Interest Rate ParityDefined along with formula and more
Aside from currency rates, interest rates may also vary from one country to another.
For example, a treasury bond in the US might yield a 4% return.
However, a similar bond in the UK might instead yield a higher return, such as 6%, or a lower one, such as 2%.
Knowing the difference in interest rates, wouldn’t it be a profitable idea to borrow money in the country with the lower interest rate, exchange it with the currency of the country with the higher interest rate, let the money earn the higher interest, then exchange the currency back to pay for the loan?
Sounds complicated, doesn’t it? While there are indeed people who engage in such a practice, there’s a reason why not everyone is doing it.
In addition to being complicated, is it really profitable?
The theory of interest rate parity says no.
According to such theory, the interest rate differential between two countries is the same as the differential between the forward exchange rate and the spot exchange rate.
As such, whether you invest using one currency or the other, the theory of interest rate parity assumes that you’ll still be earning the same amount.
But just knowing that isn’t enough to fully understand what interest rate parity is.
That’s why in this article, we’ll be taking a closer look at what interest rate parity is.
Is there a formula that supports it?
If so, what is this formula?
And how does interest rate parity?
What is its purpose?
Let’s try to answer these questions as go along with the article.
What is Interest Rate Parity (IRP)?
Interest parity is a theory concerning the relationship between the spot exchange rate and the forward exchange rate or expected spot rate, with interest rates as a basis.
It assumes that the interest rate differential between two countries is equal to the differential between the spot exchange rate and the forward exchange rate.
This results in the forward exchange rate being equal to the spot exchange rate multiplied by the interest rate of the home country then divided by the interest of the foreign country.
If interest rate parity holds true, no one should be able to make a profit just by simply borrowing money, then exchanging it into a foreign currency, then at a later date, exchanging it back to your home currency.
In a way, it prevents the exploitation of the differential between exchange rates and interest rates of two or more countries.
Interest rate parity plays an important role in foreign exchange markets as it explores the relationship between interest rates, spot exchange rates, and forward exchange rates.
It basically governs the relationship between currency exchange rates and interest rates.
If it holds true, the hedged returns from investing in different currencies should be equal regardless of their interest rates.
Do note that interest rate parity works under the assumption that the currencies are in equilibrium.
If currencies are in equilibrium, then no one should be able to profit from just exchanging money. However, without equilibrium, arbitrage in the foreign exchange market could be possible.
The Interest Rate Parity Formula
Assuming the currencies are in equilibrium, the forward exchange rate should be equal to the spot exchange rate multiplied by the interest rate of the home country and then divided by the interest of the foreign country.
Put into formula form, it should look like this:
Ft(a/b) = St(a/b) x ((1 + ia)T ÷ (1 + ib)T)
Where:
Ft(a/b) – refers to the forward exchange rate
St(a/b) – refers to the spot exchange rate
ia – refers to the interest rate of country A (foreign country)
ib – refers to the interest rate of country B (home country)
T – refers to the time until the expiration date; this usually has a value of 1
For example, let’s say that the spot exchange between the US dollar and the UK pound is at $1/£0.83 or £1/$1.20.
You currently have $1,000 which you can exchange for £830 using the current exchange rate.
Suppose that the interest rate in the US is 6%, while in the UK its 4%, let us calculate the forward exchange rate of the US dollar to the UK pound in one year.
Ft(a/b) = St(a/b) x ((1 + ia)T ÷ (1 + ib)T)
= £0.83 x ((1+.04)1 ÷ (1 + .06) 1)
= £0.8143
As per our computation, the forward exchange rate should be $1/£.081.
Let’s try if the interest parity rate holds true.
If we were to convert the $1,000 into £830 and invest it in the UK, it should grow to £863.20 in one year.
If we invest the $1,000 in the US instead, it should grow to $1,060 in one year.
Using the forward rate above, $1,060 should be convertible to £863.16.
The £0.04 difference is a result of rounding down.
With this, we can see that the interest parity rate does hold.
Covered VS Uncovered Interest Rate Parity
Interest rate parity may either be covered or uncovered.
Interest rate parity is “covered” when the no-arbitrage condition can only be satisfied with the use of forward contracts.
Forward contracts are derivative instruments that attempt to hedge against foreign exchange risk.
On the other hand, interest parity is “uncovered” when the no-arbitrage condition could be satisfied even without the use of forward contracts.
In actuality though, uncovered interest rate parity rarely holds.
The uncovered interest rate parity assumes that the exchange rate will adjust so that the IRP will hold.
Since there are no forward contracts under uncovered interest rate parity, there’s also no forward exchange rate.
Thus, we have to modify the interest rate parity formula under an uncovered IRP situation:
ST(a/b) = St(a/b) x ((1 + ia)T ÷ (1 + ib)T)
Where:
St(a/b) – refers to the spot exchange rate now
ST(a/b) – refers to the spot exchange rate at time T; if T is one year, this will be the spot exchange rate in one year
ia – refers to the interest rate of country A (foreign country)
ib – refers to the interest rate of countr0y B (home country)
T – refers to the time until the expiration date; this usually has a value of 1
This modified formula is similar to the one above.
We only need to exchange the forward exchange rate with the future spot exchange rate since, under an uncovered IRP situation, there are no forward contracts.
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University of Wisconsin "Interest Rate Parity" Page 1 . August 22, 2022
Columbia University "Uncovered interest rate parity and the term structure" Publication. August 22, 2022