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# Definition of interest rate parity (IRP)

## 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.

Key points to remember

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

## Understanding Interest Rate Parity (IRP)

Interest rate parity (IRP) plays a vital role in foreign exchange markets by linking interest rates, spot exchange rates and exchange rates.

IRP is the fundamental equation that governs the relationship between interest rates and exchange rates. The basic principle of IRP is that the hedged returns of investments in different currencies should be the same regardless of their interest rates.

IRP is the concept of non-arbitrage in foreign exchange markets (the simultaneous buying and selling of an asset to profit from a price difference). Investors cannot lock in the current exchange rate in one currency at a lower price and then buy another currency in a country with a higher interest rate.

The IRP formula is:



F

0

=

S

0

Ã—

(

1

+

I

vs

1

+

I

b

)

or:

F

0

=

Forward rate

S

0

=

Spot rate

I

vs

=

Interest rate in the country

vs

I

b

=

Interest rate in the country

b

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 the country} c & i_b = text {Interest rate in the country} b end {aligned}

F0=S0Ã—(1+Ib1+Ivs)or:F0=Forward rateS0=Spot rateIvs=Interest rate in the country vsIb=Interest rate in the country b

## Forward exchange rate

An understanding of forward rates is fundamental to IRP, especially when it comes to arbitrage. Forward exchange rates for currencies are exchange rates at a future time, as opposed to spot exchange rates, which are current rates. Forward rates are available from banks and currency brokers for periods ranging from less than a week to five years and more. As with spot currency quotes, futures contracts are quoted with a bid-ask spread.

The difference between the forward rate and the spot rate is called swap points. If this difference (forward rate minus spot rate) is positive, we speak of term premium; a negative difference is called a term.

A currency with lower interest rates will trade with a term premium compared to a currency with a higher interest rate. For example, the US dollar typically trades at a term premium against the Canadian dollar. Conversely, the Canadian dollar trades at a forward discount to the US dollar.

## Vs covered. Unhedged interest rate parity (IRP)

IRP is said to be â€œhedgedâ€ when the non-arbitrage condition could be satisfied by the use of forward contracts to attempt to hedge against currency risk. Conversely, the IRP is â€œoverdraftâ€ when the non-arbitrage condition could be satisfied without resorting to forward contracts to hedge against currency risk.

The relationship is reflected in the two methods an investor can adopt to convert foreign currencies to US dollars.

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 investment proceeds into US dollars using a forward exchange rate at the end of the investment period.

The second option would be to convert the foreign currency to US dollars at the spot exchange rate, then invest the dollars for the same term as in option A at the local risk-free (US) rate. When no arbitrage opportunity exists, the cash flows of the two options are equal.

Arbitrage is defined as the simultaneous purchase and sale of the same asset in different markets in order to take advantage of tiny differences in the quoted price of the asset. In the forex world, arbitrage trading involves buying and selling different currency pairs to exploit pricing inefficiencies.

The IRP has been criticized on the basis of the assumptions that accompany it. For example, the IRP Hedged model assumes that there are infinite funds available for currency arbitrage, which is obviously unrealistic. When futures or futures are not available for hedging, the unhedged IRP does not tend to hold up in the real world.

## Example of Covered Interest Rate Parity (IRP)

Suppose Australian Treasuries offer an annual interest rate of 1.75% while US Treasuries offer an annual interest rate of 0.5%. If an investor in the United States is looking to take advantage of Australian interest rates, they will need to swap US dollars for Australian dollars to buy treasury bills.

Subsequently, the investor should sell a one-year Australian dollar futures contract. However, under the Hedged IRP, the transaction would only have a return of 0.5%; otherwise, the no-arbitration condition would be violated.

## What is the conceptual basis of IRP?

IRP is the fundamental equation that governs the relationship between interest rates and exchange rates. Its basic principle is that the hedged returns of investments in different currencies should be the same, regardless of their interest rates. Essentially, arbitrage (the simultaneous buying and selling of an asset to take advantage of a price difference) should exist in the forex markets. In other words, investors cannot lock in the current exchange rate in one currency at a lower price and then buy another currency in a country with a higher interest rate.

## What are forward exchange rates?

Forward exchange rates for currencies are exchange rates at a future time, as opposed to spot exchange rates, which are current rates. Forward rates are available from banks and currency brokers for periods ranging from less than a week to five years and more. As with spot currency quotes, futures contracts are quoted with a bid-ask spread.

## What are redemption points?

The difference between the forward rate and the spot rate is called swap points. If this difference (forward rate minus spot rate) is positive, we speak of a term premium; a negative difference is called a term discount. A currency with lower interest rates will trade with a term premium compared to a currency with a higher interest rate.

## What is the difference between covered and uncovered IRP?

IRP is said to be hedged when the non-arbitrage condition could be satisfied by the use of forward contracts to attempt to hedge against currency risk. Conversely, IRP is discovered when the no-arbitrage condition could be satisfied without resorting to forward contracts to hedge against currency risk.

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