Hedge Funds: An Analytic Perspective (New Edition)

Hedge Funds: An Analytic Perspective (New Edition)

by Andrew W. Lo
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Princeton University Press


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Hedge Funds: An Analytic Perspective (New Edition)

The hedge fund industry has grown dramatically over the last two decades, with more than eight thousand funds now controlling close to two trillion dollars. Originally intended for the wealthy, these private investments have now attracted a much broader following that includes pension funds and retail investors. Because hedge funds are largely unregulated and shrouded in secrecy, they have developed a mystique and allure that can beguile even the most experienced investor. In Hedge Funds, Andrew Lo—one of the world's most respected financial economists—addresses the pressing need for a systematic framework for managing hedge fund investments.

Arguing that hedge funds have very different risk and return characteristics than traditional investments, Lo constructs new tools for analyzing their dynamics, including measures of illiquidity exposure and performance smoothing, linear and nonlinear risk models that capture alternative betas, econometric models of hedge fund failure rates, and integrated investment processes for alternative investments. In a new chapter, he looks at how the strategies for and regulation of hedge funds have changed in the aftermath of the financial crisis.

Product Details

ISBN-13: 9780691145983
Publisher: Princeton University Press
Publication date: 07/26/2010
Series: Advances in Financial Engineering Series
Edition description: Updated
Pages: 416
Sales rank: 788,200
Product dimensions: 6.10(w) x 9.20(h) x 1.00(d)

About the Author

Andrew W. Lo is the Harris & Harris Group Professor at the MIT Sloan School of Management, and director of the MIT Laboratory for Financial Engineering. He is the coauthor of A Non-Random Walk Down Wall Street and The Econometrics of Financial Markets (both Princeton).

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Copyright © 2010 Princeton University Press
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ISBN: 978-0-691-14598-3

Chapter One


One of the fastest growing sectors of the financial services industry is the hedge fund or alternative-investments sector, currently estimated at more than $1 trillion in assets worldwide. One of the main reasons for such interest is the performance characteristics of hedge funds-often known as "high-octane" investments: Many hedge funds have yielded double-digit returns for their investors and, in many cases, in a fashion that seems uncorrelated with general market swings and with relatively low volatility. Most hedge funds accomplish this by maintaining both long and short positions in securities-hence the term "hedge" fund-which, in principle, gives investors an opportunity to profit from both positive and negative information while at the same time providing some degree of "market neutrality" because of the simultaneous long and short positions. Long the province of foundations, family offices, and high-net-worth investors, alternative investments are now attracting major institutional investors such as large state and corporate pension funds, insurance companies, and university endowments, and efforts are underway to make hedge fund investments available to individual investors through more traditional mutual fund investment vehicles.

However, many institutional investors are not yet convinced that alternative investments comprise a distinct asset class, i.e., a collection of investments with a reasonably homogeneous set of characteristics that are stable over time. Unlike equities, fixed income instruments, and real estate-asset classes each defined by a common set of legal, institutional, and statistical properties-alternative investments is a mongrel categorization that includes private equity, risk arbitrage, commodity futures, convertible bond arbitrage, emerging-market equities, statistical arbitrage, foreign currency speculation, and many other strategies, securities, and styles. Therefore, the need for a set of portfolio analytics and risk management protocols specifically designed for alternative investments has never been more pressing.

Part of the gap between institutional investors and hedge fund managers is due to differences in investment mandate, regulatory oversight, and business culture between the two groups, yielding very different perspectives on what a good investment process should look like. For example, a typical hedge fund manager's perspective can be characterized by the following statements:

The manager is the best judge of the appropriate risk/reward trade-off of the portfolio and should be given broad discretion in making investment decisions. Trading strategies are highly proprietary and therefore must be jealously guarded lest they be reverse-engineered and copied by others. Return is the ultimate and, in most cases, the only objective. Risk management is not central to the success of a hedge fund. Regulatory constraints and compliance issues are generally a drag on performance; the whole point of a hedge fund is to avoid these issues. There is little intellectual property involved in the fund; the general partner is the fund.

