Where does a futures price come from before anyone has traded it?

Not from a forecast. A December futures price is not the market's guess at December's spot price. That misreading is common, confident and expensive. A futures price is, for the most part, an arithmetic consequence of today's spot price and the cost of holding the thing until December.

The arbitrage that sets it

There are two ways to have gold in six months' time:

• (a) Buy it now at spot, borrow the money to do so, and pay to store and insure it for six months.
• (b) Buy a six-month futures contract and leave your cash where it is meanwhile.

If (b) were meaningfully cheaper than (a), anyone able to do both would buy futures and sell physical. If it were dearer, they would do the reverse. The two routes are pinned together by that arbitrage, and the size of the gap between spot and futures is exactly the cost of route (a). That is cost of carry.

The relationship

Fair value F = S + financing + storage − income

• S — the spot price.
• Financing — interest on the money tied up in holding the physical: S × r × t.
• Storage (and insurance) — physical commodities only. Gold is cheap to store, natural gas and live cattle are not.
• Income — anything the underlying pays you while you hold it: dividends for an equity index, coupons for a bond. Income reduces fair value, because holding the physical version pays you and holding the future does not.

Worked: gold, six months out

• Spot $2,000/oz, financing rate 5% a year, storage plus insurance 0.4% a year, t = 0.5 years
• Financing: 2,000 × 0.05 × 0.5 = $50
• Storage: 2,000 × 0.004 × 0.5 = $4
• Income: none
• F = 2,000 + 50 + 4 = $2,054

The six-month future should trade near $2,054 — not because anyone expects gold to be $2,054, but because $54 is what six months of carry costs. On a 100-ounce contract that is $5,400 of carry.

Worked: an equity index, three months out

Here income bites, so the formula is usually written F = S × (1 + (r − q) × t), where q is the dividend yield.

• Index 5,000, r = 5%, q = 1.5%, t = 0.25 years
• F = 5,000 × (1 + (0.05 − 0.015) × 0.25) = 5,000 × 1.00875 = 5,043.75
• The future sits 43.75 index points above the index. At a $50 multiplier that is $2,187.50 per contract.

And notice the corollary: when dividend yield exceeds the financing rate, (r − q) turns negative and the future trades below the index. Nothing bearish is being expressed. It is subtraction.

Where the model bends

For a commodity that is genuinely scarce right now, holders derive a benefit from having the physical stuff — the ability to keep a refinery running, a bakery baking, a power station burning. That benefit behaves exactly like income: it pushes fair value down, sometimes below spot. It is called convenience yield, and unlike interest rates it is not observable. You infer it from the gap the rest of the arithmetic cannot explain.

That is why commodity curves are messier and more informative than index curves — and it is why the next lesson gives the leftover gap a name and a schedule.

In the data

The financing term in the carry arithmetic is a published rate rather than an assumption. Two versions of the dollar rate are below: the overnight fixing, and the same rate compounded over the trailing 90 days.

The overnight rate is the one quoted in the news and the wrong one for a months-long calculation: a three-month carry wants a three-month rate, and the 90-day average is the closest published figure. The two differ whenever rates are moving, which is exactly when the choice matters. Carry in another currency needs that currency's own rate — sterling's SONIA, the euro's €STR — not the dollar's.

Try it now

1. The financing leg is the 90-day average above: a compounded term rate rather than an overnight print, the one that belongs in a three-month carry calculation. Use it as r.

2. The S&P 500 index and its front futures contract are below, side by side. The future is the continuous front contract; at the end of September 2026 that is December's, which expires on 18 December. Compute fair value with the index formula above, taking t as the days from the quote to 18 December divided by 365, and q as the distribution yield of an S&P 500 fund in the second table.

3. Compare your figure to the quoted futures price. How much of the gap did carry explain? Whatever is left over is the interesting part, and it has a name.