Interest Rate Parity (IRP) Definition, Formula, and Example

What Is Interest Rate Parity (IRP)?

Interest rate parity (IRP) is a theory that the interest rate differential between two countries is equal to the differential between the forward exchange rate and the spot exchange rate.

Understanding Interest Rate Parity (IRP)

Interest rate parity (IRP) plays an essential role in foreign exchange markets by connecting interest rates, spot exchange rates, and foreign exchange rates.

It's the fundamental equation that governs the relationship between interest rates and currency exchange rates. The basic premise of IRP is that hedged returns from investing in different currencies should be the same regardless of their interest rates.

IRP is the concept of no-arbitrage in the foreign exchange markets: the simultaneous purchase and sale of an asset to profit from a difference in the price. Investors can't lock in the current exchange rate in one currency for a lower price and then purchase another currency from a country offering a higher interest rate.

The formula for IRP is:

$\begin{aligned} &F_0 = S_0 \times \left ( \frac{ 1 + i_c }{ 1 + i_b } \right ) \\ &\textbf{where:}\\ &F_0 = \text{Forward Rate} \\ &S_0 = \text{Spot Rate} \\ &i_c = \text{Interest rate in country }c \\ &i_b = \text{Interest rate in country }b \\ \end{aligned}$​F0​=S0​×(1+ib​1+ic​​)where:F0​=Forward RateS0​=Spot Rateic​=Interest rate in country cib​=Interest rate in country b​

Forward Exchange Rate

An understanding of forward rates is fundamental to IRP, especially as it pertains to arbitrage. Forward exchange rates for currencies are exchange rates at a future point in time, unlike spot exchange rates which are current rates.

Forward rates are available from banks and currency dealers for periods ranging from less than a week to five years and more. Forwards are quoted with a bid-ask spread as are spot currency quotations.

The difference between the forward rate and the spot rate is known as swap points. It's known as a forward premium if the forward rate minus the spot rate. is positive. A negative difference is a forward discount.

A currency with lower interest rates will trade at a forward premium in relation to a currency with a higher interest rate. The U.S. dollar typically trades at a forward premium against the Canadian dollar. Conversely, the Canadian dollar trades at a forward discount versus the U.S. dollar.

Covered vs. Uncovered Interest Rate Parity

The IRP is said to be "covered" when the no-arbitrage condition can be satisfied through the use of forward contracts in an attempt to hedge against foreign exchange risk.

The IRP is "uncovered" when the no-arbitrage condition could be satisfied without the use of forward contracts to hedge against foreign exchange risk.

The first option an investor can choose is to invest the foreign currency locally at the foreign risk-free rate for a specific period. The investor would then simultaneously enter into a forward rate agreement to convert the proceeds from the investment into U.S. dollars using a forward exchange rate at the end of the investing period.

The second option would be to convert the foreign currency to U.S. dollars at the spot exchange rate and then invest the dollars for the same amount of time as in option A at the local (U.S.) risk-free rate. The cash flows from both options are equal when no arbitrage opportunities exist.

IRP has been criticized based on the assumptions that come with it. The covered IRP model assumes that there are infinite funds available for currency arbitrage and this is obviously not realistic. Uncovered IRP doesn't tend to hold in the real world when futures or forward contracts aren't available to hedge.

Covered Interest Rate Parity Example

Let's assume that Australian Treasury bills are offering an annual interest rate of 1.75%. U.S. Treasury bills are offering an annual interest rate of 0.5%. An investor in the United States who wants to take advantage of Australia's interest rates would have to exchange U.S. dollars for Australian dollars to purchase the Treasury bill.

The investor would then have to sell a one-year forward contract on the Australian dollar but the transaction would have a return of only 0.5% under the covered IRP. The no-arbitrage condition would be violated otherwise.

The Bottom Line

IRP is the fundamental equation that governs the relationship between interest rates and currency exchange rates. Its basic premise is that hedged returns from investing in different currencies should be the same regardless of their interest rates.

Arbitrage or the simultaneous purchase and sale of an asset to profit from a difference in the price should essentially exist in the foreign exchange markets. Investors can't lock in the current exchange rate in one currency for a lower price and then purchase another currency from a country offering a higher interest rate.