In this paper, we analyze the tail-dependence structure of credit default swaps (CDS) and the global financial cycle for a group of eleven emerging markets. Using a Copula-CoVaR model, we provide evidence that there is a significant taildependence between variables related with the global financial cycle, such as the VIX, and emerging market CDS. These results are particularly important in the context of distressed global financial markets (right tail of the distributions of the VIX) because they provide international investors with relevant information on how to rebalance their portfolios and a more suitable metric to analyze sovereign risk that goes beyond the traditional CoVaR. Additionally, we present further evidence supporting the importance of the global financial cycle in sovereign risk dynamics.