Futures Fair Value & Rollover Cost Calculator
Compare a futures price with its cost-of-carry fair value, see the annualised basis, and work out what it costs to roll a position to the next expiry. Runs in your browser; nothing is uploaded.
A worked example
Say the spot price is ₹24,000 with 30 days to expiry, an interest rate of 7% and a dividend yield of 1.2%. The net cost of carry is 5.8% a year, so the fair value of the futures is 24,000 × e^(0.058 × 30 ÷ 365) = ₹24,114.68. If the futures trade at ₹24,150, they are ₹35.32, or 0.15%, above fair value. The basis is ₹150, which works out to 7.60% a year, and the financing rate implied by the market price is 8.78%.
Understanding the calculation
- Fair value
- Spot times e raised to (interest rate minus dividend yield) times days to expiry divided by 365. Interest and dividends are treated as continuous, annual percentages.
- Annualised basis
- (Futures price divided by spot, minus 1) times 365 divided by days to expiry. This is a simple annualisation, comparable with an interest rate.
- Implied cost of carry
- The natural log of futures over spot, divided by time in years, plus your dividend yield. It is the financing rate the market is pricing in.
- Assumptions
- A single dividend yield for the whole period, no transaction costs or borrowing constraints, and the same rate for lending and borrowing. For a single stock with a known dividend date, the real fair value will differ a little.
Common questions
What is the fair value of a futures contract?
It is the price at which buying the underlying today and holding it to expiry would cost the same as the futures. It equals the spot price grown at the financing rate, less the dividends you would collect while holding the underlying: spot times e to the power of (interest rate minus dividend yield) times time. If futures trade far from that, arbitrageurs step in.
Why do futures usually trade above spot?
Because carrying the underlying costs money. Buying futures instead of the underlying saves you the financing cost, so futures carry a premium equal to that cost, minus the dividends you would miss. That premium shrinks to zero as expiry approaches.
What is basis, and what is annualised basis?
Basis is the futures price minus the spot price. Annualised basis scales that premium to a year, so you can compare it with interest rates. When annualised basis is above the risk-free rate, futures look expensive relative to spot, and below it they look cheap.
What is the implied cost of carry?
It is the financing rate that would make the observed futures price equal to fair value, given your dividend yield. Comparing it with the rate you entered shows whether the market is pricing more or less carry than expected.
How is the rollover cost worked out?
Rolling means closing the near-month contract and opening the next month. The cost is the next-month price minus the near-month price, shown in points, as a percentage, and annualised over the days between the two expiries. It is a real cost when you are long, and a gain when you are short.
Is a difference from fair value a trading signal?
Not by itself. Small gaps are normal, and transaction costs, borrowing constraints and unknown dividends all move the real fair value. Treat the result as a reference point rather than a trade.