Strategy #0000000032 · Fixed-income relative value
Yield-curve butterfly and curvature trading
Build neutral weights from three tenors and durations, then apply curve shocks.
A yield-curve butterfly is long short- and long-end bonds and short a middle tenor, targeting curve curvature. A dollar-duration-neutral construction controls initial net market value and small parallel-rate risk, but not slope, credit, convexity or funding.
Value and dollar-duration neutrality only isolate a chosen first-order risk; non-parallel shocks, convexity and carry remain.
Three ways in
Understand the story. Then inspect the risk.
Start with a familiar situation, check the payoff, then test how the numbers change.
The idea · in two minutes
Jack expects a flatter curve; Rose checks whether he is really long duration
Three-, five- and ten-year yields define a curve segment. Jack buys the short and long ends and shorts the belly, expecting the belly to strengthen relatively. Rose asks whether notionals, duration and market value are actually balanced.
A value-neutral butterfly makes wing market values roughly equal to the belly short. Matching wing dollar-duration to the belly lowers first-order exposure to a small parallel move. It does not make the three yields move together or remove convexity and carry.
With non-parallel curve changes, P&L depends on each leg’s key-rate risk. Regression-weighted beta can shift across regimes. Execution depth, repo funding, borrow and daily marks can also break theoretical neutrality.
- Value-neutral wing weightsWith belly short market value 1, wings are w₁=(D₃−D₂)/(D₃−D₁) and w₃=(D₂−D₁)/(D₃−D₁).
- Duration-neutral + parallel shockRequire D₁<D₂<D₃; weights are value-neutral and shocks are tenor-specific.
- Default non-parallel curve, carry and costResults are per 100 units of belly-short notional, not a return on zero net initial market value.
Illustrative research examples only. They are not live signals or a recommendation.
The mechanics · payoff and exposure
P_1+P_3=P_2,\qquad P_1D_1+P_3D_3=P_2D_2,\qquad \Delta V\approx-\sum_{i=1}^{3}s_iP_iD_i\Delta y_i+\frac12\sum_{i=1}^{3}s_iP_iC_i(\Delta y_i)^2
P₁ and P₃ are long-wing market values; P₂ is the belly short. D_i are modified durations, C_i convexities and s=(+1,−1,+1) trade signs. The equalities impose value and dollar-duration neutrality; Δy_i are decimal yield moves by tenor.
Greeks: the directional intuition
- Parallel duration
- Measures sensitivity to implied volatility.
- Curve shape
- Measures sensitivity to implied volatility.
- Convexity
- Measures sensitivity to implied volatility.
- Funding and liquidity
- Measures sensitivity to implied volatility.
P_1+P_3=P_2,\qquad P_1D_1+P_3D_3=P_2D_2,\qquad \Delta V\approx-\sum_{i=1}^{3}s_iP_iD_i\Delta y_i+\frac12\sum_{i=1}^{3}s_iP_iC_i(\Delta y_i)^2
Practical context · published observations
Yield-curve butterfly and curvature trading: read the record with its caveats.
The chart uses the published figures or explicitly labelled study inputs below. A historical index or model replay is not the same as an investor’s realised account return.
互動工具是固定權重、單期間的現金債券近似；不含實際收益率曲線、key-rate interpolation、repo、借券、coupon timing、稅務或 bid/ask。duration 排序無效時不計算；結果不是歷史套利證據。 Source ↗ · Methodology ↗
Change assumptions and inspect the scenario
Inputs illustrate the strategy mechanics; they are not live quotes, forecasts or investment advice.
Variants · same family, different risk levers
Related methods share a mechanism, not every assumption.
Each row identifies what changes in its signal, construction or risk.
| Related strategy | Relationship | What changes | New cost or risk |
|---|---|---|---|
| Fifty-fifty butterfly | Equal wing dollar-duration | Uses equal wing exposures for a slope/curvature view. | May not also be zero-value and belly-duration neutral. |
| Regression-weighted butterfly | Historical beta weights | Weights wings using historical tenor-move regressions. | Betas can be unstable across regimes. |
| Maturity-weighted butterfly | Maturity-ratio weights | Uses tenor spacing as a weight proxy. | Maturity spacing ignores leg DV01/PV01 differences. |
| Nelson–Siegel curvature timing | Model signal | Times butterfly exposure from predicted curvature factors. | Factor estimation, timing overfit and costs. |
| Swap PV01 butterfly | Annuity/PV01 coordinates | Balances swap PV01 rather than notional or cash market value. | Calendars, discount curves and collateral must align. |
The tool is a fixed-weight, one-period cash-bond approximation. It omits live curves, key-rate interpolation, repo, borrow, coupon timing, taxes and bid/ask. It refuses invalid duration ordering and is not historical arbitrage evidence.
Read beyond the summary
References
Primary sources and research used to describe the strategy and its limits.
- 01Kakushadze & Serur (2018), 151 Trading Strategies, §§5.6–5.8.source
- 02Andrada-Félix, Fernandez-Perez & Fernández-Rodríguez (2015), Fixed income strategies based on Nelson–Siegel parameters.research
- 03Audrino & Serwart (2024), Yield curve trading strategies exploiting sentiment data.research
- 04Sun (2026), Shape of Yield Curves Under Instrument-Based Parallel Shifts.research