# Short butterfly spread with puts

### Goal

To profit from a stock price move up or down beyond the highest or lowest strike prices of the position.

### Explanation

A short butterfly spread with puts is a three-part strategy that is created by selling one put at a higher strike price, buying two puts with a lower strike price and selling one put with an even lower strike price. All puts have the same expiration date, and the strike prices are equidistant. In the example one 105 Put is sold, two 100 Puts are purchased and one 95 Put is sold. This strategy is established for a net credit, and both the potential profit and maximum risk are limited. The maximum profit is equal to the net premium received less commissions, and it is realized if the stock price is above the higher strike price or below the lower strike price at expiration. The maximum risk equals the distance between the center and lower strike prices less the net premium received, and a loss of this amount incurred if the stock price is equal to the center strike price (long puts) on the expiration date.

This is an advanced strategy because the profit potential is small in dollar terms and because "costs" are high. Given that there are three strike prices, there are multiple commissions in addition to three bid-ask spreads when opening the position and again when closing it. As a result, it is essential to open and close the position at "good prices." It is important to ensure the risk/reward ratio including commissions is favorable or acceptable.

## Example of short butterfly spread with puts

 Sell 1 XYZ 105 put at 6.25 6.25 Buy 2 XYZ 100 puts at 3.15 each (6.30) Sell 1 XYZ 95 put at 1.25 1.45 Net credit = 1.20

### Maximum profit

The maximum profit potential is the net credit received less commissions, and there are two possible outcomes in which a profit of this amount is realized. If the stock price is above the highest strike price at expiration, then all puts expire worthless and the net credit is kept as income. Also, if the stock price is below the lowest strike price at expiration, then all puts are in the money and the butterfly spread position has a net value of zero. As a result, the net credit, 1.20, less commissions is kept as income.

### Maximum risk

The maximum risk is equal to the difference between the center and lowest strike prices less the net credit received minus commissions, and a loss of this amount is realized if the stock price is equal to the center strike price (long puts) at expiration.

In the example above, the difference between the center and lowest strike prices is 5.00, and the net credit received is 1.20, not including commissions. The maximum risk, therefore, is 3.80 less commissions.

### Breakeven stock price at expiration

There are 2 breakeven points. The lower breakeven point is the stock price equal to the lower strike short put plus the net credit. The upper breakeven point is the stock price equal to the higher strike short put minus the net credit.

### Profit/Loss diagram and table: short butterfly spread with puts

 Sell 1 XYZ 105 put at 6.25 6.25 Buy 2 XYZ 100 puts at 3.15 each (6.30) Sell 1 XYZ 95 put at 1.25 1.25 Net credit = 1.20
Stock Price at Expiration Short 1 105 Put Profit/(Loss) at Expiration Long 2 100 Puts Profit/(Loss) at Expiration Short 1 95 Put Profit/(Loss) At Expiration Net Profit/(Loss) at Expiration
110 +6.25 (6.30) +1.25 +1.20
105 +6.25 (6.30) +1.25 +1.20
100 +1.25 (6.30) +1.25 (3.80)
95 (3.75) +3.70 +1.25 +1.20
90 (8.75) +13.70 (3.75) +1.20

### Appropriate market forecast

A short butterfly spread with puts realizes its maximum profit if the stock price is above the higher strike or below the lower strike on the expiration date. The forecast, therefore, must be for "high volatility," i.e., a stock price move outside the range of the strike prices of the butterfly.

### Strategy discussion

A short butterfly spread with puts realizes its maximum profit if the stock price is above the higher strike or below the lower strike on the expiration date. The forecast, therefore, must be for "high volatility," i.e., a stock price move outside the range of the strike prices of the butterfly.

Butterfly spreads are sensitive to changes in volatility (see Impact of change in volatility). The net price of a butterfly spread falls when volatility rises and rises when volatility falls. Consequently some traders establish a short butterfly spread when they forecast that volatility is "low" and will rise. Since the volatility in option prices typically rises as an earnings announcement date approaches and then falls immediately after the announcement, some traders will sell a butterfly spread seven to ten days before an earnings report and then close the position on the day before the report. Success of this approach to selling butterfly spreads requires that either the volatility in option prices rises or that the stock price rises or falls outside the strike price range. If the stock price remains constant and if implied volatility does not rise, then a loss will be incurred.

Patience and trading discipline are required when trading short butterfly spreads. Patience is required because this strategy profits from stock price movement and/or rising implied volatility, and stock price action can be unsettling as it rises and falls between the lower and upper strike prices as expiration approaches. Trading discipline is required, because, as expiration approaches, "small" changes in the underlying stock price can have a high percentage impact on the price of a butterfly spread. Traders must, therefore, be disciplined in taking partial profits if possible and also in taking "small" losses before the losses become "big."

### Impact of stock price change

"Delta" estimates how much a position will change in price as the stock price changes. Long puts have negative deltas, and short puts have positive deltas.

Regardless of time to expiration and regardless of stock price, the net delta of a butterfly spread remains close to zero until one or two days before expiration. If the stock price is above the highest strike price in a short butterfly spread with puts, then the net delta is slightly positive. If the stock price is below the lowest strike price, then the net delta is slightly negative. Overall, a short butterfly spread with puts profits from a stock price rise above the higher strike price or a fall below the lower strike price.

