Backtesting Systemic Risk Forecasts Using Multi-Objective Elicitability

Systemic risk measures such as CoVaR, CoES, and MES are widely-used in finance, macroeconomics and by regulatory bodies. Despite their importance, we show that they fail to be elicitable and identifiable. This renders forecast comparison and validation, commonly summarized as “backtesting,” impossible. The novel notion of <i>multi-objective elicitability</i> solves this problem by relying on bivariate scores equipped with the lexicographic order. Based on this concept, we propose Diebold–Mariano type tests with suitable bivariate scores to compare systemic risk forecasts. We illustrate the test decisions by an easy-to-apply traffic-light approach. Finally, we apply our traffic-light approach to DAX 30 and S&amp;P 500 returns, and infer some recommendations for regulators.