Interactive Portfolio Optimization Using Mean-Gini Criteria

Abstract

We study a multi-objective portfolio optimization model that employs two conflicting objectives—maximizing mean return, and minimizing risk as measured by the Gini Mean Difference (GMD). We assume that an investor’s implicit utility is a function of these two objectives and help the investor identify the optimal (i.e., most preferred) portfolio among the efficient ones. We develop an interactive solution procedure based on the concept of domination cones that can be used with a class of utility functions defined over Mean-Gini criteria. The investor’s preferences are elicited interactively through pairwise comparisons of efficient Mean-Gini portfolios based on which domination cones are derived to guide the search for the most preferred portfolio. The interactive solution method enjoys a finite convergence property. Computational results illustrating the effectiveness of the interactive procedure and the out-of-sample performance of the optimal portfolios for a range of implicit utility functions are presented. The results indicate that the optimal portfolios defined by our models consistently outperform the S&P 500 index. Further, an out-of-sample performance analysis reveals that a strategy emphasizing mean return over Gini performs best under similar market conditions over the training and testing sets, while a risk-averse strategy emphasizing Gini over mean return performs best under market reversal conditions.