g July 2008
December 2008.

−0.2898*** 0.0072 −0.3478**

4.64%

During the LTCMa,c

Unleveraged funds 0.6191*** βRMRF βSMB 0.2827*** 0.1747** βHML

Attrition rate

Before the LTCMb

Table 9. Estimation of Risk Exposures in Normal and Crisis Market Periods (for Leveraged and Unleveraged Funds). 46 XIN LI AND HANY A. SHAWKY

The Market Timing Skills of Long/Short Equity Hedge Fund Managers

47

lower than that experienced by bad market timers. However, during normal market conditions, market timing does not appear to have a significant impact on a fund’s liquidity. One possible explanation for this is that there are funds that have fairly liquid asset holdings that could easily and quickly be liquidated. These funds may have positive φ4 þ φ5 but few liquidity shocks.

Potential Impact of Leverage on Market Timing In this subsection we examine the robustness of our market timing results to the use of leverage by hedge funds. It is possible to argue that an increase (decrease) in the margin requirements during market downturns (upturns) might reduce (increase) a fund’s market exposure. As a result, it is possible that the leverage effect due to changes in the margin requirements might have a confounding effect on our findings with respect to the decrease (increase) in betas. We conduct a simple test to examine the potential influence of leverage on our results. The TASS database provides information on the use of leverage by individual hedge funds. We divided our sample into funds that reported the use of leverage and funds that reported not using leverage. We reestimated our panel data model for both samples. Table 9 presents the estimates for both levered and unlevered funds. The results indicate that the changes in the factor loadings for the three panels are very similar for both samples. This suggests that our market timing results are not attributable to a leverage effect on hedge funds during market crisis.

CONCLUSION We examine the market timing ability of hedge fund managers over the period of 1994
2011. Instead of using the standard OLS approach commonly used in the literature, we use a semiparametric panel data estimator to address the attrition problem and to enable us to compare funds’ beta before and during periods of financial crisis. The panel data model provides a more effective approach in evaluating funds’ risks over short periods of time and we find evidence for significant market timing skill in the hedge fund industry. Specifically, we show that a significant number of Long/ Short equity hedge funds change their portfolio holding and their

48

XIN LI AND HANY A. SHAWKY

correlation with the market in different stages of the market cycle. The direction of changes around the crises is consistent with our initial priors of market timing skill. After confirming the existence of market timing behavior, we estimate individual fund level regressions to evaluate the market timing skills of hedge fund managers. Building on the literature of linear market timing, we add a nonlinear feature to the regression equation to capture the funds’ concern for market variance. We find that a significant number of funds behave more conservatively when the market return is far above the average level and more aggressively when the market return is far below the average. These results contribute to the traditional linear market timing literature. Our empirical results show that there are at least 21.32% of the Long/ Short funds that exhibit good nonlinear market timing skills. At the 10% significance level, at least 267(17.00%) funds exhibit good market timing on the RMRF factor (either linear or nonlinear), with similar results for the HML factor. Market timing skill on RMRF factor plays an important role in extracting positive alpha for hedge funds. Good market timers generally outperform bad market timers by an alpha of 150bp per year and by an annualized Sharpe ratio of 100bp. Moreover, the maximum investordriven liquidity pressure for good market timers is generally lower than that of bad market timers.

NOTES 1. This model has the advantage of providing consistent coefficient estimates for short time periods and has the advantage of addressing the significant attrition problem in hedge funds. 2. Dybvig and Ross (1985) and Grinblatt and Titman (1989) pointed out that with good market timers, the Jensen’s alpha is likely to be biased downward. 3. These static multifactor models are used extensively, such as Agarwal and Naik (2004), Fung and Hsieh (2004), Jagannathan et al. (2010). Many studies use hedge fund indexes to represent hedge fund return characteristics in multifactor models. 4. Regression variables in Chen and Liang (2007) are up to the squared term. However in our regression, we use the cube term because we want to measure the managers’ relative “conservativeness” and “aggressiveness” during different market conditions, instead of treating volatility only as a market indicator. 5. Shleifer and Vishny (1997) point out that institutional investors and sophisticated arbitrageurs may avoid some arbitrage positions if they are very volatile. They point out that, “Although such positions offer attractive average returns, the volatility also exposes arbitrageurs to risk of losses and the need to liquidate the portfolio under pressure from the investors in the fund.”

The Market Timing Skills of Long/Short Equity Hedge Fund Managers

49

6. In the robustness test, we first screen funds to have 66 or more monthly returns data and then we take the first 18 observations out for each fund, making our sample still having more than 48 monthly observations for each fund. Unreported results remain substantially unchanged. 7. The “all equity funds” here include categories of Convertible Arbitrage, Long/Short Equity Funds, Event-Driven, Dedicated Short Bias, Equity Market Neutral and Emerging Markets in Lipper TASS database definitions. 8. According to Sadka (2010), the recent financial crisis events are LTCM in the fall of 1998, the quant crisis in the summer of 2007, and financial crisis in the fall of 2008. 9. Attrition rate is calculated as the number of funds becoming defunct within the year divided by the number of funds at the start of the year. 10. The constant threshold is calculated as the minimum return in the corresponding panel. 11. Fung and Hsieh (1999) have also pointed out that the mean
variance analysis preserves the utility ranking in hedge funds. 12. Best and Grauer (1991) have shown analytically and computationally that the sensitivity of asset weights in the mean
variance portfolio to changes in the mean returns of individual assets could be negative. 13. The beta change could also be in the opposite direction of the market change, but the direction should stay the same, instead of changing with the market. 14. For the φ4 þ φ5 ; ψ 4 þ ψ 5 , and μ4 þ μ5 coefficients, we use Wald test to calculate the p-value. 15. At the 10% overall significance level, we use the most conservative Bonferroni correction to adjust the significance level of individual hypothesis test to 10%/N for each of the N tests in the hypotheses family. This measure is conservative, so the real proportion of funds having good nonlinear market timing skills should actually be larger than 21.32%. 16. We carry out two joint tests for good nonlinear market timing based on the conservative Bonferroni correction significance level and take the higher percentage of the two. First test: H0 : φ4 ≤ 0; φ4 þ φ5 ≥ 0; ψ 4 þ ψ 5 ≥ 0; μ4 ≥ 0; μ4 þ μ5 ≤ 0 Second test: H0 : φ4 ≤ 0; ψ 4 ≤ 0; μ4 ≥ 0 Joint test for good linear market timing: H0 : φ2 ≤ 0; ψ 2 ≤ 0; μ2 ≥ 0 17. Less than 10% of funds show perverse market timing skills at the 10% significance level, for either of the two factors. 18. We also note that the best Sharpe ratio performer is from the “good market timer” group. 19. Except for the 75% percentile, where the alpha of good market timers is slightly less than that of the bad market timers, and for the maximum alpha where the advantage of good market timers is 1478bp per year compared to bad market timers. 20. The alpha is estimated from Fama
French three-factor model with regression Eq. (3). The reason we do not directly compare the alpha obtained from our market timing model (5) is that as our model already decomposed part of the original alpha into the market timing section and thus it is not appropriate to compare funds’ return using our alpha.

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XIN LI AND HANY A. SHAWKY

ACKNOWLEDGMENTS We are grateful to Kajal Lahiri, Bruce Dieffenbach, Terrence Kinal, Matthew Zapala, Ying Wang, and Liu Yang for valuable comments and suggestions. We thank seminar participants at SUNY-Albany. All errors are our own.

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EXTENDING THE REAL OPTIONS APPROACH BY INCLUDING INFORMATION OPTIONS Andrew H. Chen, James A. Conover and John W. Kensinger ABSTRACT Analysis of Information Options offers new tools for evaluating investments in research, mineral exploration, logistics, energy transmission, and other information operations. With Information Options, the underlying assets are information assets and the rules governing exercise are based on the realities of the information realm (infosphere). Information Options can be modeled as options to “purchase” information assets by paying the cost of the information operations involved. Information Options arise at several stages of value creation. The initial stage involves observation of physical phenomena with accompanying data capture. The next refinement is to organize the data into structured databases. Then bits of information are selected from storage and synthesized into an information product (such as a management report). Next, the information product is presented to the user via an efficient interface that does not require the user to be a field expert. Information Options are similar in concept to real options but substantially different in their

Signs that Markets are Coming Back Research in Finance, Volume 30, 53
93 Copyright r 2014 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1108/S0196-382120140000030007

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details, since real options have physical objects as the underlying assets and the rules governing exercise are based on the realities of the physical world. Also, while exercising a financial option typically kills the option, Information Options may include multiple exercises. Information Options may involve high volatility or jump processes as well, further enhancing their value. This chapter extends several important real option applications into the information realm, including jump process models and models for valuing options to synthesize any of n information items into any of m output assets. Keywords: Capital budgeting decisions; business investment policy; contingent claims; futures pricing; option pricing JEL classifications: G310; G130

INTRODUCTION Information Options involve choices in which the underlying assets are information items. Transition-phase Information Options accrue as a result of possessing information and have real options as the underlying assets. The rules governing exercise of Information Options are based on realities that exist within the information realm (infosphere). Information Options parallel real options in various applications along the value chain, but differ in their details, since real options have physical objects as the underlying assets and the rules governing exercise are based on the realities of the physical world.1 Just as real option applications offer tools for improved decision making for a variety of physical investments, Information Options offer potential improvements in decision support for those whose shareholder value results from information operations (including gathering, storing, processing, or presenting information). Information Options can be modeled as options to “purchase” information items by paying the cost of the information operations involved. Information Options arise at several stages of value creation, starting with information gathering. This first stage involves observation of physical phenomena with accompanying data capture. The next stage involves organizing the data into structured databases. The third stage involves selecting bits of information from storage and then synthesizing it into an information product (such as a report, article, or design specifications for a product to be fabricated in the physical realm). Then the information product is distributed (over information channels) and presented to the user via an

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efficient interface that does not require the user to be a field expert (presentation may involve personal interaction). In the end, the user applies the information in order to add value in the physical realm. Thus the loop is closed with value added in the physical realm. (The second section provides illustrations of Information Options in a sequential decision process.) There are some important distinctions between Information Options and real options. First, exercising an option to exchange one set of information in return for another information item does not involve destruction of the input (in contrast, an option to convert one physical commodity into another typically involves using up the input good). So, whereas many real options may be exercised only once, Information Options can have multiple exercises. Thus a given set of information items may spawn several options that can be exercised from it, and exercising one of them does not destroy the others. Therefore, the potential value generated by Information Options may be greater than in the case of real options. Additionally, options with information items as underlying assets may be more likely to involve high volatility or jump processes (compared with options that have physical items as underlying assets). For example, a new discovery might initiate a substantial jump in the value of Information Options that arise from an organization’s proprietary information. On the negative side, a discovery by a competitor might immediately reduce or eliminate the value of options that arise from an organization’s proprietary information. With the limited liability of options, such substantial movement potential translates into high option values. These characteristics of multiple exercise and high volatility could explain seemingly high market valuations for equity in companies that derive their value from information operations. Possession of proprietary databases and unique ability to process information into marketable intellectual property could support equity values that significantly exceed amounts attributable to physical assets in place or cash flows from existing physical operations. The literature of real options consistently argues that discounted cash flow (DCF) calculations underestimate net present value, and attribute the shortfall to DCF’s failure to consider the value of choice and flexibility. Yet when there have been opportunities to compare the real options evaluations with market evaluations, the real options approach also has been found to underestimate value (see Brennan & Schwarz, 1985; Paddock, Siegel, & Smith, 1988; Siegel, Smith, & Paddock, 1987). Evaluation of Information Options may help gain insight into the sources of value that are not being measured by other techniques.

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Indeed, real option applications have helped bridge the gap between finance and strategy (see Amram & Kulatilaka, 2000). Business strategy has roots in military strategy (the word “strategy” itself derives from Greek roots meaning “the art of the general”) which opens some interesting parallels. During the 1990s, the military leadership in several nations have devoted substantial resources to information warfare
that is, military actions in which the targets are information and the avenues of attack are across information channels. The U.S. Joint Chiefs of Staff have identified “Information Dominance” as one of five basic core competencies necessary for a modern military force.2 Information warfare is further differentiated from “information in warfare.” The latter involves using modern information technology to enhance effectiveness and efficiency of traditional military activities that involve applying energy to physical targets. Information warfare is distinctly different in the nature of the targets and the avenues of engagement
some information warfare specialists refer to themselves as “cyber warriors.” Similar distinctions can be drawn for business activities. “Information in business” involves using knowledge to enhance effectiveness and efficiency of business activities that involve transforming physical objects in order to add value (see, e.g., Feigenbaum, McCorduck, & Nii, 1988). (There are discussions below summarizing several real option applications that have been developed around the concept of options to exchange one asset for another, or any of n inputs into any of m output products.) “Information business” would encompass actions involving businesses whose shareholder values result from gathering, storing, processing, or presenting information
those for whom information is product as well as raw material, and information channels are the route of access and delivery. Virtual option applications can fill gaps in the analysis of value added by information in traditional business activities. Further, Information Options are uniquely appropriate for analyzing investments in information business.

OVERVIEW OF REAL OPTION APPLICATIONS, AND VIRTUAL OPTION PARALLELS Abandonment Options The first applications of option pricing theory to the valuation of real options were aimed at the option to abandon a project entirely and liquidate its assets (see Kensinger, 1980; Myers & Majd, 1990). Abandonment

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options can be evaluated using models for the values of put options. In the realm of Information Options where the underlying assets are information items, complete abandonment may not be a practical issue. When digital information is abandoned, the positive benefit is measured in terms of storage capacity released for other uses. Given the very low cost of archiving digital information, there would be little incentive to completely discard any of it (unless there is concern that it might have negative impact if later discovered, which involves issues beyond the intended scope of this chapter).

Basic Extraction Next, real option applications were developed for valuing natural resource investments such as mines and oil leases.3 Such projects can be viewed as options to buy basic commodities and evaluated using the Black
Scholes Option Pricing Model (see Brennan & Schwarz, 1985; Siegel et al., 1987). These activities occur at the beginning of the value chain.4 Rayport and Sviokla (1995) have translated the physical value chain into its parallel in the information realm. At the base of the virtual value chain are the activities that involve gathering information by observing physical phenomena. A simple call option model might be appropriate for situations in which a single information item can be “purchased” by paying the cost of observation. This is a limited scenario in the information realm, however. Alternative scenarios would include multiple information items captured by a given observation, or a choice of the most valuable of several information items derived from a given observation. These possibilities represent more complex options, some of which are examined later in this chapter. Then the decision whether to observe or not could be evaluated by comparing the value of the acquired option with the cost of observation. Also, the raw data itself may best be viewed as an option, to which we now turn.

Options to Exchange One Asset for Another Next in the ascent of real option applications along the physical value chain, options to exchange one product for another have been applied to gain insight into the value of conversion processes such as smelters or oil refineries (see Kensinger, 1987; Triantis & Hodder, 1990). Such options can be evaluated using the Margrabe (1978) model. The comparable stage in the virtual value chain involves organizing raw data into databases that

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facilitate later retrieval (as raw data is refined into information, information into knowledge, and knowledge into wisdom).5 Unlike the refining processes in the physical realm, raw data need not be destroyed in the refining (the raw data may be archived for repeated use). Thus there is not an exact parallel between the physical realm and the information realm with regard to refining processes. Rather, in the information realm, something new is created when raw data is refined, without damage to inputs. Thus, holding raw data provides the option to purchase information by paying the price of incorporating it into a structured database. Further, any given data set may represent multiple options in a package possessing an admirable quality: unexercised options need not be destroyed in the process of exercising others. Thus we should proceed to more complex options.

Multiple Exchange Options Real option analysis has been applied to activities (such as flexible manufacturing facilities) that involve transforming the least expensive of several alternative inputs into the most valuable of several possible outputs. In a move to the parallel position on the virtual value chain, an organized database (or linked set of multiple databases) provides options to select information and synthesize it into products such as reports, articles, documentaries, or books. Synthesis takes place within the infosphere, and people involved in the process can work from any physical location. The value of organized data is enhanced because exercise of any option does not destroy other options. The third section presents a discussion of options to exchange the cheapest of several inputs for the most valuable of several outputs. This discussion begins in terms of Margrabe’s (1982) generic model, which is broad enough to include a variety of probability distributions for generating prices. Then the discussion extends to an implementation using the Boyle-Tse (1990) algorithm for solving the Johnson (1987) model.

Remaining Stages of the Virtual Value Chain The next stage of the virtual value chain described by Rayport and Sviokla (1995) involves distributing the information product (report, article, design specifications for a product to be fabricated in the physical realm, etc.). This takes place in the information realm. Subsequently, the information product is presented to a user. Then in the final stage of the value chain, the

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user applies the information in the physical world, perhaps to achieve greater effectiveness or efficiency in a physical activity
so here the loop with the physical world is closed.6 An example of this final stage is using an array of sensors to gather data about the flow of electricity into and out of a transmission system, in order to optimize the generation and transmission processes. Thus recapping the virtual value chain and the Information Options represented at each stage, we start with gathering information. This first stage involves observation of physical phenomena with accompanying data capture. The second stage involves organizing the data into structured databases. The next stage involves selecting information from storage and then synthesizing it into an information product (such as a report, article, or design specifications for a product to be fabricated in the physical realm). Then the product is distributed (over information channels) and presented to the user via an efficient interface that does not require the user to be a field expert. In the end, the user applies the information successfully to add value in the physical realm. Thus the loop is closed with value added in the physical realm. To summarize the Information Options framework, we can then work backward from the final application. The effort expended in transmitting and presenting the information product can be evaluated as a decision to exercise an option
the motivation for exercise is the value added in the physical realm when the information product is applied. This value added can be evaluated as an option to convert one of n physical inputs into the most valuable of m physical outputs (without the information, one would not know how to do this). Backtracking, the price paid for the synthesis effort is defined by the value of the option just described. Backtracking further, the value of organizing the database is the value of a portfolio of options to produce information products such as reports, articles, or design specifications; and the value of raw data is represented by the value of options to convert it into organized databases.

ILLUSTRATIONS OF REAL OPTIONS AND INFORMATION OPTIONS IN SEQUENTIAL DECISION PROCESSES Information Options in Mineral Exploration As an illustration of the way virtual option analysis could enhance decision making, let us consider a sequential decision process at Royal Dutch/Shell

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that unfolded over a time period extending more than a decade. The details have been reported in the Wall Street Journal (Solomon & Fritsch, 1996). The decision process began in May 1985 with the choice of bidding on an offshore drilling lease in the Gulf of Mexico, dubbed the “Mars” field. Initial survey data had produced difficult-to-interpret data that some thought might indicate oil deposits. After winning the lease, the next choice involved exploratory drilling. The affirmative decision here resulted in discovery of a so-called elephant field; but the decision process did not end, because the site was so deep underwater. The next choice involved innovating new drilling technologies capable of developing the site. Once the technology was in hand, the final choice was when to proceed with development. The decision process begins with Shell’s efforts to map the region in preparation for the auction of drilling rights by the federal government. (The saga begins at a time when capital markets were apparently discouraging major expenditures for exploration in North America.) Geologist Roger Baker encountered many difficulties interpreting the seismic data because of distortions produced as the signals passed through the thermal layers encountered in the deepwater (such thermal layers act as lenses, but it is difficult to know how the signals are being distorted). Despite these difficulties, the company had to decide whether (and how much) to bid on the site. One can approach the problem of valuing oil leases by treating such leases as call options.7 Greater upside potential, of course, translates into higher option value. (In sealed bidding Shell paid $2.4 million for the rights to drill, a 37% premium above the minimum allowable bid, with no other company making a competing offer). The next step in the decision process involved exploratory drilling, which cost $14 million. In part, it could be justified as a means for improving the knowledge necessary to decide optimal exercise of the real option identified above. (From this point of view, the question focuses on the role of the new information in improving the ability to evaluate the option to develop the site.) In addition to learning what resources might lie in this specific deposit, however, potentially valuable lessons could be learned from comparing actual drilling data with the seismic data gathered in the initial survey. Such lessons might give Shell some competitive advantages in interpreting preliminary data on new fields to be considered in the future. How could we evaluate lessons learned concerning interpretation of seismic data from deepwater prospecting in general? Royal Dutch/Shell would have knowledge about similar information from other locations in its proprietary databases. Learning the truth about the Mars site could

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substantially enhance the value of such information. A positive outcome would identify new development options of the Siegel/Smith/Paddock variety for each such similar location (and a negative outcome here could prevent losses elsewhere). Knowing the number of similar sites in its databases, Royal Dutch/Shell could tally the options potentially available to it. The transition-phase virtual option associated with the exploratory drilling at the Mars site has this portfolio of real options as the underlying asset. Given the global scope of Royal Dutch/Shell seismic data-gathering activities, this virtual option could have substantial upside potential (hence substantial value, due to the limited downside risk). The exploratory drilling revealed that the Mars field contains 700 million barrels of oil, the biggest domestic discovery since Alaska’s Prudhoe Bay. (This is about one-third the size of all Gulf Oil Company’s recoverable reserves at the time of its merger with Chevron.) Shell’s problem was that no one had yet gained experience constructing a production platform capable of operating in such deepwater and also capable of withstanding the hurricanes that occur there. The next part of the decision process involves a multiyear research effort to design a platform. How do we evaluate the investment in research devoted to platform design? At the outset, no one knew for sure whether a successful design could be achieved with available technology, or whether a production platform could be built at a cost that would make developing the field economically viable. Strictly within the confines of the Mars field, we are still dealing with the Siegel/Smith/Paddock real option that has developed reserves as the underlying asset. The exercise price of this option is uncertain at this stage of the decision process, and the proposed research would provide new information to enlighten the evaluation of this real option. Also, however, proprietary knowledge gained from platform development efforts could be valuable in other future applications. A positive outcome could create new development options that would accrue from information about other similar deepwater sites known from Royal Dutch/ Shell’s proprietary databases of seismic observations. When the research into platform design was complete, Shell had the task of evaluating the expenditure of $1.1 billion to build a platform and drill 26 production wells (this is about $1.57 per barrel). The platform would cost $650 million and the drilling would cost another $450 million. Some of this cost would be shared with minority partner British Petroleum. The expenditures at this stage would be the largest in the whole development effort. Although this is the stage in the decision process that involves the most money, it is the least complex. The remaining decision is whether

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to exercise the real option to pay drilling costs and receive the developed reserves. At this stage there is highly refined information about the exercise price and about the value of the underlying asset, so the decision process can proceed smoothly.

