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HMRC internal manual

# Understanding corporate finance: foreign exchange: interest rate parity

## How exchange rates are determined: interest rate parity

The most important theory of how exchange rates are determined is the theory of interest rate parity. This can be illustrated by a simple example:

Suppose that a UK investor, with funds in sterling, has a free choice of whether to invest in the UK or the USA. The rate of return on risk-free US government securities is 5%, while the rate of return on UK gilts is 3%.

Let us further suppose that the spot £/US dollar exchange rate is \$1.6/£, and the 12 months forward rate is also \$1.6/£. The investor could convert the whole of her capital into dollars, and at the same time enter into a forward agreement to buy back sterling at the same rate in a year’s time. She would therefore lock in a risk-free return of 5%, compared to someone who kept their money in sterling and earned only 3% in the UK.

This state of affairs would not last long, because speculators would immediately sell sterling for dollars and invest in the US. Market pressure would drive forward exchange rates to a level where the investor in the US and the investor in the UK received equal returns.

Someone investing £100,000 in the UK would, on these figures, have cash of £103,000 at the end of the year.

The person exchanging £100,000 for dollars at a spot rate of \$1.6/£ would receive \$160,000. Investing that at 5%, they would have \$168,000 at the end of the year. In order to achieve exactly the same return as the UK investor, they would have to sell \$168,000 for £103,000, i.e. an exchange rate of \$1.6311/£.

This implies that, if the two currencies are to be in equilibrium, the 12 months’ forward exchange rate should be \$1.6311/£, that is to say dollars can be purchased more cheaply at the forward rate than at the spot rate. We say that dollars trade at a forward discount to sterling. For exchange rates and interest rates to be in equilibrium between two countries, the currency of the country with the higher interest rate should stand at a forward discount to the currency of the country with the lower interest rate.

This means that, in the long run, companies will not obtain an advantage by investing or borrowing in one currency rather than another (although they may be able to exploit short-term market imbalances). A company which invests in a strong currency may make a foreign exchange profit, but will receive a lower interest return. A company which makes its investment in a weak currency will get more interest, but will lose from depreciation of the currency.