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.

Automated summary

The security market line is usually flat or downward-sloping. We propose that probability weighting affects this relationship differently during periods of overweighting or underweighting extreme events. Overweighting inflates the probability of bad events and demands higher compensation for beta risk, while underweighting has the opposite effect. These effects offset each other when not considering probability weighting, resulting in a flat or slightly negative return-beta relationship. Our three-moment conditional capital asset pricing model for a market with rank-dependent utility agents supports these predictions, as demonstrated in our extensive empirical study.