Let’s dive deep into a comprehensive definition of a long put butterfly, a neutral options strategy designed for investors who expect the price of an underlying asset to stay relatively close to a specific strike price by the time the options expire. It’s a limited risk, limited reward strategy that aims to profit from this lack of significant price movement, specifically using put options.

Core Concept:

A long put butterfly is constructed by combining three put option contracts with the same expiration date but three different strike prices, all equidistant from each other. It involves:

1. Buying one put option with a lower strike price. This is the lower “wing” of the butterfly.
2. Selling two put options with a middle strike price. This is the “body” of the butterfly.
3. Buying one put option with a higher strike price. This is the upper “wing” of the butterfly.

The middle strike price (where you sell two puts) is the point of maximum potential profit, and it represents the price level you expect the underlying asset to be near at expiration. The lower and upper strikes act as the breakeven points and define the range of profitability.

Construction Example:

Suppose the underlying asset is trading at $50. A typical long put butterfly might be constructed with the following options, all with the same expiration date and a $5 width between strikes:

• Buy 1 Put Option with a $45 strike price.
• Sell 2 Put Options with a $50 strike price.
• Buy 1 Put Option with a $55 strike price.

Net Debit:

Establishing a long put butterfly typically results in a net debit, meaning you pay more to buy the two outer put options than you receive from selling the two middle put options. This net debit represents the maximum potential loss of the strategy (excluding brokerage commissions).

Profit and Loss Profile:

The profit and loss diagram of a long put butterfly resembles a peaked tent or an inverted “V” shape, with the peak at the middle strike price.

• Maximum Potential Profit: Occurs when the price of the underlying asset expires exactly at the middle strike price ($50 in our example). At this point:

  • The $45 put is in-the-money by $5.
  • The two $50 short puts expire worthless.
  • The $55 put expires worthless. The profit is the intrinsic value of the lower strike long put minus the initial net debit. So, Maximum Profit = (Higher Strike – Middle Strike) – Net Debit, or ($55 – $50) – Net Debit = $5 – Net Debit.

• Maximum Potential Loss: Limited to the initial net debit paid to establish the spread. This occurs if the price of the underlying asset expires at or below the lower strike price ($45) or at or above the higher strike price ($55). In these scenarios, the value of the long puts is offset by the obligation of the short puts, resulting in a net value equal to the initial cost (the debit).

• Breakeven Points: There are typically two breakeven points for a long put butterfly:

  • Lower Breakeven: Lower strike price plus the net debit. In our example, if the net debit was $1.50, the lower breakeven would be $45 + $1.50 = $46.50.
  • Upper Breakeven: Upper strike price minus the net debit. In our example, the upper breakeven would be $55 – $1.50 = $53.50.

The position is profitable if the underlying asset price expires between these two breakeven points, with maximum profit at the middle strike.

Why Use a Long Put Butterfly?

• Expectation of Low Volatility/Minimal Price Movement Around a Specific Price: This strategy is ideal when an investor has a strong conviction that the underlying asset’s price will be very close to a particular strike price by expiration.
• Lower Capital Requirement Compared to a Short Straddle/Strangle: While also betting on low volatility, a long put butterfly has a defined and limited maximum loss, unlike short straddles or strangles which have potentially unlimited losses.
• Defined Risk and Reward: Both the maximum potential profit and the maximum potential loss are known at the time the trade is entered.

Key Considerations:

• Time Decay (Theta): Time decay generally works against a long put butterfly. As the expiration date approaches, the value of the purchased outer put options will decline, eroding the potential profit if the price doesn’t move precisely to the middle strike. However, the short puts also experience time decay, which can partially offset this.
• Volatility (Vega): A decrease in implied volatility after the spread is established is generally beneficial for a long put butterfly, as it reduces the value of all the options, and the net effect can be positive if the price is near the middle strike. Conversely, an increase in implied volatility can be detrimental.
• Accuracy of Price Prediction: The strategy’s profitability is highly dependent on the underlying asset price expiring very close to the middle strike price. Even small deviations can significantly reduce or eliminate profits.
• Limited Profit Potential: The maximum profit is capped at the difference between the strikes minus the net debit.

Managing a Long Put Butterfly:

• Monitoring Price Movement: Closely tracking the underlying asset’s price relative to the middle strike price is crucial as expiration approaches.
• Taking Profits Early: If the price moves close to the middle strike price with significant time remaining, you might consider closing the position early to realize a portion of the maximum potential profit and avoid the risk of the price moving away before expiration.
• Rolling the Spread: If the price moves significantly away from the middle strike but there’s still time until expiration, you might consider “rolling” the spread by closing the existing positions and opening new ones with different strike prices or expiration dates, although this can be complex and may not always be advantageous.

Similar Strategies:

• Long Call Butterfly: Constructed with calls instead of puts, it has the same profit/loss profile but is used when a trader expects the price to stay near a specific strike price but wants to profit from a potential upward move (or lack of downward move).
• Iron Butterfly: A similar neutral strategy using both calls and puts, often established for a net credit and also profiting from low volatility around a central strike price.

In Conclusion:

The long put butterfly is a specialized options strategy for traders with a very specific and often short-term outlook on an underlying asset’s price. It offers a defined risk and reward scenario, with the maximum profit realized if the price lands precisely at the middle strike price at expiration. However, it is sensitive to time decay and requires accurate price prediction to be profitable. It’s a strategy best used when there is a high conviction of minimal price movement around a specific level.