Incorporating Skew in Hedge Fund Evaluation and Portfolio Allocation

Abstract

We have reason to believe that negatively-skewed assets are commonly overvalued, despite having significant downside risk. This paper investigates how the skewness of returns should change investors’ evaluation of and allocation to hedge funds. We first provide evidence to support the claim that many hedge funds have negatively skewed returns. We then propose a new evaluation benchmark for negatively-skewed funds. Finally, we discuss how investors can construct portfolios that take into account the skew of the underlying assets. We find that many common hedge fund indices have return distributions that resemble the shape of short put option payoffs, which are known to be left-skewed. We argue that when choosing a benchmark against which to measure a fund’s performance, investors should choose one with similar skew. Therefore, instead of measuring hedge fund performance relative to the S&P 500, we propose that funds be compared to a strategy of shorting monthly put options on the S&P 500. Not only should skew affect the way investors evaluate hedge fund performance, but it should also influence their capital allocation. We solve a mean-variance-skewness (MVS) portfolio optimization problem to construct an optimal portfolio across common hedge fund indices. We compare this optimal portfolio to the traditional Markowitz portfolio containing the same assets. The differences between these two portfolios provide evidence that incorporating skew in portfolio optimization should change how investors optimally allocate to hedge funds.