Consider a non-dividend paying stock with current price $152.62. The 1-year spot rate is 1.4% and a futures contract on the stock with maturity 1 year is trading at $159.4. Suppose you borrow so that you can buy 870 shares of the stock. Moreover, you sell 870 futures contracts. The payoff of your position at maturity is

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BlackTom AI · Accepted Answer

The question asks for the payoff of a specific trading strategy at maturity.
First, restate the setup in my own words to ensure clarity: you buy 870 shares of a non-dividend stock at 152.62 per share, financed by borrowing, and you simultaneously sell 870 futures contracts with a maturity of 1 year at a futures price of 159.4. The 1-year spot rate is 1.4%, which determines the borrowing cost.
Next, compute the amount you owe on the stock purchase when repaying the loan at maturity. The principal borrowed to buy 870 shares is 870 × 152.62 = 132,779.40. Interest on the loan for one year at 1.4% is 132,779.40 × 0.014 = 1,858.91. Therefore, the total amount due at maturity to repay the loan is 132,779.40 + 1,858.91 = 134,638.31.
Now evaluate the cash flows at maturity from the two positions:
- Stock position: you own 870 shares, so you have 870 × S_T cash from selling the stock at the then-prevailing price S_T. This cash is available to help repay the loan.
- Short futures position: you are short 870 futures contracts at F = 159.4. At maturity, the profit from a short futures position is 870 × (F − S_T) because you contract to deliver at price F but the actual spot price is S_T.
Total cash at maturity from these two components is 870 × S_T + 870 × (159.4 − S_T) = 870 × 159.4 = 138,678.00. Subtract the loan repayment amount of 134,638.31, leaving a net payoff of 138,678.00 − 134,638.31 = 4,039.69.
Therefore, the payoff of the position at maturity is 4,039.69 dollars.
Note on structure: the S_T terms cancel out when combining the stock position with the short futures payoff, which is why the payoff depends only on the initial futures price and the loan repayment amount, not on the actual terminal stock price. This type of result is typical when the stock position is exactly hedged by an offsetting futures position with the same quantity.

COEC_V 371 001 002 2025W1 Lecture 8 Practice Quiz

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