Continuous Beta, Discontinuous Beta, and the Cross-Section of Expected Stock Returns∗

Aggregate stock market returns are naturally categorized as either small or large movements. In the continuous-time model setup, we can formally identify these movements as continuous or discontinuous (jump). Using a large, novel, highfrequency dataset, I investigate how individual stocks respond to these two different market changes. I also explore whether the different systematic risks associated with those two movements are priced in the cross-section of expected stock returns. I show that the cross-section of expected stock returns reflects a risk premium for the systematic discontinuous risk but not for the systematic continuous risk. An investment strategy that goes long stocks in the highest discontinuous beta decile and shorts stocks in the lowest discontinuous beta decile produces average excess returns of 17% per annum. I estimate that the risk premium for the discontinuous risk is approximately 3% per annum after controlling for the usual firm characteristic variables including size, book-to-market ratio, momentum, idiosyncratic volatility, coskewness, cokurtosis, realized-skewness, realized-kurtosis, maximum daily return, and illiquidity. JEL classification: C13, C14, G11, G12