Interest Rate Parity

What is Interest Rate Parity?

Interest Rate Parity is a concept that links forex market rate and country’s interest rates and states that if the currencies are in equilibrium, one cannot make use of the opportunity to make profits just by exchanging money. The underlying concept is that returns from investing in various currencies should be independent of the country’s interest rates. Hence, there will be no arbitrage opportunity in the foreign exchange markets – investors cannot seek to profit by the difference between the interest rates using foreign exchange as an asset or a way to invest.

Explanation

Interest Rate Parity Formula

Interest Rate Parity Formula

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Source: Interest Rate Parity (wallstreetmojo.com)

Numerically, Interest Rate Parity can be put as –

Forward Exchange Rate (Fo) = Spot Exchange Rate (So) X (1 + Interest rate A)^n /  (1 + Interest rate B)^n

It can also be put as –

Forward Exchange Rate (Fo) / Spot Exchange Rate (So) = X (1 + Interest rate A)^n / (1 + Interest rate B)^n

The equation explains that the forward exchange rate (Fo) should equal the spot exchange rate (So) multiplied by the interest rate of country A (home country) divided by the interest rate of the country B (foreign country). The gap between Fo and So is termed as a swap. If the difference is positive, it is known as a forward premiumForward PremiumForward premium is when the future exchange rate is predicted to be more than spot exchange rate. Notation of D/F indicates that the F currency is the base currency and D currency will depreciate against it.read more; conversely, a negative difference is called a forward discount.

In cases where Interest Rate Parity stands good, it is not possible to create an arbitrage/ profit opportunity by borrowing currency A, converting into currency B and then back to home currency in the future.

Examples

You can download this Interest Rate Parity Formula Excel Template here – Interest Rate Parity Formula Excel Template

Example #1

Let us assume a spot rate of 1.13 USD/ EUR, a USD interest rate of 2% and EUR interest rate of 3%. What will be the Forward Exchange Rate after a year?

Solution

Use the below-given data for the calculation of forward exchange rate –

Interest Rate Parity Formula Example 1

Calculation of Forward Exchange Rate can be done as follows –

Example 1.1
  • = 1.13*(1+2%)^1/(1+3%)^1

Forward Exchange Rate will be –

Interest Rate Parity Formula Example 1.2
  • Forward Exchange Rate = 1.119

Similarly, we can calculate forward exchange rate for year 2 and year 3

Interest Rate Parity Formula Example 1.3

Example #2

Suppose the USD to CAD spot exchange rate is 1.25 and the one-year forward exchange rate is 1.238. Now, the interest rate for USD is 4% while it is only 3% for CAD. If IRP were to hold to true, it would mean – 1.2380 / 1.2500 should be equal to 1.03 / 1.04 which turns out to be approximately 0.99 in both the cases which confirms the validity of the Interest Rate Parity.

Example #3

Taking a step further, let us assume person A is investing USD 1,000 in a year. There are two scenarios – one, wherein we can invest in EUR and convert it into USD at the end of year 1 or two, where we can convert into USD now and invest in USD. Suppose So = 0.75 EUR = 1 USD, interest rate in EUR is 3% and USD is 5%.

Scenario 1

If the interest rate in EUR is 3%, A can invest USD 1000 or EUR 750 (taking FX rate) at 3% giving a net return of USD 772.50.

Scenario 2

Otherwise, A can invest in USD 1000 and then convert the return into a net return. Fo = 0.75 (So) X 1.03 (home currency)/1.05 (foreign currency) = 0.736

Now, USD 1000 at 5% yields USD 1050 which can be converted into EUR by using 0.736 and not 0.75 as the conversion rate.

Therefore, USD 1050 = USD 1050 X 0.736 giving a net return of approximately USD 772.50.

Relevance and Implications

  • Interest rate parity is of importance due to the fact that if the relationship does not hold good, there is an opportunity to make an unlimited profit by borrowing and investing in different currencies at different points of time, which is termed as arbitrageArbitrageArbitrage in finance means simultaneous purchasing and selling a security in different markets or other exchanges to generate risk-free profit from the security's price difference. It involves exploiting market inefficiency to generate profits resulting in different prices to the point where no arbitrage opportunities are left.read more.
  • If the actual forward exchange rate is greater than the calculated Interest Rate Parity rate – a person can borrow money, convert it using a spot exchange rate and invest in the foreign market at their interest rates. At maturity, it can be converted back to a home currency with a fixed certain profit since the locked price is greater than the calculated price. Technically, anyone and everyone would have made money by just borrowing funds and investing in different markets – which is not practical and does not hold true in the real world.
  • Interest rate parity can be also used to determine the pattern/ estimate of the foreign exchange rate at future date. For instance, if the interest rate of a home country is increasing keeping the interest rate of foreign country constant – we can speculate the home currency to appreciate in value with respect to the foreign currency. The opposite holds true if we see the interest rate of the home country decreasing.
  • Having said that, the thesis is still criticized for the assumptions it comes up with. The model assumes that one can invest in any fund and currency available in the market which is not practical and realistic. Also, when there is no scope to hedge the future/ forward contracts, the uncovered IRP stays null and void.

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