Making heads or tails of systemic risk measures

Abstract: This paper shows that the CoVaR,$\Delta$-CoVaR,CoES,$\Delta$-CoES and MES systemic risk measures can be represented in terms of the univariate risk measure evaluated at a quantile determined by the copula. The result is applied to derive empirically relevant properties of these measures concerning their sensitivity to power-law tails, outliers and their properties under aggregation. Furthermore, a novel empirical estimator for the CoES is proposed. The power-law result is applied to derive a novel empirical estimator for the power-law coefficient which depends on $\Delta\text{-CoVaR}/\Delta\text{-CoES}$. To show empirical performance simulations and an application of the methods to a large dataset of financial institutions are used. This paper finds that the MES is not suitable for measuring extreme risks. Also, the ES-based measures are more sensitive to power-law tails and large losses. This makes these measures more useful for measuring network risk but less so for systemic risk. The robustness analysis also shows that all $\Delta$ measures can underestimate due to the occurrence of intermediate losses. Lastly, it is found that the power-law tail coefficient estimator can be used as an early-warning indicator of systemic risk.