A Minimum Discrepancy Formulation of Stochastic Dominance Analysis and Implications for Asset Pricing

Abstract

In this paper, we offer a MD (Minimum Discrepancy) reformulation of the estimation and inference problem that arises in SD analysis, delivering a method that retains the desirable properties of optimal GMM while offering better higher order ones and, most importantly, without requiring the estimation of the weighting matrix, which is typically unstable and, especially when the cross-section of test-asset payoffs is large compared to the sample period length, subject to substantial sampling error. Moreover, when testing for stochastic dominance/efficiency of a given evaluated portfolio, our method makes it straightforward to impose a no short sales restriction on the admissible allocations to the test assets. While important in practice in certain circumstance, this is instead very hard, if not impossible, in a traditional GMM setting. In an empirical application using 51 years of data on portfolios formed sorting stocks on size and size and book-to-market, we find that, under decreasing absolute risk aversion (DARA) as well as more restrictive parametric specifications of the utility function, the market portfolio is stochastically dominated by the size and book to market portfolios while it compares favorably to the size portfolios.