Why is the futures price usually above spot?

When the risk-free rate exceeds the underlying's income yield (dividends, or convenience yield for a commodity), carrying the asset costs more than holding the future, so the future trades at a premium — contango.

What does a negative basis mean?

It means the futures price sits below fair-value-implied spot, i.e. income yield exceeds the risk-free rate — common for high-dividend indices or commodities in backwardation.

Is this the same as the roll yield calculator?

No — this prices one contract from spot and a rate, useful before a contract exists or to sanity-check a quote. The roll yield calculator instead compares two already-quoted contract prices to measure the cost of rolling between them.

Does this work for commodities, not just index futures?

Yes — for commodities, use storage cost minus convenience yield in place of a dividend yield; a net negative 'incomeYield' (i.e. storage costing more than convenience yield) pushes fair value further above spot.

Why is the annualised carry exactly r − q?

Because ln(fair value ÷ spot) ÷ time always equals r − q algebraically — it is the definition the formula is built from, not an approximation, so it holds exactly regardless of the time period entered.

Futures

Futures Fair Value Calculator

Calculate the cost-of-carry fair value of a futures or forward contract from spot price, risk-free rate, dividend or convenience yield and time to expiry.

Futures fair value is the theoretical price of a futures contract implied by carrying the underlying to expiry: spot × e^((risk-free rate − income yield) × time).

Fair value

$5,043.34

Basis: +$43.34
Basis %: +0.87%
Curve state: Contango

Fair value = spot × e^((risk-free rate − yield) × time). A theoretical benchmark, not a trading signal.

Worked example

An index trades at 5,000 (spot), the risk-free rate is 5%, the index's dividend yield is 1.5%, and the futures contract expires in 90 days.

Time to expiry: 90 ÷ 365 = 0.2466 years
Annualised carry (r − q): 5% − 1.5% = 3.5%
Fair value: 5,000 × e^(3.5% × 0.2466) = 5,043.34
Basis: 5,043.34 − 5,000 = +43.34 (+0.87%)

The contract's theoretical fair value is 5,043.34 — a 43.34-point premium to spot (contango) that reflects carrying the index at a 3.5% net rate for 90 days.

How this is calculated

A futures (or forward) price is tied to spot by the cost of carry — the net cost of holding the underlying to expiry:

fair value = spot × e^((risk-free rate − income yield) × time)

The risk-free rate is the cost of financing the position; the income yield (dividends for a stock index, convenience yield for a commodity) is the benefit of holding it. When the rate exceeds the yield, the future trades above spot — contango. When the yield exceeds the rate, it trades below — backwardation.

Time is expressed in years, so days to expiry is divided by 365 before it enters the formula. The gap between the fair value and spot is the basis, and dividing that annualised gap back out always returns exactly the risk-free rate minus the yield — it is the algebraic inverse of the same relationship.

When to use this calculator

Use this to sanity-check a quoted futures price against its theoretical value from spot, the risk-free rate and the underlying's income yield. It is the same 'fair value' figure financial media publish pre-market for S&P 500 futures.

It is a useful learning tool for the mechanics of cost of carry: raise the rate, lower the yield, or lengthen time to expiry one at a time and watch the fair-value premium (or discount) respond.

Traders comparing dated futures against spot use it to judge whether the market's actual basis is rich or cheap relative to the pure carry cost — a persistent gap between quoted and fair value often signals supply/demand pressure specific to that contract.

Common mistakes

Using the dividend rate for the whole year when the contract only runs partway through it — always convert days to years first (days ÷ 365).
Forgetting the yield leg entirely: without subtracting the dividend/convenience yield, the fair value overstates the true cost of carry for anything that pays income.
Comparing fair value to a stale spot print — the fair-value gap only holds relative to the current spot price, not yesterday's close.

Frequently asked questions

What is futures fair value?: It is the theoretical futures price implied by the cost of carrying the underlying to expiry: spot × e^((risk-free rate − income yield) × time). It is the same figure financial media quote as 'fair value' for pre-market S&P futures.
Why is the futures price usually above spot?: When the risk-free rate exceeds the underlying's income yield (dividends, or convenience yield for a commodity), carrying the asset costs more than holding the future, so the future trades at a premium — contango.
What does a negative basis mean?: It means the futures price sits below fair-value-implied spot, i.e. income yield exceeds the risk-free rate — common for high-dividend indices or commodities in backwardation.
Is this the same as the roll yield calculator?: No — this prices one contract from spot and a rate, useful before a contract exists or to sanity-check a quote. The roll yield calculator instead compares two already-quoted contract prices to measure the cost of rolling between them.
Does this work for commodities, not just index futures?: Yes — for commodities, use storage cost minus convenience yield in place of a dividend yield; a net negative 'incomeYield' (i.e. storage costing more than convenience yield) pushes fair value further above spot.
Why is the annualised carry exactly r − q?: Because ln(fair value ÷ spot) ÷ time always equals r − q algebraically — it is the definition the formula is built from, not an approximation, so it holds exactly regardless of the time period entered.