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Answer: Long forward with delivery price at $20; i.e., K = 20
If the commodity price stays at **$20** at maturity: - **Borrowing to buy spot** leads to a negative net profit because the loan must be repaid with interest. - **Long call option** has payoff of zero at expiry when \(S(T)=K=20\), but the option premium makes the net profit negative. - **Long forward** with delivery price 20 has payoff \(S(T)-K = 20-20 = 0\), so its net profit is the highest among the choices. Therefore, the **long forward** produces the highest future net profit.
Author: Manit Arora
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Question 137.3 A commodity has a current spot price of $20 and six-month forward price of $20 (i.e., , ). Assume the risk-free rate is constant at 4.0%. Which of the following current trades (T0) returns the highest future (net) profit if the stock price does not change during the next six months, such that S(+0.5)=S(T)=\`20`$?
A
Borrow at the risk-free rate in order to purchase spot commodity
B
Buy (long) call options with strike at $20; i.e., K = 20.
C
Long forward with delivery price at $20; i.e., K = 20
D
Each of the above have identical future (net) profits
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