Information Options in Basic Research What about the expense of Roger Baker’s initial efforts gathering information
the basic research that gave rise to the entire process we have just reviewed? Also, how does the new knowledge about interpreting deepwater seismic observations affect the value of future survey efforts? In a mature information culture, new data gathering tends to occur at the frontiers of available knowledge. When Roger Baker, for example, gathered his survey data, he applied existing methods for exploring in a new area. Roger Baker is a prospector with experience about the probability of discovery from a given search effort. This probability distribution could be treated as the underlying stochastic process in evaluating the effort as a virtual option (the underlying asset being information of value for use in bidding on a lease). Interpreting Roger Baker’s data proved challenging because of unforeseen but understandable interference by the thermal layers in the deepwater. Subsequent clarification of how to interpret this data could produce benefits in at least two ways. First, the newly acquired skill could be applied to data produced in prior deepwater surveys at other locations, with new drilling options as the result (as discussed above). Further, the new capability to interpret data changes the probability of discovery from future survey efforts, thus encouraging future prospecting.

Information Options in Human Resources Development Investments in human resources development may alter the exercise price of an organization’s Information Options. Improved engineering capabilities, for example, may reduce the exercise price for an option to derive product designs from proprietary data. Analyzing the impact on the value of an organization’s Information Options therefore could provide useful insights for decisions about investments in human resources development. Beech Aircraft Company provides an example. Brand identity was strong, with a solid reputation for product quality; but the existing product

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line was dominated by aging designs. In 1979 Beech committed to developing a revolutionary design (dubbed “Starship”) that used all-composite construction, fully computerized flight instruments, jet-fan power, and the then-radical canard architecture (on a canard aircraft, the main lifting wing is at the rear, with the horizontal stabilizer mounted on the nose). Most of the investment went into computer-aided design facilities and factory automation for handling composite materials on a large scale (which have many alternative uses, hence generating valuable real options). This effort attracted new engineering talent and revitalized the company to such an extent that Beech attracted significant attention as a strategic acquisition with several potential suitors. (Beech’s primary stockholder at the time was the founder’s widow, who wanted to retire and had significant estateplanning issues.) The result was a successful sale to Raytheon within less than a year of launching the Starship project, nearly doubling the value of Beech stock in four months. Raytheon’s acquisition came before any of the major project expenditures had been made and the project was still in its very early stages (Raytheon was the primary supplier of cockpit instruments, communications equipment, and navigation aids for the Starship project). The Starship itself had a very brief production run, but the capabilities developed during that effort have enhanced the organization in a variety of ways. Chief among the gains achieved through the Starship program was the enhanced ability to attract and retain high-quality engineering talent.8 With the engineering talent, computer-assisted design, and computerintegrated manufacturing systems (CIM) established via the Starship development program, Beech substantially reduced the costs of making improvements for existing products and developing new product designs. Highly visible among the new products that resulted is a new jet aircraft with aluminum wings and composite fuselage. Beech’s design and composite materials production capabilities have also resulted in several contracts to supply components for other manufacturers (including parts for the B-2 bomber and the C-17 cargo aircraft built for the U.S. Air Force). These capabilities directly result from the investments made in the Starship program.

Information Options in Logistics Many companies have made investments in transmitters and monitoring equipment so they can constantly track the location of shipping containers or trucks as they move about the world. There have also been investments

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to develop online searchable databases of shipping manifests so that associates can locate specific items that are present in transit. As an example of the potential value to be derived from such investments, consider a BMW dealer in Texas who has just received an order for a specific model in a particular color, with specific selections of optional equipment. Armed with the necessary access to data, the dealer can quickly locate a suitable automobile aboard a transport ship sailing across the Atlantic bound for another dealer’s inventory, query the currently designated recipient for permission, and redirect the delivery of the auto when it arrives in port. Within a collaborative network, cooperating members can use tracking systems to optimize the flow of goods through the supply channels. Information Options in Electric Power Transmission Independent power generators and utility companies offer another example of collaborative networks in which cooperating members can use monitoring systems to optimize the flow of energy through the transmission system. As current flow fluctuates over particular sectors of the grid, active flow management can divert current from “full” sectors to “needy” sectors, and reserve generation capacity can be brought online as needed. Value accrues in the form of reduced losses from overproduction, while customer demand can still be met satisfactorily. Investments in improved sensor deployment represent transition-phase Information Options. Further, archived data may be useful in analyzing seasonal or day-of-the-week fluctuations in the patterns of customer demand, improving the ability to analyze investments in new generating capacity.

MODELS FOR EVALUATING INFORMATION OPTIONS Jump Process Model In order to evaluate Information Options, let us begin with the case of a single input and single output, with the possibility for discontinuous jumps in value. Options with information items as underlying assets may be more likely to involve high volatility or jump processes (compared with options that have physical items as underlying assets). For example, a new

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discovery might initiate a substantial jump in the value of Information Options that arise from an organization’s proprietary information. On the negative side, a discovery by a competitor might immediately reduce or eliminate the value of options that arise from an organization’s proprietary information. This section presents a general valuation model for Information Options with underlying stochastic process described as a mixture of both jump and diffusion processes. When the virtual option can be exercised without destroying the input information items, then complex options can usually be represented as portfolios of several options, each one conveying the privilege to generate a single output item. For each of these individual options, the total change in the value of the underlying asset is assumed to consist of two types of changes: (1) The small and “normal” changes in the market value of the firm that are modeled as Brownian motion with a constant variance per unit time and a continuous sample path. (2) The large and “abnormal” changes in value that are due to arrival of significant unanticipated events. Given these specifications, the changes in value can be formally written as the following stochastic differential equation: dV=V = ðμ − λkÞdt þ σ dZ þ dq

ð1Þ

where V = value of the underlying asset; μ = instantaneous expected return in the value of the underlying asset; σ2 = instantaneous variance of the value of the underlying asset, conditional on no arrival of “abnormal” information; dZ = a standard Gauss
Wiener process; dq = a continuous-time Poisson process, assumed independent of dZ for simplicity; λ = the intensity of the Poisson process (the mean number of arrivals of “abnormal” information per unit time; and k = Eðγ − 1Þ; where ðγ − 1Þ is the random percentage change in the value of the underlying asset if the Poisson event occurs, and E is the expectation operator over the random variable γ. In Eq. (1) σ dZ describes the portion of value change attributable to “normal” sequential small shocks (Brownian motion). The number of

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discontinuous jumps during the infinitesimal time is either one or zero with probability λ dt and 1 − λ dt, respectively. Thus the resulting sample path would be mostly continuous, but with finite jumps of differing signs and amplitudes at discrete points. Given Vð0Þ = V and μ, λ, k, and σ are constants, the random value of the underlying asset at time t can be expressed as: VðtÞ = V exp½ðμ − σ 2 =2 − λkÞt þ σZðtÞγðnÞ

ð2Þ

where Z(t) is a Gaussian standard normal random variable with zero mean, γðnÞ = 1 if n = 0; γðnÞ = Π Nj= 1 γj for n ≥ 1 where γj are the jump amplitudes assumed for simplicity to be independently and identically distributed and n is Poisson distributed with parameter λt. Under the assumptions that the capital asset pricing model (CAPM) holds and that the jump process is diversifiable, Merton (1976) shows that the price of any contingent claim, FðV; tÞ which is a function of the value of the underlying asset and time must satisfy the following general valuation equation: 0:5 σ 2 V 2 FvvðV; tÞ þ ðr − λkÞVFvðV; tÞ þ FtðV; tÞ − rFðV; tÞ þ λEðFðVY; tÞ − FðV; tÞÞ = 0

ð3Þ

which is an integro-differential equation where the expectation is taken over the random value of the jump amplitude γ, and r is the constant instantaneous riskless rate of interest. The unique f value of the contingent claim on the underlying asset is determined by the initial and boundary conditions (which generally include Fð0; tÞ = 0 and FðV; tÞ ≤ VÞ. Additional boundaries can be stated when required by the constraints of specific situations.9

Multiple Outputs, Choice of Inputs In the case of multiple outputs ðOUT1 ; …; OUTn Þ, but only one input (IN), the end-of-period payoff can be represented by the following expression: Payoff = MaxfMax½OUT1 ; …; OUTn 
IN; 0g

ð4Þ

That is, at the time the decision is made about how to use the information in a given time period, the output with maximum value will be chosen;

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and the payoff will be the difference between the value of that output and the cost of the input. In the case of more versatile information processing systems, the optionholder has the choice in each time period to convert the lowest cost input from a set of m inputs into the highest valued output from a set of n output items, but need not exercise the option unless it is profitable to do so (a binomial illustration and numerical examples are given in the Appendix). The value of this option at any time prior to the expiration date can be solved numerically, using techniques developed by Margrabe (1982) for situations that do not involve discontinuous jumps. This scenario can be represented more compactly by supposing that the current prices at time t for the various information items form a vector, x = ½x1 ; ⋯; xn , the prices at future time T form a vector X = ½X1 ; ⋯; Xn ; and qð…Þ is a multivariate p.d.f. for the vector X, given the initial set of current prices at time zero (the vector x). The production of information outputs from the raw input can be represented by some function f ðXÞ.10 This function could be simple or quite complex. The interest rate is r for U.S. Treasury securities maturing at time T. Then, the value of an option to accomplish the optimal transformation is given by the following: Z Z ð5Þ Option value = e − rðT − tÞ ⋯ f ðXÞqðX; T =xÞdx where integration is over the n-dimensional array of future prices for all of the commodities. Margrabe proved this solution for the case of a logGaussian p.d.f.
showing that the richer the array of choices, the higher the Net Present Value (NPV) of the project. The virtual option package is a portfolio of the above options with different maturities, with one maturing in each period of the project’s life.

Implementation Using the Boyle and Tse Algorithm Johnson’s (1987) model calculates the exact value of a call option with exercise price X and time to maturity T, on the maximum of N assets with current values S1 ; S2 ; …; Sn . Computing the exact solution requires numerically evaluating N þ 1 N-dimensional standard normal distribution functions. This is practical for N < 6 on personal computers using the Schervish (1985) algorithm. Solving with N = 6 is practical only on minicomputers and mainframes, while N > 6 is practical only on super computers.

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Chen, Conover, and Kensinger (1998) have implemented the multiple exchange option framework using the Boyle-Tse (1990) algorithm for evaluating an option on the maximum or minimum of several assets. This algorithm has overcome earlier criticism that realistic problems could not be solved without consuming large amounts of computer time (the program is available from the authors upon request). CCK report the ability to solve problems with up to 1,000 different output goods at high speed on a personal computer with a math coprocessor, and have solved problems with up to 9,000 output goods in about 30 seconds on a 250 Megaherz Sun SPARC workstation. The Boyle/Tse (1990) formulation can be applied to a wide range of problems that used to be too costly (or impossible) to evaluate. Detailed description of the steps is too lengthy for this chapter, but a copy of the computer code is available upon request. What follows is a description of the principle steps of the algorithm. First, the N assets are assumed to be jointly multivariate normal. Direct evaluation of the multivariate normal distribution function is very costly for N > 6, but the maximum of two bivariate normally distributed assets is well defined. The algorithm uses a recursive technique that successively compares N assets, taken two at a time. Let us begin by assuming that MAXðx1 ; x2 Þ is normally distributed. Given this assumption, the expected value, variance, and covariance of MAXðx1 ; x2 ; x3 Þ can be approximated using the recursive relationship: MAXðx1 ; x2 ; x3 Þ = MAXðMAXðx1 ; x2 Þ; x3 Þ

ð6Þ

Then, the first four moments of the maximum of the first three assets with the fourth are calculated using: MAXðx1 ; x2 ; x3 ; x4 Þ = MAXðMAXðx1 ; x2 ; x3 Þ; x4 Þ

ð7Þ

Repeatedly applying this procedure to the remainder of N variables (using the current cumulative maximum value at each step) allows approximation of the distribution of the maximum of N jointly random normal variables. Zero strike options on lognormally distributed assets are examined by discounting (under risk neutrality) the expected value of the log of the maximum of N asset prices. For nonzero strike prices, the procedure estimates the probability that the maximum of N assets will exceed the strike price of the option. First, the recursive algorithm described above is used to

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calculate the first four central moments of MAXðx1 ; x2 ; …; xN Þ. The second step is to form a Taylor series expansion of the option pricing problem using the standardization transform in terms of the first four central moments of the maximum of N jointly multivariate normals from the first step. A Gram
Charlier expansion of the Taylor series is solved to calculate the probability that MAXðx1 ; x2 ; …; xN Þ will be greater than the exercise price. The algorithm described in Boyle/Tse (1990) is an accurate approximation that is fast enough to run on a personal computer. For N up to 50 assets, the approximation error is as low as 0.06 percent. The algorithm has four appealing characteristics: • It requires only the evaluation of univariate normal distributions that are simple and inexpensive to perform. • The algorithm runs very quickly compared to its only competitor, which is repeated simulation sampling. • The algorithm is very accurate over a wide range of the parameters. • The model predictions can be checked against independent estimates of the model prices from Monte Carlo sampling of multivariate distribution functions or direct evaluation of the distribution functions. In simulation trials to evaluate how value responds to increasing flexibility, Chen et al. (1998) report results similar to those observed in diversified portfolios of securities. At first, additional outputs or inputs add substantially to value, but after 12
15 alternatives are already available, more new alternatives add very little additional value.

Estimating the Covariance Matrix The virtual option approach requires two types of data: (1) current values for the information items involved and (2) the descriptions of the probability distributions that generate future values. The current prices themselves may be directly observable or readily proxied. Let us now consider the estimation of parameters for the covariance matrix. In the Johnson model, and the Boyle and Tse implementation, each of the n asset prices, n standard deviations and the n × n correlation matrix of each asset with the other assets must be specified. The model is very sensitive to any errors that might occur in estimating the covariance matrix. Option models that capture the value of a simple option on a single asset, such as Black
Scholes (Black & Scholes, 1973), specify the underlying

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stochastic process generating returns on the asset simply in terms of the asset’s total variability (including both systematic and unsystematic risk combined into one measure). Options to exchange one asset for another, such as Margrabe (1978), specify the underlying stochastic process in terms of the ratio of the prices of the two assets (thus the covariance of the two assets enters the calculation). Multiple exchange options are much more complex and demand careful estimation of the parameters input into the model. In well-functioning financial markets, asset prices move together when the assets are close substitutes (otherwise there would be arbitrage opportunities). This characteristic is captured in a carefully estimated covariance matrix, or in a diagonal-model approximation such as the CAPM in which variability is partitioned into systematic and unsystematic components. In order to apply the financial markets model successfully to real options or Information Options, it is necessary to insure that the variance
covariance matrix adequately captures the webwork of interrelationships among the prices for the input and output items.11 The problem can be illustrated by considering a binomial example based on a series of coin tosses, such as the illustration in the Appendix. The Johnson model is essentially an extension of such a binomial process to a very large number of coin tosses spanning the life of the option. The problem arises because there is no constraint that eliminates the possibility for one of the output prices to be inflated by a series of “heads” in the sequence of random coin tosses. When there are a hundred or more output items involved, the odds are high that within the model, one of the prices will become very large, thus inflating the calculated value of the option beyond the bounds of reason. If inputs and outputs were all publicly traded commodities, economic forces of supply and demand would prevent the price of any one of the output items from rising well beyond the others over time. One of the output items might rise substantially over a short time, but producers would increase their output of it, while reducing output of the others. Price adjustments would follow, so that the whole group of related goods would remain clustered (although relative prices would be free to fluctuate substantially within the bounds of the cluster). Chen et al. (1998) resolve this problem by defining the underlying stochastic processes using a linear model similar to the CAPM, in which there are two components defining variability: one component affects all the items in the matrix, while the other component represents the unique shocks specific to the individual items. The values the analyst must estimate, then, are the current prices of the output items, annualized standard deviations for changes in their values,

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and the correlation matrix among them. No forecasting of future prices is necessary (such forecasts, in contrast, are the essence of DCF analysis). Maintaining consistency in the estimates that are input into the model, and insuring appropriate structure of the correlation matrix, can be made a function of the software used to incorporate the exchange option models into decision-support systems. Programmers will find interesting opportunities to provide expert assistants that will quiz users, prompting them to think clearly through the underlying strategic issues.

WAYS IN WHICH THE VIRTUAL OPTION APPROACH INTEGRATES FINANCE AND STRATEGY Links with the Physical Value Chain The concept of the physical value chain, presented in Porter (1985), is a useful reference for assessing the progress that has been made up to now toward integrating finance and strategy by means of applying option pricing methodologies (see Fig. 1 for a graphic image). On a global scale, extraction or cultivation of basic commodities is at the bottom of the physical value chain. The second tier involves processing basic commodities into refined products. Next comes the fabrication of finished products. At the high end of the physical value chain come the distribution and marketing of products, and postsales servicing of customers. Thus the early commodity option applications, such as Brennan and Schwarz (1985), deal with projects at the low end of the value chain. Over time the real options literature has extended the commodity option theme to the valuation of options to exchange a group of commodities for another. Thus real option pricing applications have

Fig. 1.

Service

Distribution & Marketing

Fabrication

Refining

Basic Extraction

Technology development Human resources development

The Physical Value Chain from a Global Perspective.

Fig. 2.

Distribute

Synthesize

Select

Gather

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Organize

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The Virtual Value Chain.

extended to higher levels of the physical value chain
to the physical processing of commodities into refined products, and then to flexible production systems used in fabricating complex products. Work also continues to develop real option methods for evaluating activities at the upper end of the physical value chain: involving distribution, marketing, and service. Real option applications in evaluating support activities such as technology development or human resources development have been problematic.12 Evaluating Information Options fills important gaps by applying option analysis to activities that add value along the virtual value chain (Fig. 2). Also, evaluating Information Options provides new insight into the value of efforts to develop technology or human resources. This approach may also yield insights in evaluating efforts to improve logistics or service in the physical realm (such efforts might be analyzed as transition-phase Information Options).

The Knowledge Advantage There are several additional ways in which the virtual option approach integrates financial analysis with strategic analysis. Let’s begin with the end-of-period payoff for the simple case of a single input and a choice among multiple output items, given above in Eq. (4) and reproduced below as Eq. (8). Payoff = MaxfMax½OUT1 ; …; OUTn  − IN; 0g

ð8Þ

It can be shown that this dominates an option that includes a smaller set of output items, such as one with the following payoff: Payoff = MaxfMax½OUT1 ; …; OUTn − 1  − IN; 0g

ð9Þ

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To demonstrate this point, we compare an option which includes two output items with another that includes those same outputs plus one more, and find that the three-output option is worth more because its payoff would be greater in those states of the world in which OUT3 > IN; OUT3 > OUT2 and OUT3 > OUT1 . Therefore, we can state the following: An organization that has the same potential uses for a given information item as another organization, plus one or more additional possible uses unique to that organization, will gain a higher NPV by gathering the information. Thus, the value of obtaining information may differ from one organization to another, and organizations with more agility have an advantage in generating investor value.

A well-known property of such options, whether or not the p.d.f. is log-Gaussian, is that prior to expiration they are worth more than the present value of the spread expected at expiration (expected price of output minus expected price of input. This can be illustrated in the simple case of a single output and a single input (the argument is easily extended to the case of multiple outputs or inputs). At any given time prior to the expiration of the option, CXðOUT; IN; tÞ > e − rt ðE½OUTt  − E½INt Þ

ð10Þ

With the values of the input and output items fluctuating at random, the spread between them is free to widen or shrink. The existence of discretion allows management to take whatever profit opportunities arise when the spread is wide, but cutoff losses that would occur when the spread becomes negative. The more volatile the spread, the greater are the possible profits. Since losses are limited, however, the increased upside potential is not offset on the downside. The model therefore supports another point: The more volatile the relationship between the values of input and output items, the greater the value of a virtual option.

The more volatile each item’s price, and the lower the correlation between their prices, the more volatile the spread. Therefore, the highest option values are to be found when values of input and output are volatile, with low correlation. If there were a great many organizations engaged in the same information operations, competition among them would tend to keep the spread from fluctuating widely, and output values would be highly correlated with the input values. A low correlation would be associated with a situation in which competition is not intense. (A few years ago, for example, DuPont possessed patents that protected its capability to convert

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petroleum into a manmade substitute for wool (polyester), which gave it a significant competitive advantage for a time. As the capability diffused throughout the economy, however, the advantage dissipated.) Therefore, the model supports another point: The value of a virtual option is greater the more innovative the information operation, and the stronger the barriers to entry for potential competitors.

This statement is very similar to the lessons derived from a qualitative analysis of anecdotal evidence by Shapiro (1985) and Porter (1985). The process of estimating the matrix of correlations in a virtual option evaluation, therefore, entails a quantification of knowledge structure in the industry. This dimension is not made explicit in the DCF approach or the real options approach to management.

HURDLES TO BE OVERCOME Developing methodologies for valuing real options has helped integrate finance theory with the concepts of business strategy. In the third section, we address issues of corporate strategy that arise in the analysis of flexible production systems. Also, some potential applications of option pricing models are anticipated in other areas besides flexible manufacturing (See, e.g., Myers (1984) and Trigeorgis & Mason (1987)): • Valuing options for future growth that might arise from current activities. • Valuing the act of contingency planning, in the sense that the object of such planning is to create and manage a portfolio of strategic “real options.” • Valuing options to redeploy assets to new uses as the business environment changes. There is a hurdle that must be overcome in gaining acceptance of option techniques by decision makers, and we try to overcome it here. The powerful computers that are widely available to decision makers, coupled with improved solution algorithms, now make it possible to offer complex project evaluation techniques to practitioners in user-friendly packages. The problem is that many decision makers will face the prospect of using decision-support systems that, as far as they are concerned, are black boxes. It may be very hard for a responsible decision maker to bet a large sum of money on a

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project, based upon the output of a computerized black box that he or she does not understand well. In the Appendix, therefore, we offer simplified illustrations in hopes of building intuitive understanding among practitioners.

