Test statistics for prospect and Markowitz stochastic dominances with applications

Zhidong Bai*, Hua Li, Huixia Liu, Wing Keung WONG

*Corresponding author for this work

    Research output: Contribution to journalJournal articlepeer-review

    44 Citations (Scopus)


    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 functionsvis-à-visreturns on iShares andvis-à-visreturns of traditional stocks and Internet stocks before and after the Internet bubble.

    Original languageEnglish
    Pages (from-to)278-303
    Number of pages26
    JournalEconometrics Journal
    Issue number2
    Publication statusPublished - Jul 2011

    Scopus Subject Areas

    • Economics and Econometrics

    User-Defined Keywords

    • Hypothesis testing
    • Markowitz stochastic dominance
    • Prospect stochastic dominance
    • Risk averse
    • Risk seeking
    • RS-shaped utility function
    • S-shaped utility function
    • Test statistics


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