A number of empirical studies have reported the result that exchange rates show a delayed overshooting in response to monetary policy shocks. This result is puzzling. Economic theory suggests that the overshooting should occur immediately after the shock, not with a delay. This paper uses a 'new open economy macroeconomics' model with pricing-to-market to analyze whether the assumption of noise trading in the foreign exchange market helps to resolve the delayed overshooting puzzle. The implications of noise trading for the effects of monetary policy shocks on the nominal and on the real exchange rate are analyzed.