Modeling asymmetric comovements of asset returns

Existing time-varying covariance models usually impose strong restrictions on how past shocks affect the forecasted covariance matrix, In this article we compare the restrictions imposed by the four most popular multivariate GARCH models, and introduce a set of robust conditional moment tests to detect misspecification. We demonstrate that the choice of a multivariate volatility model can lead to substantially different conclusions in any application that involves forecasting dynamic covariance matrices (like estimating the optimal hedge ratio or deriving the risk minimizing portfolio). We therefore introduce a general model which nests these four models and their natural "asymmetric" extensions. The new model is applied to study the dynamic relation between large and small firm returns.