Systemic Risk Measurement : Multivariate GARCH Estimation of CoVaR

We modify Adrian and Brunnermeier's (2011) CoVaR, the Value-at-Risk (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 that are farther in the tail, to backtest CoVaR, and to improve its consistency (monotonicity) with respect to the dependence parameter. In addition, unlike in Adrian and Brunnermeier, the CoVaR of an institution here has a time-varying exposure to its VaR due to the time-varying correlation. We define the systemic risk contribution of an institution as the change from its CoVaR in its benchmark state, which we take 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. We also investigate the link between institutions' contributions to systemic risk and their characteristics such as size, leverage, and equity beta. Finally, using 12 months of data prior to the beginning of June 2007, we compute industry groups' pre-crisis systemic risk contributions