How is a butterfly yield curve trade constructed?

Question

AcadiFi · Accepted Answer

A butterfly trade is a three-legged position combining a bullet (body) and a barbell (wings) to bet on CURVATURE — the shape of the hump in the curve — while being duration-neutral and cash-neutral.

**Positive butterfly (expect curve to become MORE humped)**:
- Long body (e.g., 5-year)
- Short wings (e.g., 2-year and 10-year)
- Profits if belly richens relative to wings.

**Negative butterfly (expect curve to become LESS humped / flatten curvature)**:
- Short body
- Long wings
- Profits if belly cheapens relative to wings.

**Construction constraints**:
1. Duration-neutral: weighted durations offset.
2. Cash-neutral (50/50 cash weights) OR dollar-duration-weighted.

**Worked example**: Vermillion Rates Group believes the 5-year will RICHEN relative to 2-year and 10-year (positive butterfly). Current yields: 2Y = 3.85%, 5Y = 4.30%, 10Y = 4.55%. Durations: 2Y = 1.90, 5Y = 4.60, 10Y = 8.70.

Weights (50/50 wings): $50M in 2Y, $50M in 10Y, $X in 5Y. Dollar durations:
- 2Y: $50M × 1.90 = $95M DV01-equiv units
- 10Y: $50M × 8.70 = $435M
- Total wings: $530M
- Body 5Y must equal $530M: $X × 4.60 = $530M → X = $115.2M.

Short $115.2M of 5Y, long $50M of 2Y and $50M of 10Y. Cash sum: +50 +50 −115.2 = −$15.2M (net short cash — funded).

**Payoff**: If 5Y yield falls 10bps while 2Y and 10Y unchanged, 5Y short loses $115.2M × 4.60 × 0.001 = $530K (but you're short, so positive wait — let me flip: if you EXPECTED belly to richen, you go LONG body, not short).

Let me restate: POSITIVE butterfly = LONG body, SHORT wings. You profit if belly richens (yield falls relative to wings). In the example above, swap the directions accordingly.

**Risks**: If your curvature call is wrong and curve simply shifts parallel, you're near-neutral. But basis risk between on-the-run and off-the-run bonds can generate tracking error.

How is a butterfly yield curve trade constructed?

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