## What is Interest Rate Parity Theory?

Interest rate parity theory is the representation of the relationship between interest rates and exchange rates of two countries. The theory further states that the difference in interest rates differentiates the exchange rate of two countries. This implies that the currency of a high interest rate country will be at forward discount in comparison to the currency of a low interest rate country. The vice versa is also true.

In other words, the interest rate differential will be equal to the interest rate differential between two countries.

Interest rate differential = Exchange rate differential

1+rF/ 1+rD = f (F/D)/S(F/D)

where rF = interest rate of country F

rD = interest rate of domestic country

f(F/D) = spot exchange rate between the countries foreign country and domestic country

S(F/D) = forward rate between foreign country and domestic country

The theory states that the high interest rate on a currency is offset by forward premium. It is the responsibility of arbitrage that ensure that it happens.

### Example of Interest Rate Parity Theory

Suppose that the interest rate on a one year bond in India is 13 per cent while similar bond in USA pay 10 per cent interest. The spot rate for $0.1522/INR and the 1 year forward rate is $0.1455/INR. So, now if you have a choice of investment, which one you should choose?

It is clearly seen that INR is trading at a forward discount. Let’s assume that you have USA $100. If you invest $100 in USA, at the end of one year, you will receive $110.

Alternatively, you can exchange US $100 for Indian rupees at the spot rate, you will receive 100/0.1522 which equals to 657. You can invest 500 at 13 per cent for one year. At maturity, you will receive 657 *1,13 which is equals to 742. Now you can sell the Indian rupee forward and immediately receive 742 * 0.1455.

The answer is simple, what you gain on the interest rate differential, you lose on the exchange rate differential. In simple words, there is a parity between the interest rates and exchange rates.