Optimizing Benchmark-Based Portfolios with Hedge Funds

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. This article introduces a new stochastic programming model which incorporates Monte Carlo simulation and optimization to examine the effects on the optimal allocation to hedge funds given benchmark related investment objectives such as expected shortfall and semi-variance. The results show that a substantial allocation—approximately 20% to hedge funds is justified. Specifically, the return distributions of portfolios constructed using the stochastic programming model skew to the right relative to those of the optimal mean-variance portfolios, resulting in higher Sortino ratios.