Basis Convergence
The tendency of a futures price and its underlying spot price to meet as expiration nears, forcing the basis to zero at settlement.
Formula
Basis = Spot Price − Futures Price → 0 as time-to-expiry → 0
Basis convergence is the process by which the gap between a futures price and the underlying spot (cash) price shrinks toward zero as the contract approaches expiration. Basis is Spot − Futures; at the moment of settlement, a futures contract is a claim on the deliverable at the current spot, so the two prices must align or arbitrageurs would lock in a riskless profit.
Away from expiry, the basis reflects the net cost of carry — financing and storage minus any income, dividends, or convenience yield. As time to maturity falls, there is less carry left to embed, so the basis decays mechanically toward zero. This is what makes the relationship between cash and futures predictable rather than arbitrary.
For hedgers, convergence is the whole point: a short futures hedge against a physical long is only clean if the basis converges as expected. Basis risk — the chance that convergence is incomplete or erratic (a different deliverable grade, a delivery-location mismatch, or a squeeze) — is the residual exposure a hedge cannot remove.
Example
WTI crude spot is $80.00 and the expiring front-month future trades at $80.60 (basis = −$0.60) one month out. As delivery nears, carry burns off and the future drifts to $80.05 while spot sits at $80.00 — basis = −$0.05, then ~$0.00 at delivery. A hedger short the future against physical barrels captures the $0.55 convergence as the position rolls into settlement.