Basis Risk

Last lesson's airline example had a suspiciously tidy ending: whatever the spot price did, the hedged cost landed on exactly the locked-in futures price, to the penny. That tidiness relied on a hidden assumption — that the futures contract tracks the exposure perfectly, and that the hedge is closed out at precisely the moment the exposure is realized. In practice neither is quite true, and the gap between them is called basis risk.

Define the basis at any time t as

b_t = S_t - F_t,

the spot price of the asset you actually hold or need, minus the price of the futures contract you're using to hedge it. If the futures contract were on exactly your asset and expired at exactly the moment you need it, the basis would converge to zero right at expiry — spot and futures prices must agree the instant delivery happens, or an arbitrageur would trade the gap away — and the hedge would be perfect. Basis risk is what's left over when that convergence is not exact at the moment the hedger actually needs it, and it has two common causes:

The algebra of an imperfect hedge

Suppose a hedger sets up a position at time 1 (basis b_1 = S_1 - F_1) and closes it out at time 2 (basis b_2 = S_2 - F_2), before formal expiry. Take a short hedge — selling the asset at time 2 while holding a short futures position taken on at time 1. Total proceeds are the spot sale plus the futures gain:

S_2 + (F_1 - F_2) = F_1 + (S_2 - F_2) = F_1 + b_2.

Run the same bookkeeping for a long hedge (buying the asset at time 2, having bought futures at time 1) and the total cost comes out the same way:

S_2 - (F_2 - F_1) = F_1 + (S_2 - F_2) = F_1 + b_2.

Either direction, the effective price is F_1 — the price locked in at the start — plus the basis at close-out, b_2. If b_2 were known in advance, the hedge would be perfect: you'd simply add a known constant to a known futures price. The problem is that b_2 is not known when the hedge is set up — it depends on how spot and futures happen to have drifted apart by the time the position is closed. Hedging with futures doesn't eliminate price risk; it trades a large, obvious risk (the level of S_2) for a smaller, subtler one (the wobble in b_2).

Worked example: three ways the basis could land

A regional heating-oil distributor will need to buy 1,000,000 gallons of heating oil in 40 days. There's no exact futures match for local delivery, so the firm goes long 1,000,000 gallons of the standard NYMEX heating-oil future, currently trading at F_1 = \$2.00/gal, while the local spot price is S_1 = \$2.04/gal (basis b_1 = 0.04). Forty days later the firm buys the physical oil and closes the futures position. Three equally plausible outcomes for the market:

Scenario $S_2$ (local spot) $F_2$ (futures) $b_2 = S_2 - F_2$ Effective price $F_1 + b_2$
Basis unchanged $2.30 $2.26 $0.04 $2.04
Basis widens $2.30 $2.20 $0.10 $2.10
Basis narrows (turns negative) $2.30 $2.33 −$0.03 $1.97

The spot price landed on $2.30 in every scenario — yet the effective price the firm actually pays ranges from $1.97 to $2.10, a 13-cent spread on a $1,000,000-gallon position, or about \$130{,}000. Compare that to leaving the whole thing unhedged, where the price could have been anything the market did over 40 days — the hedge has collapsed a wide, unbounded risk into a narrow, bounded one. That narrow band is basis risk: real, but far smaller than the risk it replaced.

Seeing it: the basis narrows toward expiry — but wobbles on the way

Cost-of-carry arbitrage forces spot and futures prices to meet exactly at delivery, so on average the basis shrinks toward zero as expiry approaches. But "on average" hides real day-to-day noise — supply shocks, local shortages, storage costs, interest-rate moves — so the path is not a straight line. A hedger who closes out early, at some point still short of expiry, is exposed to wherever that noisy path happens to be on that particular day. Drag the sliders to see how a bigger starting basis or noisier convergence widens the range of possible close-out points.

Sometimes you can't — there is no traded futures contract on "jet fuel delivered to Newark Airport on the 14th," and there never will be, because a contract needs enough standardized volume to attract enough buyers and sellers to be liquid. Exchanges standardize contracts (a handful of delivery months, a handful of grades, a handful of delivery points) precisely so that trading concentrates into a few instruments deep enough to hedge and unwind large positions cheaply. A perfectly matched but illiquid contract would trade at a wide bid-ask spread — the transaction-cost equivalent of basis risk, and often worse. Real hedging is a trade-off: accept a little basis risk from an imperfect match, in exchange for a liquid market that lets you actually get the trade done at a fair price. The choice of which available contract minimizes that basis risk is itself a live decision — one this course quantifies precisely in the next lesson.

A common overreaction to basis risk is to conclude "well, if the hedge isn't perfect, why bother?" — and skip hedging altogether. That throws away the vast majority of the risk reduction to avoid a much smaller residual. In the heating-oil example, the unhedged firm's cost could have landed anywhere the 40-day spot price wandered — potentially a swing of tens of cents driven by a cold snap or a refinery outage. The hedged firm's cost varied by 13 cents across three basis scenarios that were deliberately chosen to look bad. Basis risk is real and worth managing, but it is a residual measured against the alternative of no hedge at all — not against some unattainable standard of perfection. A second, related mistake: basis risk does not vanish just because you rolled the hedge to a longer-dated contract or added more contracts — it comes from the mismatch in what and when, not from the size of the position.