Portfolio selection using stochastic dominance criteria

The direct application of stochastic dominance criteria to portfolio selection problems has been thought impractical because an extremely large number of combinations of returns must be considered. This paper proposes and evaluates a rigorous statistical procedure for sampling the combinations of returns on candidate risky assets so that stochastic dominance criteria may be used directly in an efficient linear programming model for portfolio selection. The sampling scheme exploits the association of the return on each candidate stock with the return on a market index in a manner analogous to the Sharpe single-index model, thereby eliminating the large number of combinations with probabilities close to or equalling zero. Portfolios computed by the proposed linear programming stochastic dominance model are compared with those computed by the single-index quadratic programming model, using 180 months of recent data on a sample of NYSE common stocks.