Crypto Futures Basis Explained: Contango, Backwardation and Convergence

Editorial responsibility: Oliver Sinz · Last verified: October 14, 2026

The basis is the gap between a futures price and the price of the asset the contract references. In crypto, respected sources quote it with opposite signs, venues measure it against different reference prices, and it applies to two instrument families, dated futures and perpetual futures, that close the gap in fundamentally different ways.

This guide sets one sign convention and uses it throughout. It shows how to normalize a premium or discount by time, how to read a futures curve without treating it as a forecast, and why a dated contract converges at expiration while a perpetual has no date on which it must. All prices below are hypothetical illustrations, not market data.

Futures Basis Defined: One Convention, Applied Consistently

This guide measures the basis as futures minus spot:

Absolute basis:     B = F − S
Percentage basis:   b = (F − S) / S

Here F is the futures price and S is the spot reference price. Both are quoted in the same currency for one unit of the underlying. Under this convention, a futures premium (F above S) is a positive basis and a futures discount (F below S) is a negative basis.

Sources differ. CME Group quotes equity index basis as futures minus spot, as this guide does. But CME's lesson on Treasury basis defines it as the cash price minus the converted futures price, and Binance Academy's basis trading article uses spot minus futures, so a market where futures trade above spot shows a negative basis. None of these is wrong, but a "basis of −2%" in one source can describe the same market as "+2%" in another. Always check which price is subtracted from which, and which spot reference was used. "Premium" and "discount" do not depend on a sign convention, which makes them safer words.

A $1,600 premium means something different at a $40,000 bitcoin price than at $80,000. Percentage basis makes contracts comparable across price levels, but not across maturities. That requires normalizing by time.

Example 1: A Bitcoin Futures Premium, a Discount, and the Annualized Basis

Assumptions (hypothetical):

• Spot reference: S = $80,000 per BTC, observed at the same moment as the futures price.
• Contract: a linear BTC futures contract quoted in USD per BTC and cash-settled in USD. Figures are per 1 BTC of notional. (Exchange contracts apply a multiplier. CME's standard bitcoin contract, for example, covers 5 BTC.)
• Time to final settlement: 91 calendar days, on a 365-day year, because crypto spot trades every day.

Premium case, with the futures at $81,600:

B = 81,600 − 80,000 = +$1,600
b = 1,600 / 80,000  = +2.00%

Simple annualized basis      = b × 365 / days       = 2.00% × 365 / 91       = +8.02%
Compounded annualized basis  = (F / S)^(365/days) − 1 = (1.02)^(365/91) − 1   = +8.27%

Discount case, with the futures at $79,200:

B = −$800,  b = −1.00%
Simple annualized = −4.01%     Compounded annualized = −3.95%

Simple annualization scales the period's percentage linearly. Compounded annualization assumes the same period ratio could be earned repeatedly and reinvested. Neither one is "correct"; each answers a different question. A quoted annualized basis should always say which method and which day count it uses.

The 8.02% figure is a normalized price relationship, not an annual yield anyone receives. Capturing even the 2.00% gap means holding spot against a short futures position until settlement, posting futures margin, paying fees and spreads, and surviving interim mark-to-market losses. Unless the spot leg is financed with borrowed money (which has its own cost), the capital tied up exceeds the spot notional, so the gross return on that capital is smaller than the quoted percentage. Harvesting the discount case requires selling or borrowing spot, with its own costs and constraints. Measuring the basis and accounting for a trade's net return are separate exercises.

Cost of Carry: What a Futures Premium Should Reflect

Standard futures pricing, as summarized in the CFA Institute's futures pricing reading, sets the futures price equal to the spot price compounded at the risk-free rate, with adjustments for the costs and benefits of carrying the asset. This guide uses a simple-interest approximation:

F* ≈ S × [1 + (r − y) × T]

Here r is the annual financing rate in the quote currency, y is the explicit annual cash yield from holding the asset (such as lending income, net of holding costs), and T is the time to settlement in years. Bitcoin has no warehousing cost, and its explicit cash yield is usually small.

Take a hypothetical financing rate of r = 4.00% and y = 0. Then F* = 80,000 × (1 + 0.04 × 91/365) = $80,797.81. The observed $81,600 sits $802.19 above that. Measured against spot on the same simple basis, the residual is 802.19 / 80,000 × 365/91 = about 4.02% annualized.

That residual is not a second return on top of the 8.02%. The quoted basis already includes the financing compensation, and this decomposition simply splits it into 4.00% financing and 4.02% of something else. In crypto, that "something else" has been large and volatile. A BIS working paper on crypto carry found that the basis averaged roughly 10% a year in its sample and at times exceeded 40%, and that interest-rate differentials explained very little of it. The authors describe the residual as a volatile convenience yield on futures, driven by trend-chasing investors' demand for leverage and by limited arbitrage capital, which they link to margin spikes, liquidation risk and the lack of cross-margining between spot and futures. Cost of carry is a benchmark that assumes a frictionless market, not a price the market is obliged to trade at.

