Futures basis

Who this page is for — Anyone comparing futures with spot, assessing a hedge, reading contango and backwardation, or analysing a roll. Basis is useful only when its formula, expiry and cash reference are stated.

Futures basis is a difference between the price of a specific futures expiry and a defined spot or cash price. On this page, Cyclepedia always uses the convention:

b = F − S

F is the price of the future for the stated expiry and S is the spot price observed at the same time and in the same unit. Under this convention, b > 0 means futures above spot and b < 0 means futures below spot.

The convention is not universal. The CFTC glossary often defines commodity basis as cash minus futures, so:

common CFTC basis = S − F = −Cyclepedia b

Two analyses can therefore describe the same market with numbers of opposite sign. Before using phrases such as “basis is rising,” state the formula, future, spot source, timestamp, currency, grade and location.

In plain terms — “Basis is +3” is not a complete statement. In Cyclepedia, it means that the specified futures expiry is three units above the stated spot price; under the cash-minus-futures convention, the same observation is −3.

Observed basis must be separated from theoretical carry, the spread between expiries and roll return.

Before calculating: make F and S comparable

The calculation requires comparable quantities:

Field	Why it matters
Future	ticker, month and year identify the exact expiry
Spot or cash	an index, auction, physical price, ETF or another proxy are not equivalent
Time	non-simultaneous quotations can create an artificial basis
Unit and currency	index points, tonnes, bushels, barrels and exchange rates require consistency
Grade and location	grade and delivery point affect the relationship for commodities
Market state	stale prices, limits or closed sessions reduce comparability

Sign example. If F = 103 and S = 100, Cyclepedia reports b = +3. The cash-minus-futures convention reports −3. Neither figure alone indicates an arbitrage or forecast: they describe the same difference with opposite orientation.

Gross basis, fair basis and net basis

To prevent “basis” from describing three different quantities, this page uses the following operational labels. They are not universal: data and formulas must retain their definitions.

1. Observed gross basis

b_gross = F − S

This is the directly observed difference. It includes expected carry and every other effect embedded in prices: financing, income, storage, supply and demand, constraints, delivery optionality and possible misalignments.

2. Model fair basis

First estimate a theoretical futures price F*, then:

b_fair = F* − S

For an equity index, in a simplified model with rate r, expected dividend yield q and time to expiry τ, expressed consistently:

F* = S × e^((r − q) × τ)

For a storable commodity, an instructional representation can add storage and insurance costs u and convenience yield y:

F* = S × e^((r + u − y) × τ)

These are not universal formulas for every contract. Discrete dividends, term-specific rates, collateral, taxes, grade, location, non-financeable costs, short-sale constraints and unobservable inputs require a suitable model.

3. Net basis or deviation from fair value

Cyclepedia uses net basis here for the deviation of observed futures from the chosen fair value:

b_net = F − F* = b_gross − b_fair

The figure depends on the model. It is not certain profit: transaction costs, actual funding, uncertain dividends, balance-sheet constraints and execution risk can create a no-arbitrage band around F*.

Verifiable example. A spot index is at 5,000; r = 4%, q = 1.5% and τ = 0.25 years, with continuous compounding and no frictions. The fair future is 5,000 × e^((0.04 − 0.015) × 0.25) ≈ 5,031.35. If the observed future is 5,036, gross basis is +36, fair basis is approximately +31.35 and net basis is approximately +4.65 points. The result measures deviation from the assumed model, not a trading recommendation.

Calendar spread and basis point are not futures-versus-spot basis

A calendar spread compares two futures in the same family with different expiries. With the convention stated:

calendar spread = F(far) − F(near)

Spot does not appear here. The spread describes the shape of the curve and can be positive, negative or change across expiries. Saying “contango” or “backwardation” therefore requires naming the points being compared; it is not the same as forecasting a market rise or fall.

A basis point, by contrast, is a unit of change in a rate or yield: 1 bp = 0.01% = 0.0001 in decimal form. Twenty-five basis points are 0.25 percentage points. The similar name does not make a futures-versus-spot difference a measure in basis points.

Basis risk in a hedge

Basis risk is the risk that the relationship between cash exposure and the future changes unexpectedly while a hedge is open. It can arise from an imperfect expiry, a correlated but non-identical asset, grade, location, currency, trading hours, settlement formula or quantities that do not align perfectly.

For an idealized short hedge, with one cash unit and a perfectly sized future, the combined change before costs is:

Δcash + short futures P&L = ΔS − ΔF = −Δb

Example. At inception S₀ = 100, F₀ = 103, so b₀ = 3. At close S₁ = 94, F₁ = 95, so b₁ = 1. The cash asset loses 6; the short future gains 8; the combined result is +2, equal to −Δb = −(1 − 3). When sizes, multipliers or assets do not match, the actual hedge ratios are required.

A hedge reduces a selected risk but partly replaces it with basis, margin, liquidity and operational risk. A historically stable basis is no guarantee that it will remain stable under stress.

Convergence: a conditional mechanism

The delivery structure or cash-settlement formula is designed to link the future with its reference market. As expiry approaches, arbitrage and settlement tend to reduce the difference consistent with that reference. “Futures and spot converge” does not mean that every series labelled spot must become identical to the future at every instant.

For physically delivered contracts, the deliverable asset, par point, grade, location and timing matter. Scarcity, congestion or unrepresentative differentials can disrupt normal convergence. A cash-settled contract converges towards its defined final reference, not necessarily towards an ETF, retail quote or different intraday index.

Basis, roll and roll yield

Rolling means closing one expiry and opening a deferred one. The different prices change the new entry point and, for an unchanged contract count, can change notional; they do not by themselves create an immediate loss.

Keep three components separate:

execution cost: bid-ask spread, commissions, slippage and leg risk;
calendar spread: observed difference between expiries at the roll;
roll yield: return component produced by the position's evolution along the curve and by the methodology used to maintain exposure.

For a long strategy that renews contracts, contango is often associated with negative roll yield and backwardation with positive roll yield, all else held constant. “Often” does not mean “always”: curve shape, spot movements, chosen tenor, weights, collateral and the roll calendar change the result.

Checklist for publishing or using a basis figure

Write the formula and sign convention.
Identify the future, expiry and spot or cash source.
Align timestamp, currency, unit, grade and location.
Distinguish gross, fair and net basis with explicit formulas.
Do not call a calendar spread or a basis point “basis.”
For a hedge, measure the change in basis and the hedge ratio.
For a roll, separate execution costs and roll yield.
Treat convergence as a relationship with the contractual reference.

Sources

U.S. Commodity Futures Trading Commission, Basics of Futures Trading — contracts, cash settlement, delivery and economic risk.
U.S. Commodity Futures Trading Commission, Futures Glossary — cash-minus-futures convention, basis risk, basis point and calendar spread.
U.S. Commodity Futures Trading Commission, The Economic Purpose of Futures Contracts — hedging, offset, delivery and convergence with the cash market.
CME Group, Mark-to-Market — daily settlement and position variation.
CME Group, Understanding Futures Expiration & Contract Roll — expiry, offset and replacement with deferred contracts.
CME Group, Cash Settlement vs. Physical Delivery — settlement references and the link between the contract and physical market.
CME Group, What is Equity Index Basis? — futures-minus-spot convention and the relationship with financing and dividends.
U.S. Commodity Futures Trading Commission, Policy Statement on Price Differentials — delivery points, grades, differentials and conditions for convergence.