We study zero interest-rate policy in response to a large negative demand shock when long-run inflation 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. Optimal policy is well-approximated by a constant calendar-based forward guidance, independent of the shock’s realized persistence. This insurance principle qualitatively and quantitatively distinguishes our paper from other recent research on bounded rationality and the forward guidance puzzle.