Futures vs. Forward Convexity Adjustment Explained
Learn why futures and economically similar forwards can diverge when daily settlement and rate sensitivity differ, with a worked DV01 hedge example and practical checks.
Direct answer
Futures and similar forwards can differ because futures gains and losses settle during the contract while forward cash flows may come later. When rates and sensitivity interact, that timing can create a convexity adjustment.
Daily settlement changes cash-flow timing
Futures use exchange settlement prices to move gains and losses through variation margin during the life of the contract.
A forward can defer most economic settlement until a later date, depending on its collateral and legal terms.
That timing difference matters because interim cash can be funded or reinvested at rates that may themselves change.
Futures vs. forwards explains the broader contract and credit differences.
Convexity is not just another name for basis
Spot-futures basis mainly compares a futures price with a spot reference and its carrying inputs.
Convexity adjustment instead asks whether two instruments with similar rate exposure respond differently as rates move and cash flows occur at different times.
Futures basis and fair value covers cost of carry separately.
Short-term rate futures show the idea clearly
CME notes that a Three-Month SOFR future has a fixed $25 value for a one-basis-point move per contract.
A swap or forward-like rate exposure can have a DV01 that changes as the rate level changes. Its value therefore bends rather than moving with one fixed dollar slope.
The resulting futures hedge ratio can change after rates move, even if the original hedge was matched closely.
Worked example: 100 contracts can become 102
Assume a forward-like rate exposure has DV01 of $2,500 per basis point. A futures contract contributes $25 per basis point.
The first-order hedge ratio is 2,500 / 25 = 100 futures contracts.
Now assume the forward-like exposure's DV01 rises to $2,550 while the futures contract remains $25 per basis point. The updated ratio is 2,550 / 25 = 102 contracts.
Keeping only 100 contracts leaves $2,550 - $2,500 = $50 per basis point of first-order mismatch. Over a 20 bp move, that approximation is $1,000 before second-order effects and costs.
The exact adjustment is model dependent
The worked example shows changing sensitivity, not a universal convexity-pricing formula.
An actual adjustment depends on product design, volatility, rate dynamics, correlation, discounting, settlement timing, collateral, and the horizon being compared.
For SOFR products, also preserve the exact contract month and reference period. SOFR futures implied rates explains that contract convention.
Use a futures-forward comparison checklist
- Match the underlying economic exposure and maturity - Record when each instrument actually exchanges cash - Compare DV01 or the relevant price sensitivity at the same market state - Check whether the sensitivity changes when rates or prices move - Separate convexity from ordinary basis and carry - Include collateral, funding, bid-ask spreads, fees, and model assumptions [!TRYMARK] Convexity checkpoint At the September 18 comparison, record DV01 of $2,500, futures BPV of $25, the 100-contract hedge, then stress DV01 to $2,550 and recalculate the hedge before comparing outcomes.
This guide explains a pricing and hedging mechanism. It does not say that one structure is universally cheaper or better.
Common questions
Are futures and forward prices always different?
No. Under simplifying assumptions they can be very close or equal. Differences become important when settlement timing, rates, collateral, and changing sensitivities affect the economics.
What is convexity bias in interest-rate futures?
It is the valuation or hedge difference that appears because a linear futures payout can be compared with a forward-like or swap exposure whose value changes nonlinearly as rates move.
Is convexity adjustment the same as cost of carry?
No. Cost of carry helps relate spot and futures values. Convexity adjustment concerns differences in cash-flow timing and nonlinear sensitivity between economically related instruments.
Can I calculate the exact adjustment from DV01 alone?
No. DV01 is useful for a local hedge comparison, but exact pricing generally needs volatility, rate dynamics, discounting, settlement, collateral, and other model assumptions.