Introduction to Corporate Finance

PART 5: SPECIAL TOPICS

The US dollar trades at a –0.25% forward discount for a six-month contract, or about –0.50% per

year. In other words, the forward discount on the US dollar is opposite in sign and similar in magnitude

to the forward premium on the yen, though the discount is always smaller in absolute value than the

premium. In general, to calculate the annualised forward premium or discount on a currency, based on

a forward contract to be executed in N days, use the following equation:

Eq. 17.1 FS

SN

− 360

×

We can calculate the annualised forward discount (or premium) on the Swiss franc (SF) relative to the US dollar

based on the rate for a three-month forward contract. For example, we could calculate that, if the spot rate

equals US$1.0312/SF, and the three-month (or 90-day) forward rate equals US$1.0321/SF. Notice that the franc

buys more dollars on the forward market than it does on the spot market, so it trades at a forward premium.

We can determine the annualised premium as follows, given that we are using a 90-day contract:

US$1.0321/SFUS$1.0312/SF

US$1.0312/SF

360

90

0.00349 0.35%

−

×= =

example

The forward discount or premium gives traders information about more than just the price of

exchanging currencies at different points in time. The forward premium is tightly linked to differences in

interest rates on short-term, low-risk bonds across countries.

One last lesson remains to be gleaned from Table 17.4. In its daily exchange rate table, the Wall Street

Journal quotes the value of the world’s major currencies relative to the US dollar. But what if someone

wants to know the exchange rate between British pounds and Canadian dollars? In fact, all the information

needed to calculate this exchange rate appears in the figure. We simply need to calculate a cross exchange

rate by dividing the US dollar exchange rate for one currency by the US dollar exchange rate for the other

currency. For example, using Friday’s US dollar spot rates, we can determine the £/C$ exchange rate:

$.

$. $

£

£

US1 5269/

US0 8038/C

=C$1.89960/

Note that, since we divided the US dollar–British pound exchange rate (quoted as US dollars per

British pound) by the US dollar–Canadian dollar exchange rate (quoted as US dollars per Canadian

dollar), the resultant cross rate is quoted as Canadian dollars per British pound. If we wanted the cross

rate quoted as British pounds per Canadian dollar, we would need to take the inverse of this (i.e. divide

the denominator by the numerator in the preceding expression).

How can we be sure that one pound buys 1.89960 Canadian dollars simply by taking this ratio?

The answer is that if the exchange rate between pounds and Canadian dollars were any other number,

then currency traders could engage in triangular arbitrage, trading currencies simultaneously in different

markets to earn a risk-free profit. Because currency markets operate virtually 24 hours per day, and

because currency trades take place with lightning speed and with very low transactions costs, arbitrage

maintains actual currency values in different markets relatively close to this theoretical ideal. As discussed

earlier, we can use this method to derive cross rates for the Australian dollar against currencies that are

not included in the RBA data (shown in Table 17.3 on page 606).

The preceding example shows that a trader could repeatedly make a profit if the exchange rates do

not change. Of course, exchange rates do change, and they change in ways that bring the market back

into equilibrium. Figure 17.2A illustrates what happens as arbitrage takes place. Compare this to

cross exchange rate
An exchange rate between
two currencies calculated
by taking the ratio of the
exchange rate of each
currency, expressed in terms
of a third currency

triangular arbitrage
A trading strategy in which
traders buy a currency in a
country where the value of
that currency is too low and
immediately sell the currency
in another country where the
currency value is too high, to
make a risk-free profit