Roughing up Beta: Continuous vs. Discontinuous Betas, and the Cross-Section of Expected Stock Returns

Motivated by the implications from a stylized equilibrium pricing framework, we investigate empirically how individual equity prices respond to continuous, or \smooth," and jumpy, or \rough," market price moves, and how these different market price risks, or betas, are priced in the cross-section of expected returns. Based on a novel highfrequency dataset of almost one-thousand individual stocks over two decades, we find that the two rough betas associated with intraday discontinuous and overnight returns entail significant risk premiums, while the intraday continuous beta is not priced in the cross-section. An investment strategy that goes long stocks with high jump betas and short stocks with low jump betas produces significant average excess returns. These higher risk premiums for the discontinuous and overnight market betas remain significant after controlling for a long list of other firm characteristics and explanatory variables previously associated with the cross-section of expected stock returns.