We show theoretically and empirically that the cross-section of stock return idiosyncratic volatilities contains useful information about the ICAPM. We construct a proxy cross-sectional bivariate idiosyncratic volatility (CBIV) for the covariance risk between the market and the unobserved hedge portfolio under the ICAPM. Consistent with the ICAPM pricing relation, CBIV is a robust and significant predictor of the equity risk premium. We further show that the return predictability of the tail index in Kelly and Jiang (2014) can be explained by the ICAPM covariance risk.

This study examines the pricing of multivariate crash risk (MCRASH) in the Chinese stock market. Our findings indicate a significantly positive influence of MCRASH on the cross-section of future stock returns, with the MCRASH premium being notably higher in China than in the US. A plausible explanation for China's higher MCRASH premium is that Chinese stocks may experience greater loss magnitudes in left-tail events, leading investors to demand higher expected returns as compensation for bearing a unit of MCRASH. Additionally, the return effect of MCRASH is found to be significantly stronger for stocks of non-state-owned enterprises and those with lower media coverage. Finally, we construct a four-factor model comprising market, size, value, and MCRASH factors, which demonstrates superior explanatory power compared with the CH3 and CH4 models proposed in the literature.