Introduction to the Put Broken Wing Butterfly

The Put Broken Wing Butterfly (BWB) is a sophisticated options trading strategy that offers a unique risk-reward profile, particularly appealing to professional traders seeking to generate income in a specific market environment. This strategy is a variation of the standard butterfly spread, but with a key modification that alters its characteristics and potential outcomes. By strategically 'breaking' one of the wings of the butterfly, traders can often establish the position for a net credit, thereby creating a trade with no upside risk and a high probability of profit.

Construction of a Put BWB

A standard put butterfly spread is constructed by selling two at-the-money (ATM) puts, buying one out-of-the-money (OTM) put, and buying one in-the-money (ITM) put. The distance between the ATM and OTM strikes is equal to the distance between the ATM and ITM strikes. This creates a symmetrical risk profile with a defined profit and loss zone.

The Put BWB, however, is constructed with unequal distances between the strikes. Specifically, the distance between the short puts and the further OTM long put is wider than the distance between the short puts and the closer OTM long put. This is why it is called a “broken wing” butterfly. The structure of a Put BWB is as follows:

• Sell two puts at strike price C.
• Buy one put at a higher strike price D.
• Buy one put at a lower strike price A, where the distance between C and A is smaller than the distance between D and C.

For example, a trader might sell two 100 puts, buy one 105 put, and buy one 90 put. In this case, the width of the upper wing (105-100) is 5 points, while the width of the lower wing (100-90) is 10 points. This asymmetry is the defining feature of the BWB.

Key Characteristics and Advantages

The primary advantage of the Put BWB is the ability to establish the position for a net credit. This is achieved by making the credit spread component of the structure (the wider wing) larger than the debit spread component (the narrower wing). When the premium received from selling the wider spread is greater than the premium paid for the narrower spread, the entire position is established for a credit. This has several important implications:

• No Upside Risk: If the underlying price rises above the highest strike at expiration, all options expire worthless, and the trader keeps the initial credit received. This is a significant advantage over a standard butterfly, which would result in a loss in this scenario.
• High Probability of Profit: Because the trade can be profitable even if the underlying moves against the desired direction (up), the probability of profit is significantly higher than that of a standard butterfly.
• Defined Risk: The maximum loss is still defined, although it is typically larger than the maximum loss of a standard butterfly.

Profit and Loss Profile

The profit and loss profile of a Put BWB is asymmetrical. The maximum profit is achieved if the underlying price is at the short strike (strike C) at expiration. The maximum loss is realized if the underlying price is at or below the lowest strike (strike A) at expiration.

Formulas

The key formulas for a Put BWB are as follows:

Maximum Profit:

Max Profit = (Strike D - Strike C) + Net Credit Received

Max Profit = (Strike D - Strike C) + Net Credit Received

Maximum Loss:

Max Loss = (Strike C - Strike A) - Max Profit

Max Loss = (Strike C - Strike A) - Max Profit

Breakeven Point:

Breakeven Point = Strike C - Max Profit

Breakeven Point = Strike C - Max Profit

Example

Let's consider a Put BWB on a stock trading at $102. A trader implements the following strategy:

• Sells 2 XYZ 100 Puts @ $2.50 each ($5.00 total credit)
• Buys 1 XYZ 105 Put @ $4.00
• Buys 1 XYZ 90 Put @ $0.50

Net Credit: $5.00 - $4.00 - $0.50 = $0.50 per share, or $50 per contract.

Maximum Profit:

Max Profit = (105 - 100) + 0.50 = $5.50 per share, or $550 per contract.

Max Profit = (105 - 100) + 0.50 = $5.50 per share, or $550 per contract.

This is achieved if XYZ is at $100 at expiration.

Maximum Loss:

Max Loss = (100 - 90) - 5.50 = $4.50 per share, or $450 per contract.

Max Loss = (100 - 90) - 5.50 = $4.50 per share, or $450 per contract.

This is realized if XYZ is at or below $90 at expiration.

Breakeven Point:

Breakeven Point = 100 - 5.50 = $94.50

Breakeven Point = 100 - 5.50 = $94.50

Data Table

The following table illustrates the profit and loss of this example at various stock prices at expiration:

As the table shows, the Put BWB offers a favorable risk-reward profile for traders who believe the underlying stock will remain within a certain range, with a slight bullish to neutral bias. The ability to structure the trade for a credit and eliminate upside risk makes it a effective tool in the professional trader's arsenal.