Empirical Tests for Stochastic Dominance Optimality
24 Pages Posted: 17 Sep 2015 Last revised: 15 May 2018
Date Written: September 15, 2015
If a given risky prospect is compared with multiple choice alternatives, then a joint test for optimality is more appropriate than a series of pairwise Stochastic Dominance tests. We develop and implement a bootstrap empirical likelihood ratio test for this hypothesis. The test statistic and implied probabilities can be computed by searching over discrete distributions that obey a system of linear inequalities using quasi-Monte Carlo simulation and convex optimization methods. An extension of the Kroll-Levy simulation experiment shows favorable small-sample properties for data sets of realistic dimensions. In an application to Fama-French stock portfolios, pairwise tests classify a portfolio of small growth stocks as admissible, whereas our test classifies the portfolio as significantly non-optimal for every risk averter.
Keywords: Decision Making under Risk, Stochastic Dominance, Empirical Likelihood
JEL Classification: C61, D81, G11
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