# Interest Rate Parity (IRP) Theory of Exchange Rate

When Purchasing Power Parity (PPP) Theory applies to product markets, Interest Rate Parity (IRP) condition applies to financial markets. Interest Rate Parity (IRP) theory postulates that the forward rate differential in the exchange rate of two currencies would equal the interest rate differential between the two countries. Thus it holds that the forward premium or discount for one currency relative to another should be equal to the ratio of nominal interest rate on securities of equal risk (and duration) denominated in two currencies.

For example, where the interest rate in India and US are respectively 10% and 6% and the dollar-rupees spot exchange rate is Rs.42.50/US \$. The 90 day forward exchange rate would be calculated as per IRP as follows:

= 42.50  (1+0.10/4)/(1+0.06/4)

= Rs.42.9250

And hence, the forward rate differential [forward premium (p)] will be;

(42.9250 – 42.50)/42.50 = 1%

And the interest rate differential will be;

(1+0.10/4) /(1+0.06/4)  – 1   = p

i.e., 1.01 – 1 = p

Therefore, p = 0.01 or 1%

Thus, If there is no parity between the forward rate differential and interest rate differential, opportunities for arbitrage will arise. Arbitrageurs will move funds from one country to another for taking advantage of disparity. But in an efficient market, with free flow of capital and negligent transaction cost, continuous arbitration process will soon restore parity between the forward rate differential and interest rate differential which is called as covered interest arbitration.

Let us take another example where the interest rate in India and the USA are 12% and 4% respectively, the dollar-rupee exchange rates are: Spot = Rs.42.50/\$.1 and Forward (90) = Rs.43.00/\$.1. The Forward rate differential and interest rate differential will be calculated as follows:

Forward rate differential = (43.00 – 42.50)/  42.50

= 0.01176 i.e., 1.176%

Interest rate differential, p = (1+0.12/4)/(1+0.04/4)  – 1

= 0.0198 i.e., 1.98%

Thus, here  there is disparity  between the forward rate differential and interest rate differential,  The interest rate differential is higher than the forward rate differential. Arbitrageurs will move funds from one country to another for taking advantage of this disparity. i.e., Funds will move from USA to India to take advantage of the higher interest rate in India

The arbitration process will be as follows:

1. Arbitrageur will borrow \$1000 from US market for a three month period at interest rate prevailing at 4%
2. Convert US Dollar into Indian Rupees at the Spot exchange rate to get Rs.42,500
3. Invest this money for a three months period in India at the interest rate prevailing  which is 12%

After three months :

1. The Arbitrageur will liquidate the rupee investment to get Rs. 43,775 (42,500+ 1275)
2. Buy US Dollar as per the forward contract at Rs.43/1\$ and receive US \$ 1,108 by converting Indian Rupees into US \$ i.e., (43,775/43) which is US\$ 1,018
3. Repay the US loan by paying US\$ 1,010, i.e., (1000 * 4% for 3 months)
4. Makes an arbitrage profit of US\$8.

This will continue where more and more arbitrageurs will enter into the market to take advantage of the disparity in interest and forward rate which ultimately has the impact on the interest rates and exchange rates as follows;

• Borrowings more in the US will raise the interest rate there
• Investing larger funds in India will lower the interest rate in India

As a result of which the interest rate differential will narrow

• Selling dollars at the spot rate will lower the spot exchange rate as the demand for forward contract is higher.
• And Buying dollars in the forward market at the forward rate will raise the forward exchange rate

As a result of which the Forward rate differential will widen.

The Interest Rate Parity (IRP) theory points out that in a freely floating exchange system, exchange rate between currencies, the national inflation rates and the national interest rates are interdependent and mutually determined. Any one of these variables has a tendency to bring about proportional change in the other variables too.

Limitations of IRP Theory: To a large extent, forward exchange rates are based on interests’ rate differential. This theory assumes that arbitrageurs will intervene in the market whenever there is disparity between forward rate differential and interest rate differential. But such intervention by arbitrageurs will be effective only in a market which is free from controls and restrictions. Another limitation is that regarding the diversity of short term interest rates in the money market (where interest rates on Treasury Bills, Commercial Paper, etc., differ) which creates problem while taking interest rate parity. Extraneous economic and political factors may sometimes enhance speculative activities in the foreign exchange market. Market expectation also has strong influence in the determination of Forward rates.

Credit: International Finance Notes-MGU