The Butterfly

The long butterfly spread is a three-leg strategy that is appropriate for a neutral forecast � when you expect the underlying stock price (or index level) to change very little over the life of the options. A butterfly can be implemented using either call or put options. For simplicity, the following explanation discusses the strategy using call options.

A long call butterfly spread consists of three legs with a total of four options: long one call with a lower strike, short two calls with a middle strike and long one call of a higher strike. All the calls have the same expiration, and the middle strike is halfway between the lower and the higher strikes. The position is considered "long" because it requires a net cash outlay to initiate.

When a butterfly spread is implemented properly, the potential gain is higher than the potential loss, but both the potential gain and loss will be limited.

The total cost of a long butterfly spread is calculated by multiplying the net debit (cost) of the strategy by the number of shares each contract represents. A butterfly will break-even at expiration if the price of the underlying is equal to one of two values. The first break-even value is calculated by adding the net debit to the lowest strike price. The second break-even value is calculated by subtracting the net debit from the highest strike price. The maximum profit potential of a long butterfly is calculated by subtracting the net debit from the difference between the middle and lower strike prices. The maximum risk is limited to the net debit paid for the position.

Butterfly spreads achieve their maxim profit potential at expiration if the price of the underlying is equal to the middle strike price. The maximum loss is realized when the price of the underlying is below the lowest strike or above the highest strike at expiration.

As with all advanced option strategies, butterfly spreads can be broken down into less complex components. The long call butterfly spread has two parts, a bull call spread and a bear call spread. The following example, which uses options on the Dow Jones Industrial Average (DJX), illustrates this point.
DJX trading @ $75.28
Buy 1 DJX 72 Call @ $6.10 x 100 $610 (wing)
Sell 2 DJX 75 Call @ $4.10 x 100 ($820) (butterfly body)
Buy 1 DJX 78 Call @ $2.60 x 100 $260 (wing)
Net Debit from Trade $50 ($870 - $820)

In this example the total cost of the butterfly is the net debit ($.50) x the number of shares per contract (100). This equals $50, not including commissions. Please note that this is a three-legged trade, and there will be a commission charged for each leg of the trade.

An expiration profit and loss graph for this strategy is displayed below.
Butterfly Chart Butterfly Graph

*The profit/loss above does not factor in commissions, interest, tax, or margin considerations.

This profit and loss graph allows us to easily see the break-even points, maximum profit and loss potential at expiration in dollar terms. The calculations are presented below.

The two break-even points occur when the underlying equals 72.50 and 77.50. On the graph these two points turn out to be where the profit and loss line crosses the x-axis.
First Break-even Point = Lowest Strike (72) + Net Debit (.50) = 72.50
Second Break-even Point = Highest Strike (78) - Net Debit (.50) = 77.50

The maximum profit can only be reached if the DJX is equal to the middle strike (75) on expiration. If the underlying equals 75 on expiration, the profit will be $250 less the commissions paid.
Maximum Profit = Middle Strike (75) - Lower Strike (72) - Net Debit (.50) = 2.50

$2.50 x Number of Shares per Contract (100) = $250 less commissions

The maximum loss, in this example, results if the DJX is below the lower strike (72) or above the higher strike (78) on expiration. If the underlying is less than 72 or greater than 78 the loss will be $50 plus the commissions paid.
Maximum Loss = Net Debit (.50)

$.50 x Number of Shares per Contract (100) = $50 plus commissions

By looking at the components of the total position, it is easy to see the two spreads that make up the butterfly.

Bull call spread: Long 1 of the November 72 calls & Short one of the November 75 calls

Bear call spread: Short one of the November 75 calls & Long 1 on the November 78 calls
Summary

A long butterfly spread is used by investors who forecast a narrow trading range for the underlying security, and who are not comfortable with the unlimited risk that is involved with being short a straddle. The long butterfly is a strategy that takes advantage of the time premium erosion of an option contract, but still allows the investor to have a limited and known risk.