Four Terms That Are Not Synonyms

• Contango and backwardation describe the slope of the futures curve across maturities.
• Positive and negative basis describe one contract relative to spot, and only under a stated sign convention.
• Positive and negative funding describe a perpetual contract's payment direction. On Binance, for example, a positive rate means longs pay shorts.
• Positive and negative carry describe the net cost or benefit of holding an asset or position. CME's equity-index lesson calls carry positive when the dividend yield exceeds the financing cost, a condition that pushes index futures to a discount. Positive carry can therefore coexist with a negative basis.

Contango vs Backwardation: Reading the Futures Curve

A futures curve plots each dated contract's price against its time to maturity, with spot as the zero-maturity point. CME's education material describes contango as futures trading above spot along an upward-sloping curve, and backwardation as futures below spot along a downward-sloping curve. Some educational sources, such as Schwab, define the terms relative to the expected future spot price, which cannot be observed directly. This guide uses the observable curve.

The price difference between two maturities is a calendar spread:

Spread(T1, T2) = F(T2) − F(T1)

A calendar spread compares two futures prices. It does not involve spot at all.

Example 2: Three Hypothetical BTC Futures Curves

Spot is $80,000 in every case. The basis is F − S, and the annualized figures are simple, on a 365-day year.

• Curve A (contango): Each contract trades at a premium to spot, and each later contract trades above the earlier one. The 91→182-day spread implies a forward rate between those dates of (83,200 / 81,600 − 1) × 365/91 = 7.86% annualized.
• Curve B (backwardation): Each contract trades at a discount, and the discount deepens with maturity.
• Curve C (humped): Every contract trades at a premium to spot, yet the back of the curve slopes down. The 182-day contract is $200 below the 91-day contract. "The 182-day future trades at a premium" is true. "The curve is in contango between 91 and 182 days" is false. The annualized basis also falls from 12.17% to 2.51% even though every basis is positive.

A curve's shape does not forecast spot prices. Futures prices embed financing costs, demand for leveraged exposure, hedging pressure and collateral constraints, not just expectations. Contango does not mean the market "expects" a higher price at expiry, and backwardation does not predict a decline. Nor does a curve shape create a trade by itself. A calendar spread position profits only if the spread moves favorably, both legs need margin, and once the near contract expires the far leg remains exposed.

Convergence at Expiration: What the Basis Converges To

A dated futures contract has a contractual final settlement price. Because every open position is closed at that price, the futures price at settlement equals the settlement reference R: the basis measured against that reference is zero. Before then, arbitrage tends to pull futures toward the reference as the remaining carry shrinks. That is a tendency, not a schedule.

The reference is a computed benchmark, not a single trade:

• CME bitcoin futures: Under CME Rulebook Chapter 350, each contract covers 5 BTC and settles in cash. The final settlement price is the CME CF Bitcoin Reference Rate (BRR) published at 4 p.m. London time on the last trading day, normally the last Friday of the contract month.
• The BRR itself: Per the CME CF Reference Rates Methodology, the BRR collects trades on approved constituent exchanges from 3:00 to 4:00 p.m. London time. It splits that hour into twelve 5-minute partitions, takes a volume-weighted median in each, and averages the twelve medians equally.
• Deribit: Per its support documentation, the delivery price is the time-weighted average of the Deribit index over the last 30 minutes before expiry (450 index values at 4-second intervals).

"Futures converge to spot" therefore means "futures converge to a specified reference." A fill on one exchange at 4:00 p.m. can differ from the BRR. CF Benchmarks notes that most U.S. spot bitcoin ETFs strike their NAV at the New York variant (BRRNY), while CME futures settle against the London BRR.

Example 3: Following One Contract to Settlement

This uses the same hypothetical USD cash-settled contract as Example 1. The path is chosen for illustration; it is not a forecast of how convergence unfolds.

Every futures price change splits exactly into a spot change and a basis change: ΔF = ΔS + ΔB.

Four lessons follow:

1. Direction and basis are different movements. Spot rose 7.5%, then partly reversed. Most of the futures move was spot movement; the basis contributed a narrowing of $1,600 over the whole period. A long futures holder gained $2,900 per BTC, less than spot's $4,500, because they paid the initial premium.
2. Narrowing is not linear. The annualized basis was 8.02% on Day 0 and 6.08% on Day 61. It could just as easily have widened. Exiting a hedged spot-plus-short-futures position on Day 61 would have locked in only the $1,170 of narrowing so far, before costs.
3. Convergence does not remove mark-to-market. A short futures leg would have paid $4,830 per BTC in variation margin by Day 61, or $24,150 per 5-BTC CME-sized contract, even though the combined position gained from the narrowing basis. The offsetting spot gain usually sits in another account or on another venue. An under-collateralized short can be force-closed before convergence ever happens.
4. Settlement tracking is a separate residual. If a hedger sells spot at $84,620 on one exchange while the futures settle at $84,500, the outcome differs by $120 per BTC. Convergence happens against R, not against the trader's own fill.

