## Forward foreign exchange rates – an alternative method

##### Published: Jun 2003

In Treasury Today September 2001, we showed how to calculate a forward foreign exchange rate using the following formula:

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

We showed that the forward outright rate is simply a function of the current spot rate and the interest rates in both currencies. We also explained that, by convention, currency pairs (e.g. GBP/EUR) are always quoted in the same way. The first named currency is known as the ‘base’ currency and the second the ‘variable’ currency.

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 are GBP/USD, EUR/USD, AUD/USD and NZD/USD.

Assume that the interest rate in the UK is 5.00% and in the Eurozone is 3.75% and the current spot rate is 1.422. GBP, as the first quoted currency, is the base currency and EUR is the variable currency – this can be remembered as the spot rate quotes the number of Euros per £1. The formula above gives the following rate for 31 days forward:

$$Forward \: outright \: rate = 1.422 \: \times \: \frac{1 \: +0.0375 \: \times \: \frac{31}{360}}{1 \: + \: 0.05 \: \times \frac{31}{360}}=1.4205$$

(Note the different year convention used for the interest calculation)

There is an alternative to this method of calculating the forward rate using the differential in the two interest rates. This calculates a ‘points adjustment’ which is then added to or some subtracted from the spot rate to provide the forward rate.

If the interest rate in the base currency is higher than that in the variable currency, then the points should be subtracted from the spot rate. This means that the forward rate will be lower than the spot rate.

If the interest rate in the base currency is lower than that in the variable currency, then the points should be added to the spot rate, making the forward rate higher than the spot rate.

We use the following equation:

Forward rate = spot rate + / – points adjustment
Where the $$points \: adjustment = spot \: rate \: \times \: interest \: differential \: \times \: \frac{days \: to \: settlement}{days \: in \: year}$$

Using the example above:

The spot rate is 1.422, the interest differential is 1.25 (which is divided by 100) and there are 31 days to settlement. In this case, there are 365 days in the year, as GBP is the base currency. Therefore the points adjustment =

$$1.422 \: \times \: \frac{1.25}{100}\: \times \: \frac{31}{365}= 0.0015$$

Because the interest rate in the base currency (GBP) is higher than the interest rate in the variable currency (EUR), the forward rate is calculated as:

$$1.422 \: – \: 0.0015 \: = \: 1.4205$$