Beta and Coskewness Pricing: Perspective from Probability Weighting

The security market line is often flat or downward-sloping. We hypothesize that probability weighting plays a role and one ought to differentiate between periods in which agents overweight extreme events and those in which they underweight them. Overweighting inflates the probability of extremely bad events and demands greater compensation for beta risk, whereas underweighting does the opposite. Unconditional on probability weighting, these two effects offset each other, resulting in a flat or slightly negative return–beta relationship. Similarly, overweighting the tails enhances the negative relationship between return and coskewness, whereas underweighting reduces it. We derive a three-moment conditional capital asset pricing model for a market with rank-dependent utility agents to make these predictions, and we support our theory through an extensive empirical study.

Funding: This work was supported by National Natural Science Foundation of China [Grants 71971083, 71931004, 72171138]; Program for Innovative Research Team of Shanghai University of Finance and Economics [Grant 2020110930]; Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science-Ministry of Education, East China Normal University; a start-up grant and the Nie Center for Intelligent Asset Management at Columbia University.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2421.