Asymmetric Returns and Optimal Hedge Fund Portfolios

THE JOURNAL OF ALTERNATIVE INVESTMENTS 9 I t is now well established that the construction of optimal hedge fund portfolios requires techniques that reach well beyond traditional mean variance analysis. For example, Brooks and Kat [2002] demonstrate that various hedge fund strategies have more downside than upside risk—returns exhibit negative skew and excess kurtosis. Lo [2001] and Anson [2002] argue much the same from a conceptual perspective. Krokhmal, Uryasev, and Zrazhevsky [2002] and Signer and Favre [2002] demonstrate that assuming normality in hedge fund returns leads to portfolios that are more risky than in the case when asymmetry is explicitly considered. If certain hedge fund strategies have more downside than upside risk, and one must take this into account in building portfolios, what is the best approach? Unfortunately, there is no easy answer. A myriad of various risk metrics and optimization approaches have been proposed as solutions. None have emerged to universal acceptance as of yet. That said, several methods appear to offer acceptable avenues for practitioners engaged in building and managing hedge fund portfolios. In this article, I leverage off of recent work and compare various optimization techniques applied to hedge fund portfolio construction. I specifically focus on strategy allocation, as opposed to the more general problem of allocating to stocks, bonds, and hedge funds, which was the thrust of most prior research. The first section provides a brief background on the issue of asymmetric returns and the implications for optimization. In the second section, I apply common portfolio optimization techniques to the hedge fund strategy allocation problem employing Duarte’s general model, which views portfolio optimization as a single problem from which other techniques fall out as special cases. The third section examines the Cornish-Fisher expansion as an efficient and promising methodology when applied to hedge fund strategies. My major conclusion is that the incorporation of asymmetry produces significantly different hedge fund portfolios than in the situation when returns are viewed as symmetric. In particular, I find that optimal hedge fund portfolios should have up to a 30% smaller allocation to distressed debt than symmetric return models indicate. This is due to the fact that downside risk for distressed debt is unusually high. The lower allocations to distressed debt are offset by larger allocations to equity market neutral, rotational, and systematic macro strategies, which produce more positively skewed portfolios.