Statistical decisions between portfolios: Mean-variance analysis revisited

The problem of choice from a given set of portfolios is a problem of ordering the proper set F of probability distribution functions. In this paper the relations between (first and second degree) stochastic dominance rules and certain mean-variance rules are explored. Conditions are given under which stochastic dominance efficient sets are contained in mean-variance efficient sets as well as conditions under which the sets coincide. In this light some recent empirical work on efficient sets of portfolios is reconsidered; theoretical and practical reasons are discussed which limit the applicability of stochastic dominance rules in portfolio analysis.