We derive empirical tests for the stochastic dominance efficiency of a given portfolio with respect to all possible portfolios constructed from a set of assets. The tests can be computed using straightforward linear programming. Bootstrapping techniques and asymptotic distribution theory can approximate the sampling properties of the test results and allow for statistical inference. Our results could provide a stimulus to the further proliferation of stochastic dominance for the problem of portfolio selection and evaluation. Using our tests, the Fama and French market portfolio is significantly inefficient relative to benchmark portfolios formed on market capitalization and book-to-market equity ratio.