How much capital should financial intermediaries hold? We propose a general equilibrium model with a financial sector that makes risky long‐term loans to firms, funded by deposits from savers. Government guarantees create a role for bank capital regulation. The model captures the sharp and persistent drop in macro‐economic aggregates and credit provision as well as the sharp change in credit spreads observed during financial crises. Policies requiring intermediaries to hold more capital reduce financial fragility, reduce the size of the financial and non‐financial sectors, and lower intermediary profits. They redistribute wealth from savers to the owners of banks and non‐financial firms. Pre‐crisis capital requirements are close to optimal. Counter‐cyclical capital requirements increase welfare.