To analyze the intertemporal interaction between the stock and bond market returns, we assume that the conditional covariance matrix follows a multivariate GARCH process. We allow for asymmetric effects in conditional variances and covariances. Using daily data, we find strong evidence of conditional heteroskedasticity in the covariance between stock and bond market returns. The results indicate that not only variances, but also covariances respond asymmetrically to return shocks. Bad news in the stock and bond market is typically followed by a higher conditional covariance than good news. Cross asymmetries, that is, asymmetries followed from shocks of opposite signs, appear to be important as well. Covariances between stock and bond returns tend to be relatively low after bad news in the stock market and good news in the bond market. A financial application of our model shows that optimal portfolio shares can be substantially affected by asymmetries in covariances. Moreover, our results show sizable gains due to asymmetric volatility timing.