Stochastic Dominance and Diversification

Abstract

Stochastic dominance (SD) rules are applicable in selection between mutually exclusive investments but, unlike the mean-variance rule, they cannot identify all possible efficient diversification strategies. Thus, SD rules can tell us whether investment F dominates investment G, or investment G dominates H, but they cannot provide us with the set of combinations of these three assets that dominate all other sets of combinations. Moreover, for two investments F and G, even if it is given that F dominates G, say by SSD, when diversification is considered, one cannot tell unequivocally whether this SSD implies that more than 50% of the wealth should be invested by all risk averters in the superior investment F. Analysis of SD and diversification has been attempted but much still has to be accomplished in this area of research. In this chapter we first discuss some published results obtained in this area, and then we will report some new results.