This study provides empirical evidence to support an explanation for the puzzling patterns described by Engel (2016) regarding interest rate differentials and foreign exchange rates; while a high-interest-rate currency tends to earn a positive excess return in the short run, its long-run excess return tends to be negative. We present an explanation of these patterns based on inflation risk premia: whereas short-term interest rates do not affect short-term inflation risk premia, they negatively affect long-term inflation risk premia. Different responses of short-term and long-term inflation risk premia generate different patterns of short-term and long-term FX excess returns.