# Short Christmas tree spread variation with calls

### Goal

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

### Explanation

A short Christmas tree spread variation with calls is a three-part strategy involving six calls. If there are four strike prices, A, B, C and D, with A being the lowest, a short Christmas tree spread variation with calls is created by selling two calls at strike A, buying three calls at strike B, skipping strike C and selling one call at strike D. All calls have the same expiration date, and the four strike prices are equidistant.

In the example above, two 95 Calls are sold, three 100 Calls are purchased, the 105 strike is skipped, and one 110 Call is sold. The position is established for a net credit, and both the potential profit and maximum risk are limited.

This is an advanced strategy because “costs” are high. Given three strike prices and six options, there are multiple commissions and 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 also important to consider the per-contract commission rate since commissions will impact the return on investment.

## Example of short christmas tree spread variation with calls

 Sell 2 XYZ 95 calls at 8.40 16.80 Buy 3 XYZ 100 calls at 4.80 each (14.40) Sell 1 XYZ 110 call at 0.95 0.95 Net credit = 3.35

### Maximum profit

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

### Maximum risk

The maximum risk is equal to the two times difference between the lowest strike price (short two calls) and the strike price of the three long calls minus the initial net credit including commissions. This loss is realized if the stock price is at the strike price of the long calls at expiration.

In the example above, the difference between the lowest strike price and the strike price of the long calls is 5.00, and the initial net credit is 3.35, not including commissions. The maximum risk, therefore, is (2 x 5) – 3.35 = 6.65 less commissions.

### 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 one-half of the net credit received for the position including commissions. In the example above, the lowest strike is 95 and the net credit for the position is 3.35. The lower breakeven point at expiration, therefore, is 96.675 (95.00 + 3.35/2).

The upper breakeven point is the stock price equal to the highest strike price minus the net credit for the position. In the example above, the highest strike is 110 and the net credit for the position is 3.35, so the upper breakeven point at expiration is 106.65 (110.00 – 3.35).

### Profit/Loss diagram and table: short Christmas tree spread variation with calls

 Sell 2 XYZ 95 calls at 8.40 16.80 Buy 3 XYZ 100 calls at 4.80 each (14.40) Sell 1 XYZ 110 call at 0.95 0.95 Net credit = 3.35
Stock Price at Expiration Short 2 95 Calls Profit/(Loss) at Expiration Long 3 100 Calls Profit/(Loss) at Expiration Short 1 110 Calls Profit/(Loss) at Expiration Net Profit/(Loss) at Expiration
115 (23.20) +30.60 (4.05) +3.35
110 (13.20) +15.60 +0.95 +3.35
105 (3.20) +0.60 +0.95 (1.65)
100 +6.80 (14.40) +0.95 (6.65)
95 +16.80 (14.40) +0.95 +3.35
90 +16.80 (14.40) +0.95 +3.35

### Appropriate market forecast

A short Christmas tree spread variation with calls realizes its maximum profit if the stock price is above the highest strike or below the lowest strike on the expiration date. The forecast, therefore, must be for “high volatility,” i.e., a price move outside the range of the strike prices of the spread.

Depending on the relationship of the stock price to the point of maximum loss (strike price of the three long calls), the forecast can have a directional bias. In the example above, if the stock price is 100 when the spread is established, then the stock must fall only five points to reach the downside point of maximum profit; however, the stock must rise 10 points to reach the upside point of maximum profit.

### Strategy discussion

A short Christmas tree spread variation with calls is the strategy of choice when the forecast is for a stock price move outside the range of the highest and lowest strike prices. Unlike a long straddle or long strangle, however, the profit potential of a short Christmas tree spread variation is limited. Also, the commissions for a Christmas tree spread variation are considerably higher than for a straddle or strangle. The tradeoff is that a short Christmas tree spread variation has breakeven points much closer to the current stock price than a comparable long straddle or long strangle.

