Taking the Risk Out of Systemic Risk Measurement

Conditional value at risk (CoVaR) and marginal expected shortfall (MES) have been proposed as measures of systemic risk. Some argue these statistics should be used to impose a “systemic risk tax” on financial institutions. These recommendations are premature because CoVaR and MES are ad hoc measures that: (1) eschew statistical inference; (2) confound systemic and systematic risk; and, (3) poorly measure asymptotic tail dependence in stock returns. We introduce a null hypothesis to separate systemic from systematic risk and construct hypothesis tests. These tests are applied to daily stock returns data for over 3500 firms during 2006-2007. CoVaR (MES) tests identify almost 500 (1000) firms as systemically important. Both tests identify many more real-side firms than financial firms, and they often disagree about which firms are systemic. Analysis of hypotheses tests’ performance for nested alternative distributions finds: (1) skewness in returns can cause false test rejections; (2) even when asymptotic tail dependence is very strong, CoVaR and MES may not detect systemic risk. Our overall conclusion is that CoVaR and MES statistics are unreliable measures of systemic risk