Contrast these statements with the following characterization of a typical institutional investor:

As fiduciaries, institutions need to understand the investment process before committing to it. Institutions must fully understand the risk exposures of each manager and, on occasion, may have to circumscribe the manager's strategies to be consistent with the institution's overall investment objectives and constraints. Performance is not measured solely by return but also includes other factors such as risk adjustments, tracking error relative to a benchmark, and peer group comparisons. Risk management and risk transparency are essential. Institutions operate in a highly regulated environment and must comply with a number of federal and state laws governing the rights, responsibilities, and liabilities of pension plan sponsors and other fiduciaries. Institutions desire structure, stability, and consistency in a well-defined investment process that is institutionalized-not dependent on any single individual.

Now, of course, these are rather broad-brush caricatures of the two groups, made extreme for clarity, but they do capture the essence of the existing gulf between hedge fund managers and institutional investors. However, despite these differences, hedge fund managers and institutional investors clearly have much to gain from a better understanding of each other's perspectives, and they do share the common goal of generating superior investment performance for their clients. One of the purposes of this monograph is to help create more common ground between hedge fund managers and investors through new quantitative models and methods for gauging the risks and rewards of alternative investments.

This might seem to be more straightforward a task than it is because of the enormous body of literature on investments and quantitative portfolio management. However, several recent empirical studies have cast some doubt on the applicability of standard methods for assessing the risks and returns of hedge funds, concluding that they can often be quite misleading. For example, Asness, Krail, and Liew (2001) show that in some cases where hedge funds purport to be market neutral (namely, funds with relatively small market betas), including both contemporaneous and lagged market returns as regressors and summing the coefficients yields significantly higher market exposure. Getmansky, Lo, and Makarov (2004) argue that this is due to significant serial correlation in the returns of certain hedge funds, which is likely the result of illiquidity and smoothed returns. Such correlation can yield substantial biases in the variances, betas, Sharpe ratios, and other performance statistics. For example, in deriving statistical estimators for Sharpe ratios of a sample of mutual funds and hedge funds, Lo (2002) shows that the correct method for computing annual Sharpe ratios based on monthly means and standard deviations can yield point estimates that differ from the naive Sharpe ratio estimator by as much as 70%.

These empirical facts suggest that hedge funds and other alternative investments have unique properties, requiring new tools to properly characterize their risks and expected returns. In this monograph, we describe some of these unique properties and propose several new quantitative measures for modeling them.

One of the justifications for the unusually rich fee structures that characterize hedge fund investments is the fact that these funds employ active strategies involving highly skilled portfolio managers. Moreover, it is common wisdom that the most talented managers are first drawn to the hedge fund industry because the absence of regulatory constraints enables them to make the most of their investment acumen. With the freedom to trade as much or as little as they like on any given day, to go long or short any number of securities and with varying degrees of leverage, and to change investment strategies at a moment's notice, hedge fund managers enjoy enormous flexibility and discretion in pursuing performance. But dynamic investment strategies imply dynamic risk exposures, and while modern financial economics has much to say about the risk of static investments-the market beta is sufficient in this case-there is currently no single measure of the risks of a dynamic investment strategy.

These challenges have important implications for both managers and investors since both parties seek to manage the risk/reward trade-offs of their investments. Consider, for example, the now-standard approach to constructing an optimal portfolio in the mean-variance sense:




where [R.sub.i] is the return of security i between this period and the next, [W.sub.1] is the individual's next period's wealth (which is determined by the product of {[R.sub.i]} and the portfolio weights {[R.sub.i]}), and U(?) is the individual's utility function. By assuming that U(?) is quadratic or by assuming that individual security returns [R.sub.i] are normally distributed random variables, it can be shown that maximizing the individual's expected utility is tantamount to constructing a mean-variance optimal portfolio [[omega].sup.*].

