CFA Level IAlternative InvestmentsHard
An analyst is pricing a one-year futures contract on a commodity using the cost-of-carry model. The current spot price is $50, the annual risk-free rate is 5%, annual storage costs are 3% of spot price, and the convenience yield is estimated at 2%. What is the theoretical one-year futures price?
- A$53.00
- B$51.50
- C$50.00
- D$54.00
Show answer & explanationAnswer & explanation
Correct answer: A. $53.00
Using the cost-of-carry model: F = S × (1 + r + storage cost − convenience yield) = $50 × (1 + 0.05 + 0.03 − 0.02) = $50 × 1.06 = $53.00. Storage costs increase the futures price (cost of holding the physical commodity), while convenience yield (the benefit of holding the physical good) reduces it.
Why the other options are wrong
- B. Fails to include storage costs in the calculation.
- C. Ignores all carry costs and yields, simply repeating the spot price.
- D. Incorrectly adds convenience yield instead of subtracting it, or double-counts a cost.
Cost-of-Carry Model for Futures Pricing
The cost-of-carry model prices a futures contract as the spot price adjusted for the net cost of holding the underlying asset: financing/storage costs increase the futures price, while convenience yield (a non-cash benefit of physical ownership) decreases it.
- F = S × (1 + r + storage cost − convenience yield)
- High convenience yield can push a market into backwardation
- Storage costs are more relevant for physical commodities than financial assets
Memory trick: Carrying costs add up, convenience yield knocks it back down.