Interest rate parity is a theory to predict forward foreign exchange rates. These foreign exchange rates are predicted based on the hypothesis that the interest rate differential between two countries should offset the forward exchange rate and the spot exchange rate.

Interest rate parity describes an ideal situation where the spot and foreign exchange rates of two countries are in equilibrium. This theory suggests a strong relationship between interest rates and exchange rates.

Spot exchange rate is the exchange rate that is currently used in the market. It is the rate at which one currency can be converted or exchanged to another currency.

The spot rate of a currency is dictated by the market. For example, the United States Dollar (USD) can be converted to Great Britain Pounds (GBP) at a rate of $1.25 USD for every £1 GBP.

On the other hand, forward foreign exchange rate is the rate at which currencies can be exchanged or converted in some point in the future.

This is different to spot exchange rates which are exchange rates of the time the exchange is taking place. Generally, the forward exchange rate is taken as the rate at which financial institutions agree to exchange currency in one year’s time.

According to the Interest Rate Parity theory, there is a direct relationship between the interest rates in two countries and the differences in the exchange rate of those countries.

This theory conveys that if the interest rates in two countries are different, then the exchange rate of the currencies of those countries will also be different in accordance with the interest rate of the countries after a specific period of time usually taken as one year.

## Arbitrage

Arbitrage is when an entity purchases or sells an asset to profit from it by exploiting the differences in the price of the asset in different markets. In perfect market conditions, arbitrage would not be possible as the price of assets across all markets will be the same.

However, due to market imperfectness, entities can make a profit off of it. This concept also relates to interest rate parity.

For example, if the interest rate in the United States of America is 12% and the interest rate in the United Kingdom is 8%, anyone can borrow money in the UK at 8% and invest it in the USA at 12% and make a 4% profit on it. However, according to Interest Rate Parity, this is not possible.

The theory suggests that while the interest rate is higher in the USA, the difference in the interest rates is offset by the exchange rates of the currencies of the two countries.

So, at the end of the year, while the person might make a 4% profit from interest earnings, it will be offset by the loss the person makes due to the fall in value of the currency of the USA.

According to the theory, the decrease in the rate of exchange will be exactly the same as the difference in interest rates, i.e. 4%.

## Interest Rate Parity: Formula

The formula to calculate the forward exchange rates under the Interest Rate Parity theory is:

**F _{0 }= S_{} x (1 + i_{a} / 1 + i_{b})**

In the formula above, **F _{}** is the forward exchange rate while

**S**is the spot exchange rate. The interest rates for Country A and Country B are represented by

_{}**i**and

_{a}**i**respectively. The interest rates can be obtained from financial institutions of the countries being considered.

_{b}The forward exchange rate quotes between two countries can also be obtained from financial institutions, for example, banks, for a range of period.

The spot exchange rates can be obtained from forex markets or financial institutions. The historical spot rates can also be easily obtained from these institutions or the internet.

The forward and spot rates of the currencies of countries with different interest rates will be different. If the difference between the forward and spot rate is greater than 0 (positive), then the difference is known as forward premium.

However, if the difference between the forward and spot rate is less than 0 (negative) then the difference is known as forwarding discount.

The forward premium or discount status of a currency depends on which currency is being evaluated.

Currencies with lower interest rates will trade at a forward premium while currencies with a higher discount rate will trade at a forward discount.

## Interest Rate Parity: Example

Spot exchange rates between two currencies, the Great Britain Pounds (£) and the United State Dollars ($) is given as below:

£1 GBP = $1.25 USD

$1 USD = £0.8 GBP

The interest rate in the United Kingdom is 8% while the interest rate in the United States is 12%. Assuming a company in the United Kingdom wants to borrow £10,000 in the UK and invest it in the United States, the forward exchange rate can be calculated first as:

F0 = S0 x (1 + ia / 1 + ib)

F0 = £0.8 x (1 + 8% / 1 + 12%)

F0 = £0.8 x (1.08 / 1.12)

F0 = £0.771

This means that the future exchange rate in a year’s time will be £0.76 for $1 instead of £0.8 for $1. As suggested before, because the interest rate of the UK is lower, the value of the GBP will rise in comparison to the US that have a higher interest rate.

So instead of the spot exchange rate is $1.25 for every £1, in a year’s time, due to interest rate differences, it will be $1.30 ($1 / £0.771) for every £1.

This means that the company must first convert the £10,000 to USD, and will receive $12,500. This $12,500 will make the company an interest income of $1,500 ($12,500 x 12%) once invested. Therefore, the company will receive a total of $14,000 ($12,000 + $1,500) in one year. After the year, when the company converts it back to GBP, it will receive approximately £10,800 ($14,000 x 0.771).

However, if the same money were invested in the UK, it would have yielded an interest income of £800 (£10,000 x 8%). This would have made the total amount of £10,800 (£10,000 + £800) at the end of the year.

This is what interest parity suggests. The difference in the interest rates of the two countries was offset by the difference in the spot exchange rate and the forward exchange rate of the currencies of the two countries in a year.

## Conclusion

The Interest Rate Parity suggests a strong relationship between the difference in spot exchange rate and forward exchange rate of currencies of two countries and the interest rate of the two countries.

It suggests that the differential of the interest rates of the two countries is offset by spot rate and forward exchange rate of their currencies.

When the theory is true, entities cannot take advantage of the interest rate differences between the two countries in an arbitrage,