Prospect and Markowitz stochastic dominance

Abstract

Levy and Levy ( , 2004 develop the Prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend Levy and Levy's Prospect Stochastic Dominance theory (PSD) and Markowitz Stochastic Dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD.Prospect theory has been regarded as a challenge to the expected utility paradigm. Levy and prove that the second order PSD and MSD satisfy the expected utility paradigm. In our paper we take Levy and Levy's results one step further by showing that both PSD and MSD of any order are consistent with the expected utility paradigm.Furthermore, we formulate some other properties for the PSD and MSD including the hierarchy that exists in both PSD and MSD relationships; arbitrage opportunities that exist in the first orders of both PSD and MSD; and that for any two prospects under certain conditions, their third order MSD preference will be 'the opposite' of or 'the same' as their counterpart third order PSD preference. By extending Levy and Levy's work, we provide investors with more tools for empirical analysis, with which they can identify the first order PSD and MSD prospects and discern arbitrage opportunities that could increase his/her utility as well as wealth and set up a zero dollar portfolio to make huge profit. Our tools also enable investors to identify the third order PSD and MSD prospects and make better choices.

Review on Efficiency and Anomalies in Stock Markets

“…On the other hand, Thaler and Johnson (1990) observed that investors are more risk-seeking on gains and more risk-averse on losses, inferring that investors have a reverse S-shaped utility function. Other academics, for example, Levy and Wiener (1998), Levy andLevy (2002, 2004), Wong and Chan (2008), and Bai et al (2011b) developed their theories based on the assumption that investors possess S-shaped or reverse S-shaped utility function.…”

Does Global Shapes of Utility Functions Matter for Investment Decisions?

“…There is an extensive body of literature that outlines the potential pitfalls of eliciting utility functions using certainty equivalent technique types of experiments (Hey et al, 2009;Morone, 2010). Hence, it would be interesting to explore to what extent our findings can be generalized to different preference elicitation methods, as well as stochastic dominance rules (Wong and Chan, 2008), as a more general approach to expected utility maximization.…”

“…Studies show that fully concave utility is equivalent to stochastic dominance (SD) and fully convex utility is equivalent to risk-seeking stochastic dominance (RSD) (Wong, 2007;Levy, 2015). On the other hand, S-shaped utility function is equivalent to prospect stochastic dominance (PSD) and reversed S-shaped utility is equivalent to Markowitz stochastic dominance (MSD) (Levy and Wiener, 1998;Levy, 2002, 2004;Wong and Chan, 2008). Recently, Bai et al (2015) has developed tests for SD and RSD and many studies (Qiao et al, 2012 andWong andZhu, 2015) have been using these tests to study preferences of investors with fully concave and fully convex utility, and MSD and PSD tests for S-shaped and reversed S-shaped utility functions (Bai et al, 2012;Fong et al, 2008).…”

Why Are Warrant Markets Sustained in Taiwan but Not in China?

“…We also note that there could be many directions for further studies. One of them is to study the preference of other types investors, for example, investors with S-shaped and reversed S-shaped utility functions, see, for example, Wong and Chan [80] and the references therein for more information.…”