CFA Level IAlternative InvestmentsHard
A commodity futures contract has a current spot price of $60 per barrel and a one-year futures price of $63 per barrel. The annual storage cost for the commodity is $1.50 per barrel, and the risk-free rate is 4%. Based on the cost-of-carry model, is the futures contract overvalued, undervalued, or fairly valued?
- AFairly valued
- BCannot be determined without knowing convenience yield.
- COvervalued
- DUndervalued
Show answer & explanationAnswer & explanation
Correct answer: D. Undervalued
The theoretical futures price (F_0) is calculated as S_0 * (1 + r_f) + storage costs. F_0 = $60 * (1 + 0.04) + $1.50 = $62.40 + $1.50 = $63.90. Since the actual futures price of $63 is less than the theoretical price of $63.90, the futures contract is undervalued.
Why the other options are wrong
- A. This would mean the actual futures price equals the theoretical price.
- B. Convenience yield is implicitly accounted for if the actual futures price deviates from the cost-of-carry model with known storage costs and risk-free rate.
- C. This would mean the actual futures price is above the theoretical price.
Cost-of-Carry Model (Commodities)
A model used to determine the theoretical futures price of a commodity, based on its spot price and the costs of holding it.
- Theoretical Futures Price = Spot Price * (1 + Risk-Free Rate) + Storage Costs.
- Excludes convenience yield in its basic form.
- If actual futures price > theoretical, it's overvalued; if actual < theoretical, it's undervalued.
Memory trick: Spot grows by risk-free, then add storage, that's fair.