Revue des sciences commerciales et de gestion
Volume 3, Numéro 1, Pages 35-68
2004-04-30

Diversification In Portfolio Selection Problems: A Definition And Some Financial Consequences.



Authors : Touati-tliba Mohamed .

Abstract

Abstract: The purpose of this article is to propose a general definition of " more diversified » in portfolio problems and relate this definition to the optimal investment strategy. Central to this concern is the identification of what it is that is diversified and what determine the desirable degree of diversification. Some partial diversification results are provided using both the general expected utility model for arbitrary distributions as well as standard parametric distributions suitable for portfolio theory emphasizing the role of different parameters in determining the degree of diversification. It is shown that if the random vector of returns Yis a mutual fund transformation of.X then every risk averse investor diversify more under X. Furthermore, for elliptical and skew-normal distributions, necessary and sufficient conditions are given to insure that short sales are not the optimal investment strategy for all risk-averse investors. We also discuss the relation between relevant parameters of two distributions that imply more diversification under one distribution rather than the other.

Keywords

Portfolio selection, Diversification, Majorization, Negative interdependence, Elliptical distributions, Skew-elliptical distributions, Separating distributions.

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