If this speculator relies on his expectations regarding the future spot rate to sell his euros and, therefore, sells those euros in the future spot market, he engages in an uncovered interest arbitrage: When a speculator has a forward contract with a predetermined forward rate at which he’ll sell currency in the future, this time he engages in covered interest arbitrage.

If a speculator doesn't have a forward contract to exchange currency at a future date, he just has his expectations regarding the future spot rate and used the future spot market to exchange currency.

Suppose that an American investor wants to make use of the differences in interest rates on the dollar and the euro, as well as the expected change in the dollar–euro exchange rate between now and sometime in the future by putting his money in a euro-denominated security. Therefore, he buys euros today, invests in the security, and, at maturity, sells his euros and converts them into dollars.

The IRP, however, assumes that the speculator gets a forward contract to exchange foreign currency in the future. Having a forward contract doesn’t solve all his problems. Nevertheless, a forward contract can limit a speculator’s exposure to unexpected and potentially large changes in future spot rates.

Now that you know about the difference between uncovered and covered interest arbitrage, when does a speculator makes a profit based on the covered interest rate arbitrage?

In order to think about your profit opportunities using the Interest Rate Parity (IRP) or the covered interest arbitrage, consider calculations of ρ and the IRP-suggested forward rate. ρ is calculated based on the interest rate differential between countries. When you plug your calculated ρ into the forward rate formula, to separate it from the bank’s forward rate, you call it the IRP-suggested forward rate.

Suppose you collect data about the relevant interest rates and the spot exchange rate. You go to the bank and ask about its forward rate. If the IRP-suggested forward rate is the same as the bank’s forward rate, the IRP holds; neither domestic nor foreign investors have an opportunity to engage in covered interest arbitrage and make profits.

In other words, neither investor can use covered interest arbitrage to enjoy higher returns than the ones provided in their home countries. In this case, the change between the forward rate and the spot rate offsets the interest rate differential between two countries.

The IRP does not hold if the bank’s forward rate does not reflect the interest rate differential. In other words, when you go to the bank and ask about its forward rate, its forward rate may be different than the IRP-suggested forward rate. In this case, either you or a foreign speculator can earn excess profits by investing in securities in the other country, but, under normal circumstances, not both of you.