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For a given set of banks, how big can losses in bad economic or financial scenarios possibly get, and what are these bad scenarios? These are the two central questions of stress tests for banks and the banking system. Current stress tests select stress scenarios in a way which might leave aside many dangerous scenarios and thus create an illusion of safety; and which might consider highly implausible scenarios and thus trigger a false alarm. We show how to select scenarios systematically for a banking system in a context of multiple credit exposures. We demonstrate the application of our method in an example on the Spanish and Italian residential real estate exposures of European banks. Compared to the EBA 2016 stress test our method produces scenarios which are equally plausible as the EBA stress scenario but yield considerably worse system wide losses.