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Risk-adjusted performance of funds of hedge funds using a modified Sharpe ratio Authors: Greg N. Gregoriou and Jean-Pierre Gueyie Source: The Journal of Wealth Management Date: Winter 2003 |
Applied to the hedge fund universe, traditional performance measures that assume a mean-variance framework suffer from some limitations, mainly due to the non-normality of returns. The authors propose an improvement to the original Sharpe ratio through the use of the modified Value-at-Risk (MVaR). The new performance measure is named the Modified Sharpe ratio.
In the equation of the modified Sharpe ratio, the modified VaR is introduced instead of the standard deviation. It is defined as follows:
Modified Sharpe Ratio = (Rp - Rf) / MVaR
where Rp is the return of the portfolio (i.e. a hedge fund or a fund of hedge funds), Rf is the risk-free rate, and MVaR is the modified VaR.
The replacement of the standard definition by the MVaR is justified by the fact that the latter takes into account skewness and kurtosis in addition to mean and standard deviation. It is of particular interest in the case of hedge funds in order to avoid underestimating risk. It should be noted that from this angle the VaR exhibits the same shortcomings as the standard deviation.
An empirical application of the modified Sharpe ratio is examined. The data, provided by Zurich Capital Markets, covers the period from January 1997 to December 2001. The whole sample contains monthly returns of 90 live funds of hedge funds, but only 30 funds are studied: the 10 funds with the largest assets under management, the middle 10 and the bottom 10 funds. The risk-free rate Rf is assumed to be nil to simplify the ranking. The MVaR is calculated at a 95% confidence level.
Comparing the average of mean returns in each of the three groups, the top group (respectively bottom funds) exhibits the highest (lowest) mean return average. On the other hand, the most negative skewness is in the bottom group, where the standard deviation is also the highest. Considering the MVaR, the bottom funds display the highest in absolute value. In short, bottom funds are more frequently affected by extreme negative returns. Mostly, empirical results for the 30 selected funds confirm that a normal Sharpe ratio overestimates the performance in comparison with the modified Sharpe ratio, except when the normal Sharpe ratio is negative.
