The financial crisis and its aftermath have raised numerous questions about the appropriate role of financial stability considerations in the conduct of monetary policy. This paper develops a simple example of the possible connections between financial stability and monetary policy. We find that even without an explicit financial stability goal for monetary policy, financial stability considerations arise naturally in the context of standard models of optimal monetary policy if the potential magnitude of financial stability shocks is affected by the stance of policy. In this case, similar to the classic analysis of Brainard (1967), policymakers may seek to reduce the variance of output by scaling back the level of policy accommodation provided today in response to an aggregate demand shock relative to the level that would otherwise be provided. However, the policy implications of this possible connection between monetary policy and financial stability are complex even in the simple example considered here. In particular, financial stability considerations may also increase the relative benefits of following a commitment policy relative to a discretionary strategy.