What is Interest Rate Parity?

Explanation

  • Put – a person who invests in a domestic country and then converts into other currencies or another who converts into other currencies and invests in the international market will yield the same return, considering all other factors constant.They are of two types – uncovered and covered interest rate parityCovered Interest Rate ParityAccording to covered interest rate parity, an investment in a foreign instrument that is completely hedged against exchange rate risk will have the same rate of return as an identical domestic instrument. Thus, the forward exchange rate can be determined based on the interest rate earned on both the domestic and foreign investments, as well as the Spot exchange rate between the two currencies.read more. The former exists when there are no covenants about the forward interest rate, and the parity is dependent only on the expected spot rate. The latter has a pre-decided contract locked in for the forward interest rate. In layman’s terms, we forecast the rates uncovered while we lock in the rates today, in covered.

Interest Rate Parity Formula

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Numerically, Interest Rate Parity can be put as –

It can also be put as –

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 country B (foreign country). The gap between Fo and So is termed a swap. A positive difference 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 impossible to create an arbitrage/ profit opportunity by borrowing currency A, converting it into currency B, and returning to the home currency in the future.

Examples

Example #1

Let us assume a spot rate of 1.13 USD/ EUR, a USD interest rate of 2%, and a 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 the forward exchange rate –

Calculation of forwarding Exchange Rate can be done as follows –

  • = 1.13*(1+2%)^1/(1+3%)^1

Forward Exchange Rate will be –

  • Forward Exchange Rate = 1.119

Similarly, we can calculate forward exchange rate for year 2 and year 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, 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 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 one 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 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 important because if the relationship does not hold well, there is an opportunity to make an unlimited profit by borrowing and investing in different currencies at different points, termed 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.Suppose the forward exchange rate exceeds the calculated Interest Rate Parity rate. In that case, a person can borrow money, convert it using a spot exchange rate and invest in the foreign market at interest rates. At maturity, it can be converted back to a home currency with a fixed profit since the locked price is greater than the calculated price. Technically, anyone and everyone would have made money by borrowing funds and investing in different markets – which is not practical and does not hold in the real world.Interest rate parity can also be used to determine the pattern/ estimate of the foreign exchange rate at future dates. For instance, if the interest rate of a home country is increasing, keeping the interest rate of a foreign country constant – we can speculate the home currency to appreciate over the foreign currency. The opposite holds if we see the interest rate of the home country decreasing.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.

This has been a guide to Interest Rate Parity and its definition. Here we discuss its formula and calculation along with practical examples. You can learn more from the following articles –

  • Put-Call ParityCurrency PegCurrency FuturesFunctional Currency