Beta risk in the cross-section of equities

We develop a conditional capital asset pricing model in continuous time that allows for stochastic beta exposure. When beta comoves with market variance and the stochastic discount factor (SDF), beta risk is priced, and the expected return on a stock deviates from the security market line. The model predicts that low-beta stocks earn high returns, because their beta positively comoves with market variance and the SDF. The opposite is true for high-beta stocks. Estimating the model on equity and option data, we find that beta risk explains expected returns on low- and high-beta stocks, resolving the “betting against beta” anomaly.