Optimal Hedge Fund Allocation with Improved Estimates for Coskewness and Cokurtosis Parameters

Abstract

Since hedge fund returns are not normally distributed, mean–variance optimization techniques are not appropriate and should be replaced by optimization procedures incorporating higher-order moments of portfolio returns. In this context, optimal portfolio decisions involving hedge funds require not only estimates for covariance parameters but also estimates for coskewness and cokurtosis parameters. This is a formidable challenge that severely exacerbates the dimensionality problem already present with mean–variance analysis. This article presents an application of the improved estimators for higher-order co-moment parameters, in the context of hedge fund portfolio optimization. The authors find that the use of these enhanced estimates generates a significant improvement for investors in hedge funds. The authors also find that it is only when improved estimators are used and the sample size is sufficiently large that portfolio selection with higher-order moments consistently dominates mean–variance analysis from an out-of-sample perspective. Their results have important potential implications for hedge fund investors and hedge fund of funds managers who routinely use portfolio optimization procedures incorporating higher moments.