In many applications involving the construction of efficient sets, the parameters of the alternatives are estimated using small examples. As a result, inefficient alternatives may be included in the sample efficient set and efficient alternatives left out. This paper investigates the effects of estimation risk when there are more than two alternatives and limited information. The study meals that estimation risk is a severe handicap to the practical implementation of stochastic dominance and mean-variance efficiency analysis.Subject Arm: portforiio AnalysLr and Risk and Uncertahty.