Beta Risk in the Cross-section of Equities

We develop a bivariate stochastic volatility model that allows for dynamic market exposure. The expected return on a stock depends on beta's co-movement with the stochastic discount factor and deviates from the standard security market line when beta risk is priced. When estimating the model on returns and options for a large number of firms we find that allowing for beta risk helps explain the expected returns on low and high beta stocks that are challenging for standard factor models. Overall, we find strong evidence that accounting for beta risk results in better model fit.