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We analyze whether four market‐based measures of the global systemic importance of financial institutions offer early warning signals during three financial crises. The tests based on the 2007–2008 crisis show that only one measure (∆CoVaR) consistently adds predictive power to conventional early warning models. However, the additional predictive power remains small and it is not normally confirmed for the Asian and the 1998 crises. We conclude that it is problematic to identify a market‐based measure of systemic importance that remains valid across crises with different features. The same criticism also applies to several conventional proxies of systemic importance, of which size is the most consistent performer.