Skip to content

    Under active development. New calculators and features ship every week. Everything currently runs free while the site matures — pricing pages are a preview, checkout is not open yet.

    Search ⌘K
    Calculates locally in your browser · duration hedge
    Treasury / futures hedge

    Treasury futures hedge calculator

    A bond portfolio can be hedged by shorting Treasury futures in the ratio of their dollar durations. This calculator computes the number of contracts, the residual exposure left by rounding, and the P&L the position produces for a given rate shift.

    Duration6.0Contract$110.00Hedge99.9%
    Contracts to short
    83.9
    Rounded: 84
    Portfolio dollar duration
    $60,000,000
    Value × modified duration
    Contract dollar duration
    $715,000
    Price × 1000 × duration / CF
    Rounding residual
    $60,000
    Exposure left after rounding
    Hedge calculation
    Duration-based ratio; the conversion factor adjusts for the cheapest-to-deliver.
    83.9 contracts
    Hedge calculation
    TermValue
    Portfolio value$10,000,000
    Portfolio duration6.00
    Portfolio dollar duration$60,000,000
    Futures price$110.00
    Futures duration6.50
    Conversion factor1.000
    Contracts83.92

    Short the futures to hedge a long bond portfolio; buy them to hedge a short position.

    Inspect the model
    Choose a quick result view, a scaled comparison, or the complete diagnostic set.
    Portfolio value change against rate shift
    Dollar duration turns a rate move into a P&L number.
    Portfolio value change against rate shift-672.00-388.80-105.60177.60460.80744.00-1.0-1.0-0.8-0.8-0.6-0.6-0.4-0.4-0.2-0.20.00.00.20.20.40.40.60.60.80.81.01.0P&L (thousands)
    Exposure by side
    Portfolio against the notional of the hedge.
    Exposure by side$0$1.417e+4k$2.835e+4k$4.252e+4k$5.670e+4k$7.087e+4kPortfolio DDPortfolio DDHedge DDHedge DDDollar duration
    Canonical equations
    The exact relationships implemented by this engine.

    N = (V·D_p) / (P·1000·D_f / CF) · Dollar duration matching.

    V × modified duration · Approximate P&L per 1% rate move.

    |N − round(N)| × contract DD · The cost of integer contracts.

    finance methodology

    A clear path from inputs to results.

    A bond portfolio can be hedged by shorting Treasury futures in the ratio of their dollar durations. This calculator computes the number of contracts, the residual exposure left by rounding, and the P&L the position produces for a given rate shift.

    Step-by-step methodWorked exampleAssumptions explained

    How to use

    1. Enter the portfolio value and its modified duration.
    2. Enter the futures price, its duration and the conversion factor.
    3. Read the contract count and residual exposure.
    4. Check the P&L for a rate shift.

    The formula

    N=V⋅DpP⋅1000⋅Df/CFN = \frac{V \cdot D_p}{P \cdot 1000 \cdot D_f / CF}

    Reference: Duration-based hedge ratio for Treasury futures; conversion factor adjusts for the cheapest-to-deliver.

    Worked example

    $10M portfolio at duration 6, futures at 110

    Inputs
    • Portfolio $10,000,000, duration 6.
    • Futures price 110, duration 6.5, conversion factor 1.0.
    Calculation path
    1. 1

      Portfolio dollar duration: 10M × 6 = $60M.

    2. 2

      Contract dollar duration: 110 × 1000 × 6.5 = $715,000.

    3. 3

      Contracts: 60M / 715,000 = 83.9.

    4. 4

      Rounding to 84 leaves about $71,500 of residual exposure.

    Result

    83.9 contracts · $715k per contract · small rounding residual.

    Interpreting the result

    The ratio equalises dollar duration, so a one-basis-point move costs the same on both sides. What it cannot remove is basis risk: the portfolio and the cheapest-to-deliver are different bonds, and their spread moves independently of the curve.

    Assumptions & limitations

    • Parallel shifts in the yield curve.
    • Stable spread between the portfolio and the CTD.
    • No margin, financing or roll costs.
    • Contract size of 1,000 per point.

    Frequently asked questions

    Why the conversion factor?

    Futures are priced off a notional bond; the factor converts the CTD price to that notional.

    Should I round up or down?

    Either; rounding leaves a small residual exposure in one direction.

    What is basis risk?

    The residual mismatch between the hedged portfolio and the futures contract.

    Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.