Flexible Manufacturing Real option analysis now includes even the complex problem of deciding how much to spend for flexible manufacturing facilities (applying option pricing methods to evaluating equipment such as computer-controlled machine tools that convert a generic input, such as a cube of steel, into any of a variety of different machined parts). Besides filling analytical gaps in cases involving application of information to enhance effectiveness of activities in the physical world, evaluating Information Options can improve decision-making concerning actions when outputs as well as inputs are exclusively information items. Option models offer the possibility of improving decision makers’ ability to analyze investments in CIM systems. Such systems are a radical departure from the familiar factory that can make only a few products, and which must operate at high volume in order to keep unit costs at an acceptable level. The new CIM systems, in contrast, are capable of processing generic inputs into a large array of different outputs and can quickly shift from one job to another. The flexible manufacturing cell at the General Dynamics plant in Fort Worth, for example, can turn raw metal blanks into any of 560 different aircraft parts; and the cost per unit is virtually the same whether the production run is for only one part or a hundred. When a part is needed, the operator selects its specifications from a computer library, feeds appropriate blanks into the queue, and within minutes the cutting tools finish the new parts. Variable cost for each unit of output is the cost of the blank input, plus the energy consumed in operating the cutting tools for the time required by that specific output (these are known quantities). Cost per unit is the same whether the operator makes one part or a hundred. Converting to another set of specifications requires only a new selection from the menu, so switching costs are virtually nil. With automated feeding of input, the equipment can be programmed for a series of selections and left to run on its own much as one would place a series of documents into the queue for a laser printer. Further, the computer control can be linked with other computers within the organization to trigger production of needed parts without human communication.

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Kaplan (1986) addresses the problems of analyzing investments in CIM projects using DCF analysis, noting the difficulty in estimating how much the inherent flexibility of such a system adds to its value. The multiple exchange option approach, however, could significantly reduce the degree to which the analysis of such investments must be left to qualitative considerations. When the U.S. Navy considered such an installation for its fleet support facilities at Norfolk, Virginia, the cost was justified by considering the new equipment to be equivalent to a “painter’s palette” for creating parts. The alternative would be a parts inventory on hand with enough depth to provide any of several hundred different parts in sufficient quantity to satisfy unpredictable requirements. Since the new machinery cost much less than a traditional parts stock, it was purchased. While this is an apt comparison, decision makers would be well served by more rigorous analytical tools based on models of options to exchange generic input for any of several output goods. Many capital budgeting decisions are concerned with systems that are used to convert one group of commodities into another
Triantis and Hodder (1990) define flexible production systems broadly enough to include refineries, chemical plants, and a range of flexible manufacturing system (FMS) installations. Inputs may be varied, too, as in the case of beverage can making equipment that can work with either steel or aluminum, whichever is cheaper. The economic life of such a system spans several time periods, and it’s worth in each single period is the value it adds to the economy by accomplishing resource conversion. In no rational case, however, would the conversion be made if a loss would result. Thus the valuation problem for flexible manufacturing facilities covers the following points: • There are options to choose the most profitable from an array of choices available at the moment. • There are options to shut down temporarily when no profitable activity is available. This issue has been examined on a slower-paced time scale by McDonald and Siegel (1985a, 1985b), but FMS systems accelerate the time scale substantially. • There are options to add new products to the repertoire by developing or purchasing additional software. This is analogous to the growth options analyzed by Majd and Pindyck (1987). The value of having access to flexible manufacturing equipment in a single future period could be conceived as an option to exchange input resources for output products. In the multiperiod case, the value could be

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represented as a portfolio of such options with different maturities, one of which matures in each period of the equipment’s life. The standard DCF investment analysis tools ignore the value of flexibility. Instead, one who uses the standard tools treats the project as a “black box” that will somehow produce a stream of future cash flows without human guidance in response to future changes in the environment. It is simply assumed that the project will be launched and then left on its own.

Limitations of the Exchange Option Approach and Directions for Further Work Despite the considerable improvement these new techniques represent, there are still some limitations. The exchange option approach offers the capability of quantifying some of the strategic aspects of a project which up to now were thought of as unquantifiable, but does not cover all the aspects that would be desirable. Writers on strategy, such as Porter (1985) and Shapiro (1985) identify cost leadership, a quality edge, or monopoly power as sources of sustained competitive advantage. The exchange option model captures some of these strategic qualities through the correlation coefficients in the joint probability function; but these parameters are presumed to be stationary in existing option pricing models. The covariance matrix could change as new competitors enter an industry and stabilize the spread between input and output prices, and a dynamic environment can be too much for existing option pricing models to handle reliably. In the option models, furthermore, the right decision about whether or not to exercise the option at maturity is assumed to be clear-cut (see Brennan & Schwarz, 1985). In the case of an option to exchange one commodity into another, the choice is plain. In the case of deciding whether or not to abandon a project completely, however, the choice may be complicated if there are ramifications of the present decision that impact the value of future choices. Although it is conceivable that these considerations could be modeled with sophisticated compound option models, in many situations the right choice is not clear, and experienced judgment is required. Another barrier yet to be broken is the problem of valuing a company’s options for future growth. The difficulty is to define and model the process that generates ideas and opportunities for future growth. In the exchange option models, the relevant process is the one that generates the future prices of the commodities; and in the abandonment option models it is the one that generates the future market value of the assets used by the project.

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The process that generates growth opportunities, however, is not so clearcut. To some extent, it may reflect physical characteristics of a company’s assets, such as the flexibility inherent in buildings or plants which are designed to easily accommodate future expansion. On the other hand, however, much of the growth potential of a company comes from its human capital
the creativity and ingenuity of the people involved with the company. Capturing such things in a mathematical model is a very challenging task, to say the least. Also, the optimal abandonment strategy needs to be worked out. The option to abandon could be incorporated into the multiple exchange problem as of n choices, at any given time period. Its exercise extinguishes future options prior to their exercise dates, however. Taking this into account would supplement the work already done by Howe and McCabe (1983). Although the efforts to capture the dimension of a project’s inherent manageability have recently begun to produce significant improvements in the techniques available to the capital budgeting analyst, there are some limitations that may never be overcome in the efforts to quantify all the strategic dimensions of business venturing. As model-builders continue to move up along the value chain in the process of quantifying the value of active management
moving from the level of extraction of basic natural resources to the refining of one commodity into another, then to fabrication of complex products, then distribution, marketing, and servicing
the elusive elements of executive judgment and competitive skills will become increasingly important.

CONCLUDING REMARKS This chapter develops the concept of Information Options for inclusion with real options in capital investment applications. Information Options involve choices in which the underlying assets are information items, and the rules governing exercise are based on realities that exist within the information realm (infosphere). Information Options differ from real options, since real options have physical objects as the underlying assets and the rules governing exercise are based on the realities of the physical world. Transition-phase Information Options accrue to the owner as a result of possessing information, and have real options as the underlying assets (transition-phase Information Options capture value at the interface where information is applied to gain advantage in the physical domain).

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The Information Options concept gains structure from the “virtual value chain” described by Rayport and Sviokla (1995). This traces the process of adding value through information operations. The first stage involves gathering information from the physical realm. The next stage involves organizing the raw data into structured databases for later retrieval. The next stage of information operations involves selecting information from the databases and organizing it into a product such as a report, article, or design specifications for a product to be fabricated in the physical realm. Then follows distribution, then presentation to the user. Effective presentation may be challenging, if the information product is presented to a decision maker who is not an expert in the field. Substantial value may hinge on how effectively and efficiently the information is conveyed to someone who lacks understanding of the basic principles that are part of an expert’s daily working knowledge. The final stage of the virtual value chain involves applying the information to gain advantage in the physical realm (this is the stage at which we encounter transition-phase Information Options). Some stages in the virtual value chain may be skipped; particularly if the person who develops an information product is also the decision maker, in which case the distribution and presentation stages can be skipped. Information Options may exist at each step from one stage of the virtual value chain to the next. Information Options can be modeled as options to “purchase” information items by paying the cost of the information operations involved. The process of gathering raw data by observations in the physical realm, for example, generates options to organize the data by paying the cost of populating an existing database or constructing a new one. Additionally, possessing the necessary organized databases generates options to develop information products such as design specifications for a product to be fabricated in the physical realm. Some information operations can be automated, and doing so reduces the cost of exercise for the Information Options an organization possesses. Thus the investment in data automation can be evaluated by measuring the change in value of the organization’s portfolio of Information Options. Information Options can be modeled as options to exchange an input such as an engineer’s time for an output item that incorporates added value. More often, there may be a choice of the most valuable among two or more output items; and there may be possibilities for choosing the least costly of two or more input items (such as when the input information is purchased). The basic research on options with multiple underlying assets has been done by Margrabe (1978, 1983), Stulz (1982), Stulz and Johnson

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(1985), and Johnson (1987). Chen et al. (1998) applied this method to evaluating real options associated with flexible manufacturing facilities. The benefit of evaluating Information Options is not only a more robust set of quantitative tools for measuring the economic value added by an organized activity, but also refined insight into the qualitative aspects of a positive net present value action. By evaluating Information Options along with real options, it is possible to draw well-founded conclusions about the effects on share value of such attributes as flexibility, innovativeness, and proprietary knowledge. An organization that possesses knowledge no one else has, for example, exclusive possession of options to apply it for advantage in the physical world. Additionally an organization with unique capability to use information (in a way no other organization can duplicate) has enhanced value through possessing a broader array of choices. The concept of the physical value chain, presented in Porter (1985), is a useful reference for assessing the progress that has been made toward integrating finance and strategy by means of applying option pricing methodologies. The real options literature has extended the concept of options to exchange one commodity for another (or one of several inputs for one of several outputs) to develop real option applications for basic extraction, refining, and flexible production systems used in fabricating complex products. Work also continues toward developing real option methods for evaluating activities at the upper end of the physical value chain: involving distribution, marketing, and service. Real option applications in evaluating support activities such as technology development or human resources development have been problematic.13 Evaluating Information Options fills important gaps by applying option analysis to activities that add value along the virtual value chain. Also, evaluating Information Options provides new insight into the value of efforts to develop technology or human resources. This approach may also yield insights in evaluating efforts to improve logistics or service in the physical realm (such efforts might be analyzed as transition-phase Information Options). Other information activities that operate at the junction of the real world and the infosphere, such as coordination of energy transmission, could become better understood via the virtual option approach. The proposed option techniques surpass the power of complex simulations. Contingency tables and dynamic programming might be used instead, but the option approach can be more efficient as well as more powerful. The more complex models require solution by numerical integration, which of course can’t be done with a simple hand-held calculator (as can the standard DCF procedures). The powerful computers that are now

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widely available to decision makers, however, make it possible to offer complex project evaluation techniques to practitioners in versatile packages with “smart” interactive interfaces.

NOTES 1. Financial options, from which the models we use are derived, have publicly traded securities as underlying assets, and the rules of exercise are set forth in written contracts. 2. “Information Dominance” includes the ability to protect and utilize one’s own information resources while denying the enemy the ability to rely upon its information resources. 3. Growth options (options to generate new activities that arise from current activities) have also been presented in terms of call options, but the identity of the underlying asset is less clear, and so the values for entry into the model are less clear than in the case of natural resource investments. 4. See Michael Porter (1985) for a description of the generic value chain. 5. This statement of the objective of information operations is from Lt. Gen. Michael Hayden, Director of the United States National Security Agency. 6. The process of adding value in the virtual value chain begins with observation drawn from the physical world. It then proceeds to several stages that take place in the infosphere: data is organized, then selected, synthesized, and distributed. Next, it is presented back into the physical realm, and applied to gain enhanced valueadded in the physical realm. 7. For details on this application, see Siegel et al. (1987). 8. The author learned this in an interview with a Beech executive who wishes to remain anonymous. 9. See Merton (1976) for further discussion of boundary conditions and valuation procedure. 10. For example, f ðXÞ = Maxð0; X2 ; X1 Þ: 11. Chen et al. (1998) discovered during simulation trials of the Boyle/Tse algorithm that the result is very sensitive to any lapses in this regard, rapidly converging toward undefined high values if the systematic linkage is inadequately captured. The intuition behind this problem is fairly clear. Without explicit linkage, as the number of inputs and outputs increases, there is an increasing probability that at least one of the several inputs will drop to a low price, while one of the outputs will rise to a high price. 12. See Amram and Kulatilaka (2000) for a discussion of appropriate tools for evaluating investments in technology development. 13. See Amram and Kulatilaka (2000) for a discussion of appropriate tools for evaluating investments in technology development. 14. Let us assume a discount rate of 10% for this example. 15. This assumption could be relaxed by treating operating costs as a negative “dividend” or by incorporating the additional inputs into a multiple exchange model (to be described later in the chapter).

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16. This assumption of independence can be relaxed to allow for more complex interrelationships among the information items. This simplifying assumption is made, however, for the binomial illustration. 17. This assumption of independence can be relaxed to allow for more complex interrelationships among the items. This simplifying assumption is made, however, for the binomial illustration.

ACKNOWLEDGMENTS We gratefully acknowledge the many helpful comments from Lenos Trigeorgis and Gordon Sick. The author appreciates Phelim Boyle’s updated, electronic algorithm supplied from the working paper version of Boyle/Tse (1990); and the updated, electronic version of the multivariate normal subroutine MULNOR supplied by Mark Schervish.

REFERENCES Amram, M., & Kulatilaka, N. (2000). Strategy and shareholder value creation: The real options frontier. Journal of Applied Corporate Finance, 13(2), 15
28. Black, F., & Scholes, M. (1973). The pricing of options and corporate liablities. Journal of Political Economy, 81(3), 637
654. Boyle, P. P., & Tse, Y. K. (1990). An algorithm for computing values of options on the maximum or minimum of several assets. Journal of Financial and Quantitative Analysis, 25, 215
228. Brennan, M., & Schwarz, E. (1985). Evaluating natural resource investments. The Journal of Business, 58, 135
158. Chen, A., Conover, J., & Kensinger, J. (1998). Valuing flexible manufacturing facilities as options. Quarterly Journal of Economics and Finance, 38, special issue on the role of competition and strategy, published by the Bureau of Economic and Business Research, University of Illinois, and JAI Press, pp. 651
674. Feigenbaum, E., McCorduck, P., & Nii, H. P. (1988). The rise of the expert company. New York, NY: Random House. Howe, K. M., & McCabe, G. M. (1983). On optimal asset abandonment and replacement. Journal of Financial and Quantitative Analysis, 18, 295
305. Johnson, H. (1987). Options on the maximum or the minimum of several assets. Journal of Financial and Quantitative Analysis, 22, 277
283. Kaplan, R. S. (1986). Must CIM be justified by faith alone. Harvard Business Review, 64(2), 87
95. Kensinger, J. (1980). Project abandonment as a put option: Dealing with the capital investment decision and operating risk using option pricing theory. Working Paper No. 80-121, Cox School of Business, Southern Methodist University (presented at the annual meeting of the Financial Management Association, October 1980).

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Kensinger, J. (1987). Adding the value of active management into the capital budgeting equation. Midland Corporate Finance Journal, 5(1), 31
42. Majd, S., & Pindyck, R. S. (1987). Time to build, option value, and investment decisions. Journal of Financial Economics, 18, 7
27. Margrabe, W. (1978). The value of an option to exchange one asset for another. Journal of Finance, 33, 177
198. Margrabe, W. (1982). A theory of the price of a claim contingent on n asset prices. Working Paper No. 8210 (September 1982). School of Government and Business Administration, George Washington University. McDonald, R., & Siegel, D. (1985a). Investment and the valuation of firms when there is an option to shut down. International Economic Review, 26, 331
349. McDonald, R., & Siegel, D. (1985b). The value of waiting to invest. Quarterly Journal of Economics, 101, 707
727. Merton, R. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3, 125
144. Myers, S. C., & Majd, S. (1990). Abandonment value and project life. Advances in Futures and Options Research, 4(1), 1
21. Paddock, J., Siegel, D., & Smith, J. (1988). Option valuation of claims on real assets: The case of offshore petroleum leases. Quarterly Journal of Economics, 103(3), 479
508. Porter, M. E. (1985). Competitive advantage. New York, NY: The Free Press. Rayport, J. F., & Sviokla, J. J. (1995). Exploiting the virtual value chain. Harvard Business Review, 73(6), 75
85. Schervish, M. J. (1985). Algorithm AS195: Multivariate normal probabilities with error bound. Applied Statistics, 34(1), 81
87. Shapiro, A. C. (1985). Corporate strategy and the capital budgeting decision. Midland Corporate Finance Journal, 3(1), 22
36. Siegel, D., Smith, J., & Paddock, J. (1987). Valuing offshore oil properties with option pricing models. Midland Corporate Finance Journal, 5(1), 22
30. Solomon, C., & Fritsch, P. (1996). Mission to mars: How shell hit gusher where no derrick had drilled before
Company makes a huge bet on untested methods to tap deep gulf well. Wall Street Journal, April 4, A1. Stulz, R. (1982). Options on the minimum or the maximum of two risky assets. Journal of Financial Economics, 10, 161
185. Stulz, R., & Johnson, H. (1985). An analysis of secured debt. Journal of Financial Economics, 14, 501
522. Triantis, A., & Hodder, J. (1990). Valuing flexibility as a complex option. Journal of Finance, 55, 549
565. Trigeorgis, L., & Mason, S. (1987). Valuing managerial operating flexibility. Midland Corporate Finance Journal, 5(1), 14
21.

FURTHER READING Amram, M., & Kulatilaka, N. (1999). Real options: Managing strategic investment in an uncertain world. Cambridge: Harvard Business School Press. Avishai, B. (1989). A CEO’s common sense of CIM: An interview with J. Tracy O’Rourke. Harvard Business Review, 67(1), 110
117.

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Bonini, C. (1977). Capital investment under uncertainty with abandonment options. Journal of Financial and Quantitative Analysis, 12, 39
54. Brennan, M., Schwarz, E., & Trigeorgis, L. (Eds.). (2000). Project flexibility, agency, and competition. Oxford: Oxford University Press. Damodaran, A. (2000). The promise of real options. Journal of Applied Corporate Finance, 13(2), 29
44. Dixit, A. K., & Pindyck, R. S. (1995). The options approach to capital investment. Harvard Business Review, 73(3), 105
115. Dyl, E. A., & Long, K. W. (1969). Abandonment value and capital budgeting (comment). Journal of Finance, 24, 88
95. Geske, R. (1977). The valuation of corporate liabilities as compound options. Journal of Financial and Quantitative Analysis, 12, 541
552. Merton, R. (1973). A rational theory of option pricing. Bell Journal of Economics and Management Science, 4, 141
183. Myers, S. C. (1977). The determinants of corporate borrowing. Journal of Financial Economics, 5, 147
175. Myers, S. C. (1984). Finance theory and financial strategy. Interfaces, January
February, 126
137. Myers, S. C., & Majd, S. (1985). Calculating abandonment value using option pricing theory. Sloan School of Management Working Paper No. 1462
83, first draft: May 1983, revised: June 1985. Pickles, E., & Smith, J. (1993). Petroleum property valuation: A binomial lattice implementation of option pricing theory. Energy Journal, 14(2), 1
26. Robichek, A. A., & VanHorne, J. C. (1967). Abandonment value and capital budgeting. Journal of Finance, 22, 577
589. Robichek, A. A., & VanHorne, J. C. (1969). Abandonment value and capital budgeting: Reply. Journal of Finance, 24, 96
97. Triantis, A. (2000). Real options and corporate risk management. Journal of Applied Corporate Finance, 13(2), 64
73. Trigeorgis, L. (1996). Real options
Managerial flexibility and strategy in an uncertain world. Cambridge: MIT Press.

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APPENDIX: ILLUSTRATIONS AND EXAMPLES OF OPTION EVALUATION The Option to Exchange One Asset for Another Here, the investment is formulated as a portfolio of options to exchange a single input for a single output. In this case the option buyer acquires the opportunity, if it is profitable to do so in the short run, to purchase the input, convert it, and sell the output (or do nothing). Moreover, the option holder has a portfolio of such options with different maturities
one for each time period in the activity’s life. More formally, there is an option in each time period to exchange the input item ðINÞ for the output item ðOUTÞ. The prices of these items are not important in and of themselves; the spread ðOUT − INÞ is what matters. When the option matures, the payoff will be the maximum of ðOUT − INÞ or 0. Using Margrabe’s (1978) model, the general form for the expression of the current value of the option would be as follows (where OUT0 and IN0 represent the present spot prices for the items). Value = α OUT0 − γ IN0

ð11Þ

The values for α and γ (which are always less than one) depend upon the time to maturity, the volatility of each price, and the correlation between the price changes of the two items. The values of α and γ are defined below. Note that the model uses the volatility of the changes in the ratio of the prices of the two items, not the volatility associated with either item by itself. If the two have a tendency to move together in close synchronization, the ratio will not be very volatile. α = Nðd1 Þ γ = Nðd2 Þ   pffi ln OUT=IN σ t pffi þ d1 = 2 σ t pffi d2 = d 1 − σ t Nð⋯Þ = normal probability density function t = time until expiration σ 2 = σ 2in þ σ 2out − 2σ in σ out ρin;out = instantaneous variance of the ratio ρin;out = correlation coefficient for the price changes

OUT IN

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ANDREW H. CHEN ET AL.

