Page "Interest rate parity" Paragraph 13

Uncovered interest rate parity asserts that an investor with dollar deposits will earn the interest rate available on dollar deposits, while an investor holding euro deposits will earn the interest rate available in the eurozone, but also a potential gain or loss on euros depending on the rate of appreciation or depreciation of the euro against the dollar.

Economists have extrapolated a useful approximation of uncovered interest rate parity that follows intuitively from these assumptions.

If uncovered interest rate parity holds, such that an investor is indifferent between dollar versus euro deposits, then any excess return on euro deposits must be offset by some expected loss from depreciation of the euro against the dollar.

Conversely, some shortfall in return on euro deposits must be offset by some expected gain from appreciation of the euro against the dollar.

The following equation represents the uncovered interest rate parity approximation.