Question

You are a U.S.-based treasurer with $1,000,000 to invest. The dollar-euro exchange rate is quoted as $1.40 = €1.00 and the dollar-pound exchange rate is quoted at $1.65 = £1.00. If a bank quotes you a cross rate of £1.00 = €1.20, how much money can an astute trader make? Be sure to keep four decimal points when computing currency rates. Be sure to calculate the intrinsic value of the British Pound and based on your calculation, determine whether British Pound is over or under priced.

Answer 1

Euro/Pound = (Euro/Dollar)*(Dollar/Pound)

= (1/1.40)*(1.65)

= 1.1786 Euro/Pound

Concert 1,000,000 into Pound and get 1,000,000/1.65 = Pound 606,060.61

Convert into Euros and get 606,060.61*1.20 = Euro 727,272.73

Convert back into USD and get 727,272,73*1.40 = $1,018,181.82

Hence, arbitrage profit = $18,181.82

British Pound is overpriced as intrinsic value is 1.1786 Euro/Pound