What is basis, and why must it collapse to zero?
Basis = spot price − futures price.
Conventions vary — commodity hedgers usually mean local cash price minus the futures price, and financial desks often quote it the other way round. Pick one, state it, and keep it. This course uses spot minus futures throughout.
Using the gold numbers from the last lesson: spot $2,000, six-month future $2,054 → basis = −$54.
Basis is not noise around a price. It is the carry, expressed as a single number — and it decays on a schedule.
Convergence is compulsory
On the last trading day, a futures contract is a claim on the underlying essentially immediately. A contract deliverable today and the physical good today are the same thing, so their prices must be the same thing. Basis goes to zero at expiry. Not approximately, not usually — by construction, enforced by anyone able to deliver into the contract or take delivery from it.
That gives basis a shape. It starts at whatever carry is worth across the contract's remaining life and grinds toward zero as that life shortens. Time is the one ingredient that reliably disappears.
Worked: basis decay on gold
Assume spot stays flat at $2,000 for six months. Heroic, and useful.
- 6 months out: F = $2,054 → basis −$54
- 3 months out: carry halves → F ≈ $2,027 → basis −$27
- 1 month out: carry is a sixth → F ≈ $2,009 → basis −$9
- Expiry: F = $2,000 → basis $0
Read what happened to the long futures holder. They lost $54 an ounce over six months — $5,400 per 100-ounce contract — with the spot price completely unchanged. Nothing went wrong. Carry was paid, on schedule, exactly as the contract required. Flip the position and the short collected precisely that.
You can lose money in futures with the spot price unchanged. That sentence is the most important line in this unit, and the next two lessons are entirely its consequences.
Why convergence matters more than it sounds
Convergence is what makes futures usable as a hedge at all. If the futures price could finish anywhere at all relative to cash, then locking in a price with futures would be theatre. Convergence is the guarantee that the two prices meet at the finish line — and therefore that a hedge placed in June still means something in November. Unit 4 depends on it completely.
Basis in the physical world
For a farmer, basis carries a second meaning: location and quality. Corn sitting in one Iowa elevator is not the standardised deliverable grade at an approved delivery point, and the difference moves with local harvest conditions, freight costs and storage availability. That local basis does not converge to zero — it converges to whatever the local cash-versus-futures relationship happens to be that November.
That surviving residual is precisely what Unit 4 calls basis risk, and it is the reason no hedge is ever perfect.
In the data
Basis is the difference between two prices observed at the same moment. The pair below is as clean as public data gets: the S&P 500 index and its front futures contract, side by side.
Index level minus futures price is the basis in index points, by this course's convention, and it is negative whenever financing costs more than the index pays in dividends. Even this pair needs care. The index stops at the New York close while the future trades almost around the clock, so a quote taken overnight folds the night's move into the gap. The same trap is larger elsewhere: a monthly average cash price set against a daily futures close, or two series on different holiday calendars, gives a number that moves for reasons that have nothing to do with carry.
Try it now
- Two lines on the same commodity are below: the front-month price itself, and a fund that holds the contracts and rolls them. Measure both across the same five years and write the two totals down.
- Now measure the gap at several shorter intervals — a quarter here, a quarter there. It is not constant, and it does not close: what you are watching is carry being paid in public, on a schedule anyone can read in advance.
- Basis on a single contract does collapse to zero, by definition, on its last day. Say in one sentence why the gap between these two lines does not, even though every individual contract inside the fund converged perfectly.