Futures Fair Price

Derivatives
Updated Apr 2026 • Has calculator

The theoretical no-arbitrage price of a futures contract based on the cost of carry.

What is Futures Price?

The futures fair price (or theoretical futures price) is derived from the cost-of-carry model, which states that the futures price equals the spot price compounded at the net carry rate over the contract's life. If the actual futures price deviates from this theoretical value, cash-and-carry arbitrage traders will push it back into line. The formula accounts for the risk-free rate and any continuous dividend yield paid by the underlying.

Formula

F = S · e^((r − q) · T)

Worked Example

Worked example — S&P 500 E-mini Futures (ES) — representative Q1 2024

Representative Q1 2024 market conditions

Step 1  S&P 500 spot level (S): 5,000
Step 2  Risk-free rate (r): 5.25% (3-month T-Bill)
Step 3  S&P 500 dividend yield (q): 1.50%
Step 4  Time to expiry (T): 90 days = 0.247 years
Step 5  Net carry: r − q = 5.25% − 1.50% = 3.75%
Step 6  F = 5,000 × e^(0.0375 × 0.247) = 5,000 × 1.00926 ≈ 5,046.3
Step 7  → If ES futures trade above this, sell futures / buy the index (cash-and-carry arb)

Source: Hull, J.C. — Options, Futures, and Other Derivatives, 11th ed., Ch. 5 (2024-01-15)

Calculate Futures Price

Current spot price of the underlying (e.g. index level or stock price)

Annual risk-free rate (e.g. 3-month T-Bill yield)

Continuous dividend yield of the underlying (use 0 for non-dividend assets)

Time to futures expiration in years (e.g. 0.25 = 3 months)

Futures Fair Price

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Not investment advice.

How to Interpret Futures Price

< -5
Deep backwardation — futures well below spot
-5 – -0.5
Backwardation — futures below spot (high dividends)
-0.5 – 0.5
Near fair value — minimal basis
> 0.5
Contango — futures above spot (positive carry)
Sources
  1. Hull, J.C. — Options, Futures, and Other Derivatives, 11th ed.
  2. CME Group — Futures Pricing
  3. Investopedia — Futures Pricing