Futures Price
The futures price is the current market price at which a futures contract—an agreement to buy or sell a specific asset at a specified future date—is trading on an exchange, reflecting the aggregate market expectation of the asset's value at the contract's delivery date adjusted for carrying costs. It is determined continuously by the interaction of buyers and sellers in the futures market and converges to the spot price at expiration.
Key takeaways
- The fair value futures price is theoretically determined by the cost-of-carry model: F = S × e^(r−q)T for financial futures, where S is the spot price, r is the risk-free rate, q is the continuous dividend yield (or foreign interest rate for currency futures), and T is time to expiration.
- For commodity futures, the cost-of-carry model incorporates storage costs and convenience yield: F = S × e^(r+u−y)T, where u is storage cost and y is convenience yield—explaining why different commodities can be in contango (u > y) or backwardation (y > u).
- Basis—the difference between the spot price and the futures price (or between prices for different delivery months)—is economically significant for hedgers: a farmer hedging wheat production is exposed to basis risk (changes in the spot-futures relationship) rather than the absolute price level once hedged.
- At expiration, the futures price must converge exactly to the spot price (for cash-settled contracts) or the deliverable asset's cash price (for physically settled contracts); failure to converge would create riskless arbitrage opportunities that market participants would immediately exploit.
- Index arbitrage—the simultaneous trading of stock index futures and the constituent stocks to exploit deviations between the futures price and the index level plus carrying costs—is a significant force keeping equity index futures prices aligned with their theoretical fair values.
Explanation
The futures price is the market's continuously quoted consensus estimate of an asset's value at a specific future date, adjusted for the costs and benefits of carrying the underlying asset from today to the delivery date. Unlike options prices, which have asymmetric payoffs and a premium structure, futures prices are symmetric—an increase in the futures price benefits long positions and harms short positions by equal amounts—and theoretically have a determinate fair value relationship to the spot price that can be derived from no-arbitrage conditions.
The cost-of-carry model is the theoretical foundation for futures pricing. For financial assets that pay a continuous income stream (such as dividend-paying equities or currency pairs), the fair value futures price is determined by the net cost of buying the asset in the spot market and carrying it to the delivery date: the buyer finances the purchase at the risk-free rate but receives dividends (or foreign interest) in return. For a stock index with continuous dividend yield q, the fair value futures price for delivery in T years is F = S × e^(r−q)T. If the actual futures price exceeds this level, arbitrageurs buy the spot index and sell futures; if below, they sell spot and buy futures. These arbitrage forces continuously drive the futures price toward its theoretical fair value.
For physically deliverable commodity futures, the cost-of-carry model must incorporate the additional economics of physical storage. A barrel of oil stored from today to three months hence incurs financing costs (the opportunity cost of the capital tied up in inventory) and physical storage costs (tank rental, insurance, handling), but also generates convenience yield—the option value of having physical supply available to avoid production disruptions or benefit from spot market shortages. When the markets in these various costs and yields are in equilibrium, the futures price settles at a level that makes indifferent the decision between holding physical inventory and buying futures.
The concept of basis is particularly important for hedgers. A corn farmer hedging production by selling December corn futures does not care about the absolute level of corn futures prices; what matters is the basis—the difference between the local cash corn price at harvest and the December futures price. If the farmer sells futures at $5.00 and the basis at harvest is −$0.20 (local cash price $4.80 below futures price), the effective selling price is $4.80. If the basis strengthens to −$0.10 (local cash $4.90), the effective selling price is $4.90—a $0.10 per bushel improvement in the hedger's outcome attributable entirely to basis movement rather than absolute price change. Basis risk is the residual risk that hedgers cannot eliminate through futures hedging.
The relationship between futures prices and expected future spot prices is a long-debated question in financial economics. The expectations hypothesis holds that futures prices equal expected future spot prices, implying no systematic risk premium for futures trading. The normal backwardation theory, associated with John Maynard Keynes, holds that commodity futures should trade below expected future spot prices because hedgers who are predominantly short (commodity producers) must offer a risk premium to attract speculators to take the other side. The insurance premium theory and more modern factor-based explanations suggest that futures risk premia arise from systematic exposure to commodity risk factors rather than simple carry relationships, and that both contango and backwardation may coexist with positive or negative expected returns depending on the prevailing factor exposures.
Formula
Fair Value Futures Price (Financial) = S × e^(r−q)×T; Fair Value Futures Price (Commodity) = S × e^(r+u−y)×T
Example
It is March 1, and the S&P 500 index stands at 5,000. The June S&P 500 E-mini futures contract (3 months to expiration) has a theoretical fair value based on the cost-of-carry model: F = 5,000 × e^(0.05 − 0.015) × 0.25 = 5,000 × e^(0.00875) = 5,000 × 1.00879 = 5,043.95, where 5% is the annualized risk-free rate and 1.5% is the annualized S&P 500 dividend yield. The actual June futures price is 5,044—essentially at fair value, reflecting the continuous index arbitrage activity that keeps futures prices aligned with their theoretical values. If the futures were mispriced at 5,060, an arbitrageur would buy the S&P 500 basket of stocks at 5,000, sell June futures at 5,060, hold until expiration receiving $75 in dividends (1.5% × 5,000 / 4), pay $62.50 in financing (5% × 5,000 / 4), and capture a riskless profit of 5,060 − 5,000 − 62.50 + 75 = $72.50 per unit.
Related terms
Arbitrage Backwardation Basis Basis Risk Chooser Option Contango Delivery Dividend Dividend Yield Exchange Futures Contract Gamma