DP
Hedging & Basis Riskintermediate

Basis

Basis is the spot price of the asset being hedged minus the futures price of the contract used, b=S−Fb = S - F (Hull convention). For a storable commodity in a normal market, basis is negative because the futures price embeds cost of carry. As expiry approaches, basis converges toward zero through arbitrage. A strengthening basis (less negative or more positive) benefits short hedgers, while a weakening basis benefits long hedgers.

Why it matters

Basis is the gap between owning the asset now and contracting to own it later. If wheat trades for A$300 spot and A$305 for delivery in three months, basis is −5-5. The gap reflects storage, insurance, and financing costs minus any convenience yield from holding the physical good. At delivery the two prices must coincide, otherwise an arbitrageur would buy the cheaper one and sell the dearer, closing the gap.

Formulas

Basis definition (Hull convention)
b=S−Fb = S - F
Some commodity-market practitioners use the opposite sign F−SF - S. Always check the convention in the source you read.
Basis at delivery
bT=ST−FT≈0b_T = S_T - F_T \approx 0
Convergence is enforced by physical delivery or cash settlement. Small frictions can leave residual basis at the last trade.
Cost-of-carry basis for a financial asset
b=S−F0=S−Se(r−q)T=S(1−e(r−q)T)b = S - F_0 = S - S e^{(r-q)T} = S\bigl(1 - e^{(r-q)T}\bigr)
rr is the risk-free rate and qq is the income yield. When r>qr > q basis is negative (contango); when q>rq > r basis is positive (backwardation).

Worked examples

Scenario

Spot wheat in Sydney trades at A$300 per tonne and the ASX Eastern Wheat 3-month future at A$305 per tonne.

Solution

Basis =300−305== 300 - 305 = A$-5 per tonne. The market is in contango, with carrying costs exceeding any convenience yield. By the delivery date the spot and futures prices should converge so that basis trends to zero.

Scenario

Crude oil spot is US$82 per barrel and the front-month WTI future is US$80 per barrel because refiners need physical oil urgently after a refinery outage.

Solution

Basis =82−80== 82 - 80 = US$+2. The market is in backwardation. A high convenience yield from holding physical oil pushes spot above futures. Short hedgers in this state benefit if basis stays positive at close.

Common mistakes

  • ✗Basis is always negative. Basis is positive in backwardation, common for oil and electricity during demand spikes, and negative in contango, common for storable grains. Sign depends on the cost-of-carry components and short-term supply or demand shocks.
  • ✗Basis and the futures-spot spread are the same thing. The market sometimes quotes F−SF - S as the carry spread; Hull uses b=S−Fb = S - F. Always confirm the sign convention before plugging into a hedging formula.
  • ✗Basis is constant once a hedge is set. Basis fluctuates daily with storage costs, financing rates, and short-term supply or demand pressures. Basis risk arises precisely because b2b_2 at hedge close is not known at the outset.

Revision bullets

  • •Basis =S−F= S - F in the Hull convention
  • •Contango has b<0b < 0, F>SF > S
  • •Backwardation has b>0b > 0, S>FS > F
  • •Converges to zero at delivery
  • •Strengthening basis helps short hedgers
  • •Weakening basis helps long hedgers

Quick check

If spot copper is US$8,000 per tonne and the 3-month copper future is US$8,080, the basis is:

Which of the following best characterises the behaviour of basis as a futures contract approaches its delivery date?

Connected topics

ConvergenceBasis Risk

In learning paths

Hedging & Risk Path

Sources

  1. Hull (2022), §3.3
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Section 3.3 defines basis, derives the strengthening and weakening cases, and links convergence to arbitrage.
  2. CME Group, Learn about Basis
    CME Group. Learn about Basis: Grains. CME Education Centre, accessed 2026.
    Practitioner-style explanation showing how basis quotes are used by grain elevators and how local supply or demand shifts move basis.
  3. Working (1953)
    Working, Holbrook. Futures Trading and Hedging. American Economic Review, Vol. 43, No. 3, 1953, pp. 314-343.
    Classic paper that reframed hedging as the management of basis rather than the elimination of price risk.
  4. ASX, ASX SPI 200 Futures
    Australian Securities Exchange. ASX SPI 200 Futures brochure. ASX.
    Lists the SPI 200 contract used in Australian equity hedging, where index basis depends on dividend yield versus the cash rate.
How to cite this page
Dr. Phil's Quant Lab. (2026). Basis. Derivatives Atlas. https://phucnguyenvan.com/concept/basis
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