Answer: Buy the forward contract and buy the zero-coupon bond

The correct answer to the question is A: Buy the forward contract and buy the zero-coupon bond. This strategy creates a synthetic long position in commodity X for a period of 6 months. The explanation for this is based on the concept of synthetic commodity positions and the relationship between forward prices and expected future spot prices. A synthetic commodity position for a period of T years can be constructed by entering into a long futures contract with T years to expiration and buying a zero-coupon bond expiring in T years with a face value of the present value of the futures price. The payoff function at time T is as follows: - Payoff from long futures position = \( St - Fo,T \), where \( St \) is the spot price of the commodity at time T and \( Fo,T \) is the current futures price. - Payoff from zero coupon bond = \( Fo,T \) When these payoffs are combined, the total payoff function equals \( (St - Fo,T) + Fo,T \) or \( St \). This results in a synthetic commodity position that mimics the payoff of owning the actual commodity. In the context of the question, the 6-month forward price of commodity X is USD 1,000, and there are six-month, risk-free, zero-coupon bonds with a face value of USD 1,000 available. By buying the forward contract and simultaneously buying the zero-coupon bond, you are effectively creating a synthetic long position in commodity X. This is because at the end of the 6-month period, the payoff from the forward contract and the zero-coupon bond will combine to give you the spot price of commodity X at that time, assuming no arbitrage opportunities and a frictionless market.

Author: LeetQuiz Editorial Team