We study zero interest-rate policy in response to a large negative demand shock when long-run expectations can fall over time. Because falling expectations make monetary policy less effective by raising real interest rates, the optimal forward guidance policy makes large front-loaded promises to stabilize expectations. Policy is too stimulatory in the event of transitory shocks, but provides insurance against persistent shocks. The optimal policy is well-approximated by a constant calendar-based forward guidance, independent of the shock's realised persistence. The insurance property distinguishes our paper from other bounded rationality papers that solve the forward guidance puzzle and generates important quantitative differences.