It is one of the great lessons of modern finance that mean-variance optimization yields benefits through diversification, the ability to lower volatility for a given level of expected return by combining securities that are not perfectly correlated. But what if the securities are hedge funds, and what if their correlations change over time, as hedge funds tend to do (Section 1.2)? Table 1.1 shows that for the two-asset case with fixed means of 5% and 30%, respectively, and fixed standard deviations of 20% and 30%, respectively, as the correlation [rho] between the two assets varies from -90% to 90%, the optimal portfolio weights-and the properties of the optimal portfolio-change dramatically. For example, with a -30% correlation between the two funds, the optimal portfolio holds 38.6% in the first fund and 61.4% in the second, yielding a Sharpe ratio of 1.01. But if the correlation changes to 10%, the optimal weights change to 5.2% in the first fund and 94.8% in the second, despite the fact that the Sharpe ratio of the new portfolio, 0.92, is virtually identical to the previous portfolio's Sharpe ratio. The mean-variance-efficient frontiers are plotted in Figure 1.1 for various correlations between the two funds, and it is apparent that the optimal portfolio depends heavily on the correlation structure of the underlying assets. Because of the dynamic nature of hedge fund strategies, their correlations are particularly unstable over time and over varying market conditions, as we shall see in Section 1.2, and swings from -30% to 30% are not unusual.

Table 1.1 shows that as the correlation between the two assets increases, the optimal weight for asset 1 eventually becomes negative, which makes intuitive sense from a hedging perspective even if it is unrealistic for hedge fund investments and other assets that cannot be shorted. Note that for correlations of 80% and greater, the optimization approach does not yield a well-defined solution because a mean-variance-efficient tangency portfolio does not exist for the parameter values we hypothesized for the two assets. However, numerical optimization procedures may still yield a specific portfolio for this case (e.g., a portfolio on the lower branch of the mean-variance parabola) even if it is not optimal. This example underscores the importance of modeling means, standard deviations, and correlations in a consistent manner when accounting for changes in market conditions and statistical regimes; otherwise, degenerate or nonsensical "solutions" may arise.

To illustrate the challenges and opportunities in modeling the risk exposures of hedge funds, we provide three extended examples in this chapter. In Section 1.1, we present a hypothetical hedge fund strategy that yields remarkable returns with seemingly little risk; yet a closer examination reveals a different story. In Section 1.2, we show that correlations and market beta are sometimes incomplete measures of risk exposure for hedge funds, and that such measures can change over time, in some cases quite rapidly and without warning. And in Section 1.3, we describe one of the most prominent empirical features of the returns of many hedge funds-large positive serial correlation-and argue that serial correlation can be a very useful proxy for liquidity risk. These examples will provide an introduction to the more involved quantitative analysis in Chapters 3-8 and serve as motivation for an analytical approach to alternative investments. We conclude by presenting a brief review of the burgeoning hedge fund literature in Section 1.4.

1.1 Tail Risk

Consider the 8-year track record of a hypothetical hedge fund, Capital Decimation Partners, LP. (CDP), summarized in Table 1.2. This track record was obtained by applying a specific investment strategy, to be revealed below, to actual market prices from January 1992 to December 1999. Before discussing the particular strategy that generated these results, consider its overall performance: an average monthly return of 3.6% versus 1.4% for the S&P 500 during the same period; a total return of 2,560% over the 8-year period versus 367% for the S&P 500; a Sharpe ratio of 2.15 versus 1.39 for the S&P 500; and only 6 negative monthly returns out of 96 versus 36 out of 96 for the S&P 500. In fact, the monthly performance history-displayed in Table 1.3-shows that, as with many other hedge funds, the worst months for this fund were August and September of 1998. Yet October and November of 1998 were the fund's two best months, and for 1998 as a whole the fund was up 87.3% versus 24.5% for the S&P 500! By all accounts, this is an enormously successful hedge fund with a track record that would be the envy of most managers. What is its secret?

