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

Abstract

This paper discusses statistical inference on the second-orderstochastic dominance (SSD) efficiency of a given portfolio relative toall portfolios formed from a set of assets. We derive the asymptoticsampling distribution of the Post test statistic for SSD efficiency.Unfortunately, a test procedure based on this distribution involveslow power in small samples. Bootstrapping is a more powerful approachto sampling error. We use the bootstrap to test if the Fama and Frenchvalue-weighted market portfolio is SSD efficient relative to benchmarkportfolios formed on market capitalization and book-tomarket equityratio. During the late 1970s and during the 1980s, the marketportfolio is significantly SSD inefficient, even if we use samples ofonly 60 monthly observations. This suggests that the size andbook-to-market effects cannot be explained by omitted risk factorslike higher-order central moments or lower partial moments.market efficiency;asset pricing;stochastic dominance;size and book-to-market effects;statistical inference