Consider a non-dividend paying stock with current price $114.15. The 1-year spot rate is 2.7% and a futures contract on the stock with maturity 1 year is trading at $123.09. Suppose you borrow so that you can buy 600 shares of the stock. Moreover, you sell 600 futures contracts. The payoff of your position at maturity is

Question

BlackTom AI · Accepted Answer

Question restatement:
- We consider a non-dividend paying stock currently priced at 114.15. The 1-year spot rate is 2.7%. A 1-year futures contract on the stock trades at 123.09. The strategy described is: borrow to buy 600 shares of the stock, and sell 600 futures contracts. The task is to determine the payoff of this position at maturity.

Option-by-option analysis:
Option A: $3,514.77
- Compute the initial investment and financing: to buy 600 shares at 114.15, you need 600 × 114.15 = 68,490. You borrow this amount to finance the purchase. 
- At maturity, you must repay the loan with interest: 68,490 × (1 + 0.027) = 68,490 × 1.027 = 70,339.23.
- Futures position: you sold (shorted) 600 futures contracts at 123.09. At settlement, you deliver your 600 shares against the futures, receiving 600 × 123.09 = 73,854. 
- Net payoff: futures receipts minus loan repayment = 73,854 − 70,339.23 = 3,514.77.
- This aligns with the idea that the stock’s future price outcome cancels in the carry, leaving the profit as the difference between the futures payoff and the financing cost.

Option B: indeterminate due to insufficient information
- The problem provides the necessary quantities (stock price, futures price, amounts, and interest rate) to compute a definite payoff. Therefore this statement is inaccurate because the information given is sufficient to determine the payoff.

Option C: $2,460.34
- If one incorrectly treated the payoff, for example, by incorrectly using the current stock price or mis-applying the futures payoff formula, one could arrive at a different figure. However, the correct calculation above yields 3,514.77, not 2,460.34. The discrepancy likely stems from mixing up which cash flows occur at maturity (delivery cash from the futures vs. loan repayment) or miscomputing interest accrual.

Option D: $4,041.99
- This value would arise from a miscalculation, perhaps by using a different interest component or mispricing the futures payoff. The correct financing of the purchase and the correct futures settle-in-cash amount must be used: 600 × 123.09 = 73,854, and loan repayment is 70,339.23, giving 3,514.77, not 4,041.99.

Summary of correct reasoning flow:
- Recognize that buying the stock costs 68,490 funded by a loan due at maturity to be repaid with interest, totaling 70,339.23.
- Recognize that shorting 600 futures at 123.09 yields a cash inflow of 73,854 at settlement when the futures are closed by delivering the 600 shares.
- The stock itself is delivered to satisfy the futures obligation, so no additional cash from the stock price at maturity enters the payoff; the stock price only affects the feasibility of delivery, not the cash difference here.
- The net payoff equals 73,854 − 70,339.23 = 3,514.77, which matches Option A.

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