We develop a conditional capital asset pricing model in continuous-time that allows for stochastic beta exposure. When beta co-moves 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...

Equity risk measured by beta is of great interest to both academics and practitioners. Existing estimates of beta use historical returns. Many studies have found option-implied volatility to be a strong predictor of future realized volatility. We find that option-implied volatility and skewness...