Tim Olson
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47 lines
2.6 KiB
Markdown
47 lines
2.6 KiB
Markdown
---
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description: "A fifty-fifty butterfly sets equal dollar durations on both wings of the barbell, making it approximately neutral to small yield curve steepening and flattening while remaining dollar-duration neutral, trading zero-cost for curve-neutrality."
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tags: [fixed-income, butterfly, duration-neutral, yield-curve, curvature]
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---
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# Fifty-Fifty Butterfly
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**Section**: 5.7 | **Asset Class**: Fixed Income | **Type**: Yield Curve / Curvature
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## Overview
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The fifty-fifty butterfly is a variation of the dollar-duration-neutral butterfly that equalizes the dollar durations of the two wings (short-maturity and long-maturity positions). This makes the strategy approximately neutral to small steepening and flattening of the yield curve (not just parallel shifts), at the cost of no longer being dollar-neutral (it is not zero-cost). It is also known as the "neutral curve butterfly."
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## Construction / Mechanics
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Using the same notation as the dollar-duration-neutral butterfly (Section 5.6), with modified durations D_1, D_2, D_3 and dollar positions P_1, P_2, P_3:
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**Equal wing dollar durations**:
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```
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P_1·D_1 = P_3·D_3 = (1/2)·P_2·D_2 (406)
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```
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This implies dollar-duration neutrality is preserved:
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```
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P_1·D_1 + P_3·D_3 = P_2·D_2
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```
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But the zero-cost condition P_1 + P_3 = P_2 is generally not satisfied.
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## Payoff / Return Profile
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- Approximately neutral to small steepening and flattening of the yield curve: the spread change between the body (T_2) and the short wing (T_1) equals the spread change between the body and the long wing (T_3).
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- Still immune to parallel shifts (dollar-duration neutral).
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- Profits from curvature changes: if the body cheapens relative to both wings, the position gains.
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## Key Parameters / Signals
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- P_1·D_1 = P_3·D_3 = (1/2)·P_2·D_2: the defining equal-wing constraint
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- T_1 < T_2 < T_3: the three maturities
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- Net cost P_2 - P_1 - P_3: non-zero unlike the dollar-duration-neutral butterfly
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## Variations
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- Dollar-duration-neutral butterfly (Section 5.6): zero-cost but not curve-neutral.
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- Regression-weighted butterfly (Section 5.8): uses empirical β to account for differential yield volatility across the curve.
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## Notes
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- The name "fifty-fifty" refers to the equal split of the body's dollar duration between the two wings.
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- Curve-neutrality is approximate and holds only for small parallel steepening/flattening moves.
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- The non-zero cost means the trader must finance the net position, which has carry implications.
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- Short-term rates are empirically more volatile than long-term rates, which limits the curve-neutrality assumption; this motivates the regression-weighted butterfly.
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