The Impact of Higher Moments on Hedge Fund Risk Exposure

Abstract

It is widely known that many hedge fund return series display significant skewness, kurtosis, and serial dependence. In addition, many hedge funds claim that their return distributions are not normal due to the use of derivatives, short sales, and rebalancing rules. Although these departures from normality do not typically invalidate the application of mean-variance analysis to portfolio formation, they often lead to higher exposure to loss than implied by the assumption of normality. In this article simulation techniques are utilized to quantify the miscalculation of exposure to loss for 31 Hedge Fund Research return series. These errors are measured for both end of horizon and within-horizon probability of loss. Results show that HFR return series tend to exhibit distributions that are far different from normal. Risk calculations performed under the assumptions that continuous returns are normally distributed significantly differently from the empirical results. However, if skewness and kurtosis for the HFR returns over the period January 1999-May 2003 are calculated, the distributions of the return series are much closer to the normal distribution and the majority of the HFR strategies exhibit positive skewness.