Statistical Inference on Stochastic Dominance Efficiency. Do Omitted Risk Factors Explain the Size and Book-to-Market Effects?

This paper discusses statistical inference on the second-order stochastic dominance (SSD) efficiency of a given portfolio relative to all portfolios formed from a set of assets. We derive the asymptotic sampling distribution of the Post test statistic for SSD efficiency. Unfortunately, a test procedure based on this distribution involves low power in small samples. Bootstrapping is a more powerful approach to sampling error. We use the bootstrap to test if the Fama and French value-weighted market portfolio is SSD efficient relative to benchmark portfolios formed on market capitalization and book-tomarket equity ratio. During the late 1970s and during the 1980s, the market portfolio is significantly SSD inefficient, even if we use samples of only 60 monthly observations. This suggests that the size and book-to-market effects cannot be explained by omitted risk factors like higher-order central moments or lower partial moments.