Systemic risk measurement: Multivariate GARCH estimation of CoVaR

We modify Adrian and Brunnermeier's (2011) CoVaR, the VaR of the financial system conditional on an institution being in financial distress. We change the definition of financial distress from an institution being exactly at its VaR to being at most at its VaR. This change allows us to consider more severe distress events, to backtest CoVaR, and to improve its consistency (monotonicity) with respect to the dependence parameter. We define the systemic risk contribution of an institution as the change from its CoVaR in its benchmark state (defined as a one-standard deviation event) to its CoVaR under financial distress. We estimate the systemic risk contributions of four financial industry groups consisting of a large number of institutions for the sample period June 2000 to February 2008 and the 12 months prior to the beginning of the crisis. We also investigate the link between institutions' contributions to systemic risk and their characteristics.

• We change the definition of financial distress in CoVaR. • We consider more severe distress events, backtest CoVaR, and improve its consistency. • Our CoVaR and VaR have a weak relation in the cross-section and in the time-series. • Depository institutions contribute the most to systemic risk. • Leverage, size, and equity beta are important in explaining systemic risk.