The investment strategy summarized in Tables 1.2 and 1.3 consists of shorting out-of-the-money S&P 500 put options on each monthly expiration date for maturities less than or equal to 3 months and with strikes approximately 7% out of the money. According to Lo (2001), the number of contracts sold each month is determined by the combination of: (1) Chicago Board, Options Exchange (CBOE) margin requirements; (2) an assumption that the fund is required to post 66% of the margin as collateral; and (3) $10 million of initial risk capital. For concreteness, Table 1.4 reports the positions and profit/loss statement for this strategy for 1992.

The essence of this strategy is the provision of insurance. CDP investors receive option premia for each option contract sold short, and as long as the option contracts expire out of the money, no payments are necessary. Therefore, the only time CDP experiences losses is when its put options are in the money, i.e., when the S&P 500 declines by more than 7% during the life of a given option. From this perspective, the handsome returns to CDP investors seem more justifiable-in exchange for providing downside protection, CDP investors are paid a risk premium in the same way that insurance companies receive regular payments for providing earthquake or hurricane insurance.

The track record in Tables 1.2 and 1.3 seems much less impressive in light of the simple strategy on which it is based, and few investors would pay hedge fund-type fees for such a fund. However, given the secrecy surrounding most hedge fund strategies, and the broad discretion that managers are given by the typical hedge fund offering memorandum, it is difficult for investors to detect this type of behavior without resorting to more sophisticated risk analytics, analytics that can capture dynamic risk exposures.

Some might argue that this example illustrates the need for position transparency-after all, it is apparent from the positions in Table 1.1 that the manager of Capital Decimation Partners is providing little or no value-added. However, there are many ways of implementing this strategy that are not nearly so transparent, even when positions are fully disclosed. For example, Table 1.5 reports the weekly positions over a 6-month period in 1 of 500 securities contained in a second hypothetical fund, Capital Decimation Partners II. Casual inspection of the positions of this one security seems to suggest a contrarian trading strategy: When the price declines, the position in XYZ is increased, and when the price advances, the position is reduced. A more careful analysis of the stock and cash positions and the varying degree of leverage in Table 1.5 reveals that these trades constitute a delta-hedging strategy designed to synthetically replicate a short position in a 2-year European put option on 10 million shares of XYZ with a strike price of $25 (recall that XYZ's initial stock price was $40; hence this is a deep out-of-the-money put).

Shorting deep out-of-the-money puts is a well-known artifice employed by unscrupulous hedge fund managers to build an impressive track record quickly, and most sophisticated investors are able to avoid such chicanery. However, imagine an investor presented with a position report such as Table 1.5, but for 500 securities, not just 1, as well as a corresponding track record that is likely to be even more impressive than that of Capital Decimation Partners, L.P. Without additional analysis that explicitly accounts for the dynamic aspects of the trading strategy described in Table 1.5, it is difficult for an investor to fully appreciate the risks inherent in such a fund.


Excerpted from HEDGEFUNDS by ANDREW W. LO Copyright © 2010 by Princeton University Press. Excerpted by permission.
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Table of Contents

