An Empirical Comparison of Stochastic Dominance among Lognormal Prospects

Abstract

l. Introduct ion The theory of portfolio selection and diversification developed by Markowitz [22] and Tobin [33] was based primarily on the criterion of meanvariance (MV) efficiency. The objective was to select an efficient set of portfolios from which every risk averter will choose the optimal portfolio which maximizes his expected utility. The MV criterion is the appropriate rule either for the case in which the utility function is quadratic or if the returns are normally distributed and risk aversion is assumed. Two approaches to the choice among risky alternatives that have been developed independently over the past two decades are the geometric mean criterion (GM) and the stochastic dominance (SD) decision model. Both can be justified by the expected utility hypothesis, with the geometric mean cri? terion following as a result of the assumption that the decision-maker has a logarithmic utility function, and the stochastic dominance models requiring the less restrictive assumption of signs of the first few derivatives of the decision-maker's utility function. This paper compares the concept of ordinary stochastic dominance to stochastic dominance of the lognormally distributed prospects from an empirical point of view. Further 1ight is also shed on the issue of applying the Markowitz-Tobin mean-variance rule