The net present value of a portfolio of such options, with one of them maturing in each period of the activity’s life (and with an initial cost of C0 ) could be represented as follows: NPV = − C0 þ ðα1 OUT0 − γ 1 IN0 Þ þ ⋯ þ ðαn OUT0 − γ n IN0 Þ

ð12Þ

The subscripts for α and γ represent the option’s maturity date. This reduces to a function of the initial cost and the current spot prices of the commodities, as follows: NPV = − C0 þ OUT0

n X i=1

αi − IN0

n X i=1

γi

ð13Þ

A more general form for the solution to the value of each of the individual options is the following: CXðOUT; IN; tÞ = e − rt ZE½MaxðOUT − IN; 0Þ Z − rt =e f ðOUT; INÞqðOUT; INÞ ∂OUT ∂IN

ð14Þ

where r = the appropriate discount rate; usually the riskless rate E = expectations operator f ðOUT; INÞ = MaxðOUT − IN; 0Þ qðOUT; INÞ = bivariate probability density function This can be solved numerically, for a variety of probability distributions. In the case of an asset with a multiperiod life, the value of the asset could be represented as a portfolio of such options, one of which matures at the end of each period. Contingency Table Example To illustrate, let us look at a simple numerical example. Consider a scenario involving a simple binomial probability distribution. We’ll assume that the output item (OUT) is currently priced at $50, and the input item (IN) is currently priced at $49 (in time period zero). At the end of time period one ðt1 Þ, the price of the output will be determined by the flip of a coin.

87

Extending the Real Options Approach

Heads, the price rises by $1; tails, it falls by $1. A second coin toss with the same rules will decide the price for the input. At the end of time period two ðt2 Þ, another round of coin tossing will take place, with the same rules. Note that in this very simplified illustration, the price movements of the two items are assumed to be independent (that is, there is assumed to be no correlation between the price changes for the two commodities). After this initial illustration there is an example which uses a modification of the Black
Scholes Option Pricing Model, and at that point we will consider a more realistic situation. The possible pairs of input and output prices at the end of the first time period are given on the first line of Table 1. On the second line is the difference ðOUT − INÞ, which represents the profit from blindly converting the input into the output. With active management, however, the conversion would not be made if a loss would result; and the third line shows the profit per unit associated with each outcome when there is active management. Table 1. Binomial Illustration of the Single Exchange Model. Possible Outcomes Input

Output t0

t1

t2

t0

t1

52

51 50

51

49

49

50

50

t2

48

49

47

48

The possible pairs of prices for the output and the input are as follows: First Period Possible pairs OUT
IN max (O
I , 0)

49,48 1 1

49,50 −1 0

51,48 3 3

51,50 1 1

Mean = 1 Mean = 1.25

Second Period Possible pairs 48,47 48,49 48,51 50,47 50,49 50,51 52,47 52,49 52,51 Frequency 1 2 1 2 4 2 1 2 1 OUT
IN 1 −1 −3 3 1 −1 5 3 1 Mean = 1 max (O
I, 0) 1 0 0 3 1 0 5 3 1 Mean = 1.4375

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ANDREW H. CHEN ET AL.

Suppose, for example, we have the opportunity to launch an activity for $2,000, which has a two-period life, zero salvage value, and the capacity to convert 1,000 units of the input into 1,000 units of the output. We will ignore taxes. Then, we would use the average prices for the input and output items to compute the expected net present value. Since the expected price for the output in each time period is $50 per unit, the expected price for the input is $49, and volume is 1,000 units, the expected profit in each period is $1,000 and the expected NPV is the following:14 NPV = − $2; 000 þ

$1; 000 $1; 000 þ = − $264:46 1:1 1:12

ð15Þ

If we recognize the value of the options, however, the expected net present value changes to the following: NPV = $2; 000 þ

$1; 250 $1; 437:50 þ = $324:38 1:1 1:12

ð16Þ

The difference is due entirely to the expected present value of the savings produced by active management. In the first period, there is a 25% probability that the operation would be suspended, avoiding a loss of $1 per unit. In the second period, there is a 25% probability of saving $1 per unit, as well as a 6.25% probability of saving $3 per unit. The present value of these savings sums to the following:       1 $1; 000 1 $1; 000 1 $3; 000 Difference = × × × þ þ = $588:84 4 1:1 4 16 1:12 1:12 ð17Þ Adding this to the figure calculated with the standard approach yields the true NPV (that is, $588:84 − $264:46 = $324:38). Thus, some activities that appear to have a negative NPV when analyzed by traditional DCF methods may actually have positive NPVs. Black
Scholes Example The simple binomial illustration is useful for building an understanding of the exchange option approach, but it downplays a very important aspect of the activity
the tendency for the prices of the input and output to move together. Such a tendency constitutes a significant part of the project’s

Extending the Real Options Approach

89

strategic environment and plays a major role in more sophisticated methods of analysis. To model a more realistic situation in the DCF format would require an intractably large number of possible pairs of prices. Margrabe’s model, however, offers a modification of the Black
Scholes Option Pricing Model, which can be used to measure the value of an option to exchange one item for another, under reasonably realistic assumptions. To illustrate this model, let’s consider an example in which the activity under consideration costs $2,000 and can convert a single input into a single output. We’ll assume the following characteristics of the situation: • The activity has a life span of two time periods. • The activity can convert 1,000 units of input into 1,000 units of the output at the end of each period. • The current input price ðINÞ is $3 per unit, and the current output price ðOUTÞ is $4 per unit. The expected rate of increase in the price of the input is 10%, it is the same for the refined product. Thus, the expected price for the input at the end of one period ðIN 1 Þ is $3.30, while ðIN2 Þ is $3.63. Likewise, ðOUT 1 Þ is $4.40 and ðOUT 2 Þ is $4.84. • Our estimate is 0.4 for the standard deviation of the rate of change in the price of input over one period ðσ in Þ. This can be understood intuitively as follows: the assumption may be thought of as saying that there is about a 2/3 probability that the price will fluctuate within a range of 40% above or below the trend line. • Our estimate is 0.2 for the standard deviation of the rate of change in the price of the output ðσ out Þ. The assumption may be thought of as saying that there is about a 2/3 probability that the price will fluctuate within a range of 20% above or below the trend line. • Our estimate is 0.5 for the correlation coefficient between the rates of change in the two items ðρin;out Þ. This also has an intuitive interpretation: about 25% ðρ2 Þ of the variation in the price of the output can be explained by variations in the price of the input. The rest of the variability associated with the output item’s price arises from other influences. • To keep the example simple, let us also assume that there are no additional operating costs beyond the cost of the input items that are placed into it.15 Given the assumptions, the variance rate to be entered into the option valuation formula would be as follows: σ 2 = 0:22 þ 0:42 − ð2 × 0:2 × 0:4 × 0:5Þ = 0:12

ð18Þ

90

ANDREW H. CHEN ET AL.

For the option that matures in one period, the steps in the valuation are as follows: lnð4=3Þ þ 0:12=2 pffiffiffiffiffiffiffiffiffi = 1:0037 0:12 pffiffiffiffiffiffiffiffiffi d2 = d1 − 0:12 = 0:6573

d1 =

ð19Þ

Option value = ð4 × 0:8422Þ − ð3 × 0:7445Þ = 1:135 The value of an option to convert one bushel of soybeans into one bushel of the refined product at the end of two periods can be calculated as follows: lnð4=3Þ þ ð0:12 × 2Þ=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi = 0:8322 0:12 × 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d2 = d1 − 0:12 × 2 = 0:3423

d1 =

ð20Þ

Option value = ð4 × 0:7973Þ − ð3 × 0:6339Þ = 1:288 Using the exchange option model to calculate the NPV of our activity, which can convert 1,000 units per period, gives the following result NPV = $2; 000 þ $1; 135 þ $1; 288 = $423

ð21Þ

If we simply considered the expected spread ðOUT − INÞ, in contrast, the expected profit would be $1,100 in period 1 and $1,210 in period 2. Then, if we used the DCF approach, we would get conflicting results. With a discount rate, for example, of 10% the DCF calculation would yield inaccurate results as follows: NPV = − 2; 000 þ

$1; 100 $1; 210 þ =0 1:1 1:12

ð22Þ

The Multiple Exchange Model The value of active management may be far greater in this later case than in the previous ones, since the activity being established has multiple possible outputs. Suppose we were considering an activity could convert INPUT1

Extending the Real Options Approach

91

into OUTPUT1 or INPUT2 into OUTPUT2 . Suppose INPUT1 and OUTPUT1 behave in the same way as two items in the coin-toss scenario from the contingency table example given earlier, while INPUT2 and OUTPUT2 are other items whose prices fluctuate independently of INPUT1 and OUTPUT1 .16 Also suppose OUTPUT2 is currently selling at $60 per unit and INPUT2 is selling at $59. At the end of the first period, the new prices will be determined by a coin toss, with the same rules as before. Then, the possible price movements can be represented as given in Table 2. The commonly used way of forecasting the next period’s cash flow from such an activity would be to compare the mean price for each item and conclude that the expected profit is $1 per unit of volume (regardless of which pair of items is chosen). Once the full range of management flexibility is taken into account, however, it can be seen that the expected payoff is $1.8125 per unit. Multiple time periods would be very complex to illustrate, even with a simple binary process. The portfolio procedure presented earlier, however, coupled with a sophisticated model of the value of a multiple-exchange option, could accomplish the necessary calculations for a range of more complex probability distributions; and capture the value of active management for more realistic situations. Establishing the activity is equivalent to purchasing a portfolio of such options with different maturities. Within each time period, it is possible that the company may have a choice among several such options. That is, the company has an option to select the highest valued of n activities. Each individual activity is an option to exchange one set of information items for another, and ownership of the activity conveys the option to pick the highest valued use in each time period. Ownership could then be modeled as a portfolio of such options with one maturing in each period of the activity’s life. The value of active management may be far greater in this later case than in the previous ones, since the activity being established has multiple functions. Suppose we were considering an activity that could convert INPUT1 into OUTPUT1 or INPUT2 into OUTPUT2 . Suppose INPUT1 and OUTPUT1 behave in the same way as the two items in the coin-toss scenario from the contingency table example given earlier, while INPUT2 and OUTPUT2 are other items whose prices fluctuate independently of INPUT1 and OUTPUT1 .17 Also suppose commodity OUTPUT2 is currently selling at $60 per unit and INPUT2 is selling at $59. At the end of the first period, the new prices will be determined by a coin toss, with the same rules as before. Then, the possible price movements can be represented as given in the tables at the top of the next page.

1,0 1

Pairs Payoff

1,1 1

49,48 1

Pairs Payoff

1,3 3

51,48 3

1,1 1

0,1 1

0,0 0

Mean payoff = 1.25

49,50 0

48

60

t0

59

61

t1

Output2

59

t0

0,1 1

3,1 3

Mean payoff = 1.8125

0,3 3

Combinations of Choices

51,50 1

3,0 3

59,58 1

3,3 3

58

60

t1

Input2

Possible pairs of prices for inputs and outputs

49

49

OUTPUT1 and INPUT1

50

51

50

t1

t0

t0 t1

Input1

Output1

Possible Outcomes

61,58 3

3,1 3

1,1 1

1,0 1

Mean payoff = 1.25

59,60 0

OUTPUT2 and INPUT2

Table 2. Binomial Illustration of the Multiple Exchange Model.

1,3 3

1,1 1

61,60 1

92 ANDREW H. CHEN ET AL.

Extending the Real Options Approach

93

The commonly used way of forecasting the next period’s cash flow from such an activity would be to compare the mean price for each item, and conclude that the expected profit is $1 per unit of capacity (regardless of which input
output pair is chosen). Once the full range of management flexibility is taken into account, however, it can be seen that the expected payoff is $1.8125 per unit of capacity. Multiple time periods would be very complex to illustrate, even with a simple binary process. The portfolio procedure presented earlier, however, coupled with a sophisticated model of the value of a multiple-exchange option, could accomplish the necessary calculations for a range of more complex probability distributions; and capture the value of active management for more realistic situations. Establishing the activity is equivalent to purchasing a portfolio of such options with different maturities. Within each time period, it is possible that the company may have a choice among several such options. That is, the option holder has an option to select the highest valued of n activities. Each individual activity is an option to exchange one set of commodities for another, and ownership of the activity conveys the option to pick the highest valued use in each period. Ownership could then be modeled as a portfolio of such options with one maturing in each period of the project’s life.

QUANTITATIVE AND COMPUTER SKILLS EMPLOYERS WANT VS. WHAT THE BUSINESS CURRICULUM CAN PROVIDE Mark Tengesdal and Adelaide Griffin ABSTRACT Employers expect today’s undergraduates to possess a certain level of math and computer skills to do their jobs well. Are we, as business programs, providing them with the information and experiences that they need to meet those expectations? Our motivation for this research study is twofold: (a) to prepare our students to be competitive in the workplace and (b) to make the highest and best use of their time while in the program. Keywords: Math and computer skills; workplace; business programs

INTRODUCTION George Koodray, VP of Communications for the New Jersey Chamber of Commerce, stated that employers all across the country say they cannot

Signs that Markets are Coming Back Research in Finance, Volume 30, 95
111 Copyright r 2014 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1108/S0196-382120140000030008

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MARK TENGESDAL AND ADELAIDE GRIFFIN

find employees with the needed skills to do their jobs. Among their complaints they list that (a) young workers are not able to think and solve complex problems, and (b) young adults lack the working knowledge needed to use common business software (Koodray, 2007). In an article examining the variables of technical change and its resulting increase in educational demands in West Germany, Alexandra Spitz-Oener (2006) found that the trend toward more analytical and interactive activities in a variety of jobs meant that skill requirements were rising faster for highly educated employees than for any other group. This research suggests that there is increasing interest in identifying desired skill categories for today’s graduates and the educational components best designed to provide them with the critical knowledge and experiences needed to prepare them for their changing work environments. Spenner (1990) suggested that the knowledge and skills individuals bring to their jobs don’t always fit what the organization requires. University business programs do not serve their students’ educational needs by teaching only the topics favored by the faculty. There has to be continuing exchange of information between industry and education. As the nature of the competitive workplace changes, so must the skill sets that are taught. Patricia Buhler (2008) described the disconnect between skill sets employers need in applicants and the ones that are possessed by the applicants. This gap becomes even more serious as the marketplace becomes more competitive globally. Skill sets include both applied skills such as math and reading and soft skills such as teamwork and communication. Organizations must possess the human capital that will allow them to adjust quickly and efficiently to sudden shifts in the market. As defined by Forret (2006), human capital is the summation of the individual’s experience, knowledge, and skills. The continuing relevant education of their employees is essential to maintaining the needed responsiveness for organizations. It’s not just the organization’s interest that is being served. Clarke and Patrickson (2008) clarified the difference between employability at the individual and at the organization levels. For the organization, employability is concerned with having the right employee mix containing the needed knowledge and skills to compete effectively. Employability at the individual level has more to do with mobility. Sandberg (2000) suggests that in a rationalist approach, those individuals with greater skill and knowledge will be more productive. As job requirements change, employees must be able to adjust quickly. If a firm is considering downsizing or outsourcing, it’s the employees with outdated skill sets who will be the first to be

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eliminated. This concept of employability extends itself to the idea of the boundaryless career in which the individual can easily shift from one job or organization to another (Arthur & Rousseau, 1996). If the employee seeks a job with another organization, she must possess an attractive mix of knowledge and skills. So everyone has a vested interest in keeping university business programs aligned with the emerging needs of employers.

PURPOSE We began our research with the intent to discover whether our program requirements provided our undergraduate students with the information they needed to be prepared for (a) the Business core curriculum and their majors, (b) career requirements following graduation, and (c) graduate school requirements should they decide to continue their formal education. We reviewed the math and computer course requirements of universities in our marketplace. The list of selected universities ran the gamut from small to large, public to private, campus-based to online, and traditional university to trade/technical school. Here is a list of our sample universities (Table 1). Table 1. Sample Universities. Austin College Baylor University DeVry University East Central University Midwestern State University Oklahoma State University Southeastern Oklahoma State University Southern Methodist University Tarleton State University Texas Christian University Texas A&M University Texas A&M University-Commerce Texas Tech University University of Dallas University of North Texas System University of Oklahoma University of Phoenix Inc. University of Texas at Arlington University of Texas at Dallas

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We found the two most popular math courses required at these universities were Statistics and Calculus. At a much lower occurrence rate, other math courses required at one or more of these universities were Precalculus; Introduction to Math Analysis; Algebra; Math Analysis for Business; Mathematical Functions; Business Math; Financial Management; Calculus and Analytic Geometry; and Matrices, Vectors, and Their Applications. The two most popular computer courses were Management Information Systems and Computer Business Applications. Additional computer courses required at one or more of the universities were Introduction to IT and Processing, Data Analysis, Database Essentials, Microcomputer Applications, Business Computer Concepts, and Operations Management.

SURVEYS Faculty Our research then shifted to inquiries of our colleagues and our customers, both internal and external. Our focus was limited to the areas of quantitative and computer skills. Softer skills such as leadership and teamwork were not studied. As the research literature shows, these skills have received increasing attention and importance in recent years. So we want to be confident that the time and effort commitment of our students in their math and computer course requirements is justified. In our first survey, the faculty was polled on what math and computer topics were necessary to prepare the students for their Business core curriculum and their major curriculum. Our findings resulted in the following recommendations. The introductory computer courses did not provide the computer literacy necessary to make Business students competitive in the business world. The applications course (Bus. 2437) focuses primarily on Microsoft applications and prepares students to work with large worksheets, many formulas, and references. It is recommended that this course be the only course option to satisfy our computer proficiency requirement. Students can also test out of the computer proficiency requirement using the CLEP test. All TWU students must take an introductory level math course (Math 1013) based on university requirements. The recommendation is to encourage them to take this during their freshman year. Our Business Analysis

Quantitative and Computer Skills

99

class (Math 2203) remains a requirement. It does not cover calculus, and the faculty survey results indicated that is acceptable. One recommendation is to rename the course so that it describes more clearly the contents of the course. Currently we require two Statistics courses. The faculty considers this beneficial for the students despite some reported overlap in content. Finally, in reviewing the Quantitative Management course (Bus. 4543), it is recommended that two levels of Quant be offered. A regular course could be offered. Then a second, Honors, section could be added and enhanced by bringing in more statistics, Excel, covering more material, and using derivatives.

Students and Supervisors In our second survey, we queried our final-semester eMBA students and their supervisors to discover whether they perceive that they possess the skill sets necessary for the quantitative and computer demands of their jobs. In two sections of the Capstone class, we have a combined total of 80 students. Three questionnaires were developed using the PsychData software. One covered Math concepts, a second covered Computer Skills, and the third focused on Quantitative Management skills. The students were divided into 3 different groups and designated to receive one of the questionnaires. In the invitation to participate in the survey, we encouraged them to give us their feedback and to send us the email address of their supervisor so that we could include them in the survey. Our interest was to see if the two views of the need for and possession of a set of skills were similar or noticeably different. We asked employers what skills they expect employees to possess, and we asked the eMBA students what skills they need to do their jobs. The focus was on the current job they hold and the current time period. A second set of questions for each group focused on the future, in terms of the employees’ promotability. We were interested in determining whether our educational curriculum was providing them the skills and knowledge needed to succeed in the future. Our graduate students were chosen as subjects because their job experiences reflect the likely future opportunities of our undergraduates. The majority of our student population lives and works within a 50-mile radius of our campus. So the experiences and perceptions of our graduate students today may well be predictive of the future experiences and perceptions of our undergraduates.

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MARK TENGESDAL AND ADELAIDE GRIFFIN

RESULTS Figs. 1
3 show the mean answers by the students and the supervisors for skill items in Statistics, Quantitative Management Analysis, and Computer, respectively. We ran some tests on the student means, but not on the supervisor means, because the supervisor samples were very small. We found that statistically all student means for being hired and for promotion were significantly different from 1, where 1 = Not Needed. Numerically, however, many of the means were not significant. In fact, for Statistics in Fig. 1, the students on average only considered Surveys and Questionnaire Design slightly above a 3 on the Likert scale. It might appear that the supervisors felt Basic Data Description was somewhat critical for both being hired and promoted, but only two supervisors responded (N = 2); so we cannot tell. In Fig. 2, students seemed to believe that Project Management was important for being both hired and promoted, as well as perhaps Quality Control and Total Quality Management, Decision Analysis, Forecasting, and Goal Programming. The supervisor means (N = 5) tended to follow the student means. Of interest were items that did not seem to be as valuable to students in Statistics such as Hypothesis Testing, as well as Confidence Intervals, Regression, and ANOVA, which are tools useful in hypothesis testing. Less critical items in Quantitative Management Analysis included Linear Programming, Queuing Theory, and Markov Analysis. These two results may be consistent with our proposal/decision to offer two levels of Quantitative Management to our students; students could either take a basic introductory level course or an advanced level course depending on their major and/or career path. In general, the students seemed to feel that computer skills were somewhat more critical than the skills in the other two areas, especially for promotion. For most current students, Statistics and Quantitative Management Analysis are not very popular courses. If they learn or believe Computer courses are important for being hired, then we might consider ways to combine Statistics and Quantitative Management topics with computer courses or coursework in order to motivate them to learn a multilayer of skills at the same time. We used repeated measures ANOVA (MANOVA) on the student survey responses to test for statistically significant differences between means. We did not run the tests on the supervisor responses because the sample sizes were too small. We first measured whether the means for being hired as

101

Quantitative and Computer Skills 1.00

2.00

3.00

4.00

5.00

Surveys and questionnaire design Basic data description (mean, median, standard deviation) Measures of position (z scores and percentiles) Frequency distribution and graphs (histograms, frequency, and cumulative distributions, times series) Probability and counting rules (factorials, permutations and combinations) Testing the difference between two means (large sample, small sample - independent and dependent) Correlation Sampling and simulation (Random, Systematic, Stratified, Cluster) Normal distribution (its properties, Standard Normal, Central Limit Theorem) Basic probability Chi-Square testing Nonparametric statistics (Sign Test, Wilcoxon Rank Sum Test) Confidence intervals (standard deviations from the mean) Hypothesis testing (z test, P-value, t test, chi-squared) Other data description (weighted mean, skewness, Chebyshev's Theorem) Simulation techniques, Monte Carlo Method Regression (coefficient of determination, standard error, R-squared) One-way Analysis of Variance (ANOVA)

Student Hire Student Promo

Other Analysis of Variance (Sheffe Test, Tukey Test, Two-Way)

Supervisor Hire

Discrete probability distributions (binomial, multinomial, Poisson)

Supervisor Promo Critical (Mean)

Fig. 1.

