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

Since hedge fund returns are not normally distributed, mean-variance optimisation techniques, which would lead to substantial welfare losses from the investor’s perspective, need to be replaced by optimisation procedures incorporating higher-order moments and comoments.


Asmerilda Hitaj

Junior researcher at the University of Milano - Bicocca (Italy).

Lionel Martellini

Professor of finance at EDHEC Business School and scientific director of EDHEC-Risk Institute.

Giovanni Zambruno

Holds the chair of Mathematical Finance at the University of Milano - Bicocca.

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.

Type: EDHEC Publication
Date: le 28/09/2010
Research Cluster : Finance

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