A view advanced in the aftermath of the late-2000s financial crisis is that lower than optimal interest rates lead to excessive risk taking by financial intermediaries. We evaluate this view in a quantitative dynamic model in which interest rate policy affects risk taking by changing the amount of safe bonds that intermediaries use as collateral in the repo market. In this model with properly-priced collateral, lower than optimal interest rates reduce risk taking. We also consider the possibility that intermediaries can augment their collateral by issuing assets whose risk is underestimated by credit rating agencies, as was observed prior to the crisis. In the presence of such mispriced collateral, lower than optimal interest rates contribute to excessive risk taking and amplify the severity of recessions.