What this calculator does
A futures price is not a forecast. It is the spot price adjusted for the cost of holding the asset until expiry: financing costs push it up, and any yield the asset pays pushes it back down.
That relationship is enforced by arbitrage rather than by opinion. At a 5 per cent financing rate against a 1.5 per cent dividend yield, a 5,000 index should trade at 5,043.94 three months out, and a market price meaningfully away from that invites a riskless trade.
The formula
The spot price is compounded continuously at the net cost of carry, being the financing rate less the yield, over the time to expiry. The difference from spot is the basis.
| Term | Meaning |
|---|---|
| Cost of carry | The financing rate less any yield, being the net cost of holding the asset. |
| Basis | The difference between the futures price and the spot price. |
| Contango and backwardation | Futures above spot is contango; below spot, which happens when the yield exceeds financing, is backwardation. |
The inputs explained
| Field | What to enter |
|---|---|
| Spot price ($) | The current spot price of the underlying. |
| Risk-free / financing rate (%) | The risk-free or financing rate, annualised. |
| Dividend yield (or storage cost, entered negative) (%) | The dividend or convenience yield. Enter a negative value for storage costs. |
| Time to expiry (years) | Time to expiry in years. Three months is 0.25. |
| Actual market futures price (optional) ($) | The actual market futures price, for comparison against fair value. |
When to use it
Checking whether a futures price is fair
A large gap from fair value is either an arbitrage opportunity or a sign something has been missed.
Understanding the basis
The gap between futures and spot is the carry cost, not a market forecast.
Rolling a position
The cost of rolling from one contract to the next follows directly from the carry.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does time to expiry change the fair value?
The same underlying at three expiries.
| Time to expiry | Fair value of the futures contract | Basis (fair value − spot) |
|---|---|---|
| 3 months | $5,043.94 | $43.94 |
| 6 months | $5,088.27 | $88.27 |
| 1 year | $5,178.10 | $178.10 |
Questions
Is a futures price a prediction of the spot price?
No, and this is the most persistent misunderstanding. It is the spot price plus the cost of carrying the asset to expiry. A futures price above spot says financing is expensive, not that the market expects a rise.
What is contango and backwardation?
Contango is futures above spot, which is normal when financing costs exceed any yield. Backwardation is futures below spot, which happens when the yield or convenience of holding the physical asset exceeds financing costs.
Why enter storage costs as a negative yield?
Because storage is a cost of holding rather than a benefit, so it works in the opposite direction to a dividend. Entering it negative raises the fair value, which is exactly the right effect for commodities.
Why do market prices deviate from fair value?
Transaction costs, borrowing constraints, dividend uncertainty and short-selling restrictions all create a band within which arbitrage is not worth executing. Deviations inside that band persist; deviations outside it usually do not.
For option pricing on the same underlying, see the Black-Scholes calculator. For the arbitrage relationship between options, see the put-call parity calculator.