CFM7037a - Understanding foreign exchange rates: how exchange rates are determined
Relationship between forward and spot rates
The difference between spot and forward rates for a particular
currency depends on the differential in interest rates between the
two countries concerned. This can be expressed mathematically as:
(1 + rs)/(1 + rf) = f/s
where rs = sterling interest rate for the period
rf = foreign currency interest rate for the period
f = forward rate of exchange for the end of the period (the
value in sterling terms of 1 unit of the foreign currency)
s = spot rate of exchange at the beginning of the period
(again, expressed as the sterling value of 1 unit of the foreign
currency).
In the example in CFM7037, you saw that an investor with
(say) £100,000 could convert it into dollars at the current
spot rate (say $1.6/£, which is equivalent to £0.625/$)
and then invest it in the US at 5% p.a., producing $168,000 at the
end of the year. If she invested it in the UK at 3%, she would have
£103,000 at the end of the year, implying a 12 month forward
exchange rate of $168,00/103,000, or $1.6310/£.
Slotting these figures into the formula gives:
(1 + 0.03)/(1 + 0.05) = f/0.625
gives a 12 month forward exchange rate of £0.6131/$, or
$1.6310/£.
Strictly, you should use the nominal interest rate –
the rate you have to pay to borrow, which takes account of
inflation – in the calculation.
Thus quoted forward rates of exchange are not “crystal
ball” predictions of what future spot rates will be. The spot
rate of exchange, on any particular day, depends on supply and
demand, and demand can be stimulated or depressed by information,
rumour or market confidence. Research indicates that, for the major
currencies, there is no good correlation between a forward price
and the eventual spot price on the delivery day.
