A broken-wing butterfly spread uses unequal distances between its three strike prices to create an asymmetric payoff. It keeps the familiar butterfly ratio: buy one option at the lower strike, sell two at the middle strike, and buy one at the upper strike, all with the same expiration.
The unequal wings change the trade’s economics. Moving one protective option farther away can reduce the entry cost or produce a net credit, but it also shifts more loss exposure to one side. A cheaper entry is not the same as a safer position.
This article focuses on call broken-wing butterflies, building on the balanced structure covered in long call butterfly spreads. The objective is to identify where the risk sits, calculate the expiration payoff, and separate that payoff from the risks of holding and closing the position.
How a Broken-Wing Butterfly Is Built
A balanced call butterfly has equally spaced strikes. Buying the 100 call, selling two 105 calls, and buying the 110 call creates two five-point wings. The middle strike is the body, where the position reaches its highest intrinsic value at expiration. The OIC long call butterfly strategy reference sets out this equal-wing construction.
A broken-wing version might replace the 110 call with the 115 call. The lower wing remains five points wide, but the upper wing becomes ten points wide. All four contracts remain in place; “broken” does not mean a protective option is missing.
Another way to read this position is as two overlapping vertical spreads:
- A five-point call debit spread: buy the 100 call and sell the 105 call.
- A ten-point call credit spread: sell another 105 call and buy the 115 call.
The wider credit spread can finance the narrower debit spread. However, above the highest strike, the credit spread’s ten-point liability exceeds the debit spread’s five-point value. That five-point difference is the exposure that the entry premium must offset.
These calculations assume matching underlyings, expirations, contract multipliers, settlement terms, and deliverables. Mixing adjusted and standard contracts can invalidate an otherwise tidy payoff calculation.
Worked Example: A Call Butterfly Opened for a Credit
Consider these hypothetical premiums, quoted per share, for options with the same expiration and a 100-share contract multiplier:
- Buy one 100 call for $7.00.
- Sell two 105 calls for $4.50 each.
- Buy one 115 call for $1.50.
The options sold bring in $9.00, while the options purchased cost $8.50. The position opens for a $0.50 credit, or $50 per butterfly. These are illustrative prices, not current market quotes. All results below exclude commissions, fees, financing, and taxes.
Maximum Profit
At an expiration price of $105, the 100 call has $5.00 of intrinsic value. Both short 105 calls and the long 115 call have zero intrinsic value.
Maximum profit = ($5.00 + $0.50) × 100 = $550.
That peak occurs at the middle strike, not throughout a broad price range. A finish above or below $105 produces a smaller profit, or a loss.
Maximum Expiration Loss
At $115 or higher, the lower call spread is worth $5.00, while the upper short call spread has a $10.00 liability. The combined intrinsic value is negative $5.00.
Maximum expiration loss = ($10.00 − $5.00 − $0.50) × 100 = $450.
The relevant amount is the difference between the wing widths, less the credit. Using the full ten-point width would overstate this position’s theoretical expiration loss. Using only the $50 entry credit would miss the risk entirely.
| Underlying price at expiration | Combined option intrinsic value | Profit or loss including $50 credit |
|---|---|---|
| $100 or below | $0 | $50 |
| $103 | $300 | $350 |
| $105 | $500 | $550 |
| $110.50 | −$50 | $0 |
| $112 | −$200 | −$150 |
| $115 or above | −$500 | −$450 |
Below $100, all options have zero intrinsic value and the credit remains. Above $105, the combined option value declines by $1 per share for each $1 increase in the underlying, until the upper protective call caps that decline at $115.
Calculating Profit, Loss, and Break-Even
For a call butterfly, label the strikes K1, K2, and K3, from lowest to highest. Let the lower width be K2 − K1 and the upper width be K3 − K2.
A general calculation starts with each option’s intrinsic value. Use D for the net entry debit per share, treating a credit as a negative debit:
Expiration profit per share = max(S − K1, 0) − 2 × max(S − K2, 0) + max(S − K3, 0) − D.
Here, S is the underlying price used for expiration settlement. Multiply the result by the contract multiplier and number of butterflies. This formula also handles unequal wings that face the other direction.
For the example’s wider upper wing and an entry credit C, the shorter formulas are:
- Maximum profit: (lower width + C) × multiplier.
- Maximum loss: (upper width − lower width − C) × multiplier, assuming a positive loss amount.
- Upper break-even: K2 + lower width + C, provided it falls between K2 and K3.
The example breaks even at $105 + $5 + $0.50 = $110.50. There is no lower break-even because the entire lower tail retains the entry credit before costs. The related guide to reading options spread payoff diagrams covers how to distinguish a profit peak from a flat tail.
