How Futures Prices Are Set: Cost of Carry, Fair Value, Basis and Convergence

A futures price is set by trading on the exchange, but arbitrage keeps it tied to the spot (cash) price through a relationship called cost of carry: the futures price is roughly the spot price plus the cost of financing and storing the asset until delivery, minus any income the asset pays in the meantime. The gap between spot and futures is the basis, and it shrinks toward zero as the contract approaches expiry.

In short: futures price ≈ spot price + financing cost + storage cost minus income (dividends, interest, or the “convenience” of holding the physical thing). For a stock index, that means spot plus interest minus dividends, which is the fair value that news anchors mention before the open. For commodities, storage and supply conditions matter, so futures can be above spot (contango) or below it (backwardation). At expiry, futures and spot converge, because a contract about to settle is effectively the spot asset.

The misconception: “the futures price is the market’s forecast”

A futures price is not a prediction of where the spot price will be. It is the price at which, today, someone is indifferent between owning the asset now and agreeing to own it later. If December gold trades above today’s gold price, that does not mean traders expect gold to rise. It mostly means that holding gold until December costs money (you could have earned interest on the cash instead), and the futures price has to reflect that.

Expectations do matter, especially for commodities that cannot be stored easily or where supply is tight, but the starting point is always the carry relationship.

The cost-of-carry idea

Imagine two ways to own one ounce of gold in six months:

Buy it now and store it. You pay the spot price today, give up the interest you would have earned on that cash, and pay for storage and insurance.
Buy a futures contract for delivery in six months. You pay nothing today (beyond margin, which is collateral, not payment) and keep earning interest on your cash.

If both routes lead to the same ounce of gold at the same date, they should cost the same. So:

Futures price = spot price + financing cost + storage cost minus income from the asset

If futures were priced higher than that, arbitrageurs would buy spot, sell futures, and lock in a riskless profit (a cash-and-carry trade). If futures were lower, they would do the reverse where they could. That trading pulls the futures price back toward fair value.

A worked example: stock index fair value

For a stock index, there is no storage cost, but there are two carry components: the interest you forgo by owning the stocks, and the dividends you receive by owning them. The futures holder pays neither and receives neither.

Illustrative inputs:

S&P 500 spot: 6,000.00
Interest rate: 4.0% a year
Dividend yield on the index: 1.3% a year
Days to the futures expiry: 90

Using simple interest:

Financing cost: 6,000 x 4.0% x 90/365 = 59.18 points
Dividends: 6,000 x 1.3% x 90/365 = 19.23 points
Net carry: 59.18 minus 19.23 = 39.95 points
Fair value: 6,000.00 + 39.95 = 6,039.95

For the E-mini S&P 500, at $50 a point, that 39.95-point premium is worth about $1,997.50 per contract. It is not a gain for anyone; it is the price of deferring the purchase.

This is why pre-market news often says futures are “above fair value” or “below fair value”. The futures price on its own says little; the comparison to fair value is the signal that the market is expected to open higher or lower than yesterday’s close. Exchanges and data vendors publish their own fair value estimates using actual dividend forecasts. More in stock index futures explained.

What happens when futures drift from fair value

Suppose, with the same inputs, the futures contract trades at 6,055.00 instead of 6,039.95: 15.05 points rich. A firm that can trade the whole index basket cheaply could:

Sell one E-mini contract at 6,055.00.
Buy $300,000 worth of the S&P 500 stocks (6,000 x $50), financing them at 4%.
Collect the dividends and hold until expiry, when the futures settle to the index.

Whatever the index does, the futures and stock positions offset. The locked-in profit is the mispricing: 15.05 x $50 = $752.50 per contract, before transaction costs. Selling futures and buying stocks pushes the futures price down and the stocks up until the gap is gone.

