The paper elicits a mechanism by which private leverage choices exhibit strategic complementarities through the reaction of monetary policy. When everyone engages in maturity transformation, authorities have little choice but facilitating refinancing. In turn, refusing to adopt a risky balance sheet lowers the return on equity. The key ingredient is that monetary policy is non-targeted. The ex post benefits from a monetary bailout accrue in proportion to the number amount of leverage, while the distortion costs are to a large extent fixed. This insight has important consequences. First, banks choose to correlate their risk exposures. Second, private borrowers may deliberately choose to increase their interest-rate sensitivity following bad news about future needs for liquidity. Third, optimal monetary policy is time inconsistent. Fourth, macro-prudential supervision is called for. We characterize the optimal regulation, which takes the form of a minimum liquidity requirement coupled with monitoring of the quality of liquid assets. We establish the robustness of our insights when the set of bailout instruments is endogenous and characterize the structure of optimal bailouts.