An Unambiguous Statement of Interest Rate Parity

Interest rate parity (IRP) states that the difference between the interest rates of two currencies equals the expected percentage change in the associated exchange rate. Unfortunately, IRP is ambiguous. There are two inconsistent values of the expected percentage change in the exchange rate, depending on which currency is treated as the numeraire. We derive a corrected IRP condition that is unambiguous but subtly different. The equilibrium interest rate differential equals the percentage difference between the spot exchange rate and the geometric mean of the future exchange rate distribution, not its expected value