Broken-wing butterfly

Definition

A broken-wing butterfly (BWB) is a butterfly whose two wings are unequal widths: the far wing on one side is placed further out (or the structure skips strikes), converting the symmetric butterfly into one that collects a credit or reduces debit by accepting more risk on one side. It is equivalently a ratio spread (strategy-ratio-spread) with the open tail bought back further away — defined risk, asymmetric by design.

How it works / structure

• Legs (put BWB example): +1 put K3 (near the money), −2 puts K2, +1 put K1, where K3 − K2 < K2 − K1 (the lower wing is “broken” wider); all same expiry.
• Payoff at expiry: profit peak at K2; on the narrow-wing side the structure often has no loss (entered at a credit); on the broken side, a defined but larger maximum loss = wing-width difference − credit.
• Parameters (engine-executable): body strike placement (delta or expected-move multiple — expected_move_pct), narrow/broken wing widths, credit floor at entry, DTE, exits (mgmt-profit-target at % of max, mgmt-time-based-exit before the expiry gamma zone, tested-side rule).
• Skew fit: put BWBs sell the smirk’s rich middle strikes and buy the cheaper far wing (opt-volatility-skew) — the credit exists because of the skew’s shape.

When it applies

Directional-lean range theses (“drifts down toward K2 but not through K1”) where a no-loss-on-one-side structure is worth the enlarged other-side risk; high-IV entries where butterfly bodies are rich; conversions of ratio spreads into defined risk. A precision structure — strike placement IS the thesis.

Risk profile & failure modes

• The broken side is the real position: the comfortable no-loss side dominates attention while the enlarged loss zone holds the actual risk; a move through the broken wing realizes the structure’s full asymmetry.
• Peak-profit mirage: like all butterflies, the tent’s peak is rarely captured; realized P&L distributions center far below max-profit marketing (strategy-iron-butterfly same caveat).
• Four-leg friction and thin wings: far OTM wings trade wide; entry/exit costs eat the small credits (ms-bid-ask-spread).
• Late gamma: the body’s short strikes steepen into expiry; time-based exits are structural, not stylistic.

Evidence & limits

Mechanics are contract arithmetic (OCC/Cboe). No public study evaluates BWBs as a class; the skew premium they harvest is measured (opt-volatility-skew citations) but structure-level edge is a per-replay question. Win-rate marketing that ignores the asymmetric loss zone is folklore, labeled as such.

Falsifiable-thesis examples

Illustrations only, not signals:

• “X will finish the cycle at or above K2 (credit kept or peak zone reached, broken wing untouched)” — falsified by a finish below K2.
• “X will not close below K1 + credit (the broken-side breakeven) on any day before expiry” — falsified by the daily closes.

Cross-references

• Symmetric parent: strategy-iron-butterfly; open-tail cousin: strategy-ratio-spread; simpler credit expression: strategy-bull-put-spread
• Pricing source: opt-volatility-skew, opt-iv-rank-percentile
• Management: mgmt-profit-target, mgmt-time-based-exit