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Interpreting the Commodity Cost-of-Carry Model and Storage Limits

Article Quant Q&A · Author: Preston Lui
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Summary

The document introduces the commodity cost-of-carry relationship, which links a futures price to spot price, financing, storage costs, convenience yield, and time to delivery. It asks whether the model implies an upper bound on futures prices and how to interpret that implication when a commodity cannot be stored for a long period.

Its agricultural example highlights a limitation in applying the formula mechanically: the model does not by itself describe what happens when storage is infeasible or unavailable over the contract horizon. The document poses the interpretation problem but does not provide an answer, supporting evidence, or an alternative model. Readers should therefore treat it as a question about the assumptions behind cost-of-carry pricing, rather than a resolved claim that futures prices become unbounded. Real-world storage constraints and changing carry inputs may require additional modeling.

Key ideas

  • The cost-of-carry relationship connects futures prices to spot prices, financing, storage, convenience yield, and time.
  • The document questions whether the formula can be applied when a commodity cannot be stored through the contract horizon.
  • It raises an interpretation problem but provides no proposed resolution or empirical evidence.
  • The formula's assumptions and practical storage constraints matter when applying it to commodity futures.

Tags

CommoditiesFuturesCarryDerivatives pricing
Full text
# Is the future cost of carry a upper bound for the future price?


# Is the future cost of carry a upper bound for the future price?












The Future cost of carry model models the future price of a commodity.

$F = Se^{((r + s - c)t)}$

Where

$F$ = the future price of the commodity

$S$ = the spot price of the commodity

$r$ = the risk-free interest rate

$s$ = the storage cost expressed as a percentage of the spot price

$c$ = the convenience yield

$t$ = time to delivery of the contract expressed as a fraction of one year

This equation sounds weird to me. For example, consider an agricultural product that you can't reasonably store for over 2 years. Then the model seems to predict the future price of that agricultural product 2 years later to be infinity. This is of course absurd.

Are there better interpretation of the formula?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.