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. If a mean-variance optimization model suggests significant allocation to hedge funds, an investor concerned about unwanted skewness and kurtosis is rightfully skeptical. We apply 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: expected shortfall, semi-variance as well as the third and fourth moments of the shortfall. Our results show that a substantial allocation - approximately 20% - to hedge funds is justified even after taken into consideration their unusual skewness and kurtosis. Moreover, results also show that our method produces a fund of funds with desired features. Specifically, our portfolios' return distributions skew to the right relative to those of the optimal mean-variance portfolios, resulting in higher Sortino ratios. Additionally, an out-of-sample backtest shows that our optimal benchmark-based portfolio achieves its goal - beating the selected benchmark.