### What Is Interest Rate Parity (IRP)?

Interest rate parity (IRP) is a theory in which the interest rate differential between two countries is equal to the differential between the forward exchange rate and the spot exchange rate. Interest rate parity plays an essential role in foreign exchange markets, connecting interest rates, spot exchange rates and foreign exchange rates.

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### The Formula For Interest Rate Parity (IRP) Is

﻿\begin{aligned} &F_0 = S_0 \times \left ( \frac{ 1 + i_c }{ 1 + 1_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}﻿

### How to Calculate Interest Rate Parity (IRP)

Forward exchange rates for currencies are exchange rates at a future point in time, as opposed to spot exchange rates, which are current rates. An understanding of forward rates is fundamental to interest rate parity, especially as it pertains to arbitrage (the simultaneous purchase and sale of an asset in order to profit from a difference in the price).

Forward rates are available from banks and currency dealers for periods ranging from less than a week to as far out as five years and beyond. As with spot currency quotations, forwards are quoted with a bid-ask spread.

The difference between the forward rate and spot rate is known as swap points. If this difference (forward rate minus spot rate) is positive, it is known as a forward premium; a negative difference is termed 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. For example, 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.

### What Does Interest Rate Parity (IRP) Tell You?

Interest rate parity is the fundamental equation that governs the relationship between interest rates and currency exchange rates. The basic premise of interest rate parity is that hedged returns from investing in different currencies should be the same, regardless of the level of their interest rates.

If one country offers a higher risk-free rate of return in one currency than that of another, the country that offers the higher risk-free rate of return will be exchanged at a more expensive future price than the current spot price. In other words, the interest rate parity presents an idea that there is no arbitrage in the foreign exchange markets. Investors cannot 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.

### Key Takeaways

• Interest rate parity is the fundamental equation that governs the relationship between interest rates and currency exchange rates.
• The basic premise of interest rate parity is that hedged returns from investing in different currencies should be the same, regardless of the level of their interest rates.
• Parity is used by forex traders to find arbitrage opportunities.

### Covered Versus Uncovered Interest Rate Parity (IRP)

The interest rate parity is said to be covered when the no-arbitrage condition could be satisfied through the use of forward contracts in an attempt to hedge against foreign exchange risk. Conversely, the interest rate parity is said to be uncovered when the no-arbitrage condition could be satisfied without the use of forward contracts to hedge against foreign exchange risk.

#### Options of Converting Currencies

The relationship can be seen in the two methods an investor may take to convert foreign currency into U.S. dollars.

One option an investor may take would be to invest the foreign currency locally at the foreign risk-free rate for a specific time 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, then invest the dollars for the same amount of time as in option A, at the local (U.S.) risk-free rate. When no arbitrage opportunities exist, the cash flows from both options are equal.

### Real World Example of Covered Interest Rate Parity (IRP)

For example, assume Australian Treasury bills are offering an annual interest rate of 1.75%, while U.S. Treasury bills are offering an annual interest rate of 0.5%. If an investor in the United States seeks to take advantage of the interest rates in Australia, the investor would have to translate U.S. dollars to Australian dollars to purchase the Treasury bill.

Thereafter, the investor would have to sell a one-year forward contract on the Australian dollar. However, under the covered interest rate parity, the transaction would only have a return of 0.5%, or else the no-arbitrage condition would be violated.

### Limitations of IRP

Interest rate parity has been criticized based on the assumptions that come with it. For instance, the covered IRP model assumes that there are infinite funds availability that can be used for currency arbitrage, which is obviously not realistic. When futures or forward contracts are not available to hedge, uncovered interest rate parity does not tend to hold in the real world.