Explanation

A synthetic long position in a commodity for a period of T years can be constructed by:

• Entering into a long forward/futures contract with T years to expiration
• Buying a zero-coupon bond expiring in T years with a face value equal to the forward price

Payoff Analysis:

• Payoff from long forward position: $S_T - F_{0,T}$

  • Where $S_T$ is the spot price at time T
  • $F_{0,T}$ is the current forward price (USD 1,000)

• Payoff from zero-coupon bond: $F_{0,T}$ (USD 1,000)

• Total payoff: $(S_T - F_{0,T}) + F_{0,T} = S_T$

This creates a synthetic commodity position where the total payoff equals the spot price of the commodity at time T, exactly replicating the payoff of owning the physical commodity.

Why other options are incorrect:

• B: Buying forward + shorting bond gives $(S_T - F_{0,T}) - F_{0,T} = S_T - 2F_{0,T}$
• C: Shorting forward + buying bond gives $(F_{0,T} - S_T) + F_{0,T} = 2F_{0,T} - S_T$
• D: Shorting forward + shorting bond gives $(F_{0,T} - S_T) - F_{0,T} = -S_T$

Only option A creates the desired synthetic long position in the commodity.