We study the possibility of (almost) self-fulfilling waves of optimism and pessimism and self-fulfilling liquidity traps in a New Keynesian model with a continuum of heterogeneous expectations. In particular, all agents choose, based on past forecasting performance, expectation values out of a distribution around the targets of the central bank. This framework allows us to explicitly model the ?anchoring? of expectations as the variance of this distribution of possible expectation values. We find that when the zero lower bound on the nominal interest rate is not binding, adequate monetary policy can prevent waves of optimism and pessimism and exclude near unit root dynamics, even when expectations are unanchored. However, as shocks bring the economy to a situation with a binding zero lower bound, there is a danger of a long lasting self-fulfilling liquidity trap that can take the form of a deflationary spiral. This can be prevented if expectations are strongly enough anchored to the targets, or if the inflation target is high enough.