Similarity between Mean-Variance and Mean-Gini: Testing for Equality of Gini Correlations

Abstract

The Mean-Variance (MV) is the most popular methodology for constructing portfolios. However, it is not consistent with the expected utility hypothesis, unless one assumes the strong assumptions of either a quadratic utility or normally distributed asset returns. The Mean-Gini (MG) is an alternative method that is consistent with expected utility theory, without the need to restrict the class of the underlying distributions. However, it is more complicated to use than MV. It turns out that under certain conditions, the construction of a MG efficient portfolio is identical in structure to the construction of a MV efficient portfolio. The aim of this paper is to develop a statistical procedure to test whether the conditions that are required for the two methods to be identical in structure hold, and to illustrate its use using data from the U. S. markets. It is found that the conditions do not hold in the market as a whole, but may hold if the portfolios are restricted to be composed of assets of a certain type. It is also found that there is a considerable loss in terms of the targets when forcing the MG to behave as elegantly as the MV.

Keywords: Mean-Variance, Mean-Gini, portfolio, beta

JEL Classification: G11