Bootstrapping a distance test for stochastic dominance analysis

A major impediment to measuring portfolio performance under stochastic dominance has been the lack of test statistics for orders of stochastic dominance above first degree. In this article, the Bootstrap method, introduced by Efron (1979), is used to estimate critical values for distance statistics in order to test the null hypothesis of no dominance, under second- and third-degree stochastic dominance, for several samples of stock returns. These test statistics, suggested by Whitmore (1978), are analogous to the Kolmogorov-Smirnov distance statistics that can be used to test for first-degree stochastic dominance. Stochastic dominance is shown to accurately assess portfolio performance of sample distributions when the population distributions are controlled and Bootstrap statistics are employed in the analysis. In addition, second- and third-degree stochastic dominance analysis of the smallfirm January anomaly indicates that, over the 23-year time period 1964 to 1986, small firms statistically dominate a diversified market index in only one calendar year.