You are a U. S.-based treasurer with $1,000,000 to invest. The dollar-euro exchange rate is quoted as $1.60 = €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 = €1.20 how much money can an astute trader make?

Answer: An astute trader can make $ 41,666.66.

Explanation: You must first change

$ 1,000,000 per pounds, which would leave a total of £ 500,000. ($ 1,000,000 / 2.00 = £ 500,000; ).

Secondly spend £ 500,000 to euros, obtaining € 600,000 (£ 500,000 x 1.20 = € 600,000; ).

Thirdly, with euros, buying dollars again, obtaining $ 960,000 (€ 600,000 x 1.60 = $ 960,000), that is, an arbitrage loss of - 40,000 in relation to the initial investment.

Finally you must return in the opposite direction:

$ 1,000,000 / 1.6 (€) / 1.2 (£) * 2 - $ 1,000,000 = $ 41,666.66 that is, an arbitrage profit.