We provide a new metric for the systemic importance of banks based on the intensity of spillovers of daily CDS movements. We denote this a bank’s Individual Systemic Risk (ISR). Our novel empirical tool uses Bayesian VAR to address the dimensionality problem in large networks of banks and maps for every pair of banks in the system the shocks that they exchange. We apply this tool to all banks that issue publicly traded CDS contracts among the world’s biggest 150 and identify which of these may trigger instability in the global financial system. Our methodology provides measures that are relatively stable across time, contain persistent information, have strong explanatory power for standard variables of systemic risk, and provided early warning signals in the case study of Deutsche Bank in mid-2016. Using our ISR measure, we demonstrate which bank- and country-specific characteristics are related to bank systemic importance. We find higher systemic importance for banks that are relatively larger, less profitable, have G-SIB status, and are headquartered in economies with fiscally strong sovereigns. We also show that there is a negative relationship between concentration in the domestic banking sector and the systemic importance of a bank. We examine the relationship of ISR to alternative systemic risk metrics.