Index futures are calculated from the current cash index, financing costs, expected dividends, and the time remaining until expiration.

The standard fair value formula is:

[ \text{Fair Value} = \text{Cash Index} \times \left[1+r\left(\frac{d}{360}\right)\right] - \text{Expected Dividends} ]

Where:

  • Cash Index is the current spot value of the index, such as the S&P 500.
  • r is the relevant short-term interest rate.
  • d is the number of days until the futures contract expires.
  • Expected Dividends are the dividends expected from the index constituents before expiration, expressed in index points.

CME Group uses this type of cost-of-carry calculation for stock index futures. The quoted futures price can trade above or below the estimated fair value because of supply, demand, liquidity and arbitrage costs.

Index Futures Calculation at a Glance

Calculation Formula What it shows
Fair futures value Cash index + financing cost - dividends The estimated futures price
Basis Futures price - cash index Whether futures trade at a premium or discount
Contract notional value Futures price × contract multiplier The exposure of one contract
Futures profit or loss Price change × contract multiplier The dollar gain or loss

Why Are Index Futures Different From the Cash Index?

Index futures are contracts that provide exposure to an index on a future date, while the cash index reflects the current value of its constituent stocks.

A futures buyer does not receive the dividends paid by the index constituents. The buyer also does not need to purchase the full stock portfolio immediately. The futures price therefore reflects:

  1. The current cash index level.
  2. The financing cost of holding an equivalent stock portfolio.
  3. The dividends that portfolio is expected to pay before expiration.

This relationship is called the cost of carry. When financing costs exceed expected dividends, index futures generally trade above the cash index. When expected dividends exceed financing costs, futures can trade below the cash index.

How Do You Calculate the Fair Value of an Index Future?

Assume:

  • Current S&P 500 cash index: 5,000 points
  • Annual interest rate: 5%
  • Time to expiration: 90 days
  • Expected dividends before expiration: 20 index points

Using the simple fair-value formula:

[ \text{Fair Value} = 5{,}000 \times \left[1+0.05\left(\frac{90}{360}\right)\right] - 20 ]

[ \text{Fair Value} = 5{,}000 \times 1.0125 - 20 ]

[ \text{Fair Value} = 5{,}042.50 ]

The estimated fair futures value is 5,042.50 points.

The calculation is:

  • Financing cost: 62.50 index points
  • Expected dividends: 20 index points
  • Net carry: 42.50 index points
  • Cash index: 5,000 points
  • Fair futures value: 5,042.50 points

If the contract trades at 5,050, it is 7.50 points above this estimate. If it trades at 5,035, it is 7.50 points below it.

What Is the Basis of an Index Future?

The basis is the difference between the futures price and the cash index:

[ \text{Basis} = \text{Futures Price} - \text{Cash Index} ]

Using the example above:

[ \text{Basis} = 5{,}042.50 - 5{,}000 = 42.50 \text{ points} ]

A positive basis means the futures price is above the cash index. A negative basis means the futures price is below the cash index.

The basis usually becomes smaller as expiration approaches because less time remains for financing costs and dividends to affect the price. At expiration, the futures contract settles against the relevant index value, so the futures price and the cash index converge.

How Is the Underlying Stock Index Calculated?

The index provider calculates the cash index before the futures price is estimated.

For a capitalization-weighted index such as the S&P 500, the basic formula is:

[ \text{Index Level} = \frac{\text{Float-Adjusted Market Capitalization}}{\text{Index Divisor}} ]

The market capitalization calculation uses the prices and eligible shares of the index constituents. The divisor scales the result into an index level and is adjusted after corporate actions, additions, deletions and other non-market events. These adjustments help prevent the index from changing because of an event that is not a market price movement.

Different indices use different methods:

  • S&P 500: float-adjusted market-cap weighted.
  • Nasdaq-100: modified market-cap weighted.
  • Dow Jones Industrial Average: price weighted.
  • Russell 2000: float-adjusted market-cap weighted.

The futures calculation uses the published cash value of the relevant index, regardless of how the index constituents are weighted.

How Is the Dollar Value of an Index Futures Contract Calculated?

The index level is quoted in points, but each futures contract has a fixed dollar multiplier:

[ \text{Contract Notional Value} = \text{Futures Price} \times \text{Contract Multiplier} ]

For example, the CME E-mini S&P 500 futures contract has a multiplier of $50 per index point. At a futures price of 5,000:

[ 5{,}000 \times $50 = $250{,}000 ]

One E-mini S&P 500 contract therefore represents approximately $250,000 of notional exposure at an index level of 5,000.

Common CME equity index futures multipliers include:

Contract Multiplier Dollar value of a 1-point move
E-mini S&P 500 $50 $50
Micro E-mini S&P 500 $5 $5
E-mini Nasdaq-100 $20 $20
Micro E-mini Nasdaq-100 $2 $2
E-mini Dow $5 $5
Micro E-mini Dow $0.50 $0.50

Micro E-mini contracts generally use one-tenth of the multiplier of the corresponding E-mini contracts.

How Are Profits and Losses Calculated?

A futures position's profit or loss equals the change in the futures price multiplied by the contract multiplier:

[ \text{Profit or Loss} = (\text{Exit Price} - \text{Entry Price}) \times \text{Multiplier} ]

For a long E-mini S&P 500 futures position:

  • Entry price: 5,000
  • Exit price: 5,020
  • Price increase: 20 points
  • Multiplier: $50

[ 20 \times $50 = $1{,}000 ]

The profit is $1,000 before commissions, exchange fees and other trading costs.

For a short position, the calculation is reversed. A 20-point decline would produce a $1,000 profit before costs.

Why Can the Quoted Futures Price Differ From Fair Value?

Fair value is an estimate, not a guaranteed trading price. The quoted futures price can differ because of:

  • Temporary imbalances between buyers and sellers.
  • Different interest-rate assumptions.
  • Changes in expected constituent dividends.
  • Market volatility.
  • Liquidity conditions.
  • The cost and risk of executing an arbitrage trade.
  • Differences between the theoretical index basket and the portfolio used for hedging.

Arbitrage activity generally pushes the futures price back toward the relationship implied by the cash index, financing costs and dividends.

Do Interest Rates or Dividends Affect Index Futures More?

Interest rates and dividends both affect index futures. Their effect depends on the time remaining until expiration.

  • Higher interest rates generally increase the futures price relative to the cash index.
  • Higher expected dividends generally reduce the futures price relative to the cash index.
  • More days to expiration increase the effect of both factors.
  • As expiration approaches, both effects move toward zero.

A useful approximation using an annual dividend yield is:

[ F \approx S \times [1+(r-q)T] ]

Where:

  • F = estimated futures price
  • S = current cash index
  • r = annual financing rate
  • q = expected dividend yield
  • T = time to expiration in years

For more precise pricing, traders generally use the estimated cash amount and timing of dividends instead of relying only on an annual dividend yield. CME's example calculates expected dividends in index points and subtracts them from the financed cash index value.

The formula estimates the relationship between the cash index and the futures price. The contract multiplier converts a price move in index points into a dollar gain or loss. The exchange determines the quoted price through market trading.