Conditional value at risk (CoVaR) and marginal expected shortfall (MES) have been proposed as stock return based measures of the systemic risk created by individual financial institutions even though the literature provides no formal hypothesis test for detecting systemic risk. We address this shortcoming by constructing hypothesis test statistics for CoVaR and MES that can be used to detect systemic risk at the institution level. We apply our tests 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 the hypothesis tests' performance for plausible alternative hypotheses finds that return skewness can cause test rejections and, even when systemic risk imparts a strong signal in stock return distributions, hypothesis tests based on CoVaR and MES may fail to detect it. Our overall conclusion is that CoVaR and MES are not reliable measures of systemic risk.
