---
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."
tags: [fixed-income, butterfly, duration-neutral, yield-curve, curvature]
---

# Fifty-Fifty Butterfly

**Section**: 5.7 | **Asset Class**: Fixed Income | **Type**: Yield Curve / Curvature

## Overview
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."

## Construction / Mechanics
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:

**Equal wing dollar durations**:
```
P_1·D_1 = P_3·D_3 = (1/2)·P_2·D_2                                  (406)
```

This implies dollar-duration neutrality is preserved:
```
P_1·D_1 + P_3·D_3 = P_2·D_2
```

But the zero-cost condition P_1 + P_3 = P_2 is generally not satisfied.

## Payoff / Return Profile
- 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).
- Still immune to parallel shifts (dollar-duration neutral).
- Profits from curvature changes: if the body cheapens relative to both wings, the position gains.

## Key Parameters / Signals
- P_1·D_1 = P_3·D_3 = (1/2)·P_2·D_2: the defining equal-wing constraint
- T_1 < T_2 < T_3: the three maturities
- Net cost P_2 - P_1 - P_3: non-zero unlike the dollar-duration-neutral butterfly

## Variations
- Dollar-duration-neutral butterfly (Section 5.6): zero-cost but not curve-neutral.
- Regression-weighted butterfly (Section 5.8): uses empirical β to account for differential yield volatility across the curve.

## Notes
- The name "fifty-fifty" refers to the equal split of the body's dollar duration between the two wings.
- Curve-neutrality is approximate and holds only for small parallel steepening/flattening moves.
- The non-zero cost means the trader must finance the net position, which has carry implications.
- Short-term rates are empirically more volatile than long-term rates, which limits the curve-neutrality assumption; this motivates the regression-weighted butterfly.