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Commodities: spot goods, storage and the futures curve

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Start with the idea

Exposure to a commodity can come from owning physical goods, holding a futures contract, or buying a fund or producer’s shares. Those positions do not have identical returns.

Symbols, units & horizon

n: signed contracts in the new maturity
M: currency per point per contract
F_roll: entry price of the deferred contract at roll time
F_later: its later exit or settlement price
C: new-leg round-trip costs in currency
Π_new: profit of this new leg, separate from the old leg’s realized P&L

When and why to use this

Use separate contract ledgers to study commodity curve exposure, carry and roll behavior.

Physical goods have grade, location, storage, insurance and delivery constraints. Gold in a vault, a crude-oil future and shares in an oil producer represent different claims. A producer’s stock also embeds operating costs, financing and management decisions.

A futures curve lists prices for different delivery dates at the same moment. Contango describes higher deferred prices relative to nearer maturities; backwardation describes the opposite ordering. Storage, financing, scarcity and convenience can affect the curve, which need not be a pure price forecast.

For a roll, closing an expiring contract and opening a deferred contract at a different price changes the exposure’s starting reference. A loss is not automatically realized equal to that price gap on the roll date. Subsequent convergence and price changes determine the new contract’s P&L.

For commodity research, track individual maturities, inventories, seasonal calendars and delivery definitions. Compare a signal against an appropriate collateralized futures benchmark, including roll execution and cash interest. A spot chart alone cannot validate a futures carry strategy.

Π_{n e w} = n M (F_{l a t e r} - F_{r o l l}) - C

Model assumptions, derivation and arithmetic

Commodities: spot goods, storage and the futures curve

Close the old contract and record its own entry-to-exit P&L separately.
For the new contract, establish a fresh entry price F_roll. Its initial price gap from the old contract is not itself this leg’s P&L.
Subtract the new entry from the later price, multiply by signed contracts and multiplier, and deduct its costs.

Work it by hand

An old contract closes at 100 and the next month opens at 102. With one contract and $10/point, the new contract has zero price P&L at entry. If it later falls to 100, this leg loses $20 before costs—even if the spot market was unchanged.

Apply it in a strategy

Choose physical, futures, fund or producer exposure explicitly.
Model grade, location, calendar and curve features causally.
Attribute returns to each actual contract and cash collateral rather than a stitched price gap.

Research deliverable

Explain the difference between a roll-date price gap and subsequent P&L on the new contract.

Mechanics & research · reviewed 12 September 2026

Official educational material checked 12 September 2026. These examples use hypothetical prices and costs. Check the actual product specification, broker terms, venue calendar and jurisdiction before building an instrument adapter. Curve terminology checked. A curve shape is not a guaranteed return.

Further reading: CME · Contango and backwardation ↗

Python implementation

Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.

def rolled_leg_profit(contracts,multiplier,new_entry,later_price,cost=0):
    if multiplier<=0 or cost<0: raise ValueError("Invalid multiplier or cost")
    return contracts*multiplier*(later_price-new_entry)-cost

print(rolled_leg_profit(1,10,102,100))

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