We propose a measure for systemic risk, \Delta-CoVaR, defined as the conditional value at risk CoVaR of the financial system conditional on institutions being under distress in excess of the CoVaR of the system conditional on the median state of the institution. From our estimates of Delta-CoVaR for the universe of publicly traded financial institutions, we quantify the extent to which characteristics such as leverage, size, maturity mismatch, and asset price booms predict systemic risk contribution. We also provide out-of-sample forecasts of a countercyclical, forward-looking measure of systemic risk and show that the 2006Q4 value of this measure would have predicted more than one third of realized \Delta-CoVaR during the financial crisis.