# Interest rate parity

Interest rate parity is an economic theory that states that the interest rate differential between two countries is equal to the differential between current and future exchange rates.

Basically what it establishes is that if there is a positive difference in interest rates, there must also be a difference in exchange rates. So that the future exchange rate is higher than the current one.

Therefore, in the country with the highest interest rate, its currency must depreciate in the future. Let's look at this analytically below.

## Interest rate parity analytically

The difference in interest rates will equal the difference in exchange rates. Therefore, the formula to calculate the future price of the exchange rate will be as follows (the spot being the current exchange rate between both currencies, d the domestic market and ext the foreign market):

Let's imagine that we want to trade in the euro currency against the dollar (€ / $). So the formula for the future exchange rate will be:

Or put another way, the interest rates will be equal to the difference in the exchange rates:

As we can see, if interest rates are higher in the US, the currency in the future also has to be higher. And this must be fulfilled to the same extent. That is, if interest rates in the US are 2% higher and the exchange rate is $ 1.20 per euro at the current time. So, the euro dollar in the future must be 2% higher than it is currently, that is, 1,224 dollars per euro (1.2 x 1.02). This implies that the dollar would depreciate 2% in the future in relation to the current rate. Mathematically it would be:

This relationship is what prevents a possible arbitrage in the currency market, because otherwise someone could finance themselves in the country that offers lower interest rates and buy the other currency obtaining a risk-free risk.

That is, arbitrage could exist when it is possible to make a profit from this spread without any risk. Investors could try to borrow in the currency with the lowest interest rate. To later invest that borrowed amount in an asset in the other currency that grants a higher interest rate. But equality in exchange rate differentials eliminates this possibility.

## Interest rate parity rates

There are two ways in which the interest rate parity theory appears in the financial world:

- Covered interest rate parity: Establishes that the future exchange rate should incorporate the difference in the interest rates of the two countries. If this does not occur, there will be a possibility of arbitration. Here the investor would not have the opportunity to make a profit by borrowing in one currency and investing in the other. This is because the cost of hedging the currency risk outweighs the potential benefit. That is, of the possible profit for investing in the currency that has a higher interest rate.
- Uncovered interest rate parity: Establishes that the difference in interest rates is equal to the expected future change in the exchange rate. That is, if the difference in interest rates is 2%, the currency with the highest interest rate should devalue 2% in the future. In this case, there is a possibility of arbitration. Well, since it is an expected exchange rate, it could happen that this devaluation is not fulfilled in the future. And therefore the investor does have a profit opportunity by borrowing in one currency and investing in another.