Symmetry vs. Asymmetry, Stochastic Dominance Optimization, and The Impact on Capital Asset Pricing

68 Pages Posted: 19 Aug 2019

See all articles by Victor Chow

Victor Chow

West Virginia University - Department of Finance

Ben J. Sopranzetti

Rutgers Business School: Newark and New Brunswick

Zhan Wang

West Virginia University, College of Business & Economics, Department of Finance, Students

Date Written: August 14, 2019

Abstract

This paper models the risk tradeoff between symmetry and asymmetry in the distribution of asset return as a core consideration for rational investor decision making under uncertainty and presents a closed-form solution for determining the optimal market portfolio using a classic utility maximization framework and stochastic dominance optimization. The optimization yields a portfolio separation for both risk-averse investors as well as those who also possess a preference for upside gains and an aversion to downside losses. In equilibrium, in addition to requiring compensation for bearing volatility risk – which is symmetrical in gains and losses – investors also require additional compensation for bearing the systematic risk associated with distributional asymmetries. The model serves as an expansion of CAPM and, as is demonstrated both theoretically and empirically, solves the long-lasting puzzle of the beta anomaly.

Keywords: Swap-Variance, Asymmetry, Expected Utility, Stochastic Dominance, Gain-Preference, Loss Aversion, CAPM

JEL Classification: D81, G02, G11, G12.

Suggested Citation

Chow, Victor and Sopranzetti, Ben J. and Wang, Zhan, Symmetry vs. Asymmetry, Stochastic Dominance Optimization, and The Impact on Capital Asset Pricing (August 14, 2019). Available at SSRN: https://ssrn.com/abstract=3437440 or http://dx.doi.org/10.2139/ssrn.3437440

Victor Chow (Contact Author)

West Virginia University - Department of Finance ( email )

P. O. Box 6025
Morgantown, WV 26506
United States

Ben J. Sopranzetti

Rutgers Business School: Newark and New Brunswick ( email )

100 Rockafeller Rd
Piscataway, NJ 08854
United States

Zhan Wang

West Virginia University, College of Business & Economics, Department of Finance, Students ( email )

Morgantown, WV 26506
United States

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