Question

You are a U.S.-based treasurer with $1,000,000 to invest. The dollar-euro exchange rate is quoted as $1.50 = €1.00 and the dollar-pound exchange rate is quoted at $2.00 = £1.00. If a bank quotes you a cross rate of £1.00 = €1.25, is there an arbitrage opportunity? If so, how much money would you make? Show all workings.

Answer 1

The $/Euro rate using the $/GBP exchange rate and
the cross rate of GBP/Euro provided by the bank =
= 2/1.25 = 1.6
The $/Euro exchange rate is 1.5.
As the rates for Euro in terms of $ are different, there
is arbitrage opportunity.
The steps would be to use the $1000000 to buy Euros
at the exchange rate to get 1000000/1.5 =	€    6,66,666.67
Use these Euros to buy GBP at the cross rate given by
the bank to get 666666.67/1.25 =	£    5,33,333.33
Finally, convert the above GBP to $ at the exchange
rate to get 533333.33*2 =	$ 10,66,666.67
Arbitrage profit = $1066666.67-$1000000 =	$        66,666.67