We study optimal monetary policy in the presence of financial stability concerns. We build a model in which monetary easing can lower the cost of capital for firms and restore the natural level of investment, but does also subsidize inefficient maturity transformation by financial intermediaries in the form of “carry trades" that borrow cheap at the short-term against illiquid long-term assets. Carry trades not only lead to financial instability in the form of rollover risk, but also crowd out real investment since intermediaries equate the marginal return on lending to firms to that on carry trades. Optimal monetary policy trades off any stimulative gains against these costs of carry trades. The model provides a framework to understand the puzzling phenomenon that the unprecedented post-2008 monetary easing has been associated with below-trend real investment, even while returns to real and financial capital have been historically high.