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Bank regulation is supposed to reduce the probability of bank failure and, if a failure occurs, to contain the damage so that system-wide problems are unlikely. The current regulatory framework, known as Basel II, is based, among other things, on risk-adjusted capital requirements. This framework has failed in the recent global financial crisis. Some believe that one of the culprits is the exclusion of so-called shadow banks (for example, hedge funds and investment banks) from regulation. We find little support for this assumption in our simulations. To the contrary, our simulations reveal that extending the same regulation to more entities is likely to produce very synchronous behaviour and thus exacerbate contagion and market crashes. On the other hand, the new size-adjusted regulation (the so-called leverage ratio) that has been proposed in Basel III appears to be more robust.