optimizing Benchmark-Based Portfolios with Hedge Funds

JOT YAU IS a professor of finance at Mbers School of Business .iiid Economics. Seattle University in Seattle, WA. ,[email protected] T he significant growth of the hedge funds industry in the past decade has heen supplemented by increased allocations to alternative investments by high-net-worth individuals as well as endowments and foundations. In recetit years, there has been a steady shift in pension plan investment strategies toward aiternative investments and/or hedge funds. For example. Ma.ssachusetts Pension Reserve Investment Managetnent in 2()0f) allocated 5.1% of its $41.9 billion plan to hedge funds. Previous studies, e.g., Kat [2005]; Till [2005|; Amenc. Giraud. Martcllini. atid Vaissie [2004]; Coleman and Mansour |2()()5|; Amenc and Martellini [2002]; Brunei [2()04[; and Lamm [2005[ have addressed the issue of including hedge funds in a standard portfolio in a mean-variance optimization framework. This article presents an optimization methodology that takes into account various quantifiable risks of portfolios with hedge funds. The Markowitz tnean-variance approach was introduced in the early 1950s as a rational tool to help guide decisions in portfolio allocation. One of its basic assumptions is that the investor's objective is defmed as the trade-off between mean return and risk measured by variance of return. This methodology has been used to determine what is often considered as the baseline asset allocation: 60% stocks and 40% bonds.' Thus, if the investor's objective is to maximize return per unit of risk, the investor can use the mean-variance approach for portfolio allocatioti. This approach is less useful, however, if the investor's preference is different from the mean-variance criterion or if the return series is not normally distributed, as in the case of hedge funds. Regarding investors' criteria for optimal portfolios, several alternative objectives have been proposed, including the minimax ratio, the mean absolute deviation ratio, and the Sortino ratio (Sharpe [1994|; Young [I998[; Sortino [2000[; and Uryasev [2000[). In addition, previous studies have considered higher moments of the return distribution in the portfolio optimization setup. For instance, Lamm [2005] uses the Cornish-Fisher approximation in an optimization where the objective function is modified value-at-risk that incorporates asymmetry explicitly. His objective function penalizes portfolios whose return distributions have negative skewness and excess kurtosis. Return distributions of traditional asset classes, e.g., stocks and bonds, have been studied extensively. Previous studies suggest that traditional asset return series arc close to noriTuil. and thus they can be well-characterized simply by their mean and standard deviation. In contrast, hedge funds typically have nonnormal return distributions marked by significant negative skewness and excess kurtosis (Ainiii and Kat [2003[ and Lo [2001]).Since mean-variance models igtiore these higher