Testing for Systemic Risk Using Stock Returns
The literature proposes several stock return based measures of systemic risk but does not include a classical hypothesis tests for detecting systemic risk. Using a joint null hypothesis of Gaussian returns and the absence of systemic risk, we develop a hypothesis test statistic to detect systemic risk in stock returns data. We apply our tests on conditional value at risk (CoVaR) and marginal expected shortfall (MES) estimates of the 50 largest US financial institutions using daily stock return data between 2006 and 2007. The CoVaR test identifies only one institution as systemically important while the MES test identifies 27 firms including some of the financial institutions that experienced distress in the past financial crisis. We perform a simulation analysis to assess the reliability of our proposed test statistics and find that our hypothesis tests have weak power, especially tests using CoVaR. We trace the power issue to the inherent variability of the nonparametric CoVaR and MES estimators that have been proposed in the literature. These estimators have large standard errors that increase as the tail dependence in stock returns strengthens.