Test Statistics for Prospect and Markowitz Stochastic Dominances with Applications

26 Pages Posted: 8 Jun 2011

See all articles by Zhidong Bai

Zhidong Bai

Northeast Normal University

Hua Li

Northeast Normal University

Huixia Liu

Northeast Normal University

Wing‐Keung Wong

Hong Kong Baptist University (HKBU)

Multiple version iconThere are 2 versions of this paper

Date Written: July 2011

Abstract

Levy and Levy (2002, 2004) 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, respectively. Davidson and Duclos (2000) develop SD tests for risk averters whereas Sriboonchitra et al. (2009) modify their statistics to obtain SD tests 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 a tool to examine the preferences of investors with S‐shaped utility functions proposed by Kahneman and Tversky (1979) in their prospect theory and investors with RS‐shaped investors proposed by Markowitz (1952a). 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 and prove the consistency of the bootstrap 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‐à‐vis returns on iShares and vis‐à‐vis returns of traditional stocks and Internet stocks before and after the Internet bubble.

Keywords: Hypothesis testing, Markowitz stochastic dominance, Prospect stochastic dominance, Risk averse, Risk seeking, RS‐shaped utility function, S‐shaped utility function, Test statistics

Suggested Citation

Bai, Zhidong and Li, Hua and Liu, Huixia and Wong, Wing‐Keung, Test Statistics for Prospect and Markowitz Stochastic Dominances with Applications (July 2011). The Econometrics Journal, Vol. 14, Issue 2, pp. 278-303, 2011. Available at SSRN: https://ssrn.com/abstract=1859841 or http://dx.doi.org/10.1111/j.1368-423X.2011.00348.x

Zhidong Bai (Contact Author)

Northeast Normal University ( email )

Changchun
China

Hua Li

Northeast Normal University ( email )

Changchun
China

Huixia Liu

Northeast Normal University ( email )

Changchun
China

Wing‐Keung Wong

Hong Kong Baptist University (HKBU)

Kowloon
Hong Kong

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