Beta and Coskewness Pricing: Perspective from Probability Weighting

Does Subjective Evaluation of Probability Impact Asset Prices? The Nobel Prize–winning capital asset pricing model (CAPM) predicts that expected excess return of any asset is positively proportional to its exposure to the overall market: the beta, leading to an upward-sloping security market line. However, this prediction is contradicted by empirical studies that the return–beta slope is often flat or even downward-sloping, a puzzle called the “beta anomaly.” The CAPM is premised upon the notion that market participants are all rational, including that they are able to objectively evaluate probabilities. However, evidence abounds that individuals are often unable to do so, examples being purchase of lottery tickets and insurance products, in which the extremely small probabilities of winning or losing big are exaggerated. This phenomenon of distorting probabilities at both tails is called “probability weighting” (PW), which is a key component of modern behavioral finance. The paper “Beta and Coskewness Pricing: Perspective from Probability Weighting” approaches the beta anomaly through PW. It offers an explanation of the beta anomaly via a new theoretical CAPM involving PW and an extensive empirical study. 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