Natural Resources: Pricing of Commodity Futures Contracts
The price of a one-year futures contract is USD 157. Assuming no storage costs or convenience yield, if the spot price is USD 148, and the risk-free interest rate is 3%, what _most accurately_ describes the potential return?
Correct!
Assuming there are no storage costs or convenience yield, the expectation is that this futures contract would earn USD 4.56 based upon the following formula:
$$\displaystyle F_0(T) = S_0e^{(r + c - i)T} = 148e^{(0.03 + 0 - 0)1} \approx 152.51 $$
It can also be approximated as:
$$\displaystyle F_0(1) \approx S_0 \times (1 + r) + c - i$$
$$\displaystyle F_0(1) \approx 148(1 + 0.03) + 0 - 0 = 152.44 $$
If the commodity is delivered at the price of USD 157, you will notice that either USD 4.49 or USD 4.56 represents the difference in value between the futures price of USD 157 and the current price of the contract. This type of return is considered an arbitrage strategy.
Keep in mind, however, the addition of storage costs and any convenience yield would lower the return, and thus the likelihood of arbitrage.
Incorrect.
This answer simply subtracts the spot price from the one-year futures contract price and does not consider the influence of the risk-free interest rate. The following formula is helpful to arrive at the correct answer:
$$\displaystyle F_0(T) \approx S_0 \times (1 + r) + c - i$$
Incorrect.
This answer uses the price of the one-year futures contract to incorrectly calculate the difference in return. The spot price should be used to calculate this difference, and the following formula is helpful to calculate the correct answer:
$$\displaystyle F_0(T) \approx S_0 \times (1 + r) + c - i$$
USD 4.50
USD 4.70
USD 9.00
