  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 summarised as `backtesting', impossible.
The novel notion of \emph{multi-objective elicitability} solves this problem.
Specifically, we propose Diebold--Mariano type tests utilising two-dimensional
scores equipped with the lexicographic order. We illustrate the test decisions
by an easy-to-apply traffic-light approach. We apply our traffic-light approach
to DAX~30 and S\&P~500 returns, and infer some recommendations for regulators.
