# Long Christmas tree spread variation with puts

### Goal

To profit from neutral stock price action near the strike price of the short puts with limited risk.

### Explanation

A long 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 long Christmas tree spread variation with puts is created by buying two puts at strike D, selling three puts at strike C, skipping strike B and buying 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 purchased, three 105 Puts are sold, the 100 strike is skipped, and one 95 Put is purchased. 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 long christmas tree spread variation with puts

 Buy 2 XYZ 110 puts at 8.25 each (16.50) Sell 3 XYZ 105 puts at 4.65 each 13.95 Buy 1 XYZ 95 put at 0.70 (0.70) Net debit = (3.25)

### Maximum profit

The maximum profit potential is equal to two times the difference between the highest strike price (long two puts) and the strike price of the three short puts minus the cost of the strategy including commissions. This profit is realized if the stock price is at the strike price of the short puts at expiration.

In the example above, the difference between the highest strike price and the strike price of the short puts is 5.00, and the cost of the position is 3.25, not including commissions. The maximum profit, therefore, is (2 x 5) – 3.25 = 6.75 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 above the highest strike price at expiration, then all puts expire worthless and the full cost of the strategy including commissions is lost. 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 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 upper breakeven point is the stock price equal to the highest strike price minus one-half the cost of the position including commissions. In the example above, the highest strike is 110 and the cost of 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 cost of the position. In the example above, the lowest strike is 95 and the cost of the position is 3.25, so the lower breakeven point at expiration is 98.25 (95.00 + 3.25).

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

 Buy 2 XYZ 110 puts at 8.25 each (16.50) Sell 3 XYZ 105 puts at 4.65 each 13.95 Buy 1 XYZ 95 put at 0.70 (0.70) Net debit = (3.25)
Stock Price at Expiration Long 2 110 Put Profit/(Loss) at Expiration Short 3 105 Puts Profit/(Loss) at Expiration Long 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 long Christmas tree spread variation with puts realizes its maximum profit if the stock price is at the strike price of the short puts at expiration. The forecast, therefore, can either be “neutral,” “modestly bullish” or “modestly bearish” depending on the relationship of the stock price to the strike price of the short puts when the position is established.

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

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

If the stock price is above the strike price of the short puts when the position is established, then the forecast must be for the stock price to fall to that strike price at expiration (modestly bearish).

### Strategy discussion

A long Christmas tree spread variation with puts is the strategy of choice when the forecast is for stock price action near the strike price of the short puts, because long Christmas tree spread variations profit primarily from time decay. They differ from butterfly spreads in two ways. First, the cost of a Christmas tree spread variation is higher than that of a butterfly spread. Second, the range of profitability for a Christmas tree variation is wider than for a butterfly. Christmas tree spread variations also differ from skip-strike butterfly spreads and standard Christmas tree spreads. Relative to skip-strike-strike butterfly spreads, Christmas tree variations have lower profit potential and also lower risk. Relative to standard Christmas tree spreads Christmas tree variations have greater risk (the net debit is higher), but the points of breakeven and maximum profit are closer to higher strike price. Christmas tree variations therefore, have a statistically higher chance of making a profit.

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 long Christmas tree spread variations when they forecast that implied volatility will fall. Since implied volatility tends to fall sharply after earnings reports, some traders will open a long Christmas tree spread variation immediately before a report and hope for little or no stock price movement and a sharp drop in implied volatility after the report. The potential profit is high in percentage terms and risk is limited if the stock price rises or falls sharply.

If implied volatility is constant, long Christmas tree spread variations do not rise noticeably in value and do not show much of a profit until it is close to expiration and the stock price is close to the strike price of the short puts. The strategy, therefore, is sometimes described as a “strategy with a low probability of a high percentage profit.”

Patience and trading discipline are required when trading long 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 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 Christmas tree spread variation with puts 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 long Christmas tree spread variation with puts, 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 Christmas tree spread variation with puts does not profit from stock price change; it profits from time decay as long as the stock price is near the strike price of the short 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.

A long Christmas tree spread variation with puts has a negative vega. This means that the net price of the position falls when volatility rises (and the long spread loses money). When volatility falls, the net price rises (and the long spread makes money). Long Christmas tree spread variations, 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 Christmas tree spread variation with puts has a net positive theta and makes money as long as the stock price is near the strike price of the short puts. If the stock price moves away from this strike price, however, the theta becomes negative as expiration approaches, and the position loses 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 long 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, then 100 shares of stock are purchased and the long puts (lowest and highest strike prices) 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 higher-strike 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 other 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 put 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 long 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 and at or above the strike price of the short puts, then the two highest-strike long puts are exercised and the other puts 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 below the strike price of the three short puts and at or above the lowest strike (one long put), then the two highest-strike long puts are exercised and the three short puts are assigned and the lowest strike put expires. The result is that 200 shares are sold short and 300 shares are purchased. The net result is a position of long 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 long Christmas tree spread variation with puts can also be described as the combination of two “narrow” bear put spread and one “wide” bull put spread. In the example above, the narrow bear put spreads are comprised of two of the long 110 Puts and two of the short 105 Puts. The wide bull put spread is comprised of the other short 105 Put and the long 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.

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.

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