### Impact of change in volatility

Volatility is a measure of how much a stock price fluctuates in percentage terms, and volatility is a factor in option prices. As volatility rises, option prices tend to rise if other factors such as stock price and time to expiration remain constant. Long options, therefore, rise in price and make money when volatility rises, and short options rise in price and lose money when volatility rises. When volatility falls, the opposite happens; long options lose money and short options make money. "Vega" is a measure of how much changing volatility affects the net price of a position.

Short butterfly spreads with puts have a positive vega. This means that the price of a short butterfly spread falls when volatility rises (and the spread makes money). When volatility falls, the price of a short butterfly spread rises (and the spread loses money). Short butterfly spreads, therefore, should be established when volatility is "low" and forecast to rise.

### Impact of time

The time value portion of an option's total price decreases as expiration approaches. This is known as time erosion. "Theta" is a measure of how much time erosion affects the net price of a position. Long option positions have negative theta, which means they lose money from time erosion, if other factors remain constant; and short options have positive theta, which means they make money from time erosion.

A short butterfly spread with puts has a net negative theta as long as the stock price is in a range between the lowest and highest strike prices. If the stock price moves out of this range, however, the theta becomes positive as expiration approaches.

### Risk of early assignment

Stock options in the United States can be exercised on any business day, and holders of short stock option positions have no control over when they will be required to fulfill the obligation. Therefore, the risk of early assignment is a real risk that must be considered when entering into positions involving short options.

While the long puts (center strike price) in a short butterfly spread have no risk of early assignment, the short puts do have such risk. Early assignment of stock options is generally related to dividends. Short puts that are assigned early are generally assigned on the ex-dividend date. In-the-money puts whose time value is less than the dividend have a high likelihood of being assigned.

If one short put is assigned (most likely the highest-strike put), then 100 shares of stock are purchased and the long puts (center strike price) and the other short put remain open. If a long stock position is not wanted, it can be closed in one of two ways. First, 100 shares can be sold in the marketplace. Second, the long 100-share position can be closed by exercising one of the center-strike long puts. Remember, however, that exercising a long put will forfeit the time value of that put. Therefore, it is generally preferable to sell shares to close the long stock position and then sell the long put. This two-part action recovers the time value of the long put. One caveat is commissions. Selling shares to close the long stock position and then selling the long put is only advantageous if the commissions are less than the time value of the long put.

If both of the short puts are assigned, then 200 shares of stock are purchased and the long puts remain open. Again, if a long stock position is not wanted, it can be closed in one of two ways. Either 200 shares can be sold in the market place, or both long puts can be exercised. However, as discussed above, since exercising a long put forfeits the time value, it is generally preferable to sell shares to close the long stock position and then sell the long puts. The caveat, as mentioned above, is commissions. Selling shares to close the long stock position and then selling the long puts is only advantageous if the commissions are less than the time value of the puts.

Note, however, that whichever method is used, selling stock and selling a long put or exercising a long put, the date of the stock sale will be one day later than the date of the purchase. This difference will result in additional fees, including interest charges and commissions. Assignment of a short option might also trigger a margin put if there is not sufficient account equity to support the stock position created.

### Potential position created at expiration

The position at expiration of a short butterfly spread with puts depends on the relationship of the stock price to the strike prices of the spread. If the stock price is above the highest strike price, then all puts expire worthless, and no position is created.

If the stock price is below the highest strike and at or above the center strike, then the highest strike short put is assigned. The result is that 100 shares of stock are purchased and a stock position of long 100 shares is created.

If the stock price is below the highest strike and at or above the center strike, then the highest-strike short put is assigned and the two center-strike long puts are exercised. The result is that 100 shares are purchased and 200 shares are sold. The net result is a short position of 100 shares.

If the stock price is below the lowest strike, then both long puts are exercised and both short puts are assigned. The result is that 200 shares are sold and 200 shares are purchased. The net result is no position, although several stock sell and buy commissions have been incurred.

### Other considerations

A short butterfly spread with puts can also be described as the combination of a bull put spread and a bear put spread. The bull put spread is the short highest-strike put combined with one of the long center-strike puts, and the bear put spread is the other long center-strike put combined with the short lowest-strike put.

The term "butterfly" in the strategy name is thought to have originated from the profit-loss diagram. The peak in the middle of the diagram of a long butterfly spread looks vaguely like a the body of a butterfly, and the horizontal lines stretching out above the higher strike and below the lower strike look vaguely like the wings of a butterfly. A short butterfly spread looks vaguely like an upside-down butterfly.

Article copyright 2013 by Chicago Board Options Exchange, Inc (CBOE). Reprinted with permission from CBOE. The statements and opinions expressed in this article are those of the author. Fidelity Investments cannot guarantee the accuracy or completeness of any statements or data.

Options trading entails significant risk and is not appropriate for all investors. Certain complex options strategies carry additional risk. Before trading options, please read Characteristics and Risks of Standardized Options. Supporting documentation for any claims, if applicable, will be furnished upon request.

There are additional costs associated with option strategies that call for multiple purchases and sales of options, such as spreads, straddles, and collars, as compared with a single option trade.

Greeks are mathematical calculations used to determine the effect of various factors on options.

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