GMM Tests for SD Efficiency of a Given Portfolio

We develop empirical tests for Second-order Stochastic Dominance (SSD) efficiency and Thirdorder Stochastic Dominance (TSD) efficiency of a given investment portfolio relative to all possible portfolios formed from a set of assets. Contrary to existing Linear Programming tests, our tests are embedded in the Generalized Method of Moments (GMM) framework, which results in superior statistical power properties and increases the comparability with existing mean-variance tests. Using these tests, we demonstrate that the mean-variance inefficiency of the CRSP all-share index relative to beta-sorted portfolios can be explained by tail risk not captured by variance.