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?

Question

Quizplus · Accepted Answer

To find out if an arbitrage opportunity exists, we can compare the cross rate with the direct exchange rate between dollars and euros.

1 euro = $1.6
1 pound = $2

Thus, 1 pound = $1.6/2 = $0.8

Now, if 1 pound is also worth €1.20, then:

1 euro = 1.20 pounds
1 pound = 1/1.20 euros = 0.8333 euros

Comparing this exchange rate with the direct exchange rate of $1.60 per euro, we can see that the cross rate of 0.8333 euro per pound is more favorable.

So, to take advantage of this arbitrage opportunity, the treasurer should:

1. Convert the $1,000,000 to pounds at the rate of $2/pound, obtaining £500,000. 
2. Convert the pounds back to euros at the cross rate of 1.20 pounds per euro, obtaining €416,667. 
3. Convert the euros back to dollars at the direct rate of $1.60 per euro, obtaining $666,667.

The profit from this series of transactions is:

$666,667 - $1,000,000 = -$333,333

Therefore, the treasurer can't make a profit from this arbitrage opportunity, and the answer is C.

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