Consider a non-dividend paying stock with current price $33.19. The 1-year spot rate is 2% and a futures contract on the stock with maturity 1 year is trading at $34.53. Suppose you borrow so that you can buy 200 shares of the stock. Moreover, you sell 200 futures contracts. The payoff of your position at maturity is

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BlackTom AI · Accepted Answer

We start by restating the setup and then compute the payoff step by step to see how the cash flows line up at maturity.

- The stock is non-dividend paying and currently priced at 33.19. You buy 200 shares, financed by borrowing. The total cost to acquire the 200 shares is 200 × 33.19 = 6,638.
- You borrow this amount at the 1-year spot rate of 2%. After 1 year, the loan repayment will be 6,638 × (1 + 0.02) = 6,638 + 132.76 = 6,770.76.
- You also sell 200 futures contracts on the stock with maturity 1 year, at a futures price of 34.53. A short futures position has a payoff at maturity of (F0 − S_T) per share, where F0 is the futures price and S_T is the spot price at maturity. Therefore, the payoff from the 200 short futures contracts is 200 × (34.53 − S_T).
- At maturity, your portfolio consists of: (i) the 200 shares worth 200 × S_T, (ii) the payoff from the short futures 200 × (34.53 − S_T), and (iii) the loan repayment of 6,770.76 that you owe.

Net payoff at maturity = [value of 200 shares] + [futures payoff] − [loan repayment]
= 200 × S_T + 200 × (34.53 − S_T) − 6,770.76
= 200 × 34.53 − 6,770.76
= 6,906 − 6,770.76
= 135.24.

Key intuition: the S_T terms cancel out because you own the stock and you have a short futures position on the same quantity of stock. The remaining cash difference comes from the fixed futures price times the quantity minus the loan repayment. This yields a deterministic payoff of 135.24 regardless of where S_T ends up, given the specified numbers.

Note on the missing options: The provided data includes an answer value of 135.24 but lists no answer choices. If options were present, you would compare each choice to the computed 135.24 payoff and identify which option matches this value. Here, the essential reasoning shows the cash flows align to yield 135.24 as the payoff at maturity.

COEC_V 371 001 002 2025W1 Lecture 8 Practice Quiz

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