Modeling asymmetric comovements of asset returns

Existing time-varying covariance models usually impose strongrestrictions on how past shocks affect the forecasted covariancematrix. In this article we compare the restrictions imposedby the four most popular multivariate GARCH models, and introducea set of robust conditional moment tests to detect misspecification.We demonstrate that the choice of a multivariate volatilitymodel can lead to substantially different conclusions in anyapplication that involves forecasting dynamic covariance matrices(like estimating the optimal hedge ratio or deriving the riskminimizing portfolio). We therefore introduce a general modelwhich nests these four models and their natural 'asymmetric'extensions. The new model is applied to study the dynamic relationbetween large and small firm returns.