Long Christmas tree spread with calls

  • The Options Institute at CBOE®

Goal

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

Explanation

Example of long Christmas tree spread with calls

Buy 1 XYZ 95 call at 8.40 (8.40)
Sell 3 XYZ 105 calls at 2.35 7.05
Buy 2 XYZ 110 calls at 0.95 (1.90)
Net debit = (3.25)

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

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

Maximum profit

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

In the example above, the difference between the lowest strike price and the strike price of the short calls is 10.00, and the cost of the position 3.25, not including commissions. The maximum profit, therefore, is 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 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 Christmas tree 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. In the example above, the lowest strike is 95 and the cost of the position is 3.25. The lower breakeven point at expiration, therefore, is 98.25 (95.00 + 3.25).

The upper breakeven point is the stock price equal to the highest strike price minus one-half of the cost of the position. In the example above, the highest strike is 110 and the cost of the position is 3.25, so the upper breakeven point at expiration is 108.375 (110.00 – 3.25/2).

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

Buy 1 XYZ 95 call at 8.40 (8.40)
Sell 3 XYZ 105 calls at 2.35 7.05
Buy 2 XYZ 110 calls at 0.95 (1.90)
Net debit = (3.25)
Stock Price at Expiration Long 1 95 Call Profit/(Loss) at Expiration Short 3 105 Calls Profit/(Loss) at Expiration Long 2 110 Calls Profit/(Loss) at Expiration Net Profit/(Loss) at Expiration
115 +11.60 (22.95) +8.10 (3.25)
110 +6.60 (7.95) (1.90) (3.25)
105 +1.60 +7.05 (1.90) +6.75
100 (3.40) +7.05 (1.90) +1.75
95 (8.40) +7.05 (1.90) (3.25)
90 (8.40) +7.05 (1.90) (3.25)

Appropriate market forecast

A long Christmas tree spread with calls realizes its maximum profit if the stock price is at the strike price of the short calls on the expiration date. 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 calls when the position is established.

If the stock price is at or near the strike price of the short calls 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 calls 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 calls 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 with calls is the strategy of choice when the forecast is for stock price action near the strike price of the short calls, because long Christmas tree spreads profit primarily from time decay. They differ from standard butterfly spreads in two ways. First, the cost of a Christmas tree spread is higher than that of a butterfly spread. Second, the range of profitability for a Christmas tree is wider than for a butterfly. Christmas tree spreads also differ from skip-strike butterfly spreads. While Christmas tree spreads have lower profit potential than skip-strike butterfly spreads, they also have lower risk.

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 long Christmas tree spreads 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 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 spreads 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 calls. 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 calls 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 calls have positive deltas, and short calls have negative deltas.

The net delta of a Christmas tree spread with calls 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 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 Christmas tree spread with calls 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 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.

Long Christmas tree spreads with calls have a negative vega. This means that the price of a Christmas tree spread falls when volatility rises (and the long spread loses money). When volatility falls, the price of a Christmas tree spread rises (and the long spread makes money). Long Christmas tree 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 Christmas tree spread with calls has a net positive theta as long as the stock price is near the strike price of the short calls. If the stock price moves away from this strike price, 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 Christmas tree 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) 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 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 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 one or both of the highest-strike 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 long Christmas tree 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 (long one call) and at or below the strike price of the three short calls, then the lowest strike long call is exercised and the other calls expire. 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 strike of the three short calls and at or below the highest strike (long two calls), then the lowest-strike long call is exercised, the three short calls are assigned and the highest strike calls expire. The result is that 100 shares are purchased and 300 shares are sold. The net result is a short position of 200 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 long Christmas tree spread with calls can also be described as the combination of one “wide” bull call spread and two “narrow” bear call spreads. In the example above, the wide bull call spread is comprised of the long 95 Call and one of the short 105 Calls. The narrow bear call spreads are comprised of the other two short 105 Calls and the two long 110 Calls.

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.