Intelligent Hedge Fund Investing - Barry Schachter, Editor

Intelligent Hedge Fund Investing
Successfully Avoiding Pitfalls through Better Risk Evaluation

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CHAPTER 9

INTRODUCTION

BIBLIOGRAPHY

ERRATA AND OTHER MATERIAL

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HOW "SHARPE" ARE FUNDS OF FUNDS
Youngju Lee and Bernard Lee

INTRODUCTION

As Lee and Lee point out, the popularity of metrics like the Sharpe Ratio is such that they are likely to continue to be used, despite the existence of known problems and the existence of alternatives. Most people hate change, and having gotten accustomed to using the Sharpe Ratio in one context, investors are loathe to stop using it in other contexts.

One practical approach to dealing with the measurement problem given this fact of human behavior is to create new metrics that have the look and feel of the discredited ones, but which address some of their problems. Another approach is to carefully identify those cases in which the familiar metric can still be used effectively.

Lee and Lee focus their attention on the use of Sharpe Ratios for performance measurement in hedge funds of funds (“FoF”). Intuition suggests that measured returns to portfolios of hedge funds should exhibit more Normally distributed returns than in the individual funds (a kind of Central Limit Theorem). If that were so, then some of the basic issues with using the Sharpe Ratio would be resolved.

However, given the problems with such return series documented elsewhere, in large part based on publicly available data on returns to hedge fund indexes, we have good reason to be skeptical. Lee and Lee offer up some hope by arguing that examining FoFs, rather than hedge fund indexes is more likely to reflect the experiences of investors, and be free of much of what is known to be problematic about published returns to hedge fund indexes.

Lee and Lee find that under pretty general conditions, the Sharpe Ratio of a portfolio of hedge funds is asymptotically Normally distributed, irrespective of the shape of the return distributions of the component funds. They then find empirical support for their results by conducting Monte Carlo simulations using a proprietary database of hedge funds. In particular, they find that FoFs that contain 40 or more (randomly selected) hedge funds have Normally distributed Sharpe Ratios.

Lee and Lee conclude that there is still room for using the Sharpe Ratio in evaluating investment performance for the FoF alternative investment vehicle.

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BIBLIOGRAPHY

Blattberg, R. C. and Gonedes, N. J., 1974, "A Comparison of the Stable and Student Distribution as Statistical Models of Stock Prices," Journal of Business, 47, pp. 244-280.
Fung, W., and Hsieh, D. A., 1999, "Is Mean-Variance Analysis Applicable to Hedge Funds?" Economics Letters 62, pp. 53-58.
http://www.GloriaMundi.org/picsresources/rb-fh.pdf
Fung, W. and Hsieh, D. A., 2000, “Performance Characteristics of Hedge Funds and Commodity Funds,” Journal of Financial and Quantitative Analysis, 35(3), pp. 291-307.
http://www.GloriaMundi.org/picsresources/rb-fh1.pdf
Fung, W. and Hsieh, D. A., 2002, “Hedge-Fund Benchmarks: Information Content and Biases,” Financial Analyst Journal, 58(1), pp. 22-34.
http://www.GloriaMundi.org/picsresources/rb-fh2.pdf
L’habitant, F. and Learned, M., 2002, “Hedge Fund Diversification: How Much is Enough?” Working Paper, Thunderbird Graduate School of International Management.
http://www.GloriaMundi.org/picsresources/rb-ll.pdf
Liang, B., 2003, “The Accuracy of Hedge Fund Returns,” The Journal of Portfolio Management, 29(3), pp. 111-121.
Lo, A., 2002, “The Statistics of Sharpe Ratio,” Financial Analyst Journal, 58(4), pp. 36-52.
Markowitz, H. M., 1999, “The Early History of Portfolio Theory: 1600-1960,” Financial Analysts Journal, 55(4), pp. 5-16.
Sharpe, W. F., 1964, “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,” Journal of Finance, 19(3), pp. 425-442.
Sharpe, W. F., 1994, “The Sharpe Ratio,” Journal of Portfolio Management, Fall, pp. 49-59.