A GMM Test for SSD Efficiency

We develop an empirical test for Second-order Stochastic Dominance (SSD) efficiency of a given investment portfolio relative to all possible portfolios formed from a set of assets. Contrary to the Linear Programming test of Post, Thierry, 2003, Empirical tests for stochastic dominance efficiency, Journal of Finance 58, 1905—1932, our test is embedded in the Generalized Method of Moments (GMM) framework. The GMM test has superior statistical properties compared to the original LP test. Using this test, we demonstrate that the anomalous size effect can be explained with risk not captured by variance alone. However, the market portfolio remains SSD inefficient relative to value and momentum portfolios due to the overvaluation of growth stocks and past losers.