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Calculating forward exchange rates - covered interest parity

Written by Mukul Pareek

Created on Wednesday, 21 October 2009 20:48

Hits: 158906

An easy hit in the PRMIA exam is getting the question based on covered interest parity right.  It will come with a couple of exchange rates, interest rates and dates, and there would be one thing missing that you will be required to calculate.  This brief write up attempts to provide an intuitive understanding of how and why covered interest parity works.  There are a number of questions relating to this that I have included in the question pool, and this article addresses the key concepts with some examples.

All that ‘covered interest parity’ means is that investing in the domestic currency would be the same as investing in a foreign currency purchased at spot, and reconverting to domestic currency at the forward rate.

A Swiss investor has CHF 1,000,000 to invest for a year.  He is considering two options:

1. He can invest this money in a local bank in Geneva, and earn an annual return of 1%.
2. Alternatively, he could convert his Swiss Francs to US dollars and place a USD deposit in New York and earn 3%.  Since he would expect to receive his investment back in USDs in the future, he would cover his risk of the exposure to the USD by selling USDs in advance at the forward rate.  A year later, when the USD deposit matures, he would convert the dollars back into francs using this forward contract he has entered into.

What covered interest parity says is that our investor would be equally well off in both the circumstances.  Even if he could earn 3% in US dollars, any advantage he might get from this higher rate of interest would be offset exactly by a poorer exchange rate when he converts his USDs to CHF.  If this were not to be true, and investing in dollars and converting back to francs later did indeed offer an advantage over investing in CHF, arbitrageurs would immediately borrow a large number of Swiss Francs, and convert them for investing in US Dollars while at the same time covering their future risk by entering into forward contracts.  This would push the forward exchange rate in a way that there would be no money to be made from this trade.

Therefore, the forward exchange rate is just a function of the relative interest rates of two currencies.  In fact, forward rates can be calculated from spot rates and interest rates using the formula Spot x (1+domestic interest rate)/(1+foreign interest rate), where the 'Spot' is expressed as a direct rate (ie as the number of domestic currency units one unit of the foreign currency can buy).

In other words, if S is the spot rate and F the forward rate, and r_f and r_d are foreign currency interst rates and domestic currency interest rates respectively, then:

Let us look at an example: If the spot CAD/USD rate is 1.1239 and the three month interest rates on CAD and USD are 0.75% and 0.4% annually respectively, then calculate the 3 month CAD/USD forward rate.

In this case the forward rate will be

It can be confusing to determine which interest rate should be considered 'domestic', and which 'foreign' for this formula.  For that, look at the spot rate.  Think of the spot rate as being x units of one currency equal to 1 unit of the other currency.  In this case, think of the spot rate 1.1239 as "CAD 1.1239 = USD 1".  The currency that has the "1" in it is the 'foreign' and the other one is 'domestic'.

It is also important to remember how exchange rates are generally quoted.  Most exchange rates are quoted in terms of how many foreign currencies does USD 1 buy.  Therefore, a rate of 99 for the JPY means that USD 1 is equal to JPY 99.  These are called 'direct rates'. However, there are four major world currencies where the rate quote convention is the other way round - these are EUR, GBP, AUD and NZD.  For these currencies, the FX quote implies how many US dollars can one unit of these currencies buy.  So a quote of ""1.1023"" for the Euro means EUR 1 is equal to USD 1.1023 and not the other way round.