Optimal Hedge Fund Allocation with Asymmetric Preferences and Distributions

Abstract

Hedge funds typically have non-normal return distributions marked by significant positive or negative skewness and high kurtosis. Mean-variance optimization models ignore these higher moments of the return distribution, and thus fail to convince investors who care about the unwanted skewness and kurtosis that hedge funds may work well in a portfolio. We use a new method which incorporates Monte Carlo simulation and optimization to solve for a variety of investment objectives and address the special issues of hedge fund allocation. We applied the new optimization model to examine the effects of semi-variance, conditional third and fourth moments on portfolio allocation with hedge funds. We show that conditional on the investor's objective, a substantial allocation to hedge funds is justified even with consideration for the highly unusual skewness and kurtosis.