Short Christmas tree spread variations differ from short butterfly spreads. The net credit received for a short Christmas tree spread variation is higher than for a short butterfly spread, but the range of loss for a short Christmas tree variation is wider than for a short butterfly. Short Christmas tree spread variations also differ from short skip-strike butterfly spreads and short standard Christmas tree spreads. Relative to short skip-strike-strike butterfly spreads, the net credit spread received for a short Christmas tree variation is higher, but the maximum profit potential is lower. Relative to short standard Christmas tree spreads, short Christmas tree variations have greater profit potential (the net credit is higher), but the points of breakeven and maximum profit are closer to lower strike price. Short Christmas tree variations therefore, have a statistically higher chance of losing money than short standard Christmas tree spreads.

Christmas tree spread variations are sensitive to changes in the volatility in option prices, which is known as “implied volatility” (see Impact of Change in Volatility). The net price of a Christmas tree spread variation falls when implied volatility rises and rises when implied volatility falls. Consequently some traders open short Christmas tree spread variations when they forecast that implied volatility will rise. Since implied volatility typically rises as an earnings announcement date approaches and then falls immediately after the announcement, some traders will sell a Christmas tree spread variation 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 Christmas tree spread variations requires that either implied volatility 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 Christmas tree spread variations. Patience is required because this strategy profits from a sharply rising or falling stock price, and stock price action can be unsettling as it rises and falls around the highest or lowest 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 Christmas tree spread variation. 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. Short calls have positive deltas, and short calls have negative deltas.

The net delta of a short Christmas tree spread variation remains close to zero until two weeks or so before expiration. As expiration approaches, if the stock price is below the lowest strike price in a short Christmas tree spread variation with calls, then the net delta is slightly negative. If the stock price is above the highest strike price, then the net delta is slightly positive. Overall, a short Christmas tree spread variation with calls profits from a sharply rising or sharply falling stock price and is hurt by time decay if the stock price is near the strike price of the long calls.

### 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 Christmas tree spread variations with calls have a positive vega. This means that the price of a Christmas tree spread variation falls when volatility rises (and the short spread makes money). When volatility falls, the price of a Christmas tree spread variation rises (and the short spread loses money). Short Christmas tree spread variations, therefore, should be opened 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 Christmas tree spread variation with calls has a net negative theta, and the position loses money, if the stock price is near the strike price of the long calls. If the stock price moves away from this strike price, however, the theta becomes positive as expiration approaches and the position makes money.

### 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 short Christmas tree spread variation with calls 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 (most likely one of the lowest-strike calls), then 100 shares of stock are sold short and the long calls and the other short calls 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 one of the long calls. 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 more than one of the short calls is assigned – there are a total of three short calls – then either more shares can be purchased or the appropriate number of 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 selling 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 short Christmas tree spread variation 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 (short two calls) and at or below the strike price of the three long calls, then the lowest-strike two short calls are assigned and the other calls expire. The result is that 200 shares of stock are sold short and a stock position of short 200 shares is created.

If the stock price is above the strike of the three long calls and at or below the highest strike (short one call), then the lowest-strike short calls are assigned, the three long calls are exercised and the highest-strike call expires. The result is that 200 shares are sold and 300 shares are purchased. The net result is a position of long 100 shares.

If the stock price is above the highest strike, then all three long calls are exercised and all three short calls are assigned. The result is that 300 shares are purchased and 300 shares are sold. The net result is no position, although several stock buy and sell commissions have been incurred.

### Other considerations

A short Christmas tree spread variation with calls can also be described as the combination of two “narrow” bear call spreads and one “wide” bull call spread. In the example above, the narrow bear call spreads are comprised of the two short 95 Calls and two of the long 100 Calls. The wide bull call spread is comprised of the other long 100 Call and the short 110 Call.

The term “Christmas tree” in the strategy name is thought to have originated from the profit-loss diagram. If the diagram is turned vertically, the uneven bulge on the diagram looks vaguely like one side of a Christmas tree.

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.

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