We consider consistent tests for stochastic dominance efficiency at any order of a given portfolio with respect to all possible portfolios constructed from a set of assets. We justify block bootstrap approaches to achieve valid inference in a time series setting. The test statistics are computed using linear and mixed integer programming formulations. Monte Carlo results show that the bootstrap procedure performs well in finite samples. The empirical application reveals that the Fama and French market portfolio is first and second-order stochastic dominance efficient, although it is mean–variance inefficient.