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

In this context, optimal portfolio decisions involving hedge fund style allocation 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 paper presents an application of the improved estimators for higherorder co-moment parameters, recently introduced by Martellini and Ziemann (2010), in the context of hedge fund portfolio optimisation. We find that the use of these enhanced estimates generates a significant improvement for investors in hedge funds. We also find that it is only when improved estimators are used that portfolio selection with higherorder moments consistently dominates mean-variance analysis from an out-ofsample perspective. Our results have important potential implications for hedge fund investors and hedge fund of funds managers who routinely use portfolio optimisation procedures incorporating higher moments.