Portfolio Rules for Conditional Stochastic Dominance: Applications to the Elliptical Distributions

Abstract

In this paper we generalize the Clark-Jokung 50% portfolio theorem(Management Science, 1999) to an arbitrary threshold and we apply it to a wide and well-known family of distributions, the elliptical distributions (multivariate normal, Student t, multivariate exponential,...). We consider the specific case of a two-asset portfolio where the cumulative conditional expected outcome on one asset is greater or equal to the cumulative conditional expected outcome of the other asset.We show that when the joint distribution of the returns of the two assets follows an elliptical distribution, the conditions for 100alpha% portfolio theorem to hold are a higher expected return for the dominant asset and that the threshold 100alpha% is less than the percentage invested in the minimum-variance portfolio.