The Mean-Variance Rule for Investors with Reverse S-Shaped Utility

Wing-Keung Wong, David Yeung and Richard Lu
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Wing-Keung Wong: Department of Finance, Fintech Center and Big Data Research Center, Asia University, Taichung City, Taiwan2Department of Medical Research, China Medical University Hospital, Taichung City, Taiwan3Department of Economics and Finance, Hang Seng University of Hong Kong, Hong Kong
David Yeung: SRS Consortium for Advanced Study, Shue Yan University, Hong Kong5Center of Game Theory, St Petersburg State University, Russia6Department of Finance, Asia University, Taichung City, Taiwan
Richard Lu: Department of Risk Management and Insurance, Feng Chia University, Taichung City, Taiwan

Annals of Financial Economics (AFE), 2023, vol. 18, issue 01, 1-16

Abstract: Our paper contributes to the literature by developing the theory of the mean-variance (MV) rules for investors with reverse S-shaped utility. To do so, we first introduce the definition of the MV rule for investors with reverse S-shaped utility. We then set up the conjecture on the preference for different prospects by using the new MV rule that they could get a higher expected utility for the preferred asset under some conditions. Thereafter, we look for the conditions that the conjecture could hold and construct a theorem for this purpose by showing that when the negative (positive) parts of the assets follow one (another) type of location-scale family or the linear combination of location-scale families, then the preferences of the assets is the same as those by using an expected utility for the investors with reverse S-shaped utility. We then extend the theory by developing some properties of portfolio diversification by using the new MV rule. The theory developed in our paper enables academics and practitioners to apply the theory developed in this paper to analyze some important empirical issues and draw inferences on the preferences of investors with reverse S-shaped utility.

Keywords: Stochastic dominance; the mean-variance rules; expected-utility maximization; risk aversion; risk-seeking; investment behaviors; investors with reverse S-shaped utility (search for similar items in EconPapers)
JEL-codes: C00 G11 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S2010495222500300

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