
Explanation:
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 creating a synthetic commodity position through a combination of a long futures contract and a zero-coupon bond.
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:
Hence, the total payoff function equals or . This creates a synthetic commodity position that replicates the payoff of owning the actual commodity.
Options B, C, and D are incorrect because they do not replicate the payoff of a long position in the commodity. Buying the forward contract and shorting the zero-coupon bond (option B) or shorting the forward contract and either buying or shorting the zero-coupon bond (options C and D) would not result in a synthetic long position in the commodity.
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A commodity trader has observed that the 6-month forward price for commodity X is currently set at USD 1,000. In addition, the trader has found a 6-month zero-coupon risk-free bond on the secondary fixed-income market, which has a face value of USD 1,000. Considering these conditions, what combination of trading actions would create a synthetic long position in commodity X for a 6-month period?
A
Buy the forward contract and buy the zero-coupon bond.
B
Buy the forward contract and short the zero-coupon bond.
C
Short the forward contract and buy the zero-coupon bond.
D
Short the forward contract and short the zero-coupon bond