Severe financial turbulence is driven by high impact and low probability events that are the hallmarks of systemic financial stress. These unlikely adverse events arise from the extreme tail of a probability distribution and are therefore very poorly captured by traditional econometric models that rely on the assumption of normality. In order to address the problem of extreme tail events in a stress testing framework, we adopt a mixture vector autoregressive (MVAR) model framework that allows for a multimodal distribution of the residuals. We use permutation tests to compare MVAR results to those of a VAR and find that mixture of distributions provides a better assessment of the impact of adverse shocks on counterparty credit risk, the real economy and banks' capital requirements. Consequently, we argue that the MVAR provides a more accurate assessment of risk owing to its ability to capture the fat tail events often observed in time series of default probabilities.