Portfolio optimization under multivariate affine generalized hyperbolic distributions

Abstract

This paper focuses on capturing the impacts of leptokurtic phenomenon and heterogeneous preferences in higher moments on asset allocation. To achieve this, we propose a utility maximization asset allocation framework under the multivariate affine generalized hyperbolic (MAGH) asset prices dynamics. With the investor’s preference given by the exponential utility, we derive the closed-form optimal asset allocations for mixed multivariate affine normal inverse Gaussian-normal model and mixed multivariate affine variance gamma-normal model, which covers Markowitz’s mean–variance model as our special case. Extensive empirical studies are conducted to assess the effectiveness of the proposed asset allocation models relative to other portfolio strategies based on the Markowitz’s mean–variance theory and the equally weighted 1/N rule. Using the out-of-sample Sharpe ratio, the certainty-equivalent return, quantile and tail metrics as the performance measures, the proposed methods are found to be very effective and robust.