# Interest rate parity

Interest rate parity |
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**Interest rate parity** is an economic concept that states the relationship between the interest rate of two different currencies. It indicates that the interest rate differential between two countries should be equal to the expected change in the exchange rate between the two currencies. In other words, the expected return on investments in any two countries, denominated in different currencies, should be the same after taking into account the differences in interest rates and expected exchange rate changes. Simply put, it states that the exchange rate should adjust to the difference in interest rate between two countries to ensure equal returns on investments.

## Example of interest rate parity

- An example of interest rate parity can be seen in the foreign exchange market. If the interest rate in the US is higher than the interest rate in the UK, then the US dollar will appreciate against the British pound, as investors will move their money to the US to take advantage of the higher interest rate. This appreciation will offset the interest rate differential, meaning that the return on investments in both countries would be equal after taking into account the exchange rate change.
- Another example of interest rate parity can be seen in the bond market. When the interest rate in the US is higher than the interest rate in the UK, investors will move their money to the US to purchase bonds and receive the higher interest rate. This will cause the prices of UK bonds to fall, as investors sell their UK bonds to purchase US bonds. This fall in the prices of UK bonds will offset the higher interest rate in the US, meaning that the return on investments in both countries would be equal after taking into account the price changes of the bonds.

## Formula of interest rate parity

The formula for Interest Rate Parity is given by:

$$ \frac{e_{t+1}}{e_t} = \frac{(1+r_{t+1})}{(1+r_t)} $$

where e is the exchange rate, and r is the interest rate.

This formula states that the expected exchange rate between two countries in the future ($$e_t+1$$) is equal to the current exchange rate ($$e_t$$) multiplied by the ratio of the future interest rate ($$r_t+1$$) to the current interest rate ($$r_t$$). This implies that the expected change in the exchange rate between two countries should be equal to the difference in their interest rates.

For example, if the interest rate in Country A is 5%, and the interest rate in Country B is 3%, then the expected exchange rate between the two countries in the future will be 1.05/1.03 = 1.02, meaning that one unit of currency from Country A will buy 1.02 units of currency from Country B.

## When to use interest rate parity

Interest rate parity can be used in a variety of contexts to help understand the relationship between two currencies. Specifically, it can be used to:

**Analyze the expected returns of foreign exchange investments**: Interest rate parity can help predict expected returns on investments in different currencies by taking into account both the interest rate differential and the expected change in exchange rate.**Determine the cost of hedging foreign exchange risk**: Interest rate parity can help identify the cost of hedging foreign exchange risk, as the difference in interest rates can be used to calculate the cost of the hedging instrument.**Identify arbitrage opportunities**: Interest rate parity can help identify arbitrage opportunities, as it can be used to compare the expected returns of investments in different currencies and identify any discrepancies that suggest an arbitrage opportunity exists.**Calculate the forward rate**: Interest rate parity can be used to calculate the forward rate, which is the expected rate at which a currency will be exchanged at a future date.**Assess the cost of borrowing in different currencies**: Interest rate parity can help identify the cost of borrowing from different countries by taking into account both the interest rate differential and the expected change in exchange rate.

## Types of interest rate parity

Interest rate parity is an economic concept that states the relationship between the interest rate of two different currencies. There are three main types of interest rate parity: covered interest rate parity, uncovered interest rate parity, and absolute interest rate parity.

- Covered Interest Rate Parity (CIP) states that the exchange rate between two countries should move in the opposite direction of the interest rate differential between them. This means that if the interest rate of one currency is higher than the other, then the exchange rate of the currency with the higher interest rate should appreciate, and vice versa.
- Uncovered Interest Rate Parity (UIP) states that the expected returns from investing in assets denominated in different currencies should be equal, regardless of the interest rate differential between the two countries. This means that the expected appreciation or depreciation of the currency with the higher interest rate should be equal to the interest rate differential between the two currencies.
- Absolute Interest Rate Parity (AIP) states that the exchange rate between two countries should move in the same direction of the interest rate differential between them. This means that if the interest rate of one currency is higher than the other, then the exchange rate of the currency with the higher interest rate should depreciate, and vice versa.

## Advantages of interest rate parity

Interest rate parity offers a number of advantages. These include:

- It helps to reduce the risk of currency fluctuations. By reducing the difference in interest rate between two countries, investors can avoid losses due to changes in the exchange rate.
- It provides investors with an efficient way to diversify their portfolios. By investing in different currencies, investors can benefit from the different interest rate structures of different countries.
- It helps to reduce the cost of borrowing for companies. Companies can borrow in the currency with the lowest interest rate and use the proceeds to invest in the currency with the higher rate. This can result in significant savings.
- It helps to create a more stable global financial system. By reducing the difference in interest rates between countries, investors can reduce the risk of currency fluctuations and make investments more secure.

## Limitations of interest rate parity

Interest rate parity is a useful tool for predicting the future exchange rate between two different currencies. However, it does have several limitations. The main limitations include:

**The assumption of perfect capital mobility**: Interest rate parity assumes that capital is perfectly mobile, meaning that investors can move their money freely between different countries without any restrictions. However, in reality, capital flows are often restricted due to a variety of factors, such as regulations, taxes, and political instability.**The assumption of no transaction costs**: Interest rate parity also assumes that there are no transaction costs when converting between two different currencies. In reality, however, there are often transaction costs involved in currency conversions, which can affect the actual return on investments.**Changes in expected exchange rate**: Interest rate parity assumes that the expected exchange rate between two currencies will remain constant. However, in reality, the exchange rate can fluctuate significantly due to a variety of factors, such as economic growth, political instability, and monetary policy.**Exchange rate risk**: Interest rate parity does not take into account the risk of exchange rate movements. In reality, exchange rate movements can cause large losses for investors, as they may not be able to predict the timing and direction of exchange rate movements.

Interest rate parity is an economic concept that states the relationship between the interest rate of two different currencies. Other approaches related to interest rate parity include:

- Covered Interest Parity (CIP) – CIP assumes that investors can move funds between two countries without incurring any costs, allowing them to enter into a risk-free arbitrage.
- Uncovered Interest Parity (UIP) – UIP assumes that there is no risk-free arbitrage. In this case, investors must take on currency risk when moving funds between countries, which means that the expected returns must be adjusted to cover the expected exchange rate changes.
- Purchasing Power Parity (PPP) – PPP assumes that the prices of goods and services should be the same between two countries, regardless of the exchange rate.
- Absolute Purchasing Power Parity (APPP) – APPP assumes that the purchasing power of a currency should be the same in two different countries, regardless of the exchange rate.

In conclusion, interest rate parity is an important economic concept that relates to the exchange rate between two different currencies. Other related approaches include CIP, UIP, PPP, and APPP, which all take into account different elements of the exchange rate.

## Suggested literature

- Du, W., Tepper, A., & Verdelhan, A. (2018).
*Deviations from covered interest rate parity*. The Journal of Finance, 73(3), 915-957.