# Long butterfly spread with calls

• The Options Institute at CBOE®

### Goal

To profit from neutral stock price action near the strike price of the short calls (center strike) with limited risk.

### Explanation

#### Example of long butterfly spread with calls

 Buy 1 XYZ 95 call at 6.40 (6.40) Sell 2 XYZ 100 calls at 3.30 6.60 Buy 1 XYZ 105 call at 1.45 (1.45) Net cost = (1.25)

A long butterfly spread with calls is a three-part strategy that is created by buying one call at a lower strike price, selling two calls with a higher strike price and buying one call with an even higher strike price. All calls have the same expiration date, and the strike prices are equidistant. In the example above, one 95 Call is purchased, two 100 Calls are sold and one 105 Call is purchased. This strategy is established for a net debit, and both the potential profit and maximum risk are limited. The maximum profit is realized if the stock price is equal to the strike price of the short calls (center strike) on the expiration date. The maximum risk is the net cost of the strategy including commissions and is realized if the stock price is above the highest strike price or below the lowest strike price at expiration.

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.

### Maximum profit

The maximum profit potential is equal to the difference between the lowest and middle strike prices less the net cost of the position including commissions, and this profit is realized if the stock price is equal to the strike price of the short calls (center strike) at expiration.

In the example above, the difference between the lowest and middle strike prices is 5.00, and the net cost of the strategy is 1.25, not including commissions. The maximum profit, therefore, is 3.75 less commissions.

### Maximum risk

The maximum risk is the net cost of the strategy including commissions, and there are two possible outcomes in which a loss of this amount is realized. If the stock price is below the lowest strike price at expiration, then all calls expire worthless and the full cost of the strategy including commissions is lost. Also, if the stock price is above the highest strike price at expiration, then all calls are in the money and the butterfly spread position has a net value of zero at expiration. As a result, the full cost of the position including commissions is lost.

### Breakeven stock price at expiration

There are two breakeven points. The lower breakeven point is the stock price equal to the lowest strike price plus the cost of the position including commissions. The upper breakeven point is the stock price equal to the highest strike price minus the cost of the position.

### Profit/Loss diagram and table: long butterfly spread with calls

 Buy 1 XYZ 95 call at 6.40 (6.40) Sell 2 XYZ 100 calls at 3.30 6.60 Buy 1 XYZ 105 call at 1.45 (1.45) Net cost = (1.25)
Stock Price at Expiration Long 1 95 Call Profit/(Loss) at Expiration Short 2 100 Calls Profit/(Loss) at Expiration Long 1 105 Call Profit/(Loss) At Expiration Net Profit/(Loss) at Expiration
110 +8.60 (13.40) +3.55 (1.25)
105 +3.60 (3.40) (1.45) (1.25)
100 (1.40) +6.60 (1.45) +3.75
95 (6.40) +6.60 (1.45) (1.25)
90 (6.40) +6.60 (1.45) (1.25)

### Appropriate market forecast

A long butterfly spread with calls realizes its maximum profit if the stock price equals the center strike price on the expiration date. The forecast, therefore, can either be “neutral” or “modestly bullish,” depending on the relationship of the stock price to the center strike price when the position is established.

If the stock price is at or near the center strike price when the position is established, then the forecast must be for unchanged, or neutral, price action.

If the stock price is below the center strike price when the position is established, then the forecast must be for the stock price to rise to the center strike price at expiration (modestly bullish).

While one can imagine a scenario in which the stock price is above the center strike price and a long butterfly spread with calls would profit from bearish stock price action, it is most likely that another strategy would be a more profitable choice for a bearish forecast.

### Strategy discussion

A long butterfly spread with calls is the strategy of choice when the forecast is for stock price action near the center strike price of the spread, because long butterfly spreads profit from time decay. However, unlike a short straddle or short strangle, the potential risk of a long butterfly spread is limited. The tradeoff is that a long butterfly spread has a much lower profit potential in dollar terms than a comparable short straddle or short strangle. Also, the commissions for a butterfly spread are higher than for a straddle or strangle.

Long 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 buy butterfly spreads when they forecast that volatility will fall. Since the volatility in option prices tends to fall sharply after earnings reports, some traders will buy a butterfly spread immediately before the report. The potential profit is “high” in percentage terms and risk is limited to the cost of the position including commissions. Success of this approach to buying butterfly spreads requires that the stock price stay between the lower and upper strikes price of the butterfly. If the stock price rises or falls too much, then a loss will be incurred.

If volatility is constant, long butterfly spreads with calls do not rise in value and, therefore, do not show much of a profit, until it is very close to expiration and the stock price is close to the center strike price. In contrast, short straddles and short strangles begin to show at least some profit early in the expiration cycle as long as the stock price does not move out of the profit range.

Furthermore, while the potential profit of a long butterfly spread is a “high percentage profit on the capital at risk,” the typical dollar cost of one butterfly spread is “low.” As a result, it is often necessary to trade a large number of butterfly spreads if the goal is to earn a profit in dollars equal to the hoped-for dollar profit from a short straddle or strangle. Also, one should not forget that the risk of a long butterfly spread is still 100% of the cost of the position. Therefore, if the stock price begins to fall below the lowest strike price or to rise above the highest strike price, a trader must be ready to close out the position before a large percentage loss is incurred.

Patience and trading discipline are required when trading long butterfly spreads. Patience is required because this strategy profits from time decay, and stock price action can be unsettling as it rises and falls around the center strike price as expiration approaches. Trading discipline is required, because, as expiration approaches, “small” changes in 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 calls have positive deltas, and short calls have negative deltas.

Regardless of time to expiration and regardless of stock price, the net delta of a long butterfly spread remains close to zero until one or two days before expiration. If the stock price is below the lowest strike price in a long butterfly spread with calls, then the net delta is slightly positive. If the stock price is above the highest strike price, then the net delta is slightly negative. Overall, a long butterfly spread with calls does not profit from stock price change; it profits from time decay as long as the stock price is between the highest and lowest strikes.

### 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.

Long butterfly spreads with calls have a negative vega. This means that the price of a long butterfly spread falls when volatility rises (and the spread loses money). When volatility falls, the price of a long butterfly spread rises (and the spread makes money). Long butterfly spreads, therefore, should be purchased when volatility is “high” and forecast to decline.

### 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 long butterfly spread with calls has a net positive 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 negative 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 calls in a long butterfly spread have no risk of early assignment, the short calls do have such risk. Early assignment of stock options is generally related to dividends. Short calls that are assigned early are generally assigned on the day before the ex-dividend date. In-the-money calls whose time value is less than the dividend have a high likelihood of being assigned.

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

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

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

### Potential position created at expiration

The position at expiration of a long butterfly spread with calls depends on the relationship of the stock price to the strike prices of the spread. If the stock price is below the lowest strike price, then all calls expire worthless, and no position is created.

If the stock price is above the lowest strike and at or below the center strike, then the lowest strike long call is exercised. 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 above the center strike and at or below the highest strike, then the lowest-strike long call is exercised and the two middle-strike short calls are assigned. 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 above the highest strike, then both long calls (lowest and highest strikes) are exercised and the two short calls (middle strike) are assigned. The result is that 200 shares are purchased and 200 shares are sold. The net result is no position, although several stock buy and sell commissions have been incurred.

### Other considerations

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

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 highest strike and below the lowest strike look vaguely like the wings of a butterfly.