Mean-Extended Gini Portfolios Personalized to the Investor’s Risk-Gain Profile

Abstract

Since Shalit and Yitzhalit (1984) the Mean-Extended Gini (MEG) has been proposed as a workable alternative to the classical Markowitz mean-variance CAPM. Although MEG keeps under control the risk belonging to the left-tail of the return distribution, small attention is reserved to potential gains belonging to the return right-tail. A generalization of MEG able to select personalized optimal mean-risk and/or mean-gain portfolios is proposed. We give evidence that if the portfolio distributions are symmetrical and/or the investor has a moderate risk-gain profile, then the efficient mean-risk portfolio always coincides with the worst inefficient mean-gain portfolio. Vice versa, if we concern more realistic scenarios admitting the existence of asymmetrically distributed assets and/or investors with very defensive or very aggressive investment profiles, portfolios which are optimal under both criteria may exist.

Keywords: extended gini index, MEG, risk-aversion and gain-properness

JEL Classification: G10, G11, G12,G29