# Arbitrage profit

The annual interest rates are 5% in the United States and 4 % in France. Assume that your bank can borrow or lend at these rates. The spot foreign exchange rate is $1.241/€. If the one-year forward rate is$1.282/€, explain how the bank could arbitrage using a sum of $1 million. What spread could be earned? 1. Borrow USD 1,000,000 at 5% for 1 year. 2. Sell USD, buy EUR spot at 1.241, so you will get 1,000,000/1.241 = EUR 805,801.77. 3. Invest the EUR at 4% for 1 year. 4. Enter into 1 year forward contract to sell EUR and buy USD at 1.282. 1 year later: 1. EUR investment = EUR 805,801.77 × 1.04 = EUR 838,033.84 2. Sell EUR at 1.282 => 838,033.84 × 1.282 = USD 1,074,359.38 3. Pay USD Loan => USD 1,000,000 × 1.05 = USD 1,050,000 Profit = USD 1,074,359.38 - USD 1,050,000 = USD 24.359.38 Thank you! 1 Like If we apply the standard interest parity formula, then the forward exchange rate should be as follows: Forward = 1.241 * 1.05/1.04 =1.253 What this shows is that some valued counterparty will be willing to pay us$1.282 for a single Euro instead of $1.253, so you better believe I want to sell them a bunch of Euros a year from now! At time 0 Borrow USD 1,000,000 Convert into EUR 805,801.77 (current rate USD1.241/EUR) Invest @ 4% Enter Forward USD 1.282/EUR Hi, At time 1 Receive EUR 838,033.84 (principal + interest 4%) Convert into USD 1,074,359.39 (using forward USD 1.282/EUR) Repay loan USD 1,050,000 principal + interest 5%) Arbitrage USD 24,359.39 Regards. Hi, Thanks a lot! Could someone help solve this please? You go to a bank and are given these quotes: You can buy a euro for 15 pesos. The bank will pay you 14 pesos for a euro.  You can buy a U.S. dollar for 0.11 euros. The bank will pay you .10 euros for a U.S. dollar. You can buy a U.S. dollar for 11 pesos. The bank will pay you 10 pesos for a U.S. dollar.  You have$5,000. Can you use triangular arbitrage to generate a profit? If so, explain the order of the transactions that you would execute and the profit that you would earn. If you cannot earn a profit from triangular arbitrage, explain why.

If said bank exists, please let me know. I’m going all in.

1. Take the $5,000 and convert it to pesos. \$5,000 \times 10 = 50,000 ~pesos

1. Then take the 50,000 pesos and convert it to euro.

50,000 ~pesos / 15 = EUR 3,333.33

1. Lastly, convert the euro back to USD.

EUR 3,333.33 / 0.11 = \\$ 30,303.03

Profit = 30,303.03 - 5,000 = …

1 Like

Thank you!

Hi

I have made a youtube video explaining triangular arbitrage in a very straightforward and simple way. Check it out here, and let me know what you guys think and if you found it useful.

I cant post links but search for this vid: CFA Level 2 - Economics | Arbitrage Triangle Explained

Kind Regards