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Recent theoretical and empirical work in portfolio theory has exhibited a natural evolution from the two-moment EV model popularized by Markowitz through the higher moment models to selection on the basis of the entire probability function. This latter approach, referred to as the Stochastic Dominance (SD) approach to portfolio selection, has been shown to be theoretically superior to all of the "moment methods" and has been the focus of an increasing volume of empirical work. In comparison with the EV model, however, the SD approach has one potentially significant deficiency from the standpoint of empirical testing. With a given set of portfolios to evaluate, the computer processor time required for the determination of the EV efficient set is quite short. One can calculate and sort means and variances on several hundred portfolios in a matter of seconds. In contrast, the processor time required for the determination of the SD efficient set for the same number of portfolios can be prohibitive. The purpose of this paper is to examine the factors responsible for the relatively time-consuming nature of empirical tests of SD efficiency and to present the major results of our search for efficient algorithms for conducting SD tests. Section I briefly examines the time-consuming nature of the tests for SD efficiency. Section II presents and evaluates; our most efficient algorithms for obtaining true SD efficiency results. Section lit examines an approach that yields approximate SD efficiency results with further reductions in required processor time. [ABSTRACT FROM AUTHOR]