We document a drift in exchange rates before monetary policy changes across major economies. Currencies tend to depreciate by 0.8 percent over ten days before policy rate cuts and appreciate by 0.5 percent before policy rate increases. We show that available fixed income instruments allow to accurately forecast monetary policy decisions and thus that the drift is foreseeable and exploitable by investors. Our baseline specification of a trading strategy constructed by going long in currencies against USD before predicted local interest rate hikes and short in currencies before predicted cuts earns on average a statistically significant excess return of 38 basis points per ten-day period after trading costs. We further demonstrate that this return is robust to the choice of holding horizon and monetary policy forecast rule. Our results thus pose a major challenge for the risk-based explanations of the exchange rate dynamics and highlight an important side effect of monetary policy decisions.