Abstract If a given risky prospect is compared with multiple choice alternatives, then a joint test for optimality is more appropriate than a series of pairwise Stochastic Dominance tests. We develop and implement a bootstrap empirical likelihood ratio test for this hypothesis. The test statistic and implied probabilities can be computed by searching over discrete distributions that obey a system of linear inequalities using quasi-Monte Carlo simulation and convex optimization methods. An extension of the Kroll–Levy simulation experiment shows favorable small-sample properties for data sets of realistic dimensions. In an application to Fama–French stock portfolios, pairwise tests classify a portfolio of small growth stocks as admissible, whereas our test classifies the portfolio as significantly non-optimal for every risk averter.