What Is the Basis in Futures?

Spot minus futures, and why it converges.

The futures basis is the difference between the spot price of an asset and the price of a futures contract on that same asset. Using the convention here — basis = spot price − futures price — a positive basis means the futures is trading below spot, and a negative basis means futures trade above spot. (Some markets invert this and define basis as futures minus spot; the math is symmetric, but knowing which convention a counterparty is using matters.) A single number, but it encodes the entire cost of carry embedded in a contract, and understanding it is prerequisite to any serious hedging program. Use the futures pricing calculator to plug in live carry assumptions before the next section.

How the futures basis reflects net carry

A futures price is not a forecast of where spot will trade at expiration — it is today's spot price adjusted for the net cost of carrying the asset from now until delivery. Under the classic cost-of-carry model:

F = S · e^{(r + u − y)·T}

where S is spot, r the risk-free rate, u the proportional storage or financing cost, y the convenience yield or dividend yield, and T the time to delivery in years. Rearranging:

Basis = S − F = S · (1 − e^{(r + u − y)·T})

For typical financial assets where storage cost is zero, the basis simplifies to S minus the futures price, which is pulled below spot by the interest rate (you can invest the cash you would otherwise tie up in the physical asset). When dividends or convenience yields exceed the risk-free rate, futures trade below spot and the basis turns positive — a condition called contango and backwardation depending on the shape of the forward curve. The basis is therefore just the carry expressed as a price level rather than a percentage.

Convergence and the arbitrage that enforces it

At delivery, basis must equal zero. The futures contract obligates the short to deliver the actual commodity or financial instrument, and the long to pay the futures price. If the futures price differed from spot at expiration, cash-and-carry arbitrage would eliminate the gap instantly. If futures were above spot, buy the asset, short the futures, and pocket the difference at delivery. If futures were below spot, sell the asset short, buy the futures, and receive the asset at below-market cost. Both trades are risk-free at expiration, so any deviation collapses immediately. This is what the concept of fair value formalises: the futures price that leaves no cash-and-carry profit on the table.

Before expiration, the basis decays along a roughly predictable path. A six-month futures contract on an equity index carrying 5 percent financing will have a basis that tightens day by day as T shrinks toward zero. Traders call this basis roll — the profit or loss on a position that comes purely from time passing, independent of any move in spot.

Basis risk in hedging

If the asset you are hedging and the asset deliverable under the futures contract are identical, a perfectly sized short futures position eliminates price risk completely. In practice they rarely are. A wheat processor might hedge with CBOT wheat futures while holding a different grade at a different location. A portfolio manager might short S&P 500 futures against a portfolio that does not perfectly replicate the index. In both cases the hedge leaves residual exposure — basis risk — because the spot price of the hedged asset and the futures price can move independently.

Basis risk does not mean hedging is pointless. It means the hedge replaces large directional price risk with a smaller, slower-moving spread risk. The key relationship is:

Effective purchase price = futures price + basis at lift

If you lock in a short hedge today at a known basis and the basis does not change by the time you lift the hedge, your effective sale price equals exactly what you targeted. The risk is that the basis strengthens (spot rises relative to futures, helping a short hedger) or weakens (spot falls relative to futures, hurting a short hedger) before you close.

Strengthening vs weakening basis

Basis strengthening means the basis becomes less negative or more positive — spot gains on futures. Basis weakening means the opposite. Whether strengthening helps or hurts depends on your position:

• Short hedger (selling the physical, long the basis): benefits from a strengthening basis. Spot outperforms futures, so the effective sale price improves.
• Long hedger (buying the physical, short the basis): benefits from a weakening basis. Futures decline faster than spot, reducing the effective purchase cost.

A simple rule: whoever has made the physical transaction that mirrors the futures position gains when the basis moves in their favour, and loses when it moves against them. Quantifying that exposure requires estimating the likely basis at hedge lift — historical basis data for the specific location, grade, or asset class is the standard input.

Worked example: basis risk in an equity hedge

A portfolio manager holds a $50 million equity portfolio with a beta of 1.15 against the S&P 500. She wants to hedge downside risk over three months. The S&P 500 index is at 5,000; the three-month futures contract trades at 5,060 (financing exceeds dividend yield slightly). Basis = 5,000 − 5,060 = −60.

The number of contracts to short, adjusting for beta:

N = (Portfolio value × Beta) / (Futures price × Multiplier) = ($50,000,000 × 1.15) / (5,060 × $250) = 45.5 → 46 contracts

Three months later the index has fallen to 4,700. The futures contract, now at expiration, trades at 4,700 (basis = 0 by convergence). The hedge gain on 46 short contracts is (5,060 − 4,700) × 250 × 46 = $4,140,000. The portfolio, with beta 1.15, fell roughly 6.9 percent, a loss of approximately $3,450,000. Net result: the hedge more than offsets the loss, with the overage attributable to the beta mismatch and rounding on contract count.

If the portfolio's correlation to the index had drifted — say the manager was overweight technology stocks that fell 10 percent while the index fell 6 percent — the futures gain would have covered only part of the loss. That gap is basis risk in the hedging sense: the spread between what was hedged and what was owned.

Basis vs calendar spread

The basis measures the gap between spot and a single futures contract. A calendar spread measures the gap between two futures contracts with different delivery dates — for example, the December contract minus the March contract. The two are related but distinct. The calendar spread reflects the carry between the two delivery periods; the basis reflects total carry from now to the front delivery. When the front contract expires and rolls, the old calendar spread becomes the new basis. Traders who target roll yield — the return from holding a futures position through successive contract expirations — are essentially trading the calendar spread, not the spot-futures basis. Conflating them leads to errors in both strategy design and P&L attribution.