Multivariate Inference for Dynamic Systemic Risk Measures

Abstract

We provide statistical inference for marginal expected shortfall (MES) and delta conditional value-at-risk ($\Delta$CoVaR) measures, which are semiparametrically estimated by a two-step procedure in a multivariate GARCH-type framework. We establish the asymptotic properties and illustrate how the estimation uncertainty can be decomposed into dynamic univariate marginal and time-varying dependence components. Moreover, we propose tests for differences in systemic risk in order to construct confidence sets for companies' ranks in systemic risk rankings. In an empirical application based on 50 large US financial institutions, our framework provides novel evidence on the informativeness of such rankings. Our findings highlight the importance of accounting for time-varying return dependence in systemic risk estimators. to cryptocurrency ETFs.