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For more than three decades, empirical analysis of stochastic dominance was restricted to settings with mutually exclusive choice alternatives. In recent years, a number of methods for testing efficiency of diversified portfolios have emerged, which can be classified into three main categories: 1) majorization, 2) revealed preference and 3) distribution-based approaches. Unfortunately, some of these schools of thought are developing independently, with little interaction or crossreferencing among them. Moreover, the methods differ in terms of their objectives, the information content of the results and their computational complexity. As a result, the relative merits of alternative approaches are difficult to compare. This paper presents the first systematic review of all three approaches in a unified methodological framework. We examine the main developments in this emerging literature, critically evaluating the advantages and disadvantages of the alternative approaches. We also point out some misleading arguments and propose corrections and improvements to some of the methods considered.

This paper points out the importance of Stochastic Dominance (SD) efficient sets being convex. We reviewclassic convexity and efficient set characterization results on SD efficiency of a given portfolio relative to adiversified set of assets and generalize them in the following aspects. First, we broaden the class ofindividual utilities in Rubinstein (1974) that lead to two-fund separation. Secondly, we propose a linearprogramming SSD test that is more efficient than that of Post (2003) and expand the SSD efficiency criteriadeveloped by Dybvig and Ross (1982) onto the Third Order Stochastic Dominance and further toDecreasing Absolute and Increasing Relative Risk Aversion Stochastic Dominance. The efficient sets forthose are finite unions of convex sets.