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 :clown_face: 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!