Basis and Convergence at Expiry
The futures price isn't the same as the spot price, and the gap between them is the basis. As expiry approaches, the futures price moves toward spot.
Risk warning: forex, CFDs, options, futures and crypto assets usually involve leverage or high volatility, and you can lose more than you put in. This lesson only teaches the concepts; all numbers are for illustration and are not investment advice.
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Text version · Futures Basics, lesson 5: “Basis and Convergence at Expiry”
The futures price isn't the same as the spot price, and the gap between them is the basis. As expiry approaches, the futures price moves toward spot.
Basis = spot − futures
basis measures how far futures are from spot. When futures cost more, it's contango (negative basis); when they cost less, it's backwardation (positive basis).
They always meet at expiration
On expiration day, futures are just “spot for immediate delivery”, so the two prices have to be the same; otherwise there'd be a risk-free arbitrage. That's why the basis converges to 0 over time.
Where contango comes from: cost of carry
Futures ≈ spot + the cost of carry until expiration (storage, insurance, interest on the money). The closer to expiration, the less cost is left to pay, so the contango naturally shrinks.
Key takeaways
- Basis = spot price − futures price.
- Futures above spot is contango (negative basis); futures below spot is backwardation (positive basis).
- Contango comes mainly from the cost of carry, like storage and financing. The less time left, the smaller the carry cost.
- At expiry the futures price converges to spot and the basis goes to 0; otherwise there'd be a risk-free arbitrage.
Try it yourself
You can do these exercises in this lesson's interactive simulation:
- Click “Example: spot $100 / futures $104”: what's the basis? Is it contango or backwardation?
- Press ▶ and pause with 30 days left: how far has the basis shrunk from −$4? What fraction of the original is it?
- Switch to “Backwardation”: is the basis positive or negative now? And at expiration?
- Drag the initial gap to $8 and play again: no matter how big the gap, does it still converge at expiration?
Quiz and explanations
- 1. Spot is $100 and futures are $104. What's the basis?
- Answer: −$4.$100 − $104 = −$4: the futures are in contango.
- 2. As expiry approaches, the futures price will…
- Answer: Converge toward the spot price.At expiry the two must match, or there'd be a risk-free arbitrage.
- 3. Spot is $100, futures are $104 and expiry is 60 days away. If the basis converges evenly over time, roughly what's the basis with 15 days left?
- Answer: −$1.Only 15/60 = 1/4 of the time is left, so the basis shrinks to −$4 × 1/4 = −$1.
Terms in this lesson
- backwardation (Backwardation): A market where futures (or later months) trade below spot (or nearer months).
- basis (Basis): Spot price − futures price; it converges toward zero by expiration.
- cost of carry (Cost of Carry): The storage, insurance and financing costs of holding a physical commodity.
- contango (Contango): A market where futures (or later months) trade above spot (or nearer months).
- futures (Futures): Standardized exchange-traded contracts to buy or sell an asset on a future date at a price fixed today.
- spot (Spot): A trade delivered and paid for right away (or very soon); its price is the spot price.