Multiple Equilibria in a Simple Asset Pricing Model with Foresight∗

Motivated by recent Federal Reserve’s unconventional monetary policies, this paper explicitly models the central bank’s large-scale asset purchases(LSAPs) along with its foresight brought by forward guidance by characterizing the central bank’s actions as a liquidity trader who sends signals to the public q period in advance. Assuming negative-exponential utility with Gaussian uncertainty(CARA-Normal framework), we show that there are exactly two stationary equilibria(one stable and one unstable) in the single period model, with the effects of introducing foresight makes the stable equilibrium more stable and the unstable equilibrium more unstable. Extending the single period model to the N -period dynamic model will possibly yield 2max(N−q,1) equilibria, both in the case of expected terminal wealth maximization and intertemporal expected utility maximization.