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Basis risk

Basis risk is the uncertainty left when an exposure and its hedge move differently. A spot–futures ledger shows what remains after the main price move is offset.

Basis risk is the uncertainty that remains when an exposure and the instrument used to hedge it do not move together as intended. A hedge can offset most of a price change while leaving a gain or loss from the changing relationship between the two prices.
In a spot–futures hedge, define the basis as
bt=St−Ft,b_t=S_t-F_t,
where StS_t is the spot price of the exposure and FtF_t is the price of the particular futures contract used. Both must be expressed in compatible units and currency. This article uses spot minus futures throughout; some markets use the opposite sign. The CFTC glossary describes basis risk as uncertainty in how that spread changes during the hedge.

The move that survives the hedge

Suppose a firm owns 100 physical units and shorts a linear futures position covering exactly 100 units. The hedge starts at time 0 and is closed at time 1, before the futures contract expires. These are synthetic prices, not market observations. Ignore funding, transaction costs, storage, income and the timing of variation-margin cash flows.
Quote, USD per unitAt openingAt close
Spot price SS100105
Futures price FF102106
Basis S−FS-F−2−1
The physical holding gains 100(105−100)=500100(105-100)=500 dollars in price value. The short future loses 100(106−102)=400100(106-102)=400 dollars. The combined price result is +USD 100.
Synthetic 100-unit long physical and short futures hedge. Spot rises from 100 to 105 and futures from 102 to 106 USD per unit. Basis rises from −2 to −1. Physical price gain of USD 500 plus futures loss of USD 400 leaves USD 100.
Synthetic 100-unit long physical and short futures hedge. Spot rises from 100 to 105 and futures from 102 to 106 USD per unit. Basis rises from −2 to −1. Physical price gain of USD 500 plus futures loss of USD 400 leaves USD 100.
Original synthetic one-period hedge, with equal physical and futures quantities. Quotes are USD per unit; gains and losses are USD. Funding, costs, storage, income and the timing of variation margin are excluded.

For a fixed quantity QQ, the price gain on the physical holding plus the short futures result is

Π=Q(S1−S0)+Q(F0−F1)=Q[(S1−F1)−(S0−F0)]=Q(b1−b0).\begin{aligned} \Pi&=Q(S_1-S_0)+Q(F_0-F_1)\\ &=Q\big[(S_1-F_1)-(S_0-F_0)\big]\\ &=Q(b_1-b_0). \end{aligned}
Here the basis increases by USD 1 per unit, leaving 100×1=100100\times1=100 dollars. An increase is called a strengthening of the basis—even when, as here, it remains negative.
The positive outcome does not make basis risk a source of guaranteed profit. If the closing spot price had instead been 103 while the same future closed at 106, the closing basis would have been −3 and the combined price result −USD 100. Before the outcome is known, it is the uncertainty in the residual that matters. A nonzero opening basis alone does not establish risk: a known closing basis would permit a known effective price under these assumptions.

A seller and a buyer read the same spread differently

For a seller who shorts futures, the cash sale price plus the futures gain per unit is

S1+(F0−F1)=F0+b1.S_1+(F_0-F_1)=F_0+b_1.
In the example, selling the physical units at 105 and paying the 4-per-unit futures loss produces an effective sale price of USD 101 per unit. The opening physical price was 100, which explains the 1-per-unit combined gain. It would be wrong to call the final physical sale proceeds alone the hedged result.
A buyer protecting a future purchase uses a long future. Its purchase cost less the futures gain also equals F0+b1F_0+b_1. Thus a stronger-than-expected closing basis improves a short hedger's sale receipt but raises a long hedger's purchase cost. CME's basis explanation develops this seller–buyer distinction.

Why a close match can still leave a gap

The local cash price can reflect grade, freight, storage and local supply conditions that differ from the futures benchmark. Hedging one commodity with a related commodity adds another mismatch. Closing before expiry leaves uncertainty in the cash–futures relationship on that particular date.

Convergence concerns the contract's specified deliverable or settlement reference at expiry. It does not imply that every local grade, location or sale date has zero basis. Nor does a high historical correlation alone promise a reliable hedge: the size of the price moves, hedge quantity and stability of the relationship matter too.

The ledger above uses equal quantities so its residual is exactly the change in basis. With another hedge quantity, the combined result is more generally QSΔS−QFΔFQ_S\Delta S-Q_F\Delta F. Contract sizing and basis uncertainty should therefore be examined together.

Daily settlement creates an additional concern: the futures loss may require cash before the physical asset is sold. That is funding liquidity risk, even when the overall hedge offsets price movements well. The Forwards and Futures lesson, available with a free signed-in account, develops those payoff and settlement mechanics.

Sources

  • John C. Hull, Options, Futures, and Other Derivatives, 9th ed., Global Edition, Pearson, 2018, §3.3, pp. 76–79: basis convention, effective hedged prices, contract choice and cross hedging. The ledger here is original and synthetic.
  • CFTC: Futures Glossary — Basis and Basis Risk: cash-minus-futures terminology and uncertainty between establishing and lifting a hedge.
  • CME Group: Learn about Basis: Grains: local price components and the different effects of basis changes on buyers and sellers.
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