## Calculating a forward exchange rate – the forward outright

##### Published: Sep 2001

Foreign exchange transactions that are settled ‘spot’ are (with the exception of USD/CAD trades) settled two working days after the trade is agreed. It is also possible to agree the trade of one currency for another to be settled at any point in the future. Any such transaction is referred to as a ‘forward outright’ transaction.

The forward exchange rate is a function of the spot rate and the interest rates on the two currencies. It is not based on price predictions at all.

By convention, currency pairs (e.g. GBP/USD) are quoted in the same way. The first named currency is known as the ‘base’ currency and the second the ‘variable’ currency.

$$Forward \: outright \: rate = spot \:rate \: \times \: \frac{1 \: + \: variable \: currency \:interest \:rate \: \times \: \frac{days\: in \: settlement}{days \:in \:year}}{1 \: + \: base\: currency \:interest \: rate \: \times \:\frac{days\: in \: settlement}{days \:in \:year}}$$

To give a worked example, assume that a UK-based treasurer knows that the company will need dollars in one month’s time. The treasurer could enter into a spot agreement now and then put the dollars on deposit for a month. However, this means that these balances will be unavailable for a month. The alternative is to enter into a forward agreement with the settlement date in one month’s time. This has the effect of fixing the rate as of today’s spot rate, but it allows the treasurer to use that cash in the month up to settlement date.

Note that in most cases the convention is that, in the currency pair, it is the USD that is quoted first and is, therefore, the base currency. The most common exceptions, apart from GBP/USD, are EUR/USD, AUD/USD and NZD/USD.

Assume that the interest rate in the UK is 5.00% and in the US is 3.75% and the current spot rate is 1.422. GBP, as the first quoted currency is the base currency, and USD is the variable currency – this can be remembered as the spot rate quotes the number of dollars per £1.

##### In this case:
$$Forward \: outright \: rate = 1.422\: \times \: \frac{1 \: + \: 0.0375 \: \times \: \frac{31}{360}}{1 \: + \: 0.05 \: \times \: \frac{31}{360}}$$
##### Conventional calculator

Using a conventional calculator, press the following buttons:

• 0.05 x 31 ÷ 360 + 1 = M + C
• 0.0375 x 31 ÷ 360 + 1 = ÷ MR =
• x 1.422 = this should give the result  1.420
##### Scientific calculator

Using the scientific calculator on a Windows computer (Start, Programs, Accessories, Calculator, View, Scientific), you would need to press the following keys:

• 1.422 * 1 + 0.0375 * 31 / 360 / 1 + 0.05 * 31 / 360 this should give the result  1.420
##### HP12C

Using an HP12C (or a similar calculator using Reverse Polish Notation):

• .0375  ENTER  31 x 360 ÷ 1 + .05 ENTER  31 x 360 ÷ 1 + ÷ 1.422 x this should give the result  1.420

Note that the value of the currency with the lower interest rate will appreciate relative to the other currency. This is logical. Assume that GBP/USD = 1.50 – spot £100 would be worth $150. If UK interest rates are 10% and US interest rates are 5%, then in a year’s time the original £100 would be worth £110 and the$150 would be worth $157.50, so the effective forward rate then would be 1.43, a relative depreciation in sterling. If rates were 5% in the UK and 10% in the US, then the USD would depreciate. The original £100 would be worth £105 and the$150 would be worth \$165, an effective forward rate of 1.57.

This change in the interest rate provides compensation to the party buying the currency with the lower interest rate. Having bought the currency with the lower interest rate, the party will earn relatively less interest income than would have been the case had the foreign exchange trade not taken place. The compensation is that, in the future, relatively less of the lower interest rate currency will be required to purchase the same quantity of the higher interest rate currency.