Assessing the Contribution of Hedge Funds to Portfolio Management Beyond the Mean-Variance Framework

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Based on an analysis that goes beyond the mean-variance framework, we investigate the relative performance of US hedge funds as compared to that of US stocks. As opposed to traditional buy-and-hold portfolios, hedge funds display option-like payoffs, making their returns skewed and possibly with no zero excess kurtosis. Because of these atypical characteristics, recent literature (see for example Fung and Hsieh, 2000; Brooks and Kat, 2002; Lhabitant, 2004; Agarwal and Naik, 2004) underlines the drawback of limiting the assessment of hedge funds’ performance to the first two moments of their return distributions (i.e. the mean and the variance), hence making the use of traditional measures questionable when it comes to appraising the performance of hedge funds.

To date, several analyses have been carried out to find a more appropriate way to assess the performance of hedge funds (see for example Sortino and Price, 1994; Leland, 1999; Dowd, 2000). The techniques used in those studies cover, on top of the first two moments, the skewness and/or kurtosis and even higher moments and aim at better reflecting the return distributions of hedge funds. In this same perspective, this paper uses the Data Envelopment Analysis (DEA) to investigate the relative performance of hedge funds under a framework that goes up to the fourth moment of their return distribution.

Based on monthly returns from a sample of 856 hedge funds and 490 stocks covering the period of January 1999 – February 2014, we apply a directional DEA model to compare the performance of hedge funds to that of stocks both under a mean-variance framework and under a four-dimensional framework. Empirical findings from this study show that hedge funds appear significantly more efficient than stocks when only the mean and the variance of returns are considered. However, this higher efficiency disappears as far as the skewness and the excess kurtosis are taken into account. Results from this empirical analysis are in line with the recent literature as they highlight the importance of considering the skewness and the excess kurtosis when assessing the performance of hedge funds.

Afrae Hassouni