Question

The sales manager of a US company trades iPhones in three different markets, Europe
(Eurozone), UK and the USA, has just received a total amount of $1million from the selling
of 1,000 iPhones (each iPhone costs $1,000). He has a week available until the payment of
firm’s suppliers and employees’ salaries. The current exchange rates between the currencies
of the three markets (USD $, euro € and GBP £), are: ?€⁄$
1 = 0.9110, ?€⁄£
2 = 1.1712 and
?$⁄£
3 = 1.2910.

a) If no transaction costs exist, could the manager take advantage of an arbitrage
opportunity? Explain. [Mark 1.5]

b) When will there not be any room for profits? That is, there is no arbitrage opportunity.
[Mark 0.5]

c) Suppose now that there is a cost each time currency is being traded, i.e., either bought or
sold. Moreover, this transaction cost is equal to 1% of the value of currency that is traded.
What will the manager’s decision be in this case? [Mark 1.0]

Note: Round your answers to the third decimal point.

Answer 1

a) Yes, he can make a profit as follows:

Euro / Dollar	0.911
Euro / Pound	1.1712
Dollar / Pound	1.291
Cross rate: Dollar / Pound = (Euro / Pound) / (Euro / Dollar)
	1.1712 / 0.911
	1.285620198
There's clearly a difference between the direct Dollar / Pound and the cross rate
What the sales manager can do is as follows:
Sell $1M and get Euro	911000	1m / 0.911
Sell these Euros and get Pound	777834.6995	911000 / 1.1712
Sells these Pounds and get Dollars	1004184.597	777834.7 * 1.291
He can clearly make a profit of $4185

b) there will be no arbitrage opportunity when the cross rate is equal to the direct rate

c) Since the profit is only 0.418% ($4185 on $1M), the manager will not do these trades (the cost of these 3 trades will be 3%, i.e., almost $30,000)