Statistics.

a group were different from the means for promotion as a group. The results are shown at the bottom of each table, Tables 2
4, and called “view.” The Statistics grouped means and the Quantitative Management grouped means for being hired and for being promoted were not different. Their respective p values were 0.728 and 0.169. The Computer hire means

102

MARK TENGESDAL AND ADELAIDE GRIFFIN 1.00

2.00

3.00

4.00

5.00

Project Management (Program Evaluation and Review Technique, PERT, Critical Path Method, subprojects, milestones, resource leveling)

Quality Control and Total Quality Management (process variability)

Decision Analysis (Decision Trees)

Forecasting (time series models, moving averages, trends, seasonal variation adjustments) Goal Programming (equally important multiple goals, ranking goals with priority levels, weighted goals) Transportation and Assignment Models (Northwest Corner Rule, Stepping Stone Method, Least-Cost Solution, Modified Distribution or MODI method, Vogel's Approximation Method) Inventory Control Models (Economic Order Quantity or EOQ, Reorder point, Quantity Discount Models, Safety Stocks, Just in Time Inventory Control, Resource Planning) Probability concepts (mutually exclusive events, statistically independent vs. dependent events, Bayes' Theorem, random variables, probability distributions, Binomial Distribution, Normal Distribution, Exponential Distribution, Poisson Distribution Regression Models (Regress X on Y, ANOVA)

Network Models (Minimal-Spanning Tree Technique, Maximal-Flow Technique, Shortest-Route Technique) Markov Analysis (states, state probabilities, transition probabilities, equilibrium)

Nonlinear Programming

Linear Programming models (minimization or maximization solutions) Waiting Lines and Queuing Theory (Fixed Time Increment and Next Event Increment Simulation Models, Simulation Mode for Maintenance, Operational Gaming, and Systems Simulation)

Student Hire Student Promo

Linear Programming: The Simplex Method (minimums and maximums, Dual Formation Procedures, Karmarkar's Algorithm)

Supervisor Hire Integer Programming (Branch and Bound Method, Mix Integer Programming, 0-1 Binary Variables Modeling)

Supervisor Promo Critical (Mean)

Fig. 2.

Quantitative Management.

and promotion means, however, were different from each other. The p value was 0.005. This suggests that the students on average believe that in general computer skills are more important for being promoted than for being hired in the first place. Thus, our more ambitious students probably will benefit from a solid foundation in these computer skills, and we

103

Quantitative and Computer Skills 1.00

2.00

3.00

4.00

5.00

Calendars, appointments, tasks in MS-Outlook Word (tables, charts, headers, footers, and watermarks) Share data among software applications of Access, Excel, and Word Worksheets (with embedded charts) Import text, files, and tables into a PowerPoint presentation Worksheets/Workbooks (with formulas, functions, formatting, Web queries) Form letters (merging to email addresses using groupware contact lists) What-if analysis (with charting and large spreadsheets) Create, sort, and query worksheet database Create templates and work with multiple worksheets and workbooks Create a graphic slide show presentation on the Web Deliver a presentation using these skills Add Excel charts, Word tables, hyperlinks, and embedded fonts Use clip art in a slide show Use diagrams and custom animation, sound effects, and transition in slides Link Excel worksheet to Word document and use Web discussion server Create database using a select query window Use a design template and text slide layout to create graphic presentation Newsletter (with desktop publishing techniques) Maintain a database using design and update features Create database using design and datasheet views Group merge in slide shows and reviewing/rejecting comments Create Database reports, forms, and combo boxes Integrate software projects (Word, Excel, Access) into website

Student Hire

Create an application system using macros, wizards, and switchboard manager Dynamic Web pages using Excel

Student Promo

Financial functions (data tables, amortization schedules, and hyperlinks in worksheets)

Supervisor Hire

Publish Data Access pages to the Web

Supervisor Promo Enhance forms with OLE fields, hyperlinks and subforms

Critical (Mean)

Fig. 3.

Computers.

probably should make sure that the computer courses they take do include all the items with sufficiently high means for promotion. Next we measured whether there were any differences between item means. The results are shown at the bottom of each table, Tables 2
4,

1.65 1.29 1.69 1.33 1.93 1.93 1.38 1.72 1.54 1.41 1.53 1.57 1.51 1.41

2.39 2.39 2.39 2.33 2.22 2.22 2.17 2.17 2.17 2.11 2.00 2.00 1.94 1.89

2.56 2.50 2.17 2.61 2.06 2.00 2.44 2.44 2.17 2.44 2.17 1.94 2.17 2.06

3.00 2.78 2.44 2.67 2.33 2.50

Mean

1.72 1.38 1.62 1.50 1.75 1.75 1.72 1.82 1.25 1.69 1.50 1.55 1.69 1.51

1.68 1.66 1.50 1.61 1.46 1.89

SD

Promotion

3.00 4.00 3.00 2.00 2.50 3.00 2.50 3.50 2.50 3.00 1.00 1.00 3.50 3.00 2.50 1.50 2.50 2.50 2.50 2.50

−0.11 −0.07 0.14 −0.18 0.11 0.14 −0.18 −0.18 0.00 −0.22 −0.11 0.04 −0.14 −0.11

Mean

0.04 0.07 0.14 −0.04 0.18 −0.06

dc SD

2.12 0.71 2.12 2.83 0.00 0.00 0.71 2.83 2.12 0.71 2.12 2.12 2.12 2.12

2.83 1.41 2.83 0.00 2.12 2.83

Hire

3.00 3.50 3.00 3.00 2.50 1.00 3.50 3.00 3.00 3.00 2.50 2.50 2.50 3.00

3.00 4.00 3.00 3.00 3.00 3.00

Mean

2.83 2.12 2.83 2.83 2.12 0.00 2.12 2.83 2.83 1.41 2.12 2.12 2.12 2.83

2.83 1.41 2.83 1.41 2.83 2.83

SD

Promotion

Supervisors (n = 2)

b

a

Scale 1 = Not needed to 5 = Critical. Means are from a MANOVA Item × View (hire vs. promotion); view, F = 0.125; p = 0.728, item, F = 1.60, p = 0.174, item × view F = 905, p = 0.514, pooled SD = 1.60; column LSDs at p < 0.05 are 0.25 for students. c Cohen’s d, and effect size that is the standardized mean difference.

1.73 1.57 1.81 1.50 1.75 1.66

3.06 2.89 2.67 2.61 2.61 2.41

Survey and questionnaire design Basic data description (mean, median, standard deviation) Measures of position (z scores and percentiles) Frequency distribution and graphs (hstgrm, frqncy cmltv, time sries) Probablility and counting rules (fctorials, permutation, combinations) Testing the difference between two means (lrg/smll smpl
indpndt/ dpndt) Sampling and simulation (Random, Systematic, Stratified, Cluster) Correlation Normal distribution (properties, Std Normal, Central Limit Theorem) Basic probability Nonparametric statistics (Sign Test, Wilcoxon Rank Sum Test) Chi-square testing Confidence intervals (standard deviations from the mean) Hypothesis testing (z test, p value, t test, chi-squared) Other data description (weighted mean, skewness, Chebyshev’s Thrm) Simulation techniques, Monte Carlo Method Regression (coefficient of determination, Standard error, R-squared) One-way Analysis of Variance (ANOVA) Other Analysis of Variance (Sheffe Test, Tukey Test, Two-Way) Discrete probability distributions (binomial, multinomial, Poisson)

SD

Mean

Hire

Studentsb (n = 18)

Statistics.

Itemsa

Table 2. 104 MARK TENGESDAL AND ADELAIDE GRIFFIN

1.25

1.23 1.37 1.39 1.46 1.74

1.68

1.97

1.71 1.61 1.82

3.89 3.74 3.58 3.58 3.16

3.05

3.00

2.63 2.63 2.56

SD

4.00

Mean

Hire

2.44

2.95 2.63

3.05

3.42

3.32

3.58

4.05 3.68 3.79

4.26

Mean

2.80

2.40 2.40

1.90 −0.03

1.81 −0.19 1.80 0.00

2.00

3.00

1.50 −0.23

0.07

1.80

1.70 −0.10

1.69

3.80

0.00

1.39

3.20 3.60 3.60

1.51 −0.10 1.34 0.03 1.18 −0.13

Mean

1.00

0.89 0.89

1.48

1.41

0.84

1.30

1.48 0.89 0.55

1.14

SD

2.20

2.50 2.20

2.80

3.20

2.20

3.80

3.40 3.80 3.40

3.60

Mean

1.30

1.29 0.84

1.30

1.48

1.10

0.84

1.52 0.84 0.55

1.14

SD

Promotion

Supervisors (n = 5) Hire

3.60

d

c

1.15 −0.16

SD

Promotion

Studentsb (n = 19)

Quantitative Management.

Project Management (Program Evaluation and Review Technique, PERT, Critical Path Method, subprojects, milestones, resource leveling) Quality Control and Total Quality Management (process variability) Decision Analysis (Decision Trees) Forecasting (time series models, moving averages, trends, seasonal variation adjustments) Goal Programming (equally important multiple goals, ranking goals with priority levels, weighted goals) Transportation and Assignment Models (Northwest Corner Rule, Stepping Stone Method, Least-Cost Solution, Modified Distribution or MODI method, Vogel’s Approximation Method) Inventory Control Models (Economic Order Quantity or EOQ, Reorder point, Quantity Discount Models, Safety Stocks, Just in Time Inventory Control, Resource Planning) Probability concepts (mutually exclusive events, statistically independent vs. dependent events, Bayes’ Theorem, random variables, probability distributions, Binomial Distribution, Normal Distribution, Exponential Distribution, Poisson Distribution) Regression Models (Regress X on Y, ANOVA) Network Models (Minimal-Spanning Tree Technique, Maximal-Flow Technique, Shortest-Route Technique) Markov Analysis (states, state probabilities, transition probabilities, equilibrium)

Items

a

Table 3. Quantitative and Computer Skills 105

1.74 1.50 1.68

1.71 1.59

2.42 2.11

SD

2.53 2.47 2.42

Mean

Hire

2.74

2.63

2.63 2.79 2.68

Mean

2.00 1.40

1.77 −0.13 1.97 −0.39*

Mean

0.55

0.71

1.22 0.89 1.30

SD

1.80

2.00

1.80 2.60 2.20

Mean

0.84

0.71

0.84 1.34 0.84

SD

Promotion

Supervisors (n = 5) Hire

2.00 2.40 2.20

d

c

1.92 −0.06 1.84 −0.19 1.80 −0.16

SD

Promotion

Studentsb (n = 19)

b

a

Scale 1 = Not needed to 5 = Critical. Means are from a MANOVA Item × View (hire vs. promotion); view, F = 2.09; p = 0.169, item, F = 7.59, p = 0.0001, item × view F = 0.633, p = 0.781, pooled SD = 1.62; column LSDs at p < 0.05 are 0.31 for students. c Cohen’s d, an effect size that is the standardized mean difference. p < 0.05 (*)

Nonlinear Programming Linear Programming models (minimization or maximization solutions) Waiting Lines and Queuing Theory (Fixed Time Increment and Next Event Increment Simulation Models, Simulation Mode for Maintenance, Operational Gaming, and Systems Simulation) Linear Programming: The Simplex Method (minimums and maximums, Dual Formation Procedures, Karmarkar’s Algorithm) Integer Programming (Branch and Bound Method, Mix Integer Programming, 0-1 Binary Variables Modeling)

Items

a

Table 3. (Continued ) 106 MARK TENGESDAL AND ADELAIDE GRIFFIN

1.50 1.41 1.41 1.54 1.69 1.60 1.50 1.54 1.57 1.70 1.85 1.61 1.73 1.67 1.72 1.69 1.69 1.62

4.15 3.90 3.90 3.80 3.70 3.65 3.60 3.55 3.55 3.55 3.55 3.55 3.50 3.40 3.30 3.00 3.00 3.00

Calendars, appointments, tasks in MS Outlook Word (tables, charts, headers, footers, and watermarks) Share data among software applications of Access, Excel, and Word Worksheets (with embedded charts) Import text, files, and tables into a PowerPoint presentation Worksheets/Workbooks (with formulas, functions, formatting, Web queries) Form letters (merging to email addresses using groupware contact lists) What-if analysis (with charting and large spreadsheets) Create, sort, and query worksheet database Create templates and work with multiple worksheets and workbooks Create a graphic slide show presentation on the Web Deliver a presentation using these skills Add Excel charts, Word tables, hyperlinks, and embedded fonts Use clip art in a slide show Use diagrams and custom animation, sound effects, and transition in slides Link Excel worksheet to Word document and use Web discussion server Create database using a select query window Use a design template and text slide layout to create graphic presentation

SD

Mean

Hire

3.00 3.60

3.45

1.69 1.60

1.67

1.53 1.43 1.15 1.54 1.54

1.23

3.85 3.70 3.95 3.95 3.45 3.50

1.52

1.46

1.45 1.39 1.51

1.34 1.36 1.23

SD

3.75

3.65

3.70 4.05 3.80

4.30 3.45 3.85

Mean

Promotion

Studentsb (n =20)

Computer.

Itemsa

Table 4.

2.57 3.00 3.57 2.57 3.86 3.29 3.43 2.71 2.71

−0.13 −0.19 −0.10 −0.26 −0.29 −0.03 −0.13 −0.29

2.71 3.86

3.57

−0.03

0.00 −0.39

3.29 4.00 3.00

5.00 3.86 3.57

−0.10 0.29 0.03 0.06 −0.23 −0.10

Mean

dc SD

1.11 1.07

1.25

1.27 1.35 1.38 0.98 0.95

0.53 0.82 1.27

1.40

0.95 1.15 0.82

0.38 1.07 1.62

Hire

3.00 3.67

3.29

3.29 4.00 3.71 3.71 3.29

3.43

3.14

3.00

3.57 4.00 3.43

4.86 3.86 3.57

Mean

1.63 1.21

1.60

1.38 1.29 1.11 1.11 1.38

1.27

1.21

1.15

0.79 1.00 1.13

0.90 0.90 0.98

SD

Promotion

Supervisors (n =7)

Quantitative and Computer Skills 107

1.57 1.39 1.69 1.71

2.45 2.45 2.30 2.25

2.95 2.40

3.15 3.20

3.05 3.15 3.00 3.05 3.00 3.45 2.65

Mean

1.67 1.79

1.76 1.47

1.50 1.66 1.69 1.43 1.67 1.79 1.69

SD

Promotion Mean 3.57 2.86 2.57 3.14 3.00 2.86 2.86 2.57 2.67 3.00 2.14

dc −0.10 −0.26 −0.19 −0.24 −0.23 −0.60* −0.10 −0.45* −0.48* −0.42* −0.10

SD

1.91 1.77

1.13 0.52

1.72 1.07 1.13 1.21 1.10 1.35 1.68

Hire

2.43 2.57

2.57 3.00

3.29 2.57 3.00 3.14 3.29 3.00 2.71

Mean

1.40 1.72

1.72 1.15

1.11 1.40 1.63 1.35 0.95 1.15 1.38

SD

Promotion

Supervisors (n =7)

b

a

Scale 1 = Not needed to 5 = Critical. Means are from a MANOVA Item × View (hire vs. promotion); view, F = 10.79; p = 0.005, item, F = 7.61, p = 0.0001, item × view F = 1.68, p = 0.043, pooled SD = 1.55; column LSDs at p < 0.05 are 0.33 for students. c Cohen’s d, an effect size that is the standardized mean difference. p < 0.05 (*)

1.55 1.77 1.69 1.67 1.66 1.74 1.67

2.90 2.75 2.70 2.68 2.65 2.53 2.50

Newsletter (with desktop publishing techniques) Maintain a database using design and update features Create database using design and datasheet views Group merge in slide shows and reviewing/rejecting comments Create Database reports, forms, and combo boxes Integrate software projects (Word, Excel, Access) into website Create an application system using macros, wizards, and switchboard manager Dynamic Web pages using Excel Financial functions (data tables, amortization schedules, and hyperlinks in worksheets) Publish Data Access pages to the Web Enhance forms with OLE fields, hyperlinks and subforms

SD

Mean

Itemsa

Hire

Studentsb (n =20)

Table 4. (Continued ) 108 MARK TENGESDAL AND ADELAIDE GRIFFIN

Quantitative and Computer Skills

109

and called “item.” An item mean is defined as the average of the hiring mean and the promotion mean for each item. There was no difference between Statistics item means, but the p values for Quantitative Management and for Computers were both 0.0001. This means that the students as a group believed at least Quantitative Management skills in Project Management were more critical than the skill Integer Programming. Computer skills in Calendars, Appointments, and Tasks in MS Outlook were more critical than Computer skills in Enhancing Forms with OLE Fields, Hyperlinks and Subforms. There may be more differences between item means, but the test did not tell how many. When designing Quantitative Management and Computer courses, the significance of these results suggest to some degree that we can use the item means for the various skill items as a guide to decide on what to include and what we may exclude from a course because of its less critical nature and the limited time available to our students. We also tested whether any item for promotion was more critical than any item for being hired, and at the same time whether any item for being hired was more critical than any item for being promoted. The results are shown at the bottom of each table, Tables 2
4, and called “item × view.” We find significant differences in Computer skills (p value is 0.043). First look at results from measuring Cohen’s d, the standardized mean difference between a skill item’s importance for being hired and its importance for being promoted. Cohen’s d is negative and significant at 5 percent for Integrating Software Projects into a Website (d = −0.60), Dynamic WebPages using Excel (d = −0.45), Financial Functions (d = −0.48), and Publishing Access Pages to the Web (d = −0.42). The negative values mean that students on average believed these particular skills were more important for promotion than for being hired. We can compare these four skills to the Computer skill with the highest positive Cohen d, which is using Word (d = 0.29), even though its difference is not significant. Its positive value indicates that students on average probably believed using Word was more critical for being hired than for being promoted. For the aforementioned test, at least the skill of Integrating Software Projects into Websites, if not all four skills, was more critical for promotion while at least one skill item, which must be an aptitude for using Word, was more critical for being hired. Presumably, before one can be promoted, he/she must first be hired. Thus any skill that would be required for being hired would also be required for being promoted. For our ambitious students, however, we

110

MARK TENGESDAL AND ADELAIDE GRIFFIN

must make sure that we design courses for them that include important skills critical for being promoted that the less ambitious students (in terms of advancing in careers that require such quantitative skills) would not need. These probably include the four computer skills mentioned in the previous paragraph and possibly Integer Programming in Quantitative Management Analysis. For example, if we create two levels of the Quantitative Management Analysis course, the higher level probably should include Integer Programming while the lower level would not.

CAVEAT In interpreting these results we need to be aware of the following caveats. First, do the respondents know what each item is? The authors considered providing greater definitions and examples of each item, but weighed that against the increased response rate associated with a simpler and less time-consuming survey. We hope that we were close to the optimal balance between the two, without too much loss of comprehension of the terms and without too large a drop in the response rate. Second, it is difficult to translate what the numbers on the scale mean to each respondent and then how to interpret the mean. Third, are the students aware of how much they use each skill? Perhaps they don’t directly use a skill at their job, but would they be as effective in their job without having learned the skill, either in how they communicate ideas and concepts with their co-workers and superiors, or in the way they comprehend their projects, tasks, and job environment (i.e., would they not be as effective a worker without having once learned the skill?). Fourth, our sample sizes were not as large as we would like. Even though the response rate was very high for students, higher numbers would have allowed us to make more definite conclusions. Of course higher samples from supervisors would have been preferred. Finally, in using our results, we must be aware of something similar to a selection bias. The respondents answered according to the jobs they currently hold. If they indicated that a particular skill was not needed at their job, would they still be better off (and perhaps in a different higher paying job or position) if they had had the skill? If this is true, then we may still want to include the quantitative courses in the curriculum.

Quantitative and Computer Skills

111

REFERENCES Arthur, M. B., & Rousseau, D. (Eds.). (1996). The boundaryless career. New York, NY: Oxford University Press. Buhler, P. (2008). Managing in the new millennium; The skills gap: How organizations can respond effectively. Supervision, 69, 19
23. Clarke, K., & Patrickson, M. (2008). The new covenant of employability. Employee Relations, 30, 121
141. Forret, M. L. (2006). The impact of social networks on the advancement of women and racial/ethnic minority groups. In M. Karsten (Ed.), Gender, ethnicity, and race in the workplace (pp. 149
166). Westport, CT: Praeger. Koodray, G. (2007). Mission critical: Training students in math and science. NJBIZ, 20, 22
23. Sandberg, J. (2000). Understanding human competence at work: An interpretative approach. Academy of Management, 43, 9
25. Spenner, K. I. (1990). Skill: Meaning, methods, and measures. Work and Occupations, 17, 399
421. Spitz-Oener, A. (2006). Technical change, job tasks, and rising educational demands: Looking outside the wage structure. Journal of Labor Economics, 24, 237
270.

