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

In the example above, one 110 Put is sold, the 105 strike is skipped, three 100 Puts are purchased, and two 95 Puts are sold. The position is established for a net debit, 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 with puts

 Sell 1 XYZ 110 put at 8.25 8.25 Buy 3 XYZ 100 puts at 2.10 each (6.30) Sell 2 XYZ 95 put at 0.70 each 1.40 Net credit = 3.35

### Maximum profit

The maximum profit potential is 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 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 Christmas tree spread 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 difference between the highest strike price (short put) and the strike price of the three long puts minus the initial net credit including commissions. This loss is realized if the stock price is at the strike price of the long puts at expiration.

In the example above, the difference between the highest strike price and the strike price of the long puts is 10.00, and the initial net credit is 3.35, not including commissions. The maximum risk, therefore, is 6.65 less commissions.

### Breakeven stock price at expiration

There are two breakeven points. The upper breakeven point is the stock price equal to the highest strike price minus the net credit received for the position less commissions. In the example above, the highest strike is 110 and the net credit received for the position is 3.35. The upper breakeven point at expiration, therefore, is 106.65 (110.00 − 3.35).

The lower breakeven point is the stock price equal to the lowest strike price plus one-half of the net credit received. In the example above, the lowest strike is 95 and the net credit received is 3.35, so the lower breakeven point at expiration is 96.675 (95.00 +3.35/2).

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

 Sell 1 XYZ 110 put at 8.25 8.25 Buy 3 XYZ 100 puts at 2.10 each (6.30) Sell 2 XYZ 95 put at 0.70 each 1.40 Net credit = 3.35
Stock Price at Expiration Short 1 110 Put Profit/(Loss) at Expiration Long 3 100 Puts Profit/(Loss) at Expiration Short 2 95 Puts Profit/(Loss) at Expiration Net Profit/(Loss) at Expiration
115 +8.25 (6.30) +1.40 +3.35
110 +8.25 (6.30) +1.40 +3.35
105 +3.25 (6.30) +1.40 (1.65)
100 (1.75) (6.30) +1.40 (6.65)
95 (6.75) +8.70 +1.40 +3.35
90 (11.75) +23.70 (8.60) +3.35

### Appropriate market forecast

A short Christmas Tree spread with puts 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 puts), 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 with puts 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 is limited. Also, the commissions for a Christmas tree spread are considerably higher than for a straddle or strangle. The tradeoff is that a short Christmas tree spread has breakeven points much closer to the current stock price than a comparable long straddle or long strangle.

Short Christmas tree spreads differ from short butterfly spreads in two ways. First, the credit received for a short Christmas tree spread, and therefore the profit potential, is higher than for a short butterfly spread. Second, however, the range of loss for a short Christmas tree is wider than for a butterfly. Short Christmas tree spreads also differ from short skip-strike butterfly spreads. Short Christmas tree spreads have lower risk than short skip-strike butterfly spreads, but they also have lower profit potential.

Christmas tree spreads 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 falls when implied volatility rises and rises when implied volatility falls. Consequently some traders open short Christmas tree spreads 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 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 spreads 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 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 strike price of the short puts 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. 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.

The net delta of a Christmas tree spread 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 with puts, 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 with puts 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 puts.

### 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 spreads with puts have a positive vega. This means that the price of a Christmas tree spread falls when volatility rises (and the short spread makes money). When volatility falls, the price of a Christmas tree spread rises (and the short spread loses money). Short Christmas tree spreads, 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 with puts has a net negative theta if the stock price is near the strike price of the long puts. If the stock price moves away from this strike price, 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 in a short Christmas tree 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), then 100 shares of stock are purchased and the long puts and the other short puts 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 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 more than one of the short puts is assigned – there are a total of three short puts – then either more shares can be sold or one or both of the lowest-strike 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 long puts.

Note, however, that whichever method is used, selling stock and selling the long put or exercising the 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 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 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 (short put) and at or above the strike price of the long puts, 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 strike price of the long puts and at or above the lowest strike, then the highest-strike short put is assigned and the three long puts are exercised. The result is that 100 shares are purchased and 300 shares are sold. The net result is a position of short 200 shares.

If the stock price is below the lowest strike, then all three long puts are exercised and all three short puts 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 with puts can also be described as the combination of a “wide” bull put spread and two “narrow” bear put spreads. In the example above, the wide bull put spread is comprised of the short 110 Put and one of the long 100 Puts. The narrow bear put spreads is comprised of the other two long 100 Puts and the two short 95 Puts.

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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