Before revision:  We show that the three widely-used systemic risk measures  conditional value-at-risk (CoVaR), conditional expected shortfall (CoES) and marginal expected shortfall (MES), which measure the risk of a position Y given that a reference position X is in distress, fail to be identifiable and elicitable on their own. As a remedy, we establish the joint identifiability of CoVaR, MES and (CoVaR, CoES) together with the value-at-risk (VaR) of the reference position X . While this resembles the situation of the classical risk measures expected shortfall (ES) and VaR concerning identifiability, a joint elicitability result fails.
After revision:  We show that the three widely-used systemic risk measures conditional value-at-risk (CoVaR), conditional expected shortfall (CoES) and marginal expected shortfall (MES), which measure the risk of a position Y given that a reference position X is in distress, fail to be identifiable and elicitable . We establish the joint identifiability of CoVaR, MES and (CoVaR, CoES) together with the value-at-risk (VaR) of the reference position X . While this resembles the situation of the classical risk measures expected shortfall (ES) and VaR concerning identifiability, a joint elicitability result fails.