What are the channels through which monetary policy affects financial stability? Can (and should) central banks prevent financial crises by deviating from price stability? To what extent may monetary policy itself unintentionally breed financial vulnerabilities? We answer these questions using a New Keynesian model with capital accumulation and endogenous financial crises due to adverse selection and moral hazard in credit markets. Our findings are threefold. First, monetary policy affects the probability of a crisis both in the short run (via aggregate demand) and in the medium run (via capital accumulation). Second, the central bank can reduce the incidence of crises in the medium run by tolerating higher inflation volatility in the short run. Third, prolonged periods of loose monetary policy followed by a sharp tightening can lead to financial crises.