# 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 that exists between current and future exchange rates .

Basically what it establishes is that if there is a positive difference in interest rates it will also have to be in exchange rates. So that the future exchange rate is higher than the one that currently exists.

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

## Analytical interest rate parity

The difference in interest rates will be equal to the difference in exchange rates. So 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 must also 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 should be 2% higher than it is today, 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 the one that avoids 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 risk-free risk.

That is, arbitration could exist when it is possible to obtain a benefit from this differential without any risk. Investors may try to borrow in the lower interest rate currency. To later invest that amount borrowed 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 theory of interest rate parity 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 happen 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 currency risk outweighs the potential benefit. That is, the possible benefit of 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 exchange rate change. In other words, if the interest rate difference is 2%, the currency with the highest interest rate should devalue 2% in the future. In this case there is a possibility of arbitration. As 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. ##### byAbdullah Sam
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