SAMPLING ERROR IN FIRST ORDER STOCHASTIC DOMINANCE

This study analyzes the standard method of testing for first order stochastic dominance from a statistical viewpoint and applies a boundary crossing algorithm to approximate the resulting error probabilities. Error probabilities can be estimated even when the two distributions are not equal. This approach, which is useful when large sample simulations are not feasible, helps clarify some of the unusual results obtained by Kroll and Levy in an earlier study.     

MARGINAL CONDITIONAL STOCHASTIC DOMINANCE,STATISTICAL INFERENCE,AND MEASURING PORTFOLIO PERFORMANCE

A simple statistical test is developed for marginal conditional stochastic dominance (MCSD). The MCSD is an extension of second‐degree stochastic dominance. As such, without specification of the return‐generating process, it can rank securities according to marginal changes of return distributions conditionally to the distribution of the market proxy, thereby proving a powerful technique for measuring portfolio performance. Although the MCSD test is asymptotic and conservative, under both the hypotheses of homoskedasticity and heteroskedasticity, it has power to detect the dominance alternative for samples with more than 300 observations. For an illustration, the MCSD test is applied to international equity markets. The test is able to show that nine of twenty‐eight equity markets are dominated by the world market. JEL classification: G11, C49     

STOCHASTIC DOMINANCE AND MEAN VARIANCE RULES IN THE SELECTION OF RISKY INVESTMENTS

This paper reexamines the methods of stochastic dominance and mean-variance analysis for the selection of risky investments. It takes as its starting point the paper by Gandhi and Saunders in the Spring 1981 issue of this journal in which they argued for the superiority of stochastic dominance analysis. In this paper the countercase is put forward for the use of mean-variance analysis. It is argued that while naive application of mean-variance criteria to the ranking of projects in isolation might lead to erroneous decisions, in the presence of reasonably sized capital markets rules based on mean-variance analysis still remain a more practical tool.     

ON STOCHASTIC DOMINANCE ANALYSIS OF DAY-OF-THE-WEEK RETURN PATTERNS

Studies show that significant differences exist among return distributions of days of the week. While these results are ubiquitous, their validity depends on the robustness of statistical procedures used. Virtually every day-of-the-week study has used mean/variance analysis despite it being well documented that daily return distributions are nonnormal. This study uses stochastic dominance analysis, which is not distribution dependent, to test for a day-of-the-week effect. Results indicate that the day-of-the-week effect is robust and that previous findings are not artifacts deriving from violations of distributional assumptions.     

MOVING STOCHASTIC DOMINANCE: AN ALTERNATIVE METHOD FOR TESTING MARKET EFFICIENCY

The purposes of this study are: (1) to propose a more general method—moving stochastic dominance (MSD)—for testing market efficiency, (2) to compare and contrast the MSD method with the cumulative average residual (CAR) risk-return analysis, and (3) to illustrate the MSD methodology on a sample of stock splits. The constant CAR analysis results are consistent with previous studies. The moving CAR results are in conflict with previous studies and indicate that investors are worse off after a stock split irrespective of the subsequent dividend change. The MSD results indicate that investors are approximately equally well off irrespective of the subsequent dividend change.