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A new study by Lionel Martellini, Scientific Director of EDHEC-Risk Institute, with Giovanni Zambruno and Asmerilda Hitaj of the University of Milano – Bicocca, entitled “Optimal Hedge Fund Allocation with Improved Estimates for Coskewness and Cokurtosis Parameters,” supported by Newedge Prime Brokerage as part of the research chair on “Advanced Modelling for Alternative Investments,” aims to enhance understanding of the dynamic and non-linear relationship between hedge fund returns and the returns on underlying fundamental systematic factors, and to analyse the implications for managing portfolios that include hedge funds.
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. 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. The paper presents an application of the improved estimators for higher order co-moment parameters, recently introduced by Martellini and Ziemann (2010), in the context of hedge fund portfolio optimisation. The authors find that the use of these enhanced estimates generates a significant improvement for investors in hedge funds. They also find that it is only when improved estimators are used that portfolio selection with higher order moments consistently dominates mean-variance analysis from an out-of-sample perspective. The results have important potential implications for hedge fund investors and hedge fund of funds managers who routinely use portfolio optimisation procedures incorporating higher moments.
A copy of the EDHEC-Risk Publication “Optimal Hedge Fund Allocation with Improved Estimates for Coskewness and Cokurtosis Parameters” can be downloaded via the following link:
A copy of the working paper “Improved Estimates of Higher-Order Comoments and Implications for Portfolio Selection” can be downloaded via the following link:
This research was supported by Newedge Prime Brokerage as part of the “Advanced Modelling for Alternative Investments” research chair at EDHEC Risk Institute.
