Question

You are a U.S.-based treasurer with $1,000,000 to invest. The dollar-euro exchange rate is quoted as $1.20 = €1.00 and the dollar-pound exchange rate is quoted at $1.80 = £1.00. If a bank quotes you a cross rate of £1.00 = €1.50 how much money can you make via triangular arbitrage (in terms of dollars)?

• 1,160,000

• 0

• 500,000

• 250,000

Can you tell me if my math is correct? Answer is 0

Steps:

Convert USD 1,000,000 to Euro using the exchange rate of USD 1.20 = 1 Euro. So we will have 1,000,000/1.20 = Euro 833,333.33

Convert EUR 833,333.33 to GBP using the exchange rate of EUR 1.50 = GBP 1 . So we will have 833,333.33/1.50 = GBP 555,555.56

Convert GBP 555,555.56 to USD using the exchange rate of USD 1.80 = GBP 1 . So we will have GBP 555,555.56 x 1.80= USD 1,000,000

Arbitrage profit = 1000000 - 1000000 = 0

Answer #1

dollar-euro exchange rate | $1.20 = €1.00 | |||||||

dollar-pound exchange rate | $1.80 = £1.00. | |||||||

therefore implied cross rate = | 1.8/1.2 | 1.5 | ||||||

Pound - Euro |
||||||||

bank quotes | £1.00 = €1.50 | |||||||

We can see that implied cross rate is equal to the bank quote therefore, there is no arbitrage profit opportunity | ||||||||

Profit = | 0.00 | |||||||

Your computed answer is correct | ||||||||

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