THE UNEASY CASE FOR REAL ESTATE INVESTMENTS C. Sherman Cheung and Peter Miu ABSTRACT Real estate investment has been generally accepted as a value-adding proposition for a portfolio investor. Such an impression is not only shared by investment professionals and financial advisors but also appears to be supported by an overwhelming amount of research in the academic literature. The benefits of adding real estate as an asset class to a well-diversified portfolio are usually attributed to the respectable risk-return profile of real estate investment together with the relatively low correlation between its returns and the returns of other financial assets. By using the regime-switching technique on an extensive historical dataset, we attempt to look for the statistical evidence for such a claim. Unfortunately, the empirical support for the claim is neither strong nor universal. We find that any statistically significant improvement in risk-adjusted return is very much limited to the bullish environment of the real estate market. In general, the diversification benefit is not found to be statistically significant unless investors are relatively risk averse. We also document a regime-switching behavior of real estate returns similar to those found in other financial assets. There are two distinct states of the real estate market. The low-return (high-return)

Signs that Markets are Coming Back Research in Finance, Volume 30, 113
148 Copyright r 2014 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1108/S0196-382120140000030009

113

114

C. SHERMAN CHEUNG AND PETER MIU

state is characterized by its high (low) volatility and its high (low) correlations with the stock market returns. We find this kind of dynamic risk characteristics to play a crucial role in dictating the diversification benefit from real estate investment. Keywords: Real estate; portfolio diversification; regime switching JEL classifications: G10; G11

INTRODUCTION The lackluster performance of the stock markets in the past two decades has led fund managers to turn to alternatives to stocks, such as hedge funds, private equity, and real estate, to enhance the performance of pension funds. Real estate has long been accepted as a legitimate alternative to stocks with good diversification benefits. Eichholtz and Hartzell (1996) find negative correlations between stock returns and real estate returns based on the appraised value for the United States, United Kingdom, and Canada. Quan and Titman (1999) find the time-series correlations between stock returns and real estate returns not to be statistically significant for 16 of the 17 countries examined in their study. Brounen and Eichholtz (2003), for example, show that real estate improves the risk-return tradeoff of investors in the United States and the United Kingdom under the mean-variance framework. Kallberg, Liu, and Greig (1996) likewise show that real estate belongs to a portfolio of an investor with bonds and stocks. MacKinnon and Zaman (2009), and Fugazza, Guidolin, and Nicodano (2007) further show that US and European real estates, respectively, provide diversification benefits when the US-focused or European-focused investors have long investment horizons and real estate returns are predictable. Brounen, Prado, and Verbeek (2010) demonstrate the use of real estate investments in the hedging of pension funds with explicit liability feature. Similarly, Chun, Sa-Aadu, and Shilling (2004) demonstrate the attractive properties of real estate investment in an institutional investor’s portfolio. There seems to be no doubt whatsoever about the diversification benefits of real estate. The concern raised in several studies is the optimal weight of real estate in a mixed-asset portfolio.1 Besides domestic real estate investment, there is also a substantial literature on the benefit of international real estate investment. One would

The Uneasy Case for Real Estate Investments

115

expect international real estate assets to have lower correlations of returns and higher diversification benefits due to the local nature of the real estate markets. A real estate boom in China, for example, does not always imply a similar boom in the United States. Further, investing in international real estate is less common than investing in international stocks and thus real estate markets may not be as well integrated globally as stock markets. This means more diversification benefits from investing in international real estate. Eichholtz (1996a), for example, find correlations between international real estate returns to be significantly lower than correlations between international common stock or international bond returns. Hoesli et al. (2004) provide evidence of the diversification benefits of both domestic and international real estate in mixed-asset portfolios from the perspective of investors in seven countries on three continents. Liu and Mei (1998) find that it is the unpredictable component of real estate returns that accounts for the diversification benefits of real estate investments. Ziobrowski and Curcio (1991) surprisingly find no diversification benefits to UK and Japanese investors when adding US real estate to a well-diversified portfolio of their own respective domestic financial assets. According to them, it is the volatility of the US currency value that makes US real estate unattractive to either Japanese or UK investors. Further, Japanese or UK investors holding also financial assets in addition to US real estate will encounter higher correlations among US assets induced by the fluctuations in the common US currency value embedded in all US assets. This can limit the distinctiveness of US real estate to Japanese or UK investors.2 Ziobrowski and Ziobrowski (1993) and Ziobrowski, Ziobrowski, and Rosenberg (1997) do not find the use of currency options or swaps to be an effective solution to the currency problem. Existing finance literature, especially that on domestic real estate investment that is uncontaminated by currency risk, seems to suggest that real estate improves the risk-adjusted return of investors due to its low correlations with other asset classes and its respectable returns. There are, however, several unresolved issues in the literature that preclude a quick and easy conclusion. First, almost all of the authors fail to perform any statistical test on the increase in risk-adjusted returns when real estate is added to an existing portfolio.3 It is well known that when an extra asset class is added to the portfolio, the in-sample performance analysis of the optimal portfolio ought to result in a risk-adjusted return no lower than that before the asset class is added. The issue is whether such improvement is too large to be explained by chance and this can only be settled by statistical tests.

116

C. SHERMAN CHEUNG AND PETER MIU

Instead of looking for the optimal weight, the present study addresses the more basic question of whether or not real estate offers any statistically significant diversification benefits at all. Second, recent studies indicate that correlations among international equity returns are higher during bear markets than during bull markets.4 This type of regime-switching correlation behavior will mean lower diversification benefits from international investments when investors face a bearish environment at home. The diversification conjecture based on static correlation assessments may therefore be erroneous. Do real estate investments display the same type of regimeswitching behavior?5 To what extent does real estate offer real diversification benefits and how robust are these benefits over time and across regimes? To preview the findings of our study, the major conclusion is that real estate appears to be a redundant asset class. We examine different proxies of real estate investments including the securitized US real estate investment trusts (REITs) and international real estate stocks as well as nonsecuritized US direct real estate investments. Both REITs and international property stocks do not offer any statistically significant diversification benefits to an existing portfolio of US equities, US bonds, and international equities. Since the returns on the direct investment in real estate is based on the appraised value that tends to be “smoothed,” we make the necessary adjustment to obtain the “unsmoothed” value before it is used to form our investment portfolios. With proper correction made to the appraised value, the benefit for a portfolio investor from directly investing in real estate also appears to be questionable. Our findings, therefore, leave an interesting puzzle as to why investors would hold real estate investments when the empirical support is not there. We also detect that the regime-switching behavior of REITs is similar to that of other financial assets documented in the literature. Specifically, correlations of real estate with stocks are higher in a bearish REIT market and therefore stocks offer no escape to real estate investors when confronted with a bearish real estate market. Correlations of real estate with stocks fall in a bullish real estate market when diversification is least needed. Interestingly, our regime-switching analysis enables us to show that REITs offer statistically significant diversification benefits to a well-diversified investor only in a bullish real estate market. This appears to suggest that real estate is attractive if an investor can successfully time the real estate market. Those investors who perceive real estate to be a stable asset in a volatile world will be sadly disappointed by the evidence in this study.

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117

OPTIMAL PORTFOLIO OF OUR REPRESENTATIVE US INVESTOR In this study, we consider a representative US investor holding US equities, non-North American equities, and US government bonds. For this representative investor, we examine the effects on the risk-return tradeoff of adding real estate to the existing portfolio. Specifically, we first estimate the maximum Sharpe ratio of the portfolio with the three existing assets as our baseline. We then re-estimate the maximum Sharpe ratio when real estate is added to the representative investor’s baseline portfolio. Any statistically significant improvement in the Sharpe ratio will prove that real estate indeed adds diversification benefits to the investor’s portfolio. To obtain the maximum Sharpe ratio with short sales allowed, we first derive the vector of weights for the tangency portfolio as:6 w=

Σ − 1 ðz − Rf ⋅1Þ B − A⋅Rf

ð1Þ

where z is the vector of mean returns Σ is the variance
covariance matrix of returns 1 is the unit vector Rf is the constant risk-free rate A = 10 ⋅Σ − 1 ⋅1 B = 10 ⋅Σ − 1 ⋅z. The Sharpe ratio of the tangency portfolio is then equal to: Θp =

z p − Rf z0 :w − Rf = σp ðw0 ⋅Σ⋅wÞ0:5

ð2Þ

where zp and σ p are, respectively, the mean and standard deviation of the return of the tangency portfolio. Let us define T as the number of monthly observations. Also, let Θ1 be the Sharpe ratio of the tangency portfolio before the addition of real estate and Θ2 be the Sharpe ratio after the addition. The null hypothesis to be tested is H0: Θ1 = Θ2. When short sales are allowed, the test statistic

118

C. SHERMAN CHEUNG AND PETER MIU

presented in Gibbons, Ross, and Shanken (1989) and Jobson and Korkie (1989) is given by: F = ðT − 4Þ ×

Θ22 − Θ21 1 þ Θ21

ð3Þ

where F follows a F-distribution with 1 and T-4 degrees of freedom. Since it is rare to short sell an entire asset class directly, we consider the portfolio allocations when short sales are disallowed.7 When short sales are disallowed, the weights of the tangency portfolio can be solved with the extra inequality constraint that the vector of weights is nonnegative. The distribution of the test statistic F in Eq. (3) is however unknown and has to be simulated before hypothesis tests can be conducted. As suggested by Glen and Jorion (1993), simulations can be done by first estimating the means, variances, and covariances using historical data. Expected return of the additional asset class (i.e., real estate in this study) is then modified so that the original tangency portfolio is still mean-variance efficient after the additional asset class is included. This in effect ensures the null hypothesis is satisfied in the subsequent simulation exercise. With these modified parameters, T random samples of joint returns are drawn from a multivariate normal distribution. Based on these simulated returns, a new set of means and variance
covariance matrix are estimated. Sharpe ratios of the tangency portfolios with and without the additional asset class can then be estimated. Finally, the value of the test statistic F in Eq. (3) is computed and recorded. The empirical distribution of the statistic can then be generated under the null hypothesis by repeating this process 1,000 times.

DATA Our proxies for US and non-North American equities are monthly total returns series of the CRSP value-weighted return index and MSCI-EAFE return index, respectively. We use the total return series of the intermediate government bonds provided by the Ibbotson SBBI Yearbook to serve as a proxy for the monthly returns on US government bonds. Obtaining return data on real estate investments is somewhat more complicated than return data on equities. Several indices are used as proxies for real estate investment. In the main analysis of this study, we use the popular All REITs monthly return series published by the National Association of Real Estate

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Investment Trusts (NAREIT). All the above data are from January 1972 to December 2009. Unfortunately, using securitized real estate such as REITs and publicly-traded real estate companies are not without their problems. Liu and Mei (1992) find that the returns on REITs resemble the returns on small cap stocks. There seems to be a general consensus that REITs and publiclytraded real estate companies are hybrid assets of stocks and real estate (see, for example, Brounen and Eichholtz, 2003; Eichholtz and Hartzell, 1996). To ensure the robustness of our conclusions, we also use alternative real estate return series. For international real estate, the monthly return series based on the FTSE EPRA/NAREIT Developed Index, which provides investors with a diverse representation of publicly-traded equity REITs and listed property companies globally, is our proxy for global real estate investments. The monthly return series of FTSE EPRA/NAREIT Developed ex US Index is our proxy for non-US real estate investments. Both FTSE EPRA/NAREIT indices are available from January 1990 to December 2009.8 The All REITs monthly return series, the FTSE EPRA/NAREIT Developed Index, and FTSE EPRA/NAREIT Developed ex US Index represent securitized investments in real estate rather than direct investments. Thus, besides using different securitized real estate returns in verifying the robustness of our results, we also consider the return from direct investment in real estate based on the Property Index of the National Council of Real Estate Investment Fiduciaries (NCREIF). The NCREIF Property Index is a quarterly total rate of return measure of investment performance of a very large pool of individual commercial real estate properties acquired in the private market for investment purposes only.9 The data cover a period from 1978 to 2009 inclusively. Since the NCREIF Property Index is based on the appraised value that tends to be “smoothed”, we make the necessary adjustment to obtain the “unsmoothed” value before it is used to form our investment portfolios. In addition to the appraised value index, we also use the MIT’s transaction based index (TBI) as an alternative proxy for direct real estate investment. The MIT TBI quarterly data cover a period from the second quarter of 1984 to the last quarter of 2009.

DIVERSIFICATION BENEFIT OF REAL ESTATE Full Sample Result Using US REITs Panel A in Table 1 contains the descriptive statistics for each asset class. The All REIT monthly return series of the NAREIT is used as a proxy for

Summary Statistics and Diversification Effects of Real Estate Based on the Full Sample (REITs is Based on the All REIT Index of NAREIT).

CRSP VW Intermediate Government bonds MSCI-EAFE REITs

0.0090 0.0464 1.000

0.0064 0.0163 0.095 1.000

Intermediate Government Bonds 0.0089 0.0500 0.618 0.061 1.000

MSCI-EAFE 0.0086 0.0520 0.617 0.117 0.438 1.000

REITs

0.0646 0.0690 0.0752 0.0847 0.1015 0.1382 0.2838 0.5385 0.1186

0.0000 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060 0.0070 0.0046a

0.8465 0.8379 0.8256 0.8066 0.7734 0.7005 0.4118 0.0000 0.7394

Intermediate Government bonds 0.0669 0.0698 0.0739 0.0802 0.0913 0.1156 0.2120 0.3510 0.1026

MSCIEAFE 0.0220 0.0234 0.0254 0.0285 0.0339 0.0457 0.0925 0.1105 0.0394

REITs 0.4312 0.3678 0.3048 0.2422 0.1807 0.1218 0.0722 0.0460 0.1459

Sharpe ratio

0.0784 0.0837 0.0911 0.1027 0.1229 0.1673 0.3442 0.6261 0.1436

CRSP VW

0.8525 0.8442 0.8324 0.8142 0.7823 0.7123 0.4331 0.0000 0.7496

Intermediate Government bonds

Portfolio weights

0.0691 0.0721 0.0765 0.0831 0.0948 0.1205 0.2228 0.3739 0.1068

MSCIEAFE

Portfolios without REITs

0.4305 0.3672 0.3041 0.2416 0.1801 0.1212 0.0715 0.0457 0.1452

Sharpe ratio

0.3170 0.3340 0.3450 0.3550 0.3570 0.3630 0.3600 0.4000 0.3620

GJp-value

a The last row corresponds to a level of risk-free interest rate of 0.46%/month which equals to the mean return on short-term treasuries over the sample period.

CRSP VW

Risk-free rate

Portfolio weights

Portfolios with REITs

Panel B: Diversification benefits of REITs: Portfolio weights and Sharpe ratios of tangency portfolios with and without REITs are reported at different levels of monthly risk-free interest rates. Optimal portfolios are obtained with short-sale disallowed and based on the full sample period from January 1972 to December 2009. The p-values of Glen and Jorion (GJ) tests on equal Sharpe ratios are also reported

Mean Standard deviation Correlation

CRSP VW

Panel A: Summary statistics of monthly total returns on different assets (January 1972
December 2009)

Table 1. 120 C. SHERMAN CHEUNG AND PETER MIU

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real estate as an asset class in Table 1. The US equities (i.e., the CRSP value-weighted return index), EAFE equities, and REITs all display similar monthly standard deviations and monthly mean returns of about 5% and 0.9%, respectively, over our sample period.10 US government bonds stand out as a distinct asset class with both lower risk and returns. REITs have a reasonable correlation of 0.617 with US equities and even lower correlations with EAFE equities (0.438) and US bonds (0.117). With competitive risk-return profile and reasonable correlation structure, there is no a priori reason to reject the diversification benefit of REITs. One simple way to test the diversification benefits is to estimate and compare the Sharpe ratios of the tangency portfolios with and without real estate using historical average return of T-bill for Rf in Eq. (2). This ex post approach is the most common practice and is also used here. In addition to using historical T-bill returns, we also consider the resulting Sharpe ratios at different values of Rf. By varying Rf, we in effect trace out the efficient frontier by solving for different tangency portfolios.11 This approach allows us to solve for different optimal portfolios on the frontier for investors with different risk aversion parameters. Thus, we can ascertain the degree of diversification benefits to investors with different degrees of risk aversion based on the Sharpe ratios and their statistical significance. This should be a useful exercise as real estate, especially the direct type represented by the NCREIF Property Index, is considered to be a safe investment suitable for conservative investors. By allowing for different degree of risk aversion, we can detect if the diversification benefits are different for investors with different degrees of risk aversion. The detailed results are reported in Panel B of Table 1. Column 1 lists the various levels of Rf being considered, with the last number (0.46%/month) being the ex post historical average. As previously discussed, we solve for the respective optimal portfolios while disallowing short sales. The optimal allocations to various asset classes for the case with and without real estate are reported in columns 2
5 and columns 7
9, respectively. When REITs are added, the allocation is about 3.94% based on the case of historical T-bills returns being used to compute the Sharpe ratio. Note that the optimal allocation in REITs increases as the risk-free rate increases. An increase in the risk-free rate corresponds to an investor with a higher risk tolerance. This should come as no surprise as REITs display equity-like risk and return characteristics and therefore are attractive to aggressive investors. The Sharpe ratios corresponding to the cases with and without REITs are reported in columns 6 and 10. In all cases, the addition of REITs leads to a marginal improvement in

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the Sharpe ratio. This confirms the well-known fact stated earlier that whenever the estimation of the input parameters, the optimization, and the performance measure are done over the same sample period as in the studies mentioned earlier, the performance of the optimized portfolios with the extra asset class cannot be inferior by construction. Any conclusion based on this observed improvement in performance is meaningless without statistical testing. The results of the statistical tests based on the simulation method of Glen and Jorion (1993) described earlier are reported in the last column of Panel B. The improvement in Sharpe ratio is not statistically significant in all cases.12 This conclusion contradicts the conventional wisdom that real estate belongs to any investor’s portfolio. One possible reason for the insignificant diversification benefit documented here is due to using REITs as a proxy for real estate investments. As mentioned earlier, there is evidence to suggest that REITs are really hybrid assets of stocks and real estate. The affinity to stocks may undermine the ability of REITs to provide adequate diversification benefits when pure real estate investment may be a viable addition to any well-diversified portfolio of equities and bonds. The insignificant diversification benefit may also be the result of the changing correlation behavior of real estate and other asset classes over the course of bullish and bearish states of the financial markets. Ample evidence has been reported in the literature supporting the regimeswitching behavior for international stock markets. Specifically, a bearish domestic stock market tends to be associated with higher correlations with other international stock markets.13 This more intense synchronization of various asset classes in a bearish environment can reduce the diversification benefits of real estate when diversification is needed most. Real estate can in fact be an attractive asset class in a “normal” stock market when returns are positive. Dynamic correlation behavior of real estate investment return has been documented in a number of empirical studies. For example, Clayton and MacKinnon (2001) find the sensitivity of REIT returns to the returns on other financial assets to be time-varying. Eichholtz (1996b) finds covariances of international property shares to be unstable. While they fail to model the time-varying risk behavior as we do below, their results argue against the use of static correlations as in Table 1.14 They also do not examine the effects of the dynamic correlation behavior on the diversification potential of REITs. The use of a poor proxy for real estate and the time-varying portfolio risk characteristics could distort the conclusion on the diversification effectiveness of real estate reported in Table 1. We will test these possible reasons for our results by using a regime-switching model and various alternative indices as proxies for real estate investments.

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Regime-Switching Model of the Return on Stock Index Financial markets in general are characterized by bullish and bearish environments often reflecting the underlying economic fundamentals. Hamilton (1989) in a seminal paper introduces the regime-switching approach to capture different economic regimes. Specifically, he uses a Markov switching regression to characterize changes in the parameters of an autoregressive process in order to capture, for example, the fast versus slow growth phase of an economy. The switch between the two phases is governed by the outcome of a Markov process. The idea of regime-switching has been applied to finance by, for example, Ang and Bekaert (2002), Ramchand and Susmel (1998), and Longin and Solnik (1995, 2001) to produce rich empirical results regarding diversification benefits of international stock markets in both bullish and bearish environments. Given that regimeswitching behavior has a definite effect on the diversification effectiveness of international stocks, it is natural to examine whether such behavior also undermines the diversification benefits of real estate. To assess the diversification benefits under different stock market regimes, a number of tests are first conducted to check for autocorrelation and heteroscedasticity in the time-series of US equity returns as proxied by the CRSP value-weighted return index. These tests enable us to develop an appropriate regime-switching (RS) model. Summary statistics are computed for the time-series of monthly total returns on the US stock index from January 1972 to December 2009 and the results are reported in Table 2. For autocorrelation, Durbin
Watson (DW) statistic on the serial correlation, p-values corresponding to Breusch (1978) and Godfrey (1978) LM test statistics as well as Ljung and Box (1979) Q-test for the higherorder serial correlation are reported. Except for the Ljung and Box Q-test, the results suggest we cannot reject the hypothesis of zero autocorrelation. The Ljung and Box Q-test rejects the zero autocorrelation hypothesis, however. We proceed to model the regime-switching effect based on zero autocorrelation and report our results based on that. We also rerun the analyses while explicitly modeling for the first-order autocorrelation effect. The conclusions are unaffected and therefore we do not report the results of these additional analyses here. For heteroscedasticity, test for first-order autoregressive conditional heteroscedasticity (ARCH) is conducted. The corresponding p-value is also reported in Table 2 and confirms the statistical significance of the ARCH effect. Given these test results, we propose a model for the monthly total return on the stock index (rt) that encompasses both the regime-switching and ARCH effects. The model is therefore

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Table 2. Summary Statistics of Time-Series of Monthly Total Returns on the CRSP Value-Weighted Portfolio (January 1972
December 2009). Mean (%) Standard deviation (%) Skewness Kurtosis Autocorrelation tests DW statistic BG (p-value) Ljung
Box (p-value) ARCH test ARCH1 (p-value)

0.900 4.644 −0.591 5.256 1.750 0.233 0.035 0.034

Notes: • DW: the standard Durbin
Watson statistic on serial correlation. • BG: p-value corresponding to the Breusch (1978) and Godfrey (1978) LM test statistic for higher-order serial correlation. • Ljung
Box: p-value corresponding to Ljung and Box (1979) Q-test of higher-order serial correlation. • ARCH1: p-value of test for first-order autoregressive conditional heteroscedasticity (ARCH).

flexible enough to allow for both state- and time-varying expected returns and volatilities. We model the return on the stock index as: rt = μðSt Þ þ ɛt ðSt Þ

ð4Þ

where St = 1 or 2 (the two possible states of the stock index), and μðSt Þ is the expected return, which is contingent on the realization of the particular state at time t.15 The residual ɛt ðSt Þ is the unexpected return at time t, which is assumed to be normally distributed with mean zero and conditional variance ht ðSt Þ, ɛ t ðSt Þ ∼ Nð0; ht ðSt ÞÞ

ð5Þ

We specify a state-dependent ARCH(1) process similar to the set up in Gray (1996), ht ðSt Þ = cðSt Þ þ aðSt Þ⋅ðɛt − 1 Þ2

ð6Þ

The Uneasy Case for Real Estate Investments

125

To complete the specification, the switching of regimes is assumed to follow a Markov chain with constant transition probabilities. Pr½St = 1jSt − 1 = 1 = P Pr½St = 2jSt − 1 = 1 = 1 − P Pr½St = 2jSt − 1 = 2 = Q