If the same strikes instead cost a $0.40 debit, maximum profit would fall to $460 and maximum expiration loss would rise to $540. Its break-even prices would be $100.40 and $109.60. Below $100, the position would lose the $40 debit rather than retain a credit.
Unequal Wings Do Not Guarantee a Credit
A broken-wing butterfly describes strike spacing, not an entry price. The premiums determine whether the package trades for a debit or credit.
Moving the upper long call farther away generally reduces its purchase cost relative to a closer call, with other inputs unchanged. Whether that reduction is enough to turn the whole position into a credit depends on the prices of all three option series.
The opposite arrangement also exists: a wider lower wing and narrower upper wing. A 100/110/115 call butterfly has ten points below the body and five above it. It should not be assigned the credit-entry formulas from the earlier example. Cboe’s circular on complex-order price protections includes this unequal-wing call construction as a debit strategy when buying the wings and selling the body.
Put broken-wing butterflies use the same buy-one, sell-two, buy-one ratio. A put version with a wider lower wing can concentrate expiration loss below the body while retaining an entry credit above the highest strike. Calculate the actual legs rather than carrying call formulas across unchanged. Calls and puts with unequal wings need not have the same entry premium.
What Changes Before Expiration?
The expiration table is not a forecast of the price available when closing early. Before expiration, each option can retain time value, so reaching the body strike does not automatically deliver maximum profit.
The position’s net sensitivities come from adding the long options’ Greeks and subtracting twice the middle option’s Greeks. Unequal spacing changes those totals. A broken-wing butterfly is not automatically neutral, always helped by time decay, or always harmed by rising implied volatility.
Assess the current position and alternative underlying prices using delta, gamma, theta, and vega for options spreads. In particular, check whether the exposure changes sharply as the underlying approaches the short strike or the wider wing.
A useful stress test asks what the spread could cost to close after an adverse move, with less time remaining and different implied volatility. Testing only the favorable expiration peak leaves out the part of the trade most likely to demand a decision.
Execution: Trade the Package, Not Just the Displayed Credit
A net limit order lets the trader specify an acceptable package price while preserving the intended ratio. Cboe’s complex-order documentation describes executions within a net price and ratio, including partial executions that preserve the proportions.
For the example, the order ticket should show one long 100 call, two short 105 calls, and one long 115 call. Check the credit or debit designation before submission. A reversed ticket changes the strategy rather more than a typo should.
Placing the legs separately can leave a temporary position without the intended protection. It also allows prices to change between fills. A package order does not guarantee execution, and a displayed midpoint is not a promised fill.
Compare the executable entry and exit prices. A theoretical $50 credit offers little comfort if transaction costs and the cost of closing consume most of it.
Assignment, Expiration, and Account Risk
With American-style options, either short call can be assigned before expiration. The protective calls do not automatically exercise just because a short call is assigned. The resulting stock obligation may require action even though the original options package had a bounded expiration payoff; FINRA’s guidance on assignment in multi-leg positions addresses this separation.
Near the middle strike at expiration, uncertainty over whether zero, one, or both short calls are assigned can leave unwanted stock exposure. The $450 maximum loss calculation assumes the complete position’s expiration economics are realized. It is not a guarantee against losses on stock left after options expire or after protective legs are removed.
Check exercise style, settlement method, exercise deadlines, and account procedures before entry. Do not assume every index option or every equity option follows identical arrangements.
Buying-power requirements also deserve a separate check. Firms can impose higher margin requirements, and transaction costs can turn an apparent profit into a loss. These considerations are addressed in OCC’s options risk disclosure, including costs and margin.
Sizing and Managing the Unequal Risk
Size the example around its $450 theoretical expiration loss, plus costs and an allowance for execution uncertainty, rather than around the $50 received. Ten butterflies collect $500 but create $4,500 of theoretical expiration loss before costs.
Set an exit decision before entering. That might involve an acceptable closing cost, a change in the price outlook, or a deadline before expiration. No universal profit target or loss multiple follows from the strategy’s name.
Track the entire cash flow when adjusting. If the position opens for a $50 credit and later costs $125 to close, the realized loss is $75 before fees. Opening a replacement spread does not erase it. The distinction between closing and rolling an options spread matters when assessing the next trade.
A broken-wing butterfly can exchange a lower entry cost for greater exposure on one side while retaining a profit peak near the body. Judge that exchange using both tails, realistic execution prices, and settlement obligations. The entry credit is one number in that assessment, not the verdict.