Why the futures basis converges, and what the term structure tells a carry desk

The basis is the difference between a futures price and the spot price of the thing it references. On the expiry date the two are the same instrument, so the basis must be zero. That single fact is what makes a dated future a carry instrument rather than a bet: whatever the basis is today, its path ends at a known point on a known date.

CME Group’s educational material on convergence puts it plainly. Futures positions can be converted into cash at expiration, so at expiration futures and spot converge to the same level, and it is that predictability that lets hedgers rely on the relationship between cash and futures. In digital assets the same logic applies to the quarterly and monthly contracts listed on derivatives venues, with one difference that matters: the basis is far more volatile than in most traditional markets.

What sets the basis

In a textbook market the futures price equals spot plus the cost of carrying the asset to expiry: financing, storage and insurance, less any income the asset pays. For a financial future the cost of carry is mostly an interest rate differential, which is why CME’s treatment of FX futures pricing is a treatment of interest rates. Digital assets have no storage cost and, in their unstaked form, no income, so the carry should be close to a funding rate for dollars.

It is usually far above that. The BIS study of crypto carry attributes the gap to a convenience yield: leveraged traders want long exposure, the futures market is where they get it, and the capital willing to sell them that exposure and hold spot against it is limited. The basis is therefore a price for leverage set by the balance between speculative demand and arbitrage capital, and it moves with sentiment. When the market is euphoric the curve steepens; after a crash it flattens or inverts, with futures trading below spot.

Reading the term structure

Line up the basis for each listed expiry and you have a term structure. When later expiries trade at progressively higher prices the curve is in contango; when they trade lower it is in backwardation. The shape carries information a single number cannot. A steep front end with a flat back end says demand for leverage is concentrated in the near term. A curve that is rich at the back but flat at the front says the market expects conditions to change. A curve that is inverted at the front after a sharp fall says leveraged longs have been liquidated and shorts now dominate.

• Contango: later expiries priced above nearer ones; the market is paying to be long over time
• Backwardation: later expiries priced below nearer ones; the market is paying to be short, or to hold spot
• Roll yield: the gain or cost of moving a position from an expiring contract to the next one
• Calendar spread: a long in one expiry against a short in another, a position on the shape of the curve rather than its level

The perpetual as the zero-maturity point

A perpetual future is the front of the curve compressed to a point: its basis is paid out continuously as funding rather than accrued to an expiry. Comparing the funding a perpetual pays with the annualized basis of a dated contract on the same asset is therefore a comparison between two prices for the same thing, leverage over time. When they disagree, a desk can hold the cheaper one against the richer one, short the dated future and long the perpetual or the reverse, and collect the difference with limited directional exposure. That is a term-structure trade, and it has the same risks as any calendar spread: the two legs can diverge further before they converge, and the margin on each is assessed separately.

What a carry desk does with this

Convergence is the only certainty in the trade, and it is only certain at expiry. Between now and then the basis can widen against a position, and a desk that has sold a rich future against spot must be able to hold both legs through that widening. The discipline is therefore about time and margin rather than direction: choosing an expiry whose basis compensates for the capital tied up until it converges, sizing the short so that a widening does not force a margin call the spot leg cannot answer, and deciding in advance whether the position will be held to expiry or rolled. The basis is a price for leverage. A carry desk is in the business of supplying it, and the term structure tells the desk what it is being paid and for how long.