Hedge Funds Portfolio Selection with Higher-Order Moments: A Non-Parametric Mean-Variance-Skewness-Kurtosis Efficient Frontier
29 Pages Posted: 2 Mar 2005
Date Written: February 2005
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: Suggested Citation