We measure the systemic importance of all banks that issue publicly traded CDS contracts among the world’s biggest 150. Systemic importance is captured by the intensity of spillovers of daily CDS movements. Our new empirical tool uses Bayesian VAR to address the dimensionality problem and identifies banks that may trigger instability in the global financial system. For the period January 2008 to June 2017, we find the following: A bank’s systemic importance is not adequately captured by its size. European banks have been the main source of global systemic risk with strong interconnections to US banks. For the global system, we identify periods of increased interconnections among banks, during which systemic and idiosyncratic shocks are propagated more intensely via the network. Using principal components analysis, we identify a single dominant factor associated with fluctuations in CDS spreads. Individual banks’ exposure to this factor is related to their government’s ability to support them and to their retail orientation but not to their size.