Risk Measures for Hedge Funds: a Cross‐sectional Approach

Abstract

"This paper analyses 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 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." Copyright 2007 The Authors Journal compilation (c) 2007 Blackwell Publishing Ltd.

A Correction for Classic Performance Measures

“…In such a case, mean and variance moments are no more sufficient to describe assets' risk levels so that returns' volatility (i.e., standard deviation) misestimates hedge fund risks (Kat, 2005;Khanniche, 2008;Liang & Park, 2007). Therefore, the significance of the higher moments above-mentioned biases the ranking inferred from the previous Gaussian-based performance measures.…”

“…Namely, the mean-variance framework underestimates the downside risk as represented by the risk related to negative outcomes (Agarwal & Naik, 2004). And, the left-tail risk as represented by the skewness statistic may grow as the portfolio's (i.e., the fund's) diversification level increases (Harvey, Liechty, & Müller, 2004;Liang & Park, 2007). By the way, Goldman (2003) and Hull (2006Hull ( , 2007 show that probability-based measures such as…”

“…Indeed, Liang and Park (2007) show expected shortfall and tail risk measures to capture strongly the left-tail risk describing the cross-sectional discrepancies in hedge fund returns. Moreover, in terms of risk measure effectiveness, expected shortfall is better than VaR for measuring downside risk whereas the Cornish-Fisher setting is better than both expected shortfall and tail risk measures (after controlling for hedge funds' style, liquidity, age, and size features).…”

Efficient hedge fund style allocations: A rules-based model

“…As we allocate across different hedge fund styles, our analysis is restricted to market illiquidity. In addition, there is a growing literature that analyses the liquidity of hedge funds (as measured by various forms of share restrictions) and the relationship to returns (Aragon, 2007;Liang and Park, 2007;Khandani and Lo, 2011;Teo, 2011 andMaier et al, 2012). 7.…”

Spicing Up a Portfolio with Commodity Futures: Still a Good Recipe?

“…20 Favre and Galeano [2002]; Bali, Gokcan, and Liang [2007]; and Liang and Park [2007] use the Cornish-Fisher expansion to extend the value-at-risk (VaR) concept to a four-moment MVaR to explicitly incorporate the presence of nonnormal skewness and kurtosis.…”