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? Group of answer choices No arbitrage is possible $41,667 $40,000 $1,160,000

Answer 1

$41,667

Step-by-step explanation:

First and foremost, in order to profit from the arbitrage opportunity, we need to first of all convert dollars to euro using the exchange rate below

$1.60 = €1.00

$1,000,000 in euros= $1,000,000*€1.00/$1.60=€625,000

Next we convert the euros to pounds using the rate quoted by the bank below:

£1.00 = €1.20

€625,000 in pounds=€625,000*£1.00/€1.20=£ 520,833.33

Lastly, we convert the pounds sterling back to dollars using the below exchange rate

$2.00 = £1.00

£ 520,833.33 in dollars=£ 520,833.33*$2/£1.00=$ 1,041,666.67

Profit from the arbitrage=$ 1,041,666.67 -$1,000,000.00

Profit from the arbitrage=$41,667(rounded to a whole dollar amount)