Broken-wing butterflies and cheap directional bets

A symmetric butterfly has equal wings and a debit. Move one wing further out and the structure changes character: it can be entered for a credit, it loses its risk on one side entirely, and it becomes a way to sell premium with a much smaller worst case than a credit spread. Push the whole butterfly out of the money instead and it becomes the cheapest way to bet on a specific target. Both are the same three-strike idea with the strikes chosen on purpose.

The broken-wing put butterfly

XYZ at $50, 45 days, IV 30%. Buy the $47 put, sell two $44 puts, buy the $40 put. The upper wing is 3 wide, the lower wing 4 wide.

The extra dollar of width on the lower wing is what pays for the structure: the $40 put is cheaper than the $41 put would have been, so the whole thing nets a small credit instead of a small debit. Put skew helps here, because the lower strikes are relatively rich to sell against.

Broken-wing put butterfly 47/44/40 for 0.10 credit

  +310 |               /\
       |              /  \
  +10  |_____________/    \
    0  |-------------------\-X--------   X = 40.90
       |                    \
  -90  |                     \________
       +---+---+---+---+---+---+---+---+
       36  38  40  42  44  46  48  50  52   XYZ at expiry

Read the shape: no risk on the upside, a small profit ($10) if the stock rallies or sits still, a large profit ($310) if it drifts down to $44, and a capped loss of $90 only if it falls through $40.90. Compare with the 44/40 bull put spread alone, which would collect about $0.35 with a max loss of $3.65; the broken-wing butterfly is that spread plus a long 47/44 put spread that costs $0.45 and cuts the max loss from $365 to $90 while adding the $310 peak. You gave up $0.25 of credit for that.

The decomposition is the way to think about every broken wing: a debit spread near the money plus a wider credit spread further out, sized so the credit pays for the debit. The credit spread's width beyond the debit spread's width is the max loss.

Margin depends on the broker. Some recognize the structure and hold the true max loss ($90); others hold the wider wing minus the total credit ($390). Check before sizing.

When it fits: you are neutral to mildly bearish, you want to sell downside premium, and you want the worst case to be a number you can shrug at. The call-side version (buy $53 call, sell two $56 calls, buy $60 call) is the mirror for a neutral-to-mildly-bullish view, though call skew usually makes it harder to get for a credit.

The cheap directional butterfly

Now the other use. XYZ at $50, and you have a target: $60 within 45 days, from a chart pattern, a catalyst, whatever your process produces. A long $55 call costs $0.70. A butterfly centered on the target costs less and pays more if the target is hit.

Buy the $55 call at $0.70, sell two $60 calls at $0.15, buy the $65 call at $0.04. Debit $0.44.

Max loss $44, max profit $456, a payout of more than 10 to 1 at the target. The cost is the upside beyond $63: the long call keeps making money through $70 and the butterfly gives it all back. If your process says "$60, then I do not know," the butterfly is the honest expression of that. If it says "$60 at least," buy the call.

Probability check, as always. $60 is about 1.9 standard deviations away; the chance of finishing inside $55.44–$64.56 is roughly 13%, and the average profit inside is about $2.30. Expectancy: 0.13 × $230 − 0.87 × $44 ≈ −$8, near zero. The 10:1 payout is fair compensation for a 1-in-8 shot. What the structure adds is cost control: you can hold the view for $44 instead of $70, and be wrong many times for the price of being right once.

Two practical notes. The far wing ($65 call at $0.04) is often quoted $0.02 bid / $0.06 ask; the whole butterfly should be entered as one order at a net price, never legged. And out-of-the-money butterflies keep almost none of their value until the last week even when the stock is heading toward the target, because the two short $60 calls hold their extrinsic value; a butterfly that is "working" can show a loss for weeks. Judge it at expiration or at a set multiple of the debit, not day to day.

Key idea: A broken-wing butterfly is a near-the-money debit spread financed by a wider, further-out credit spread; it removes risk on one side, collects a small credit, and caps the worst case at the difference in wing widths. An out-of-the-money butterfly centered on a target is the cheapest way to hold a price-and-date view, paying 10:1 or more at the pin in exchange for giving up everything beyond it.

Try it: Build the 47/44/40 broken-wing put butterfly in the options profit calculator and confirm the credit, max loss and lower breakeven. Then build a symmetric 47/44/41 butterfly and note the debit and the loss on a rally. Finally, pick a target price on a stock you follow and price the butterfly centered on it against the single call at the lower wing; compare max loss, payoff at the target, and payoff 10% beyond it.

Recap

• A broken-wing butterfly widens one wing so the structure nets a credit; risk on the narrow side disappears and the max loss is the difference in wing widths minus the credit.
• 47/44/40 put broken wing on a $50 stock: credit $0.10, max profit $310 at $44, max loss $90 below $40.90, nothing to lose on a rally.
• Think of it as a debit spread near the money paid for by a wider credit spread further out; check how your broker margins it.
• An OTM butterfly centered on a target pays 10:1 or more at the pin for a small debit, with expectancy near zero and no upside beyond the far wing.
• Enter as one order; judge OTM butterflies at expiration or a debit multiple, since they show little value until the final week.