This paper disentangles direct spillovers and common factors as sources of correlations in simultaneous heteroscedastic systems. While these different components are not identifiable by standard means without restrictions, it is shown that they can be pinned down by specifying the variances of the latent idiosyncratic and common shocks as ARCH-type processes. Applying an adapted Kalman filter estimation method to Dow and Nasdaq stock returns, predominant spillovers from the Dow and substantial rising factor exposure are found. While the latter is shown to prevail in the recent global financial crisis, volatility in the dot-com bubble period was driven by Nasdaq shocks.