Test Statistics for Prospect and Markowitz Stochastic Dominances with Applications

Levy and Levy (2002, 2004) and others extend the stochastic dominance (SD) theory 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 (RS-shaped) utility functions. Davidson and Duclos (DD, 2000) and others develop an SD test for risk averters while Sriboonchita, et al. (2009) modify their statistic to obtain an SD test for risk seekers. In this paper, we extend their work by developing new statistics for both PSD and MSD of the first three orders. These statistics provide tool to examine the preferences of investors with RS-shaped investors propose by Markowitz (1952a) and investors with S-shaped utility functions proposed by Kahnemann and Tversky (1979) in their prospect theory. We also derive the limiting distributions of the test statistics to be stochastic processes. In addition, we propose a bootstrap method to decide the critical points of the tests. To illustrate the applicability of our proposed statistics, we apply them to study the preferences of investors with the corresponding S-shaped and RS-shaped utility functions vis-`a-vis returns on iShares and vis-a-vis returns of traditional stocks and Internet stocks before and after the Internet bubble