List of Tables xi

List of Figures xvii

List of Color Plates xxi

Acknowledgments xxiii

Chapter 1: Introduction 1

1.1 Tail Risk 7

1.2 Nonlinear Risks 13

1.3 Illiquidity and Serial Correlation 25

1.4 Literature Review 30

Chapter 2: Basic Properties of Hedge Fund Returns 34

2.1 CS/Tremont Indexes 37

2.2 Lipper TASS Data 40

2.3 Attrition Rates 43

Chapter 3: Serial Correlation, Smoothed Returns, and Illiquidity 64

3.1 An Econometric Model of Smoothed Returns 66

3.2 Implications for Performance Statistics 70

3.3 Estimation of Smoothing Profiles 75

3.4 Smoothing-Adjusted Sharpe Ratios 79

3.5 Empirical Analysis of Smoothing and Illiquidity 83

Chapter 4: Optimal Liquidity 97

4.1 Liquidity Metrics 98

4.2 Liquidity-Optimized Portfolios 105

4.3 Empirical Examples 107

4.4 Summary and Extensions 117

Chapter 5: Hedge Fund Beta Replication 121

5.1 Literature Review 123

5.2 Two Examples 124

5.3 Linear Regression Analysis 126

5.4 Linear Clones 138

5.5 Summary and Extensions 164

Chapter 6: A New Measure of Active Investment Management 168

6.1 Literature Review 170

6.2 The AP Decomposition 172

6.3 Some Analytical Examples 181

6.4 Implementing the AP Decomposition 186

6.5 An Empirical Application 193

6.6 Summary and Extensions 197

Chapter 7: Hedge Funds and Systemic Risk 198

7.1 Measuring Illiquidity Risk 200

7.2 Hedge Fund Liquidations 203

7.3 Regime-Switching Models 211

7.4 The Current Outlook 215

Chapter 8: An Integrated Hedge Fund Investment Process 217

8.1 Define Asset Classes by Strategy 221

8.2 Set Portfolio Target Expected Returns 222

8.3 Set Asset-Class Target Expected Returns and Risks 222

8.4 Estimate Asset-Class Covariance Matrix 223

8.5 Compute Minimum-Variance Asset Allocations 224

8.6 Determine Manager Allocations within Each Asset Class 225

8.7 Monitor Performance and Risk Budgets 227

8.8 The Final Specification 227

8.9 Risk Limits and Risk Capital 229

8.10 Summary and Extensions 235

Chapter 9: Practical Considerations 237

9.1 Risk Management as a Source of Alpha 237

9.2 Risk Preferences 239

9.3 Hedge Funds and the Efficient Markets Hypothesis 242

9.4 Regulating Hedge Funds 250

Chapter 10: What Happened to the Quants in August 2007? 255

10.1 Terminology 260

10.2 Anatomy of a Long/Short Equity Strategy 261

10.3 What Happened in August 2007? 269

10.4 Comparing August 2007 with August 1998 273

10.5 Total Assets, Expected Returns, and Leverage 276

10.6 The Unwind Hypothesis 281

10.7 Illiquidity Exposure 284

10.8 A Network View of the Hedge Fund Industry 286

10.9 Did Quant Fail? 292

10.10 Qualifications and Extensions 298

10.11 The Current Outlook 300

Chapter 11: Jumping the Gates 303

11.1 Linear Risk Models 305

11.2 Beta Overlays 308

11.3 Hedging Long/Short Equity Managers 310

11.4 Dynamic Implementations of Beta Overlays 317

11.5 Conclusion 319

Appendix 323

A.1 Lipper TASS Category Definitions 323

A.2 CS/Tremont Category Definitions 325

A.3 Matlab Loeb Function tloeb 328

A.4 GMM Estimators for the AP Decomposition 330

A.5 Constrained Optimization 332

A.6 A Contrarian Trading Strategy 333

A.7 Statistical Significance of Aggregate Autocorrelations 334

A.8 Beta-Blocker and Beta-Repositioning Strategies 335

A.9 Tracking Error 339

References 341

Index 355

What People are Saying About This


Lo offers a truly unique perspective. He examines the properties of returns and illiquidity in great detail and introduces an innovative concept of mean-variance-liquidity optimization, something that no other book on hedge funds has addressed.
Narayan Y. Naik, London Business School

Richard Bookstaber

Andrew Lo's Hedge Funds is likely to be the high-water mark in the analysis of hedge funds for years to come. Focusing on hedge fund returns and trading strategies, risk characteristics, and potential for illiquidity, Lo brings to bear his always fresh and insightful thinking.
Richard Bookstaber, author of "A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation"


This book provides a useful and very timely overview of key aspects of the hedge fund industry. It summarizes the basic properties of hedge fund returns, discusses why traditional performance measures may be misleading when analyzing hedge fund performance, and highlights important issues such as serial correlation, return smoothing, and illiquidity.
Markus K. Brunnermeier, Princeton University

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