Question

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? Multiple Choice • No arbitrage is possible 0 $1,160,000 0 $41,667 0 $40,000

Answer 1

First Convert $ into €

1 € = $ 1.60

$ 1,000,000 = € 1,000,000 / 1.60

= € 625,000

Now, Covert € into £

1 £ = € 1.20

€ 625,000 = £ 625,000 / 1.20

= £ 520,833.33

Finally, convert £ into $

1 £ = $ 2

£ 520,833.33 = $ 520,833.33 * 2

= $ 1,041,666.67

Therefore,

Net Gain = $ 1,041,666.67 - $ 1,000,000

= $ 41,666.67

If we first convert $ into £, then it incurs a loss of $40,000.