# Interest Rate Parity Formula – What is Interest Rate Parity?

## What Is Interest Rate Parity (IRP)? Interest rate parity (IRP) is the fundamental equation that governs the relationship between interest rates and currency exchange rates. Interest rate parity (IRP) plays an essential role in foreign exchange markets. It connects interest rates with spot exchange rates and foreign exchange rates. According to IRP theory, the interest rate differential between two countries is equal to the differential between the forward exchange rate and the spot exchange rate. The basic premise of interest rate parity is that hedged returns from investing in different currencies should be the same, regardless of their interest rates. Parity is used by forex traders to find arbitrage opportunities.

There is an underlying concept behind interest rate parity.  It doesn’t matter whether a person invests money in their home country and then converts those earnings to another currency.  Or, converts the money first and invests the money overseas. Interest rates and forward currency rates are intertwined.  Therefore, the investor makes the same amount of money either way.

IRP is 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 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. (Source: investopedia.com)

## Interest Rate Parity Formula

Before looking at the interest rate parity formula, it’s helpful to explain the terminology used.

Spot exchange rates are the current exchange rates, while forward exchange rates refer to the future exchange rate of a currency. Banks and currency dealers offer forward rates from days to years, quoted at a bid-ask spread. The difference between a spot rate and a forward rate is called a swap point. When the difference is positive, it’s called a forward premium. A negative difference is a forward discount. When a currency with lower interest rates is compared to one with higher rates, it trades at a forward premium.

There are different interest rate parity equations for covered and uncovered IRP. Covered IRP shows the forward exchange rate.  The uncovered IRP shows the spot exchange rate. Below is the uncovered interest rate parity formula

### F = S (1+ia / 1 + ib)

• F = Forward rate
• S = Spot rate
• ia = Interest rate in country a
• ib = Interest rate in country b

Forward exchange rates for currencies are exchange rates at a future point in time.  This is in contrast to spot exchange rates, which are current rates. An understanding of exchange rates is fundamental to IRP, especially as it pertains to arbitrage. 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 more. 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.  On the other hand, 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. (Source: ibid)

## Covered Interest Rate Parity (IRP) vs Uncovered

### What Is Covered Interest Rate Parity?

Covered interest rate parity refers to a theoretical condition.  It is where the relationship between interest rates and the spot and forward currency values of two countries are in equilibrium. The covered interest rate parity condition means there is no opportunity for arbitrage using forward contracts.  Arbitrage often exists between countries with different interest rates. The IRP 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.

### Uncovered Interest Rate Parity

Conversely, 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 relationship is reflected in the two methods an investor may adopt to convert foreign currency into U.S. dollars.

• Invest locally – One option an investor may take 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.
• Convert the currency – 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.

In reality, there is often very little difference between uncovered and covered interest rate parity because the expected spot rate and forward spot rate are usually the same. The difference is that with covered interest parity, you are locking in future rates today. With uncovered interest parity, you are simply forecasting what rates will be in the future. (Source: thebalance.com)

## Why Interest Rate Parity Matters

Without interest rate parity, banks could exploit differences in currency rates to make easy money.

For example, assume you could pay \$1.39 for a British pound. Without interest rate parity, an American bank could lock in a one-year forward contract at that rate. Then, it could accept \$1 million in deposits and promise a 3% return. Using that \$1 million, it could buy 730,000 pounds and invest it in a British bank. If British banks pay a 5% interest rate, the American bank could end up with 766,500 British pounds. Then, it could convert that back to U.S. dollars, ending up with a total of \$1,065,435, or a profit of \$65,435.

The theory of interest rate parity is based on the notion that the returns on an investment are “risk-free.” In other words, in the examples above, investors are guaranteed 3% or 5% returns. In reality, there is no such thing as a risk-free investment. But, when the economies and monetary systems of countries are stable, investors can feel very confident about the returns on treasury bonds. In fact, U.S. Treasury bonds never default, and therefore they are viewed worldwide as risk-free. There are many other highly rated countries, including many in Europe, with bonds that are considered free of risk. (Source: ibid)

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

According to the Covered Interest Rate theory, the exchange rate forward premiums (discounts) nullify the interest rate differentials between two countries. In other words, covered interest rate theory says that the difference between interest rates in two countries is nullified by the spot/forward currency premiums.  The result is that the investors could not earn an arbitrage profit. tp

### Example

Assume Apple Inc., the U.S.-based multinational, has to pay the European employees in Euro in a month’s time. Apple Inc. can do this in different ways:

• Scenario 1 – Apple can buy Euro forward a month (30 days) to lock in the exchange rate. Then it can invest this money in dollars for 30 days after which it must convert the dollars to Euro. This is known as covering, as now Apple Inc. will have no exchange rate fluctuation risk.
• Scenario 2 – Apple can also convert the dollars to Euro now at the spot exchange rate. Then it can invest the Euro money it has obtained in a European bond (in Euro) for 1 month.  In effect, it will have an equivalent loan of Euro for 30 days. Then Apple can pay the obligation in Euro after one month.  It is also known as covering because by converting the dollars to Euro at the spot rate, Apple is eliminating the risk of exchange rate fluctuation. Under this model, if Apple Inc. is sure that it will earn interest, it may convert fewer dollars to Euro today.
• Scenario 3 – Apple Inc. can invest the money in dollars and change it for Euro at the time of payment after one month. This method is known as uncovered, as the risk of exchange rate fluctuation is imminent in such transactions.

## Uncovered Interest Rate Parity (UIP)

UIP Theory says that the expected appreciation or depreciation of a particular currency is nullified by lower or higher interest.

### Uncovered UIP Example

Assume the nominal interest rate in the US is 6% per annum, and the nominal interest rate in India is 14% per annum. Since the nominal interest rate in India is higher, the investor will perceive it to be beneficial to borrow in USD and invest that in INR, and then reconvert the investment proceeds to USD to make a profit from the difference.

Say, for example, the investor borrows USD1,800 and converts it in INR at a spot rate of INR70/USD. He would need to repay USD1,860 after a year. So, he invests INR126,000 at a rate of 14% per annum. As a result, by the end of the year, he will receive INR143,640.  Now, when he tries to reconvert the investment proceeds back to USD, the uncovered interest rate parity condition will come into play, and the nominal interest rate difference will rise in order to eliminate the difference. The investor will then neither be better off nor worse off and will not make any profit as the difference in interest rates will be adjusted according to the no-arbitrage condition of UIRP. (Source: corporatefinanceinstitute.com)

## Interest Rate Parity – Final Words

Interest rate parity says there is no opportunity for interest rate arbitrage for investors of two different countries. But this requires perfect substitutability and the free flow of capital. In reality, it turns out that sometimes there are arbitrage opportunities. This comes when the borrowing and lending rates are different, allowing investors to capture riskless yield. IRP has been criticized based on the assumptions that come with it. For instance, the covered IRP model assumes that there are infinite funds available for currency arbitrage.  This assumption is obviously not realistic. When futures or forward contracts are not available to hedge, uncovered IRP does not tend to hold in the real world.

As an example, the covered interest rate parity fell apart during the financial crisis. However, the effort involved to capture this yield usually makes it more trouble than it is worth pursuing.

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