Test Statistics For Prospect And Markowitz Stochastic Dominances With Applications

Levy and Levy(2002,2004) and others extend the stochastic dominance (SD) theo-ry for risk averters and risk seekers by developing the prospect SD (PSD) and Markowitz SD (MSD) theory for investors with S-shaped and reverse S-shaped utility functions. Davidson and Duclos (2000) and others develop a SD test for risk averters while Wong, et al.(2007) develop a SD test for risk seekers. In this paper, we extend their work by developing new statistics for ASD, DSD, PSD and MSD of the first three orders. One could then use these statistics to identify preferred assets for risk averters, risk seekers, and investors with S-shaped and reverse S-shaped utility functions. To illustrate the use-fulness of our proposed statistics, we use the SD test statistics to study the preferences of investors with the corresponding S-shaped and reverse S-shaped utility functions vis-a-vis returns of traditional stocks and Internet stocks before and after the Internet bubble and subprime crisis.