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THE MEAN-GINI EFFICIENT PORTFOLIO FRONTIER

By Haim Shalit and Shlomo Yitzhaki

Abstract

A main advantage of the mean-variance (MV) portfolio frontier is its simplicity and ease of derivation. A major shortcoming, however, lies in its familiar restrictions, such as the quadraticity of preferences or the normality of distributions. As a workable alternative to MV, we present the mean-Gini (MG) efficient portfolio frontier. Using an optimization algorithm, we compute MG and mean-extended Gini (MEG) efficient frontiers and compare the results with the MV frontier. MEG allows for the explicit introduction of risk aversion in building the efficient frontier. For U.S. classes of assets, MG and MEG efficient portfolios constructed using Ibbotson (2000) monthly returns appear to be more diversified than MV portfolios. When short sales are allowed, distinct investor risk aversions lead to different patterns of portfolio diversification, a result that is less obvious when short sales are foreclosed. Furthermore, we derive analytically the MG efficient portfolio frontier by restricting asset distributions. The MG frontier derivation is identical in structure to that of the MV efficient frontier derivation. The penalty paid for simplifying the search for the MG efficient frontier is the loss of some information about the distribution of assets. 2005 The Southern Finance Association and the Southwestern Finance Association.

DOI identifier: 10.1111/j.1475-6803.2005.00114.x
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