Introduction to Corporate Finance

17: International Investment Decisions

Figure 17.2B, which illustrates how the same transaction would take place if there were no arbitrage

opportunities. As traders in New York sell US currency in exchange for pounds, the pound appreciates vis-

à-vis the US dollar, and the exchange rate will rise from US$1.5269/£ to some new, higher level. Likewise,

as traders in London sell pounds in exchange for Canadian dollars, the pound will depreciate against the

Canadian currency, and the exchange rate will fall below C$1.9100/£ to a lower level. Finally, as traders reap

profits in New York by selling Canadian and buying US currency, the exchange rate between Canadian and

US dollars will fall from US$0.8038/C$. Though we cannot say exactly how much each of these exchange

rates will move, we can say that, collectively, they will move enough to reach a new equilibrium in which

the cross exchange rate in New York and the exchange rate quoted in London will be virtually identical.

FIGURE 17.2A TRIANGULAR ARBITRAGE

The exchange rates in New York imply that one British pound should buy 1.89960 Canadian dollars. If a bank in London offers to sell C$1.9100 for one
pound, then traders can make an instant profit by selling US dollars for pounds in New York, converting those to Canadian dollars in London, and then
selling the Canadian dollars for US dollars back in New York. The effect of these trades in New York will be to raise the US dollar pound exchange rate
above 1.5269 and to push the exchange rate between US and Canadian dollars below 0.8038. In London, the value of the pound will fall below C$1.9100.

C$1.9100 = £1

US$1.5269

£0.8038 < C$1.9100/£

Exchange rate: US$ £

(US$1.5269 = £1)

Exchange rate: US$ C$

(US$0.8038 = C$1)

Step 1:

sell US$1,000,000

for £654,922

Step 3:

sell C$1,250,901

for US$1,005,474

(i.e. US$5,474 arbitrage profit)

Step 2:

sell £654,922

for C$1,250,901

Exchange rate: £ C$

(C$1.9100 = £1)

US$1.5269 = £1

US$0.8038 = C$1

Suppose that on Friday 5 June 2015, a trader learns
that the exchange rate offered by a London bank is
C$1.9100/£ rather than C$1.89960/£, as calculated
previously. What is the arbitrage opportunity? First, note
that the figure C$1.9100/£ is ‘too high’ relative to the
theoretically correct rate. This means that in London, one
pound costs too much in terms of Canadian dollars. In
other words, the pound is overvalued, and the Canadian
dollar is undervalued. Therefore, a trader could make a
profit by executing the following steps.

1 Convert US dollars to British pounds in New York

at the prevailing spot rate, as given in Table 17.4

(on page 607). Assume that the trader starts

with US$1 million, which will convert to £654,922

(US$1,000,000 ÷ US$1.5269/£).

2 Simultaneously, the trader sells £654,922 in

London (because pounds are overvalued there) at

the exchange rate of C$1.9100/£. The trader will

then have C$1,250,901.

3 Convert the Canadian dollars back into US

currency in New York. Given the spot rate of

US$0.8038/C$ in Table 17.4, the trader will receive

US$1,005,474 (C$1,250,901× US$0.8038/C$).

After making these trades, all of which can occur

with the touch of a keystroke, the trader winds up

US$5474 richer, all without taking risk. As long as

the exchange rates do not change, the trader could

keep making a profit over and over again. This is

an arbitrage profit, and this trading strategy is an

example of triangular arbitrage.

example