Risk Measures for Hedge Funds: A Cross-Sectional Approach

Abstract

This paper analyzes the risk-return trade-off in the hedge fund industry. We compare semi-deviation, value-at-risk (VaR), Expected Shortfall (ES), and Tail Risk (TR) with standard deviation at the individual fund level as well as the portfolio level. Using the Fama and French (1992) methodology and the combined live and defunct hedge fund data from TASS, we find that the left-tail risk captured by the Expected Shortfall (ES) and Tail Risk (TR) explains the cross-sectional variation in hedge fund returns very well, while the other risk measures provide statistically insignificant or marginally significant results. During the period between January 1995 and December 2004, hedge funds with high ES outperform those with low ES by an annual return difference of 7%. We provide empirical evidence on the theoretical argument by Artzner et al. (1999) that ES is superior to VaR as a downside risk measure. We also find the Cornish-Fisher (1937) expansion is superior to the nonparametric method in estimating ES and TR.

Keywords: hedge funds, cross-section of expected returns, conditional VaR, downside risk, Cornish-Fisher expansion

JEL Classification: G11, G12, C31