Both the literature and new empirical evidence show that exchange rate regimes differ primarily by the noisiness of the exchange rate, not by measurable macroeconomic fundamentals. This motivates a theoretical analysis of exchange rate regimes with noise traders. The presence of noise traders can lead to multiple equilibria in the foreign exchange market. The entry of noise traders alters the composition of the market and generates excess exchange rate volatility, since noise traders both create and share the risk associated with exchange rate volatility. In such circumstances, monetary policy can be used to lower exchange rate volatility without altering macroeconomic fundamentals.