The global financial crisis that started in mid-2007 illustrates the relevance of systemic risk. One key driver of the systemic instability that materialised in the crisis was the elevated level of stress in large banks. We use EVT to analyse the effect of size on banks’ univariate and systemic risk across ten countries as well as across the EU. Our findings show that size has little impact on banks’ univariate risk (as measured by VaR), but that large banks have significantly higher systemic risk. Furthermore, systemic risk has significantly increased for banks of all sizes since the beginning of the crisis.