Spot EURUSD is 1.0800, the one year dollar rate is 5.00% and the one year euro rate is 3.00%, both simple. The one year forward trades at 1.1050. Compute the fair forward and the profit on EUR 10m of the arbitrage, and give one reason the gap can persist.

Spot EURUSD is 1.0800, the one year dollar rate is 5.00% and the one year euro rate is 3.00%, both simple. The one year forward trades at 1.1050. Compute the fair forward and the profit on EUR 10m of the arbitrage, and give one reason the gap can persist.

Approach: Build the forward from the two funding legs, then run the full four leg cash flow on the stated size so the profit comes out in dollars rather than in rate terms.

$41,500. Covered interest parity gives F = S * (1 + r_USD)/(1 + r_EUR), so 1.0800 * 1.05/1.03 makes the fair forward 1.10097 and the forward points 209.7. The traded forward of 1.1050 is 0.00403 too high, so you sell euros forward. Borrow $10.8m at 5% and owe $11.34m, buy EUR 10m spot and invest at 3% to hold EUR 10.3m, then deliver those euros at 1.1050 for $11.3815m, which leaves $41,500. The gap can persist because the arbitrage consumes balance sheet: the cross-currency basis has been persistently negative for dollar funding since 2008, as banks charge for the balance sheet and regulatory capital that the spot and forward legs use, so parity holds only net of that charge.

Follow-up: The dollar funding is available only for three months while the forward runs a year. How do you run the trade and what risk does the maturity mismatch add?

Key concepts: covered interest parity, forward points, cross-currency basis, arbitrage profit.