ð7Þ

Pr½St = 1jSt − 1 = 2 = 1 − Q In other words, if we are currently in state “1,” the probability of remaining in the same state is given by P and the probability of transitioning to state “2” is therefore given by 1 − P. On the other hand, if we are currently in state “2,” Q denotes the probability of staying in state “2.” Note that high estimated values of P and Q imply regime persistency. The RS model built on the seminal work of Hamilton (1989) allows data to be drawn from two possible distributions (i.e., regimes). At a given point in time, there is a nonzero probability that the process given by Eqs. (4)
(6) will stay in the same state or switch to the other state in the next period. Our objective here is to find out the risk-return characteristics of various asset classes and their correlations in each of the two regimes and examine their portfolio implications. The estimates of µ and c in each of the two states will give us an indication of the risk-return profile of the US stock market in the two states of the world. Further, the regimes can be efficiently and endogenously determined by the stock return data alone without reference to other economic information. Finally, the RS model can be exploited ex ante to enhance the return of the portfolio in different regimes as demonstrated by Ang and Bekaert (2002). Filtering technique similar to that of Gray (1996) and Hamilton (1989) is used to conduct the maximum likelihood estimation of the parameters. This approach is also adopted by Ramchand and Susmel (1998) and Ang and Bekaert (2002). We estimate the parameters governing Eqs. (4)
(7) and the results are reported in Table 3. From Table 3, state “1” can be characterized by both its low expected return and high-return volatility. The estimate of µ in state “1” is negative 0.78% per month and that of c is 0.44%. On the other hand, state “2” is the state when expected return is high and volatility is low. The estimate of µ in state “2” is 1.49% per month and the constant variance component based on the estimate of c is 0.11%. Based on the average values of ht reported in Table 3, the average variance of the US stock market return in

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C. SHERMAN CHEUNG AND PETER MIU

Table 3. Maximum Likelihood Parameter Estimates and Asymptotic Standard Errors (in italic) of Regime-Switching ARCH(1) Model of the CRSP Value-Weighted Portfolio Returns. rt = μðSt Þ þ ɛt ðSt Þ where ɛt ðSt Þ ∼ Nð0; ht ðSt ÞÞ and ht ðSt Þ = cðSt Þ þ aðSt Þ⋅ðɛ t − 1 Þ2

μ c a Transition probability Average ht (×10−3)

St = 1

St = 2

−0.0078 0.0193 0.0044 0.0018 0.0470 0.1309 P = 0.829 0.205 4.491

0.0149 0.0023 0.0011 0.0003 0.0071 0.0487 Q = 0.942 0.029 1.160

The transition probability P captures the repeat of state “1” and (1 − P) captures transition from state “1” to state “2.” The transition probability Q represents the repeat of state “2” and (1 − Q) denotes the transition from state “2” to state “1.”

the bearish regime (i.e., state “1”) is about four times that of the bullish regime (i.e., state “2”). The contrast in the risk-return profile of the two states is in fact quite stark.16 The persistency of regime as indicated by the high values of P and Q is statistically significant in both states. Since our objective is to examine the diversification benefits of real estate in different market regimes, we need a way to classify the stock return series into bullish and bearish regimes. Fortunately, as a byproduct of the maximum likelihood estimation, the endogenously determined probability of realizing a particular state or regime can also be extracted at any point in time. For example, the filter probability, PrðSt = 1jrt − 1 ; rt − 2 ; rt − 3 ; …; r0 Þ, represents the conditional probability that stock return is in state “1” at t given the observed time-series of returns up to the beginning of that period. Alternatively, we can compute the smooth probability, PrðSt = 1jrT ; rT − 1 ; rT − 2 ; …; r0 Þ, in which the inference about the state is now based on all return data up to the end of the sample period (i.e., up to time T). The evolution of the smooth probability over time is governed by both the magnitudes of the transition probabilities (i.e., P and Q) defined in Eq. (7) and the prevailing return on the stock index. For example, the higher the values of P and Q, the more persistent is the smooth probability given the lower

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The Uneasy Case for Real Estate Investments

chance of switching between the two states. A large jump in the return on the stock index will however disrupt the persistency of the smooth probability. The realization of a high (low) return at time t will lead us to assign a lower (higher) probability of state “1” being realized at time t (i.e., the value of the smooth probability at time t). The smooth probability therefore captures our assessment of the relative chances of the two states being realized in a particular month given all the observations of the returns on the stock index. The smooth probabilities are plotted in Fig. 1. A probability close to unity (zero) suggests it is very likely the stock index is in state “1” (state “2”). State “1” (state “2”) represents a bearish (bullish) regime. Fig. 1 captures the history of the US stock market quite well. Note that, for example, the smooth probability approaches one (i.e., we are almost sure that state “1” has been realized) during some of the recent bear markets, such as the one caused by the Russian financial crisis in 1998, the one in early 2000s caused by the tech bubbles, and the one in 2008 caused by the housing crisis.

1.0

0.8

0.6

0.4

0.2

0.0 Jan-72

Jan-77

Jan-82

Jan-87

Jan-92

Jan-97

Jan-02

Jan-07

Fig. 1. Time-Series Plot of Smooth Probabilities of Realizing State “1” (i.e., “LowReturn High-Volatility” Regime) of the CRSP Value-Weighted Portfolio Returns over the Sample Period from January 1972 to December 2009, as Implied by the Estimated Regime-Switching ARCH(1) Process as Reported in Table 3. A Probability Close to Unity (Zero) Therefore Suggests a Very High Likelihood of Realizing State “1” (State “2”) within That Monthly Period.

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C. SHERMAN CHEUNG AND PETER MIU

State-Contingent Results and the Significance of the Choice of Real Estate Investment Proxy To examine if the diversification benefits behave differently across the two regimes of the stock market, we need to partition the stock return data into two regimes. The estimated smooth probabilities reported in Fig. 1 will be a useful tool. A higher probability of realizing regime 1 (the low-return state) can be thought of as a bearish stock market, whereas a lower probability can be considered as a bullish stock market. A smooth probability of 0.5 indicates equal probabilities of realizing regimes 1 and 2. The return series of all asset classes can then be partitioned into two subsamples corresponding to the low- and high-return regimes based on whether the smooth probability of the stock market in each month is higher or lower than 0.5.17 With these two subsamples of return data corresponding to the two regimes, the analysis performed above on the diversification benefits of adding real estate is repeated for each of the two regimes. The results for the low-return state and high-return state are reported in Tables 4 and 5, respectively. According to Panel A in Table 4, all equities and REITs display negative returns in the bearish US stock market.18 All our asset classes also have higher volatilities compared to those in Tables 1 and 5. When the stock market is in the low-return state, US equities, EAFE equities, and REITs perform extremely poorly with average monthly losses of 1% or higher. In the case of the high-return state for the US equities, Panel A in Table 5 indicates positive mean returns for all our asset classes with lower volatilities. Recent studies on regime-switching behavior also indicate that correlations among international equity returns are higher during bear markets than during bull markets. According to Panels A in Tables 4 and 5, the correlations among equities and REITs tend to be higher (lower) in a bearish (bullish) stock environment. The heightened correlations in a bearish US stock market can reduce the diversification benefits of REITs and possibly explain the absence of overall diversification benefits reported in Table 1. Panels B in Tables 4 and 5 provide the outcomes of the portfolio optimization with and without REITs for our representative investor. Panel B in Table 4 indicates the investor should be 100% into bonds in a bearish US stock market. REITs therefore become a redundant asset.19 Any notion of real estate being a stable asset class in a volatile financial world is simply not borne out by the evidence in Table 4. Panel B in Table 5 provides a ray of hope for REITs in a bullish US stock market. REITs significantly

CRSP VW Intermediate Government bonds MSCI-EAFE REITs

0.0090 0.0219 0.011 1.000

−0.0159 0.0740 1.000

−0.0141 0.0705 0.758 −0.033 1.000

MSCI-EAFE −0.0099 0.0880 0.663 0.106 0.598 1.000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060 0.0070 0.0044a

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Intermediate Government bonds 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

MSCIEAFE 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

REITs 0.4097 0.3642 0.3186 0.2730 0.2274 0.1818 0.1362 0.0906 0.2081

Sharpe ratio

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

CRSP VW

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Intermediate Government bonds

Portfolio weights

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

MSCIEAFE

Portfolios without REITs

0.4097 0.3642 0.3186 0.2730 0.2274 0.1818 0.1362 0.0906 0.2081

Sharpe ratio












GJ p-value

The last row corresponds to a level of risk-free interest rate of 0.44%/month which equals to the mean return on short-term treasuries within the subsample.

a

CRSP VW

Risk-free rate

Portfolio weights

Portfolios with REITs

Panel B: Diversification benefits of REITs: Portfolio weights and Sharpe ratios of tangency portfolios with and without REITs are reported at different levels of monthly risk-free interest rates. Optimal portfolios are obtained with short-sale disallowed and based on the subsample corresponding to the low-return state of the CRSP VW index. The p-values of Glen and Jorion (GJ) tests on equal Sharpe ratios are also reported

Mean Standard deviation Correlation

Intermediate Government Bonds

CRSP VW

REITs

Summary Statistics and Diversification Effects of Real Estate Based on the Low-Return State of the CRSP VW Index (REITs is Based on the All REIT Index of NAREIT).

Panel A: Summary statistics of monthly total returns on different assets for the subsample corresponding to the low-return state

Table 4. The Uneasy Case for Real Estate Investments 129

CRSP VW Intermediate Government bonds MSCI-EAFE REITs

0.0154 0.0334 1.000

0.0058 0.0144 0.220 1.000

Intermediate Government Bonds 0.0149 0.0414 0.444 0.157 1.000

MSCI-EAFE

0.0134 0.0363 0.515 0.169 0.233 1.000

REITs

0.5647 0.5142 0.4432 0.3359 0.1552 0.0000 0.0000 0.0000 0.0000

Intermediate Government bonds

0.1150 0.1276 0.1452 0.1719 0.2169 0.2556 0.2536 0.2530 0.2556

0.1214 0.1315 0.1456 0.1669 0.2029 0.2266 0.2114 0.1898 0.2322

MSCI- REITs EAFE 0.5877 0.5281 0.4719 0.4207 0.3762 0.3400 0.3053 0.2708 0.3531

Sharpe ratio

0.9638 0.9097 0.8743 0.8719 0.9362 0.9787 0.8818 0.7861 1.0152

Excess return (%)

1.6401 1.7227 1.8526 2.0726 2.4885 2.8786 2.8882 2.9031 2.8754

Standard deviation (%)

0.2752 0.3108 0.3614 0.4386 0.5712 0.7154 0.7204 0.7227 0.7148

CRSP VW

0.6052 0.5561 0.4864 0.3800 0.1973 0.0000 0.0000 0.0000 0.0000

Intermediate Government bonds

Portfolio weights

0.1196 0.1331 0.1522 0.1814 0.2315 0.2846 0.2796 0.2773 0.2852

MSCIEAFE

Portfolios without REITs

0.5719 0.5131 0.4577 0.4073 0.3640 0.3296 0.2973 0.2651 0.3417

Sharpe ratio

0.9485 0.8951 0.8611 0.8619 0.9349 1.0218 0.9221 0.8222 1.0594

Excess return (%)

1.6584 1.7446 1.8813 2.1159 2.5685 3.1001 3.1010 3.1014 3.1000

Standard deviation (%)

0.0190 0.0230 0.0320 0.0410 0.0510 0.0760 0.1200 0.1630 0.0600

GJ pvalue

The last row corresponds to a level of risk-free interest rate of 0.46%/month which equals to the mean return on short-term Treasuries within the subsample.

0.1988 0.2267 0.2660 0.3252 0.4251 0.5178 0.5350 0.5573 0.5122

0.0000 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060 0.0070 0.0046a

a

CRSP VW

Risk-free rate

Portfolio weights

Portfolios with REITs

Panel B: Diversification benefits of REITs: Portfolio weights and Sharpe ratios of tangency portfolios with and without REITs are reported at different levels of monthly risk-free interest rates. Optimal portfolios are obtained with short-sale disallowed and based on the subsample corresponding to the high-return state of the CRSP VW index. The p-values of Glen and Jorion (GJ) tests on equal Sharpe ratios are also reported

Mean Standard deviation Correlation

CRSP VW

Panel A: Summary statistics of monthly total returns on different assets for the subsample corresponding to the high-return state

Table 5. Summary Statistics and Diversification Effects of Real Estate Based on the High-Return State of the CRSP VW Index (REITs is Based on the All REIT Index of NAREIT).

The Uneasy Case for Real Estate Investments

131

improve the Sharpe ratios at low levels of risk-free rate.20 To understand the rationale for the significant diversification benefits for the risk averse investors, we also provide the excess return (columns 7 and 13) and the standard deviation of return (columns 8 and 14) used to compute the Sharpe ratio of the tangency portfolio.21 Columns 7 and 8 together with columns 13 and (14) offer useful insights into the risk and return characteristics of the resulting portfolio as REITs are introduced. Comparing column 7 with column 13, the presence of REITs at the expense of lower return bonds increases the excess returns at low levels of the risk-free rate. Since the correlations of REITs and equities are weakened in a bullish stock market, columns 8 and 14 indicate that the presence of REITs also lowers the risk of the portfolio. This simultaneous reduction in risk and increase in returns at lower levels of risk-free rate explain the significant improvement in the Sharpe ratios for investors who are relatively more risk averse. On the other hand, the tangency portfolios correspond to higher levels of Rf are chosen by individuals who prefer higher risk-return portfolios. Panel B indicates that bonds are completely displaced by equities and REITs at higher levels of Rf. Adding more REITs to a portfolio of equities is no longer desirable as the returns on REITs are not as attractive as those of equities. The role of REITs at higher levels of Rf becomes one of risk reduction as indicated in columns 8 and 14. The differences in the Sharpe ratios are no longer statistically significant at higher levels of Rf. It is marginally statistically insignificant based on the ex post value of Rf of 0.46%/month. For real estate to make a meaningful contribution to a welldiversified portfolio, it must enhance the return, while at the same time able to lower the risk of the portfolio. Based on our findings, such benefit can only be realized by those investors who are more risk averse and thus rationally invest in bonds in forming their optimal portfolios. Even for this “lucky” group of investors, the benefit from investing in real estate fizzles in the bearish state of the stock market. By allowing for different degrees of risk aversion and using the regime-switching approach, we can better detect the potential benefits of investing in real estate. Our results contradict Chun et al. (2004) conclusion that real estate pays off when the benefits are most needed. They show that real estate performs well when the consumption growth opportunities are low. What they fail to do is to explicitly account for the interaction among assets in different phases of market environments as done in the present study. As mentioned earlier, international real estate has been considered as a better asset class for portfolio diversification than domestic real estate (see, e.g., Eichholtz, 1996a). To examine the diversification benefits of

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international real estate, we rerun the above experiment with the FTSE EPRA/NAREIT Developed Index instead of the popular All REITs monthly return series published by the NAREIT. Table 6 reports the descriptive statistics of the returns on this global real estate index and the correlation of its returns with other asset classes over the full sample period.22 Note that the monthly returns based on the FTSE EPRA/NAREIT Developed Index produce the worst mean return and the highest risk among all asset classes under consideration. The FTSE EPRA/NAREIT Developed Index also has higher correlations with US and EAFE equities than the US All REITs reported in Table 1, albeit the sample periods under consideration are different. For example, the FTSE EPRA/NAREIT Developed Index has a correlation of 0.773 with international equities (i.e., MSCI-EAFE) compared to 0.438 for US All REITs reported in Table 1 and a marginally higher correlation with US equities than US All REITs (0.662 vs. 0.617). To find out if this global real estate index can significantly enhance the risk-adjusted return of our representative US investor holding a diversified portfolio of US equities, EAFE equities, and US government bonds, we repeat the above analysis as reported in Table 1 Panel B but with this global index as our proxy for real estate investment. The global index is found to be a redundant asset and is excluded from the optimal portfolios at all levels of risk-free interest rate (the results are thus not reported here). This conclusion can be attributed to the undesirable risk-return characteristics of the global index as reported in Table 6.23 As explained earlier, the FTSE EPRA/NAREIT Developed Index represents both publicly-traded REITs and listed property companies. The property companies included in the index represent both property investors and property developers. Property developers do not display the same steady cash flows and same risk-return characteristics as REITs. REITs and property investors are covered by rental contracts and their cash flows are thus less sensitive to economic cycles.24 Since property developers, like public companies, are more likely to be driven by economic fundamentals, they are more correlated with the equity market. Another reason for the weak diversification effectiveness of the FTSE EPRA/NAREIT Developed Index to our representative US investor may be the fact that the index consists of a significant amount of US real estate exposure. To eliminate the contamination caused by US real estate exposure, we rerun our analysis using the FTSE EPRA/NAREIT Developed ex US Index as our proxy for real estate investment. We find that using this global ex US index does not enhance the attractiveness of real estate

CRSP VW Intermediate government bonds MSCI-EAFE

0.0078 0.0449 1.000

CRSP VW

0.0055 0.0133 −0.087 1.000

Intermediate Government Bonds 0.0034 0.0546 0.662 −0.003 0.773

1.000

FTSE EPRA/ NAREIT Developed Index

0.0046 0.0504 0.739 −0.070

MSCI-EAFE

0.787

0.0038 0.0594 0.638 0.016

FTSE EPRA/ NAREIT Developed ex US Index

Summary Statistics of Monthly Total Returns on Different Assets (January 1990
December 2009).

Mean Standard deviation Correlation

Table 6.

The Uneasy Case for Real Estate Investments 133

134

C. SHERMAN CHEUNG AND PETER MIU

investment for our representative US investor. It is again excluded from the optimal portfolios at all levels of risk-free interest rate (detailed results not reported). It is not surprising given the similarity of the descriptive statistics of the two global real estate indices (see Table 6). The risk-return characteristics of the global real estate index are essentially the same whether the US real estate sector is excluded or not. Both global real estate indices display the highest risk and the lowest return among all asset classes under consideration. Regime-switching analysis (not reported here) performed confirms the exclusion of the FTSE EPRA/NAREIT Developed ex US Index from the optimal portfolios in both the bullish and bearish states of the US stock markets.25 Given the equity-like behavior of the marketable real estate as reported in the literature, it is natural to find out how real estate investments based on the appraised value perform in a diversified portfolio. To address this issue, we use the quarterly Property Index constructed by the National Council of Real Estate Investment Fiduciaries (NCREIF) as our proxy for real estate investment returns. The full sample analysis based on the index is reported in Table 7.26 The descriptive statistics in Panel A point to the potential of the NCREIF index in a diversified portfolio. The index has a slightly better return and lower risk than US bonds. Its correlations with other asset classes are low. From Panel B, the NCREIF index indeed enters the optimal portfolios and offers significant diversification benefits except when the risk-free rate is high. The optimal portfolios at high risk-free rates are for those investors with high risk tolerance. These investors will exclude bonds or bond-like assets like the NCREIF index from their optimal portfolios as confirmed by the results of Table 7. Based on the ex post risk-free rate (see last row of Panel B), the Sharpe ratio with the optimal investments in real estate is indeed (statistically) significantly higher than the corresponding Sharpe ratio without real estate. While the quarterly NCREIF index series is not long enough to perform regime-switching analysis, the results reported in Table 7 are the most hopeful results so far for real estate. Unfortunately, directly using the NCREIF index as a proxy for real estate investment returns is not without some well-known problems. As recognized by Eichholtz and Hartzell (1996), Geltner (1993), and Stevenson (2000), among others, an appraised index such as the NCREIF index used in this study is biased due to appraisal smoothing and other problems. Our encouraging conclusions based on that index might therefore be overstated. To remove the appraisal smoothing bias, we use the method described in Geltner, MacGregor, and

0.0202 0.0342 0.006 1.000

Intermediate Government Bonds 0.0293 0.0975 0.742 0.038 1.000

MSCI-EAFE 0.0215 0.0228 0.081 −0.069 0.117 1.000

NCREIF

0.0496 0.0557 0.0672 0.0967 0.3401 1.0000 1.0000 0.0858

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 0.0138a

0.2977 0.2929 0.2839 0.2608 0.0707 0.0000 0.0000 0.2694

Intermediate Government bonds 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

MSCIEAFE 0.6527 0.6514 0.6489 0.6424 0.5892 0.0000 0.0000 0.6448

NCREIF 1.1815 0.9083 0.6366 0.3697 0.1390 0.0692 0.0113 0.4352

0.1793 0.1970 0.2297 0.3117 0.8831 1.0000 1.0000 0.2816

CRSP VW

0.8053 0.7878 0.7553 0.6742 0.1081 0.0000 0.0000 0.7040

Intermediate Government bonds

0.0154 0.0152 0.0149 0.0142 0.0088 0.0000 0.0000 0.0144

MSCIEAFE

0.6911 0.5368 0.3848 0.2397 0.1273 0.0692 0.0113 0.2746

Sharpe ratio

0.0000 0.0000 0.0000 0.0010 0.2750

0.0010

GJ p-value

The last row corresponds to a level of risk-free interest rate of 1.38%/quarter which equals to the mean return on short-term treasuries over the sample period.

a

CRSP VW

Riskfree rate

Portfolio weights

Portfolio weights

Sharpe ratio

Portfolios without NCREIF

Portfolios with NCREIF

Panel B: Diversification benefits of the NCREIF: Portfolio weights and Sharpe ratios of tangency portfolios with and without the NCREIF are reported at different levels of risk-free interest rates. Optimal portfolios are obtained with short-sale disallowed and based on the full sample period from 1978 Q1 to 2009 Q4. The p-values of Glen and Jorion (GJ) tests on equal Sharpe ratios are also reported

CRSP VW Intermediate Government bonds MSCI-EAFE NCREIF

0.0310 0.0863 1.000

CRSP VW

Panel A: Summary statistics of quarterly total returns on different assets (1978 Q1 to 2009 Q4)

Summary Statistics and Diversification Effects of Real Estate Based on the Full Sample of the NCREIF Property Index.

