Backtesting Marginal Expected Shortfall and Related Systemic Risk Measures

This paper proposes an original approach for backtesting systemic risk measures. This backtesting approach makes it possible to assess the systemic risk measure forecasts used to identify the financial institutions that contribute the most to the overall risk in the financial system. Our procedure is based on simple tests similar to those generally used to backtest the standard market risk measures such as value-at-risk or expected shortfall. We introduce a concept of violation associated with the marginal expected shortfall (MES), and we define unconditional coverage and independence tests for these violations. We can generalize these tests to any MES-based systemic risk measures such as SES, SRISK, or ∆CoVaR. We study their asymptotic properties in the presence of estimation risk and investigate their finite sample performance via Monte Carlo simulations. An empirical application is then carried out to check the validity of the MES, SRISK, and ∆CoVaR forecasts issued from a GARCH-DCC model for a panel of U.S. financial institutions. Our results show that this model is able to produce valid forecasts for the MES and SRISK when considering a medium-term horizon. Finally, we propose an original early warning system indicator for future systemic crises deduced from these backtests. We then define an adjusted systemic risk measure that takes into account the potential misspecification of the risk model.