Hedge Funds Portfolio Selection with Higher-Order Moments: A Non-Parametric Mean-Variance-Skewness-Kurtosis Efficient Frontier

29 Pages Posted: 2 Mar 2005

See all articles by Emmanuel Jurczenko

Emmanuel Jurczenko

Glion Institute of Higher Education

Bertrand B. Maillet

EMLyon Business School (Paris Campus)

Paul Merlin

TEAM/CNRS and SAMOS /MATISSE

Date Written: February 2005

Abstract

This paper proposes a non-parametric optimization criterion for the static portfolio selection problem in the mean-variance-skewness-kurtosis space. Following the work of Briec et al. (2004-a and 2004-b), a shortage function is defined in the four-moment space that looks simultaneously for possible improvements in the expected portfolio return, variance, skewness and kurtosis directions. This new approach allows us to solve for multiple competing and often conflicting asset allocation objectives within a mean-variance-skewness-kurtosis framework. The global optimality is here guaranteed for the resulting optimal portfolios. We also establish a link to a proper indirect four-moment utility function. An empirical application on funds of hedge funds serves to provide a three-dimensional representation of the primal non-convex mean-variance-skewness-kurtosis efficient portfolio set and to illustrate the computational tractabilty of the approach.

Keywords: Shortage Function, Efficient Frontier, Skewness, Kurtosis

JEL Classification: G110, G120

Suggested Citation

Jurczenko, Emmanuel and Maillet, Bertrand B. and Merlin, Paul, Hedge Funds Portfolio Selection with Higher-Order Moments: A Non-Parametric Mean-Variance-Skewness-Kurtosis Efficient Frontier (February 2005). Available at SSRN: https://ssrn.com/abstract=676904 or http://dx.doi.org/10.2139/ssrn.676904

Emmanuel Jurczenko

Glion Institute of Higher Education ( email )

Route de Glion 111
Montreux, 1823
Switzerland

Bertrand B. Maillet (Contact Author)

EMLyon Business School (Paris Campus) ( email )

23 Avenue Guy de Collongue
Ecully, 69132
France

Paul Merlin

TEAM/CNRS and SAMOS /MATISSE ( email )

3, rue Michel-Ange
Paris cedex 16, 75794
France

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