8.2 Interest rate parity

The process described above of moving from one currency to another in order to

take advantage of a higher interest rate in another country is known as uncovered

interest rate arbitrage.

In this discussion, we have made two simplifying assumptions. Firstly, we have

ignored transaction costs. As we have seen in our discussion of the expression of

exchange rates, there is always a difference between the bid and offer rates of exchange.

This difference is a cost to investors engaged in uncovered interest arbitrage and so,

in practice, the prot opportunity disappears before we reach full parity. In other

words, the expected losses from moving from one currency to another and back

include the spread between bid and offer rates of exchange.

Secondly, we have ignored differences in default risk. We have assumed above

that the only difference between German and British securities is the difference in

interest rates – that is, we have assumed the two types of securities to be perfect sub-

stitutes for each other. In practice, there may be a considerable difference in the default

risk attached to the two securities. For example, German investors may demand a

risk premium before they are willing to hold British securities, not just because of

the foreign exchange risk but also because of a difference in default risk. In this case,

we certainly do not reach uncovered interest parity. Even if the two securities are

objectively very similar, German investors may well feel that they have more informa-

tion about the risks associated with the German securities and demand a higher

interest rate on British securities before they begin to think of buying them.

The existence of forward exchange markets allows a third strategy, one that over-

comes the risk associated with uncovered interest arbitrage. A third investor, Z, realises

that he can buy sterling securities and, at the same time, sell sterling three months

forward at an agreed rate of exchange. This means that he is able to calculate exactly

how many euro he will receive when the securities mature in three months’ time

and so can make a precise comparison between the number of euro he would receive

from buying UK securities and from leaving his money invested at home in German

securities. This comparison will be inuenced by:

l	the difference in interest rates on UK and German securities; and

l	the difference between the spot and three-month forward exchange rates for sterling against the euro.

Assume that the £ and the euro were trading with no forward premium or dis-

count (spot and forward rates were exactly the same) but that euro interest rates were

higher than sterling interest rates. Clearly, then, Z’s investment strategy would be

better than X’s since Z could take advantage of the higher interest rates in the UK

without taking on any foreign exchange risk. In the jargon, he would have locked

in to the existing spot exchange rate of £1 a1.50. However, this position would not

last for very long. A large number of investors would see the benets of Z’s strategy

and would follow suit. In other words, they would sell German securities (forcing their

price down and pushing the yield on them up); buy sterling spot (forcing up the spot

exchange rate of sterling above a1.50); buy UK securities (forcing their price up and the

yield on them down); and to cover their exchange rate risk sell sterling three months

forward (forcing down the three-month forward exchange rate of sterling below a1.50).

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Chapter 8 • Foreign exchange markets

Thus, the interest rate differential between UK and German securities would be reduced

and, at the same time, a discount would develop on three-month forward sterling.

Both developments would be reducing the protability of Z’s strategy.

This process would continue until the rates of return on the strategies chosen by

X and Z came into equality (with some small allowance, as above, for transaction

costs and any perceived difference in default risk). We would then have established

covered interest parity.

Covered interest parity:When the gains from investing in a country with a higher

interest rate are equal to the forward discount on that country’s currency.

What would be the nal outcome? Euro interest rates started below £ interest

rates but euro interest rates rose while £ interest rates fell. Thus, the interest rate

differential between the two countries would have been reduced. The spot exchange

rate of £ rose but the three-month forward rate fell, establishing a discount on three

month forward sterling. This establishes a general rule:

The currency of the country in which interest rates are higher will be trading at a forward

discount; the currency of the country with the lower interest rates will be at a forward

premium.

Box 8.3 provides an illustration of the way in which spot and forward exchange

rates are reported in the Financial Times.

Box 8.3

Spot and forward rates of exchange

At the close of business of the London forex market on 26 May 2006, the spot exchange

rate of the US dollar against sterling, as reported in the Financial Timesof 27/28 May, stood

at £1 $1.8550. The one-month forward exchange rate was £1 $1.8558. In other words,

the dollar was trading one month forward at a discount against sterling (more dollars would

be required to buy a given amount of sterling one month forward than spot). Alternatively,

we could say that sterling was at a forward premium. We can easily calculate the one-

month forward discount on US dollars in percentage per annum terms.

In money terms, the discount was $1.8550 $1.8558 $0.0008. Remember that this

was the discount for one month. To convert this into an annual discount we need to multiply

by 12, giving us $0.0096. We then need simply to divide this by the spot exchange rate

of $1.8550 and multiply by 100 to obtain a percentage. This gives us 0.5175 per cent

per annum.

The general rule stated above suggests that one-month interest rates on US dollars

must have been well above those in the UK at the time. A look at the international currency

rates on the same date conrms this. At the close of trading on 26 May 2006, the

mid-point of one-month interest rates on the US dollar was 5.05 per cent; on sterling it

was 4.59 – a difference of 0.46 per cent. Allowing for transaction costs, we can accept

that covered interest parity applied, with the interest rate differential between the two

currencies being nearly equal to the forward discount on US dollars.

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