Perpetual Futures: A Premium Without an Expiration Date

A perpetual contract has no settlement date, so its gap to the reference is an instantaneous premium or discount:

Perpetual premium (+) or discount (−):   p = (P − I) / I

Here P is the perpetual price and I is the exchange's index price. P should be stated as either the last traded price or the mark price, because the two can differ. With no maturity, there is no natural time over which to annualize p. Nothing forces p to zero on any particular date. He, Manela, Ross and von Wachter note that, unlike fixed-maturity futures, perpetuals are not guaranteed to converge to spot. They also find that deviations from no-arbitrage prices are larger than in traditional currency markets.

Funding supplies the anchoring incentive instead. Binance's funding documentation describes the payments as designed to anchor the perpetual to the spot index. A positive rate means longs pay shorts, and the payment equals position notional (mark price × size) times the rate, by default every 8 hours. The rate is not simply the current price gap. It starts from a premium index that compares depth-weighted impact bid and ask prices with the price index, sampled every 5 seconds and time-weighted over the interval. It then adds the difference between a 0.01%-per-8-hours interest rate and that premium index, clamped to ±0.05%, subject to contract caps. On an 8-hour interval, whenever the premium index sits between −0.04% and +0.06%, funding simply equals 0.01%. Bybit uses a similar structure with its own limits. Intervals, caps and inputs differ by venue and change over time.

Example 4: A Premium That Does Not Have to Close

Assume, purely for illustration, a funding rate of +0.03% per 8-hour interval while the premium is positive. This rate is an assumption and is not derived from the table. A 1 BTC long marked at about $80,240 would pay 80,240 × 0.0003 = $24.07 per interval, or about $72.22 per day if both the rate and the price held constant.

Funding makes holding the long more expensive, which can attract sellers and narrow the gap. Here the premium widened anyway at t1, then flipped to a discount at t2. No contractual date forced either outcome. A hedged position that exits at any of these moments realizes whatever premium prevails then, on top of the funding it paid or received along the way.

Side by Side: Basis, Calendar Spreads and Perpetual Premiums

Crypto Market Structure That Moves the Basis

• Trading and clearing calendars. CME now lists its crypto futures and options for 24/7 trading, apart from short maintenance halts. Trades from Friday evening through Sunday evening carry the next business day's trade date, with clearing and settlement processed then. A weekend basis can therefore be observed continuously, but margin flows from weekend moves arrive later, and weekend liquidity can differ from spot venues.
• Fragmented references. The BRR, Deribit's index and Binance's price index draw on different sets of exchanges. Pairing one venue's futures with another venue's spot mixes two references.
• Quote and settlement currency. Many crypto-native contracts are quoted and margined in stablecoins, so a basis measured against USD spot also embeds the stablecoin's exchange rate. Inverse (coin-margined) contracts quote in USD, so basis arithmetic on quoted prices is the same, but their P&L is paid in the coin and is non-linear in price.
• Collateral separation. Spot holdings and futures margin often sit at different venues, so gains on one leg cannot instantly cover losses on the other. The BIS paper links persistent crypto carry to these margin and capital frictions.
• Variability. CF Benchmarks measured the CME front-month annualized basis near 25% in February 2024, above 20% in November 2024 and briefly below zero in March 2025. These are historical observations, not current conditions.

From Quoted Basis to Realized Outcome

Even convergence that works exactly as designed only fixes the endpoint of a price relationship. Between a quoted basis and any realized result sit the actual holding period, fees and slippage on both legs, the capital and financing actually deployed, variation-margin calls and liquidation risk on the short leg during rallies, the gap between your fills and the official reference, counterparty and venue risk, and, for perpetuals, funding that changes every interval.

Net-return accounting for spot–futures and spot–perpetual positions is a separate topic from measurement. This site's workbench models hypothetical perpetual, spot-hedge and funding-spread scenarios under stated assumptions. It does not construct futures curves, track live basis, or simulate dated-futures settlement.

Key Takeaways

• State the convention. This guide uses B = F − S, so a premium is positive. Many sources use S − F.
• Annualized basis is a normalized price ratio. Quote it with its method (simple or compounded) and day count, and never read it as a guaranteed return.
• Contango and backwardation describe the curve's slope across maturities. A contract can trade at a premium to spot while part of the curve slopes down.
• Dated futures converge to a contractual reference rate at settlement, but interim mark-to-market, margin and liquidity risks remain.
• A perpetual's premium has no expiry-driven convergence. Funding creates an incentive toward the index, and how a given premium translates into funding depends on each venue's published formula.