The economic theory of interest rate parity states that the difference between the interest rate in two countries is equal to the differential between the forward rate and the spot rate of those two countries. This equality does not always exist, and thus allows traders to arbitrage option positions to earn riskless returns.
For interest rate parity to exist, there must be easy capital mobility between countries, along with complete substitutability of assets. For instance, a deposit in a foreign bank is considered the same as a deposit in a domestic bank. If the nominal returns were different between the domestic and foreign deposits, investors would move their money to the bank paying the higher nominal return.
Interest rate parity exists when the expected nominal rates are the same for both domestic and foreign assets. Any difference is due to expected appreciation or deprecation in the foreign or domestic currencies. For instance, if the domestic interest rate is 8%, and the foreign interest rate is 5%, this means that the market expects the foreign currency to appreciate by 3%, or conversely, investors expect the domestic currency to depreciate by 3%.
In that scenario, it doesn’t matter if an investor invests in a timed foreign deposit and then converts the foreign currency to his domestic currency, or invests in a timed domestic deposit and then converts the domestic currency to the foreign currency. With interest rate parity, either option produces the exact same cash flow.