Mean‐extended Gini portfolios personalized to the investor's profile

Shalit and Yitzhaki presented the mean‐extended Gini (MEG) as a workable alternative to the Markowitz mean‐variance approach in 1984. Since then, the challenge has been to extend the MEG approach. The purpose of this paper is to propose a generalization of the MEG approach for making customized optimal asset allocation to control both down‐performance and/or up‐performance.

The MEG approach is used to make strategical allocation tailored to the investor risk aversion and gain propensity measured by characteristic parameters of the extended Gini measures.

The authors set up two optimization problems: the former focused on controlling the risk, the latter on emphasizing the potential gains. Sufficient conditions such that the efficient MEG‐risk frontier coincides with the inefficient MEG‐gain frontier are stated. In the realistic scenarios that portfolios have asymmetrical distributions and/or the investor profile is very conservative or very aggressive, the desirable occurrence that a portfolio is optimal under both optimizations may occur.

The main contribution of this research is to have pointed out that optimal allocation must be tailored to both the investor's risk and gain profile; and, that the optimality may be not preserved if the investor's risk‐gain profile changes. So, the statement “optimal allocation” should be reworded as “optimal allocation personalized to the investor's risk‐aversion and gain‐propensity”.