Basis & carry

Spot–Futures Arbitrage

Explore cash-and-carry and reverse carry, dated futures versus perpetual funding, basis calculations, margin requirements and liquidation risks.

Mechanics & mathematicsHypothetical examples

What Is It?

Spot–futures arbitrage compares immediate ownership of an asset with a contract for exposure at a later date. Cash-and-carry buys spot and sells an expensive dated future; reverse cash-and-carry borrows and shorts spot while buying a cheap future. The intended spread is evaluated after financing and implementation costs.

Basis is defined here as futures price minus spot price; some markets use the opposite convention. Dated contracts settle against a specified deliverable or reference price. Perpetual contracts have no expiry, so funding payments encourage alignment but do not create a fixed convergence date.

How It Works

For a matched, linear cash-and-carry hedge, a spot price rise increases the asset value while reducing the short future's value. At expiry, selling or delivering the asset offsets the futures settlement only to the extent that asset, quantity, currency and reference price match.

Cost of carry links a forward price to financing, income and storage. Convenience yield can be a non-cash benefit rather than a tradeable return, and staking yield is not automatically available on the exact asset used in a hedge. Futures daily margining can also make a forward-price formula an approximation when interest rates are stochastic.

A long-spot/short-perpetual position may receive positive funding under the venue's convention, but funding can reverse sign. Its P&L also depends on the entry-to-exit basis change. Annualizing one observed payment does not lock in a year of income.

Mathematical Formula

F_0=S_0 e^{(r+u-q)T},\qquad b_0=F_{\mathrm{market}}-S_0

Use deterministic continuously compounded rates, replicable carry, compatible settlement and feasible borrowing. S is spot, r financing, u storage/carry costs, q income yield and T years. A simple-rate expression is a first-order approximation.

\Pi_T=F_{\mathrm{sell}}-S_{\mathrm{buy}}e^{rT}-C_T

For one matched linear unit, no asset income/storage and terminal convergence, cash-and-carry profit deducts funding and all remaining costs measured at expiry. Reverse carry requires separate borrow fees and the rate actually earned on short proceeds.

\Pi_{\mathrm{perp}}\approx Q(b_{\mathrm{entry}}-b_{\mathrm{exit}})+\sum_j H_j-C

H is signed funding cash received by the hedge, Q is matched asset quantity and C includes fees, financing and borrow costs. This linear-contract approximation is not valid unchanged for inverse or quanto contracts.

Worked Example

Illustrative prices · not market data

Assume one BTC costs 60,000, a matched three-month future can be sold at 61,500, financing is 5% continuously compounded, and there is no spot income. All amounts use the same settlement currency.

The financed spot cost at expiry is 60,000 × exp(0.05 × 0.25) = 60,754.7071.
The terminal gross basis profit before financing is 1,500; after financing it is 745.2929.
If total remaining entry, exit, slippage and settlement costs measured at expiry are 120, the modeled net profit is 625.2929 per BTC.
The simple annualized quoted basis is (61,500 / 60,000 − 1) / 0.25 = 10%. This is not the net return on total committed capital.

The result assumes matched settlement and adequate collateral throughout. A liquidation before expiry can destroy the hedge even though its terminal replication looked profitable.

Execution Considerations

Match contract multipliers, settlement currency and delta exposure; inverse futures require different sizing and rebalancing. Reserve initial margin plus a liquidity buffer for variation margin. Spot profits held elsewhere may not be available to meet an immediate futures margin call.

Reverse carry needs committed asset borrow, realistic recall terms and the actual rebate on collateral. Compare net P&L with total capital tied up in spot, margin and buffers. Rebalancing a hedge changes turnover and costs; high nominal leverage alone does not establish capital efficiency. A simple annualized basis is (F/S − 1)/T, while the continuously compounded implied carry is ln(F/S)/T. Neither is a net investment return. Annualizing a perpetual funding observation by multiplying it by payment intervals is only an extrapolation, not a forecast or a locked rate.

Risks & Limitations

Basis widening, liquidation, changing margin requirements, venue default and settlement-index mismatch survive a delta hedge. Cash-settled convergence is to the contractual index, not necessarily the price at which your spot inventory can be sold.

Perpetual funding is uncertain and may become a payment. Dated futures reduce maturity uncertainty but do not remove financing, delivery, liquidity or operational risk. Trades with imperfect hedges or uncertain borrowing are practical basis trades rather than locked frictionless arbitrages.

Frequently Asked Questions

Is a perpetual funding trade the same as dated cash-and-carry?

No. A perpetual has no scheduled terminal convergence. Future funding and the eventual closing basis remain uncertain.

Can a hedged position be liquidated?

Yes. Margin is assessed under the venue's collateral rules. An offsetting spot asset may not protect a short derivative account from a cash shortage.

Is the displayed basis an annual investment return?

No. It excludes some costs and may use a different capital denominator. A fair comparison includes funding, margin buffers and the length of the actual holding period.

Explore the Existing Tool

Dashboard available · connection required

The BTC spot–futures dashboard requires a connected ticker service. A basis display is not evidence of an executable dated-futures arbitrage or a guaranteed funding return.

Open Spot–Futures Dashboard

References & Further Reading

Background sources for the concepts above. Apply the assumptions stated in this guide to each formula.

CME Group: Financing and Bond Basis Trading

Educational material only; not investment advice or an offer to trade. Examples are hypothetical. Trading involves execution, financing and capital-loss risks; no return is guaranteed.