Question

1)The forward price of wheat for delivery in four months is $6.25 per bushel, while the spot price is $5.90. The four-month interest rate is 5% per annum. Is there an arbitrage opportunity in this market if wheat may be stored costlessly? If so, show the cash flows involved in the arbitrage and show how would you take advantage if this opportunity.

Answer 1

Effective 4 months rate = 5%/3 = 0.01666666667 = 1.666666667%

Forward price = Spot * e^(rt)

Forward price = 5.9 * 2.7182818285^(0.01666666667 * 1)

Forward price = $5.9991573493

The quoted forward price of $6.25 is higher than what it should have been. So, there is an arbitrage opportunity.

Step 1: Borrow $5.9 dollars at 1.666666667% for four months and buy wheat

Step 2: Enter four-months forward contract to sell wheat at $6.25 per bushel

Step 3: Borrowed amount with interest = 5.9991573493

Step 4: Get $6.25 by selling wheat and repay $5.9991573493

The difference is your profit: 6.25 - 5.9991573493 = $0.2508426507