Index Futures Fair Value: A Cost-of-Carry Example
Equity index futures fair value relates a futures price to the current index level, financing costs and expected dividends over the contract period. The simplest cost-of-carry model provides a theoretical benchmark, not a guaranteed tradable price or a forecast of where the index will settle. Dividend timing, funding access and contract specifications can create differences.
Why futures and spot index values differ
A stock index is a calculation based on constituent share prices; futures are exchange-traded agreements with their own expiries, margins and settlement rules. Holding a basket of shares requires financing and may provide dividend cash flows. Futures pricing incorporates the economics of obtaining equivalent exposure until delivery or cash settlement. An index future above today’s index level does not necessarily express bullish sentiment.
Simplified cost-of-carry formula
With continuously compounded rates and dividend yield, an educational fair-value approximation is F = S × exp[(r − q)T], where S is the spot index level, r is financing and q is expected continuous dividend yield. The model assumes dividend yield is a continuous rate, though actual dividends arrive at discrete dates. Exact contract prices also depend on index composition, funding, margining and market-specific settlement mechanisms.
Worked example: three months to expiry
Suppose a fictional index is at 5,000, annual financing is 4%, annual dividend yield 2% and T is 0.25 years. Fair value is approximately 5,000 × exp[(0.04−0.02)×0.25] = 5,025.06. The theoretical futures basis is about 25.06 index points above spot. This does not mean the market expects the cash index to rise by 25 points in three months. If expected dividends increase, the theoretical future becomes lower under otherwise identical assumptions.
What is basis?
Basis is a difference between a futures contract and a relevant cash index or instrument, using an explicitly stated subtraction convention. Some sources calculate futures minus spot; others use spot minus futures. Financing and dividends explain part of normal basis for equities, but short-term technical and liquidity effects can also matter. When comparing basis across dates, use the same contract maturity and timestamps.
Dividends and discrete cash flows
Real-world index constituents pay dividends on varying ex-dividend dates. A more precise model discounts the anticipated dividends during the remaining futures term rather than assuming a constant yield. Changes in dividend forecasts can therefore move the fair-value estimate even if interest rates are unchanged. Special dividends and corporate actions require treatment consistent with the index provider’s rules.
Why arbitrage is not free
In theory, a large futures premium relative to carry can encourage purchases of a share basket and sales of the futures, while a discount can encourage reverse trades. Execution costs, balance-sheet usage, shorting restrictions, funding spreads, taxes, settlement and tracking differences can prevent perfect convergence at all times. The quoted spot index cannot necessarily be bought instantly at the displayed level.
Expiry and continuous futures charts
A futures series rolls from one contract to the next when the current contract approaches expiry. The jump between contracts reflects a new maturity and its cost-of-carry relationship; it should not be confused with a sudden underlying index return. Historical charts that adjust continuous contracts can follow different methods. For an actual fair-value calculation, use the exact futures expiry and price rather than a synthetic continuous chart value.
How to calculate a sound fair-value benchmark
Record the specific index, index level, futures contract code, expiry, rate curve and expected dividends. Convert all quantities into consistent currency and time units. Compute the theoretical futures price, compare with tradable bid and ask quotes and account for funding and transaction costs. Treat large apparent discrepancies as research questions rather than guaranteed arbitrage.
Index futures fair-value sensitivity
Hypothetical index at 5,000, 0.25 years to expiry; prices use F = S × exp[(r − q)T].
| Assumption | Financing rate | Dividend yield | Theoretical futures |
|---|---|---|---|
| Base case | 4.0% | 2.0% | 5,025.06 |
| Higher financing | 5.0% | 2.0% | 5,037.64 |
| Higher dividends | 4.0% | 3.0% | 5,012.52 |
| Equal finance and dividend | 4.0% | 4.0% | 5,000.00 |
The sensitivity illustrates how carry inputs affect a theoretical quote: increasing financing costs raises the model price, while increasing dividend yield lowers it, all else equal. Actual equity index futures involve discrete constituent dividends, market-specific financing, settlement and trading costs. A futures premium over the cash index is not by itself a bullish forecast. Confirm the exact contract maturity and use contemporaneous cash and futures prices before discussing a market basis.
For useful background on the related economic concepts, explore index futures pricing and expiry.
Frequently asked questions
Does a futures premium mean the index will rise?
No. Interest-rate and dividend carry often explain a premium.
What lowers equity index futures fair value?
Higher expected dividends reduce fair value, holding other variables fixed.
Why can futures basis move near expiry?
Carry decreases as time passes, while liquidity and delivery or settlement effects can also influence prices.
Sources and further reading
For a broader foundation, see Stock Index Weighting Explained.