Before revision:  The theoretical results relate the dependence consistency of CoVaR using conditioning on X>=VaR_\alpha(X) to well established results on concordance ordering of multivariate distributions or their copulas.
After revision:  We prove general results that relate the dependence consistency of CoVaR using conditioning on X>=VaR_\alpha(X) to well established results on concordance ordering of multivariate distributions or their copulas.