On the Relative Effectiveness of Stochastic Dominance Rules: Extension to Decreasingly Risk-Averse Utility Functions

Abstract

In our theoretical work on DSD ([17], [18], [19]), specially constructed examples were used to demonstrate that DSD is stronger than TSD. The results of the present paper imply that similar examples also arise naturally from realworld data. They also suggest that such examples are rare. In the specific cases studied here, the differences between these two stochastic orderings are real, but small, and TSD would likely be a suitable approximation to DSD for practical purposes. The differences between the resulting efficient subsets seem relatively less important as the size of the initial portfolio universe increases. For example, the percentage reduction in the efficient TSD subset for a 1000-portfolio problem is smaller than for a typical 100-portfolio problem. This was found to be true throughout the preliminary phases of the study, as well as in the final phase reported here. The (to us) disappointing performance of DSD resulted primarily from the left-tail problem, which became increasingly prevalent as the initial portfolio set expanded. This suggests that DSD would be most useful in problems of choice among relatively few alternatives, perhaps of the capital budgeting type. In addition, there are numerous nonfinancial problems in which DSD could prove to be useful in ranking alternative management policies. Finally, the greater strength of DSD may remain important in theoretical investigations, especially for situations in which the left-tail problem is absent.