In this paper we model how the existence of different beliefs about the underlying fundamental value of a currency affects the dynamics of the exchange rate. We find that a divergence of beliefs creates the potential for waves of optimism and pessimism that alternate in an unpredictable way. These waves are disconnected from the underlying (objective) fundamental value. We also find that in such a world there is sensitivity to initial conditions, i.e. small changes in beliefs can fundamentally alter the time path of the exchange rate.