As observed in Section 4.2, the rank correlations between the Sharpe ratio and the other performance measures are very high (except the Treynor ratio). The results thus prove to be very robust regarding a variation of the hedge fund portion in the portfolio.
Our second additional robustness check for this decision-making situation involved variations of the reference portfolio. For example, we altered the portfolio weights in the reference portfolio to 40% stocks, 40% bonds, 10% real estate, and 10% cash, which are probably more realistic values for a US bank. Again, our results were similar to those described above (see Table 6).
5. Conclusion
The main result from our empirical investigation is that the choice of performance measure does not affect the ranking of hedge funds as much as one would expect after studying the performance measurement literature. It appears that, even though hedge fund returns are not normally distributed, the first two moments (i.e., mean and variance) describe the return distribution sufficiently well.
A possible explanation might be that hedge fund returns are elliptically distributed. Note that mean-variance analysis can be used for elliptical distributions, and not only for multivariate normal distributions.[14] Lhabitant (2004, p. 312) finds evidence for elliptically distributed hedge funds returns. He observes a good statistical fit using the lognormal, the logistic, the Weibull, or the generalized beta distribution, which all belong to the group of elliptical distributions. For our data set we can confirm this finding.
What are the implications of our results? From a practical point of view, the choice of performance measure does not have a crucial influence on the relative evaluation of hedge funds. For example, in the portfolio context there are 98 hedge funds among the top 100 funds according to an evaluation made using the Sharpe ratio, which are also among the top 100 funds according to an evaluation made using Omega. Taking into account that the Sharpe ratio is the best known (see Modigliani and Modigliani, 1997) and best understood performance measure (see Lo, 2002), it might be considered superior to other performance measures from a practitioner’s point of view.
Furthermore, from a theoretical point of view, the Sharpe ratio is consistent with expected utility maximization under the assumption of elliptically distributed returns. Even without the assumption of elliptically distributed returns, Fung and Hsieh (1999) have shown that mean-variance analysis of hedge funds approximately preserves the ranking of preferences in standard utility functions.
We thus conclude that from a practical as well as from a theoretical point of view the Sharpe ratio is adequate for analyzing hedge funds. As shown by Dowd (2000), the Sharpe ratio can be used both when the hedge fund represents the entire risky investment and when it represents only a portion of the investor’s risky investment.
2646 M. Eling, F. Schuhmacher / Journal of Banking & Finance 31 (2007) 2632–2647
Acknowledgements
The authors thank the participants of the Financial Management Association European Conference (Stockholm, June 2006), the Research Workshop on Portfolio Performance Evaluation and Asset Management (Madrid, May 2006), the 9th Conference of the Swiss Society for Financial Market Research (Zu¨rich, April 2006), the 10th Symposium on Finance, Banking, and Insurance (Karlsruhe, December 2005), and the German Operations Research Society Conference 2005 (Bremen, September 2005). We are grateful to two anonymous referees and to Giorgio P. Szego¨, the editor of this journal. We also thank Florian Hach (ehedge) and Dee Weber (CISDM) for providing the data.
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