Test Statistics for Prospect and Markowitz Stochastic Dominances with Applications

36 Pages Posted: 20 Nov 2007 Last revised: 2 Oct 2010

See all articles by Zhidong Bai

Zhidong Bai

Northeast Normal University

Huixia Liu

Northeast Normal University

Wing-Keung Wong

Asia University, Department of Finance

Hua Li

Northeast Normal University

Multiple version iconThere are 2 versions of this paper

Date Written: November 16, 2007

Abstract

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.

Keywords: Prospect stochastic dominance, Markowitz stochastic dominance, risk seeking, risk averse, S-shaped utility function, reverse S-shaped utility function, test statistics, hypothesis testing

JEL Classification: C14, G12, G15

Suggested Citation

Bai, Zhidong and Liu, Huixia and Wong, Wing-Keung and Li, Hua, Test Statistics for Prospect and Markowitz Stochastic Dominances with Applications (November 16, 2007). Available at SSRN: https://ssrn.com/abstract=1030728 or http://dx.doi.org/10.2139/ssrn.1030728

Zhidong Bai (Contact Author)

Northeast Normal University ( email )

Changchun
China

Huixia Liu

Northeast Normal University ( email )

Changchun
China

Wing-Keung Wong

Asia University, Department of Finance ( email )

Taiwan
Taiwan

Hua Li

Northeast Normal University ( email )

Changchun
China

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