# Short Christmas tree spread variation with puts

- The Options Institute at CBOE®

### Goal

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

### Explanation

#### Example of short christmas tree spread variation with puts

Sell 2 XYZ 110 puts at 8.25 | 16.50 |

Buy 3 XYZ 105 puts at 4.65 | (13.95) |

Sell 1 XYZ 95 put at 0.70 | 0.70 |

Net credit = | 3.25 |

A short Christmas tree spread variation 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 variation with puts is created by selling two puts at strike D, buying three puts at strike C, skipping strike B and selling one put at strike A. All puts have the same expiration date, and the four strike prices are equidistant.

In the example above, two 110 Puts are sold, three 105 Puts are purchased, the 100 strike is skipped, and one 95 Put 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.

### 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 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 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 two times the difference between the highest strike price (short two puts) 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 5.00, and the initial net credit is 3.25, not including commissions. The maximum risk, therefore, is (2 x 5) – 3.25 = 6.75 plus 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 one-half the net credit received for the position including commissions. In the example above, the highest strike is 110 and the net credit received for the position is 3.25. The upper breakeven point at expiration, therefore, is 108.375 (110.00 − 3.25/2).

The lower breakeven point is the stock price equal to the lowest strike price plus the net credit received. In the example above, the lowest strike is 95 and the net credit received is 3.25, so the lower breakeven point at expiration is 98.25 (95.00 +3.25).

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

Sell 2 XYZ 110 puts at 8.25 each | 16.50 |

Buy 3 XYZ 105 puts at 4.65 each | (13.95) |

Sell 1 XYZ 95 put at 0.70 | 0.70 |

Net credit = | 3.25 |

Stock Price at Expiration | Short 2 110 Put Profit/(Loss) at Expiration | Long 3 105 Puts Profit/(Loss) at Expiration | Short 1 95 Put Profit/(Loss) at Expiration | Net Profit/(Loss) at Expiration |
---|---|---|---|---|

115 | +16.50 | (13.95) | +0.70 | +3.25 |

110 | +16.50 | (13.95) | +0.70 | +3.25 |

105 | +6.50 | (13.95) | +0.70 | (6.75) |

100 | (3.50) | +1.05 | +0.70 | (1.75) |

95 | (13.50) | +16.05 | +0.70 | +3.25 |

90 | (23.50) | +31.05 | (4.30) | +3.25 |

### Appropriate market forecast

A Christmas tree spread variation 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 variation 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 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. Long puts have negative deltas, and short puts have positive 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 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 variation 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 spread variations 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 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 puts has a net negative theta, and the position loses money, 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 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 puts in a short Christmas tree spread variation with puts 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 one of the highest-strike puts), 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 the appropriate number of 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 variation 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 two puts) and at or above the strike price of the long puts, then the two highest-strike short puts are assigned. The result is that 200 shares of stock are purchased and a stock position of long 200 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 two highest-strike short puts are assigned and the three long puts are exercised. The result is that 200 shares are purchased and 300 shares are sold. The net result is a position of short 100 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 variation with puts can also be described as the combination of two “narrow” bull put spreads and one “wide” bear put spread. In the example above, the narrow bull put spreads are comprised of the two short 110 Puts and two of the long 105 Puts. The wide bear put spread is comprised of the other long 105 Put and the short 95 Put.

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.