Mean Standard deviation Correlation

Table 7. The Uneasy Case for Real Estate Investments 135

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C. SHERMAN CHEUNG AND PETER MIU

Schwann (2003) to recover the underlying true return from the return based on the smooth index as follows: rtu =

rt a⋅rt− 1 − 1−a 1−a

ð8Þ

where rtu is the unobserved true return, rt is the observed return based on the appraised value, and a is the smoothing parameter. By assuming rt follows a first-order autoregressive (AR) process: rt = α0 þ α1 ⋅rt− 1

ð9Þ

The parameter a can be estimated by using the slope coefficient, α1, when applying an ordinary least square (OLS) regression to the first-order AR process.27 The results based on the “unsmoothed” NCREIF return index constructed according to the above method are reported in Table 8. Consistent with the results reported in Stevenson (2000), the volatility of real estate investments based on the unsmoothed returns reported in Panel A is much higher than the “smoothed” volatility reported in Table 7 (0.0697 vs. 0.0228). Panel B reports the diversification benefits of real estate based on the unsmoothed NCREIF return series. Real estate offers significant diversification benefits at lower levels of risk-free rate but no meaningful diversification benefits at higher levels of risk-free rate. Based on the ex post risk-free rate, the Sharpe ratio of the optimal portfolio allowing for the investment in real estate is not significantly higher than that without real estate. This last statistic is hardly encouraging. As an alternative way to avoid the potential bias arisen from the appraisal process, we also repeat the above analysis by using the MIT TBI index as the proxy of real estate return. The results reported in Table 9 are somewhat similar to those reported in Table 8 for the “unsmoothed” NCREIF return index. Real estate represented by the MIT TBI index enters the optimal portfolio only at very low levels of risk-free rate (lower than 0.50%/quarter) and plays no role at all other levels of risk-free rate. The diversification benefits are statistically insignificant at all levels of risk-free rate. The overall case for real estate thus far is relatively dismal. REITs as an asset class offer no significant diversification benefits based on overall sample of almost four decades. REITs definitely do not help when stock

0.0203 0.0343 0.004 1.000

Intermediate Government Bonds 0.0288 0.0977 0.749 0.040 1.000

MSCI-EAFE 0.0199 0.0697 0.178 −0.192 0.160 1.000

NCREIF

0.1233 0.1400 0.1718 0.2564 0.8464 1.0000 1.0000 0.2245

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 0.0138a

0.6920 0.6825 0.6645 0.6164 0.1536 0.0000 0.0000 0.6345

Intermediate Government bonds 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

MSCIEAFE 0.1847 0.1775 0.1637 0.1272 0.0000 0.0000 0.0000 0.1410

NCREIF 0.7766 0.5979 0.4220 0.2550 0.1330 0.0749 0.0171 0.2950

0.1949 0.2128 0.2456 0.3266 0.8463 1.0000 1.0000 0.2971

CRSP VW

0.8051 0.7872 0.7544 0.6734 0.1537 0.0000 0.0000 0.7029

Intermediate Government bonds

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

MSCIEAFE

0.6951 0.5414 0.3901 0.2457 0.1330 0.0749 0.0171 0.2804

Sharpe ratio

0.0000 0.0070 0.0500 0.2340


0.1640

GJ p-value

The last row corresponds to a level of risk-free interest rate of 1.38%/quarter which equals to the mean return on short-term treasuries over the sample period.

a

CRSP VW

Riskfree rate

Portfolio weights

Portfolio weights

Sharpe ratio

Portfolios without NCREIF

Portfolios with NCREIF

Panel B: Diversification benefits of the NCREIF: Portfolio weights and Sharpe ratios of tangency portfolios with and without the NCREIF are reported at different levels of risk-free interest rates. Optimal portfolios are obtained with short-sale disallowed and based on the full sample period from 1978 Q2 to 2009 Q4. The p-values of Glen and Jorion (GJ) tests on equal Sharpe ratios are also reported

CRSP VW Intermediate Government bonds MSCI-EAFE NCREIF

0.0315 0.0865 1.000

CRSP VW

Panel A: Summary statistics of quarterly total returns on different assets (1978 Q2
2009 Q4)

Summary Statistics and Diversification Effects of Real Estate Based on the Full Sample of the Unsmoothed NCREIF Property Index.

Mean Standard deviation Correlation

Table 8. The Uneasy Case for Real Estate Investments 137

0.0196 0.0287 −0.184 1.000

Intermediate Government Bonds 0.0273 0.1008 0.761 −0.108 1.000

MSCI-EAFE 0.0057 0.0625 0.141 −0.088 0.087 1.000

MIT TBI

0.1554 0.1755 0.1957 0.2461 0.8305 1.0000
0.2024

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 0.0111a

0.7996 0.8187 0.8043 0.7539 0.1695 0.0000
0.7976

Intermediate Government bonds 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000

MSCIEAFE 0.0450 0.0058 0.0000 0.0000 0.0000 0.0000
0.0000

MIT TBI 0.8593 0.6295 0.4365 0.2488 0.1013 0.0441
0.3947

0.1674 0.1771 0.1958 0.2462 0.8305 1.0000
0.2024

CRSP VW

0.8326 0.8229 0.8042 0.7538 0.1695 0.0000
0.7976

Intermediate Government bonds

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000

MSCIEAFE

0.8240 0.6295 0.4365 0.2488 0.1013 0.0441
0.3947

Sharpe ratio

0.242








GJ p-value

The last row corresponds to a level of risk-free interest rate of 1.11%/quarter which equals to the mean return on short-term treasuries over the sample period.

a

CRSP VW

Risk-free rate

Portfolio weights

Portfolio weights

Sharpe ratio

Portfolios without MIT TBI

Portfolios with MIT TBI

Panel B: Diversification benefits of the MIT TBI: Portfolio weights and Sharpe ratios of tangency portfolios with and without the MIT TBI are reported at different levels of risk-free interest rates. Optimal portfolios are obtained with short-sale disallowed and based on the full sample period from 1984 Q2 to 2009 Q4. The p-values of Glen and Jorion (GJ) tests on equal Sharpe ratios are also reported.

CRSP VW Intermediate Government bonds MSCI-EAFE MIT_TBI

0.0289 0.0875 1.000

CRSP VW

Panel A: Summary statistics of quarterly total returns on different assets (1984 Q2
2009 Q4)

Summary Statistics and Diversification Effects of Real Estate Based on the Full Sample of the MIT TBI.

Mean Standard deviation Correlation

Table 9. 138 C. SHERMAN CHEUNG AND PETER MIU

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139

markets are bearish and diversification is most needed. Moreover, the diversification benefits of REITs are marginally insignificant based on the ex post risk-free rate in a bullish stock market environment. Global real estate is no better. The only evidence we can document in favor of real estate occurs when the appraised value based on the NCREIF returns is used. It is however well known that the appraised value is biased. When the bias is removed, the diversification benefits based on the ex post risk-free rate are no longer statistically significant. The only weak case we can mount in favor of real estate is for conservative investors with high risk aversion holding REITs in a bullish stock market or holding direct investments in real estate. What if our representative portfolio investor can successfully time the real estate market? How significant will be the diversification benefit of including real estate investment in the portfolio under this situation? To address this issue, we perform a regime-switching analysis for real estate investment return. In the literature, regime-switching models have been applied to most other asset classes to gain a better understanding of their risk-return characteristics and to explore their investment implications. It will be useful to perform similar analysis for real estate. Furthermore, dynamic correlation behavior of real estate investment return has been documented in a number of empirical studies. For example, Eichholtz (1996b) finds the variances and covariances to be unstable over time for a set of international real estate returns. By using the regime-switching model, we hope to accommodate the reported instability and produce better portfolio results. As explained earlier, the first step to come up with a reasonable model for regime-switching analysis is to examine the univariate characteristics of the REITs return series. To ensure the statistical power of our analysis, we use the monthly data of the US All REIT index of NAREIT from January 1972 to December 2009 as our proxy of REITs return. This is the longest data series among all the real estate return proxies considered in this study. A number of tests are first conducted to check for autocorrelation and heteroscedasticity in the returns of REITs. The results in Table 10 suggest we can reject the hypothesis of zero autocorrelation. The presence of autocorrelation calls for the introduction of a lag return in Eq. (4) to allow for the autocorrelation effect. For heteroscedasticity, the test for first-order ARCH effect is conducted. The corresponding p-value is also reported in Table 10 and confirms the statistical significance of the ARCH effect. The significant ARCH effect is no different from what is reported earlier in the case of US equity return. Given these test results, we propose a model for the monthly

140

Table 10.

C. SHERMAN CHEUNG AND PETER MIU

Summary Statistics of Time-Series of Monthly Total Returns on US All REITs (January 1972
December 2009).

Mean (%) Standard deviation (%) Skewness Kurtosis Autocorrelation tests DW statistic BG (p-value) Ljung
Box (p-value) ARCH test ARCH1 (p-value)

0.864 5.198 −0.425 10.843 1.760 W1∧ ), yet not as much as in Scenario II due to expected monitoring and enforcement costs. Interestingly, co-owner #1 bears only half the combined costs, in present value terms, of her expected total consumption of perks and expected monitoring and enforcement. For #2, S2 = S2∧ −

and

            P M V∧ V V∧ V − −φ = −φ = ð1 − λÞ 2 2 2 2 2 2

159

Dividend Irrelevance and Firm Control

2

0

W2 = S2 þ 4ðW2∧ − S2∧ Þ þ φ@

13

2

0

13

V∧ A 5 V∧ = S2 þ W2∧ − 4S2∧ − φ@ A5 2 2 0 1 ½P þ M A = S2 þ W2∧ − S2 − @ 2 0 1 ½P þ M A = W2∧ − @ 2

Here the dollar value of #2’s ownership interest falls, by possibly even more than in Scenario II, to S2 and he must sell possibly an even larger proportion ðλ; λ ≥ γÞ of his ownership interest to artificially create the dividend of the size he desires to receive. As in Scenario II, his incremental wealth increases from its initial level ð = W2∧ − S2∧ Þ by the dollar amount of the dividend. However, the level of his total wealth falls (i.e., W2 < W2∧ ) due to the negative effects on the ownership interests of co-owners #1 and #2 of: (i) #1’s expected perk consumption and (ii) expected monitoring and enforcement of the contract. As does co-owner #1, #2 bears half the combined costs, in present value terms, of (i) and (ii). Finally, for the new co-owner (#3), very simply 

   V∧ V S3 = φ =λ 2 2

and

W3 = W3∧ ;

and the value of the firm is reduced, possibly even relative to its reduced value in Scenario II, such that now V = V∧ − P − M. Note in this theoretical framework that, at least as of the moment of #2’s decision to sell, #3’s ownership interest and wealth level is totally unaffected by #1’s expected perk consumption and expected monitoring and contract enforcement. Dividend policy matters, but only to the two co-founding owners.

DISCUSSION We now extend the analysis by introducing collusion, via a “confidence factor,” into financial markets, which moves us away from arms-length

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STEVEN A. DENNIS AND WILLIAM STEVEN SMITH

transactions. Trust is very important, especially within the context of small business. Many deals involving small businesses are consummated via handshakes. We can let CFacij ; 0 ≤ CFacij ≤ 1, denote the confidence that party i has in party j. A value of zero for the confidence factor indicates no confidence whatsoever, whereas a value of 1 represents complete confidence in the other party, as in the case where one party regards another as a close trusted friend or family member. There are currently three parties in our example, co-owners #1 and #2, and a third party (potential future co-owner #3) interested in buying an ownership interest from co-owner #2. The value for CFac21 reflects the confidence that co-owner #2, who wishes to create the dividend, has in his co-owner, #1. The value for CFac23 is a measure of the confidence that co-owner #2 has in the third party, potential future co-owner #3, etc. Table 1 identifies the relevant confidence factors and their associated scenario outcomes. Recall that co-owner #1 has no desire to create a homemade dividend and never possesses less than half an ownership interest in the firm. Again, although #1 may not be unilaterally able to impose a change in established policy, she can always unilaterally prevent other co-owners from doing so. Therefore, the level of trust she has in the other co-owner(s), as would be reflected in CFac12 and CFac13, is irrelevant to the analysis.

Table 1.

Relationships among Scenario Outcomes and Confidence Factors.

Scenario Outcome

2 Co-Owners

I

CFac21 = 1

II

CFac21 < 1

III




3 Co-Owners CFac21 < 1 and 3  CFac23 = 1 4 CFac31 < 1 5 or CFac31 = 1 CFac32 < 1 CFac32 = 1  CFac31 = 1 CFac32 < 1  CFac31 < 1 CFac32 < 1 2

CFacij denotes the confidence that co-owner i has in co-owner j. There are up to three co-owners: co-owner #1 who wishes to retain at least half ownership of the firm, #2 who wishes to sell some of his ownership interest to create an artificial (or homemade) dividend, and #3 who wishes to purchase an ownership interest from #2.

Dividend Irrelevance and Firm Control

161

If we assume that co-owner #1 is someone co-owner #2 can trust completely, so that CFac21 = 1, then “collusion” (cooperation) of the two co-owners results in creation of the dividend for #2 with #1 agreeing not to consume perks. Co-owner #2 sells to co-owner #1, and we have Scenario I above. Since no perks are consumed, no value is “destroyed” via the dividend creation process. One might consider such a scenario with family members. A father might sell an ownership interest to his son when nearing retirement, trusting the son not to consume perks, rightly or wrongly. A sibling might sell an interest to another sibling to create a homemade dividend, again trusting his/her sibling not to consume perks. If, however, CFac21 < 1, then the dollar “cost” to co-owner #2 (in Scenario II) of less than complete confidence in #1 is reflected in the difference between the levels of W2* for Scenarios I and II. Specifically, that difference equals P/2, that is, half the cost of the perks that #1 is expected to consume in Scenario II. This cost could induce #2 to decide to sell to a third party, potential future co-owner #3. When selling to a third party (in which case, CFac21 < 1), other confidence factors also become important. For CFac23 = 1; CFac32 = 1, and CFac31 < 1, co-owner #2 and potential future co-owner #3 can trust each other to vote to thwart #1’s intention to consume perks. As a result of collusion of #2 and #3, the effects on firm value and the total wealth of each of the two co-founding owners are the same as in Scenario I (i.e., none). This might be the case if co-owners #1 and #2 are not family and #2 sells to a third party who is a trusted family relation. Interestingly, if co-owner #2 sells to a third party where CFac31 = 1 and CFac32 < 1 (regardless of the value for CFac23 ), then collusion of co-owners #1 and #3 causes the effects on firm value and the total wealth of the two co-founding owners to be the same as in either Scenario I or II, depending upon any previous agreement between #1 and #3 regarding perk consumption. If the effects are to be the same as in II, then #3 pays #2 an amount for the ownership interest that is discounted to reflect the above-mentioned mutually agreed level of perk consumption into the future. In fact, #1 can even agree in advance to share perks with #3 (still at the expense of #2). However, for CFac31 < 1 and CFac32 < 1 (regardless of the value for CFac23 ), we have Scenario III. The third party (future co-owner #3) contracts for a level of perk consumption, and then pays a value for the ownership interest that discounts future perk consumption plus associated “deadweight” costs. Even if perk consumption is contracted to be at zero, the value of the firm is reduced by these deadweight cost of monitoring and enforcing the contract. This is consistent with Myers and Majluf’s (1984)

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STEVEN A. DENNIS AND WILLIAM STEVEN SMITH

conclusions that outside equity will be expensive to procure, relative to internally generated funds. If indeed CFac31 < 1 and CFac32 < 1, then the dollar “cost” to #2 (in Scenario III) of less than complete confidence in #1 is reflected in the difference between the levels of W2* for Scenarios I and III. Specifically, that difference equals (P + M)/2, that is, half the combined expected future perk consumption and associated deadweight costs. The cost of #1’s expected perk consumption (P) in Scenario III must be less than that from Scenario II such that the sum P + M in Scenario III is no greater than P from Scenario II. Otherwise, #2 would be better off selling to #1 rather than to a third party (potential co-owner #3). Overall therefore, if CFac32 < 1 (with any value for CFac31), then the dollar cost to #2 (across both Scenarios II and III) of less than complete confidence in #1 is equal to the minimum of P/2 from Scenario II and (P + M)/2 from Scenario III. Note that each of co-owners #1 and #2 will prefer “inside money,” someone who trusts him, or her, completely. As ownership interests are sold to “outsiders,” a market for those interests is made at a lower price, reducing the wealth of both co-owners #1 and #2. Moreover, #2 will likely need to sell a larger proportionate ownership interest to generate a homemade dividend of a given dollar size. Note also that any ownership interest in the firm has two prices, one if sold to a third party who completely trusts either co-owner #1 or #2, and another if sold to an outsider who completely trusts neither of these two co-founding owners. This may be a reason for the existence of “sale restrictions” in company bylaws, which restrict the selling of shares to outside parties.

CONCLUSION We have shown that when firm control is important, dividend policy is relevant because owners of a firm where control is important have limited abilities to create a homemade dividend. In our example concerning co-founders of a firm, any attempt to create a homemade dividend may decrease the value of the firm because the selling of any ownership interest allows the controlling co-founder to consume (additional) perks. Therefore, we have shown that an implicit assumption in Miller and Modigliani (1961) is that ownership is sufficiently diffuse such that control issues can be ignored.

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We introduce a “confidence factor” into financial markets, and we show that if the selling co-founder can completely trust the other co-founder, then the two partners can cooperate to create a homemade dividend costlessly. However, if the partners trust each other less than completely, a co-founder may decide to sell the ownership interest to a third party. If an ownership interest can be sold to a third party who completely trusts either of the co-founders, and especially the selling co-founder, then the homemade dividend may be created costlessly. Conversely, if the third party completely trusts neither of the co-founders, then he pays a price for the ownership interest that reflects the discounted value of future perk consumption and any “deadweight” costs of monitoring and enforcing the contract. Even if future perk consumption is contracted at a rate of zero, the value of the firm is reduced by these deadweight costs. Therefore, each of the co-founding owners loses wealth in the transaction. Moreover, there are two prices for any ownership interest in the firm that is sold to a third party, one if the interest is sold to an “insider” and another if the interest is sold to an “outsider.” Therefore, it may be value enhancing for the co-founders to negotiate a dividend policy when the firm is founded. In this case, the dividend policy is relevant, and it reflects the desired dividend for both parties and the bargaining power between the two. It seems, therefore, that dividend policy for a firm where control is important is idiosyncratic to the owners of the firm.

REFERENCES Brav, A., Graham, J. R., Harvey, C. R., & Michaely, R. (2005). Payout policy in the 21st century. Journal of Financial Economics, 77(3), 483
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315. DeAngelo, H., DeAngelo, L., & Stulz, R. M. (2006). Dividend policy and the earned/contributed capital mix: A test of the life-cycle theory. Journal of Financial Economics, 81(2), 227
254. Fama, E. F., & French, K. R. (2001). Disappearing dividends: Changing firm characteristics or lower propensity to pay? Journal of Financial Economics, 60(1), 3
43. Grullon, G., Michaely, R., & Swaminathan, B. (2002). Are dividend changes a sign of firm maturity? Journal of Business, 75(3), 387
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Jensen, M. C., & Meckling, W. H. (1976). Theory of the firm: Managerial behavior, agency costs and ownership structure. Journal of Financial Economics, 3(4), 305
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425.

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APPENDIX A. Composition of PVGO Let rc denote the continuously compounded nominal return per year, constant over time, the ownership requires for the firm’s investment opportunity set (IOS) into the future. Thus, recalling that r is the annually compounded return required by the ownership, r = erc − 1. Also, let r t represent the continuously compounded return the ownership expects the IOS to provide over future year t, such that r t > r t þ 1 > rc for t = 1; …; n − 1 and r t = rc for all t > n and some arbitrary n >> 1 (recall assumptions 5 and 6 in section “Development of a Formal Model”). Since ownership maintains a policy of retaining (and re-investing) all the firm’s earnings ðcurrent earnings ≡ E0 Þ, 2 3 r1 E1 E ðe Þ 0 5 þ PVGO þ PVGO = 4 V∧ = r r 8 9 0 since the difference within the braces f•g on the righthand side (RHS) of A2 is positive (recalling the specification of r t ). Interestingly, the first expression within braces f•g on the RHS of A1 reflects that the ownership expects PVGO to have dropped to zero by time n
1 (recall r t = rc for all t > n), where n is the future moment the ownership expects the firm to attain the “maturity stage” of its life cycle. This result implies that firm value expected as of n
1 can be derived as if ownership had decided to receive as dividends all earnings per year expected subsequently.

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B. Effect of One-Time Dividend on Dividend Relevance Now, suppose the ownership decides to pay itself a one-time dividend equal to some proportion, 1 − ∝, 0 < ∝ < 1, of current earnings ðE0 Þ: Accordingly, letting the subscript ∝ refer to the moment immediately after the decision, E1ð∝Þ = E0 þ ∝E0 ðer1 − 1Þ = E0 ½1 þ ∝ðer1 − 1Þ such that 2 3 r1 E0 ðe Þ5 þ PVGO ∝ V∝ = 4 r  Pn  rt − rc ðn − 1Þ 2 E0 ½1 þ ∝ðe − 1Þ e r1

=

r

ðB1Þ

implying  Pn    E0 r − r ðn − 1Þ r1 r t c 1 ½1 þ ∝ðe − 1Þ e 2 PVGO∝ = −e r

ðB2Þ

Comparing A2 and B2, since ∝ < 1 implies er1 > 1 þ ∝ðer1 − 1Þ, it must be true that PVGO > PVGO∝ and thus V∧ > V∝ . The decision causes firm value to fall, ex-dividend, by the difference PVGO − PVGO∝ . Indeed, as we can readily show, V∧ − V∝ ð = PVGO − PVGO∝ Þ 0 1  Pn  E0 = @ A e 2 rt − rc ðn − 1Þ ðer1 − 1Þð1 − ∝Þ r

ðB3Þ

which exceeds E0 ð1 − ∝Þ, the dollar amount of the dividend. Hence, firm value falls, ex-dividend, by more than the amount of the dividend (paid from earnings), implying dividend policy is relevant where PVGO > 0.

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However, if it’s actually the case that r t = rc for all t (as would generally be the case for a firm that had reached the maturity stage of its life cycle), then PVGO = 0. B3 reduces to E0 ð1 − ∝Þ, recalling r = erc − 1, reflecting that firm value falls, ex-dividend, by only a dollar amount equal to the dividend. Thus, dividend policy is irrelevant where PVGO = 0.