In this paper, we extend the concept of the news impact curve of volatility developed by Engle and Ng (1993) to the higher moments and co-moments of the multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model with non-normal innovations. For this purpose, we present a new methodology to describe the joint distribution of GARCH processes in a non-normal setting. Then, we provide expressions for the response of the moments of the subsequent distribution to a shock. This tool enhances the understanding of the temporal evolution of the joint distribution. We use our methodology to provide stylized facts for the four largest international stock markets. In particular, we document the persistence of large (positive or negative) daily returns. In a multivariate setting , we find that foreign holdings provide a good hedge against changes in domestic volatility after good shocks but a bad hedge after crashes. Finally, using generalized impulse responses, we show that the effect of shocks on the higher moments of the distribution is short-lasting.