If futures traded below fair value, the trade runs in reverse (sell stocks, buy futures), which is harder for most firms, because it requires stock they can sell or borrow. In practice, large banks and trading firms with low costs keep index futures within a narrow band around fair value. The band is wider when funding is expensive or markets are stressed.

Commodities: storage and the convenience yield

For a storable commodity, the carry includes physical costs.

Illustrative crude oil example, for one month:

Spot crude: $70.00 a barrel
Financing: $70.00 x 4.0% / 12 = $0.23
Storage and insurance: $0.50 a barrel per month
Full-carry futures price: $70.00 + $0.23 + $0.50 = $70.73

Per WTI contract of 1,000 barrels, that full carry is about $730.

The full-carry price is an upper limit, not a forecast. If futures traded far above it, traders with storage would buy oil, store it, and sell futures. But futures can trade well below full carry, even below spot. That happens when having the physical commodity on hand is valuable right now: a refinery that runs out of crude has to shut down. Economists call this benefit the convenience yield. When supplies are tight, convenience yield is high and near-term contracts can trade above later ones.

The two shapes of the futures curve that result have names, contango and backwardation, and get their own article: contango and backwardation.

Gold: close to pure carry

Gold is plentiful in storage and costs little to keep relative to its value, so its futures usually trade close to full carry. Illustrative: spot gold at $4,000 an ounce and a 4% rate implies a six-month futures price around $4,000 + ($4,000 x 4% x 0.5) = $4,080. On one COMEX contract of 100 ounces, that is a premium of $8,000 over spot. Real prices also reflect lease rates and storage costs. See gold futures explained.

Basis

Basis is the difference between a cash price and a futures price. In agricultural markets it is usually quoted as:

Basis = local cash price minus futures price

A grain elevator in Iowa might quote “20 under December,” meaning its cash bid is 20 cents per bushel below the December corn futures price. Basis reflects transport costs to the delivery points, local supply and demand, and storage. For stock indexes, basis is usually discussed as the futures premium over spot (the 39.95 points above).

Hedgers care about basis because a futures hedge protects against changes in the futures price, not changes in basis. More in basis.

Convergence at expiry

As expiry approaches, the time left to carry the asset shrinks, so the carry shrinks too. Using the same index inputs:

Days to expiry	Financing (points)	Dividends (points)	Fair value premium (points)	Fair value
90	59.18	19.23	39.95	6,039.95
60	39.45	12.82	26.63	6,026.63
30	19.73	6.41	13.32	6,013.32
10	6.58	2.14	4.44	6,004.44
0	0	0	0	6,000.00

(This holds the spot price at 6,000 for illustration; in reality it moves every second.)

At expiry the futures contract must equal the spot price. A cash-settled contract is settled to the index itself. A physically delivered contract delivers the actual commodity, so if futures were above spot at the last moment, anyone could buy spot, deliver it, and pocket the difference. This is convergence, and it is what keeps futures honest. How settlement works is covered in physical vs cash settlement.

What can go wrong

Convergence can be violent. Near expiry, if few participants can take delivery, the futures price can be pushed far from where anyone expected. The May 2020 WTI contract settled at minus $37.63 a barrel on April 20, 2020, the day before expiry, because holders could not find storage. See negative oil prices in April 2020.
Carry changes. Interest rates, dividend forecasts and storage costs change, so fair value moves even if spot does not.
Local basis can blow out. Weather, transport bottlenecks, or a local plant closure can widen basis sharply, so a hedge may not protect a farmer’s actual sale price as much as expected.
Fair value is not a buy or sell signal. Small gaps from fair value are often within trading costs and are arbitraged away by firms with lower costs than any individual.

The short version

Futures prices are set by trading, but arbitrage anchors them to spot through cost of carry: financing plus storage minus income. That gives index futures a calculable fair value and commodity futures an upper bound, with convenience yield explaining why some commodity futures trade below spot. Basis is the gap between cash and futures, and it converges toward zero at expiry because a contract about to settle is the spot asset.