We propose a new methodology based on copula functions to estimate CoVaR, the Valueat-Risk (VaR) of the financial system conditional on an institution being under financial distress. Our Copula CoVaR approach provides simple, closed-form expressions for various definitions of CoVaR for a broad range of copula families and allows the CoVaR of an institution to have time-varying exposure to its VaR. We extend this approach to estimate other "co-risk" measures such as Conditional Expected Shortfall (CoES). We focus on a portfolio of large European banks and examine the existence of common market factors triggering systemic risk episodes. Further, we analyse the extent to which bank-specific characteristics such as size, leverage, and equity beta are associated with institutions' contribution to systemic risk and highlight the importance of liquidity risk at the outset of the financial crisis in summer 2007. Finally, we investigate the link between macroeconomy and systemic risk and find that changes in major macroeconomic variables can contribute significantly to systemic risk.

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