# Interest Rate Parity

Interest rate parity (IRP) is a concept which states that the interest rate differential between two countries is the same as the differential between the forwarding exchange rate and the spot exchange rate. Put simply, the interest rate parity suggests a relationship between interest rates, spot exchange rates, and forward exchange rates—which means investors can be indifferent to interest rates between countries.

This essentially means that if the IRP theory is true, then it does not really matter whether an investor converts his money into a foreign currency and invests the same into that foreign country, or invests the money in the home country and then converts the proceeds into the foreign currency, as he would be earning exactly the same amount of money in both the situations.

When the exchange rate risk is ‘covered’ by a forward contract, the condition is called covered interest rate parity. When the exposure to foreign exchange risk is uncovered (when no forward contract exists) and the IRP is to be based on the expected future spot rate, it is called an uncovered interest rate parity.

## Interest Rate Parity Formula

$F_{0} = S_{0} \times \bigg( \dfrac{1 + i_{a}}{1 + 1_{b}} \bigg)$
• F0 = Forward Exchange Rate
• S0 = Spot Exchange Rate
• ia  = Interest rate of country A (quote currency)
• ib  = Interest rate of country B (base currency)

The spot exchange rate refers to the current exchange rates prevalent between any two countries and the forward exchange rate is the exchange rate between the two currencies at any future point in time.

Both spot and forward exchange rates are usually available with financial institutions such as banks and currency dealers. In fact, one can get forward rate quotes between two countries for periods ranging from a week to as long as five years.

If the difference between the forward rate and the spot rate is positive, then the currency is said to be trading at a forward premium, but if the difference between the forward rate and the spot rate is negative, then the currency is said to be trading at a forward discount.

Normally, the currency with the lower interest rates will trade at a forward premium while the currency with the higher interest rates trades at a forward discount.

The interest rate of country A is the interest rate in the foreign country where the investor hopes to invest and the interest rate of Country B is the interest rate in the home country of the investor.

## Interest Rate Parity Example

You are provided with the following details. Calculate the forward exchange rate as per the interest rate parity concept.

Using the formula, we can work out the forward rate using the numbers in the table:

$Forward\: Exchange\: Rate = 0.7864 \times \bigg( \dfrac{1 + 0.03}{1 + 0.05} \bigg) = 0.771421$

Since the difference between the forward exchange rate and the spot exchange rate is negative, it indicates that the dollar is trading at a forward discount as compared to the Euro.

Let us illustrate the IRP concept by considering two situations:

Situation 1:  If an investor were to invest $1000 in a 5% interest bearing instrument in the United States for one year, and exchange the sum earned into Euros in one year, he would have earned$1050 [1000+ (1000*5%)] in one year. Converting this earned amount of $1050 into Euros would mean using the IRP forward exchange rate of 0.771421. That would earn him 809.992 Euros (1050* 0.771421) Situation 2: Say, the investor decides to convert his$1000 into Euros and invest the money in a 3% interest bearing instrument in Germany, and exchange the sum earned back into US Dollars after one year. Converting \$1000 in the spot exchange rate of 0.7864 would give him 786.4 Euros (1000*0.7864). When he invests this 786.4 Euros in a 3% interest bearing instrument in Germany for one year, he will receive the same 809.992 Euros [786.4 + (786.4*3%)] after one year.

In essence, if the IRP concept were to hold, the investor would earn the same amount of money in both currencies irrespective of the exchange rates.

## Interest Rate Parity Analysis

The IRP concept implies that the concept of arbitrage does not exist which means that investors will not be able to profit from the difference in the interest rates of different currencies. If the IRP concept does not hold up, then it gives opportunities for investors and forex traders to make riskless profits.

Continuing with the above example, say the investor locks up his forward contract for the IRP forward exchange rate of 0.771421 (Euro/USD) but the actual forward exchange rate turns out to be 0.7899, which is higher than the locked forward rate of 0.771421. So instead of earning 809.992 Euros (1050* 0.771421), he would be earning 829.395 Euros (1050* 0.7899). This basically means the investor can make a profit by exploiting the difference in the forward rates.

Despite its importance, IRP comes with its own set of limitations.

1. IRP assumes that capital can freely move across countries.
2. The other assumption is that of perfect asset substitutability which essentially means that IRP assumes that domestic and foreign assets can be perfectly substituted for one another.

But that is not always the case due to various external risks including liquidity risks, political risks, costs, and taxation.

Despite the limitations, covered interest rate parity holds true in many situations when there is scope for free capital movement and limited capital controls. But uncovered interest rate parity rarely works in real-life situations due to the presence of multiple risk factors.

## Interest Rate Parity Conclusion

To sum up:

• Interest Rate Parity suggests that the difference in interest rates between two countries is equal to the difference between the forward exchange rate and the spot exchange rate
• IRP helps define the relationship between interest rates, spot rates, and forward rates and suggests that there will be no scope for arbitrage in interest rate differentials since the difference in the exchange rates would be reflected as either forward premium or forward discount.
• Interest Rate Parity can be either covered interest rate parity or uncovered interest rate parity depending upon the existence or non-existence of a forward contract
• IRP is based on assumptions of capital mobility and asset substitutability

## Interest Rate Parity Calculator

You can use the interest rate parity calculator below to work out the forward exchange rate and determine if it is trading at a forward premium or a forward discount by entering the required numbers.