Welcome to Christmas in May, folks – this week’s installment of my series on butterflies deals with the Christmas tree strategy. (If you’re just catching up, make sure to check out my earlier posts on long butterfly spreads and skip-strike (aka broken-wing) butterflies.

Back to Christmas trees, though. Incidentally, I’m not really sure why it’s called a “Christmas” tree, since the profit and loss graph looks more like the leaning tower than a Christmas tree, but creativity is not most market marker’s strong suit. Much like the skip-strike, the Christmas tree is usually performed with a bullish or bearish bias: usually traders use calls if slightly bullish and puts if slightly bearish. The Christmas tree is usually done for a net debit to the account, and after the trade is paid for there is no additional margin.

A butterfly with a twist

The Christmas tree is basically a standard butterfly with a twist. This twist reduces the overall cost of the butterfly, but does also reduce the range of prices that the underlying could trade in and still be profitable.  The basic format for a standard butterfly is 1x2x1 - the twist comes in with that ratio, since Christmas trees are constructed on a 1x3x2 ratio instead. For example, with the stock near or below 40 we would buy one of the 37.50 calls, sell three of the 42.50 calls and buying two of the 45 calls. Here’s a rule-of-thumb to help you remember the Christmas tree’s ratio: the number of contracts on the “outside” or bought options (37.50 and 45 strikes) added together should equal the number of contracts sold at the middle strike (42.50 strike).

Why the different strike widths?

You might have noticed that the width between the 37.50 strike and the 42.50 strike is 5 points, while the width between the 42.50 and 45 strikes is only 2.50. This slightly different spacing between the strikes is the other main difference between a Christmas tree butterfly and the “standard” butterfly. The best way to understand what this does to the trade is to break it down into the two most basic spreads that create this butterfly: a long spread combined with two short spreads, or a bullish call spread combined with two bearish call spreads.

Buy 1 37.50 call
Sell 1 42.50 call

This spread by itself is a bullish trade. The max the spread can be worth is 5 points, which is found by taking the difference between the strikes (42.50 minus 37.50 =  5). Ideally an investor putting on this long spread would like the stock to be above the 42.50 strike at expiration.

The next spread embedded in the trade is a short spread. The max this spread can LOSE is 2.50; this happens if the stock finishes above 45 at expiration. 

Sell 1 42.50 call
Buy 1 45 call

So far we have established there are two different types of spreads in this butterfly: one long spread that can earn a max 5 points and one short spread that could lose a max 2.50. So here’s the trick: because of the ratio 1x3x2 it turns out we’re doing two short spread for each long spread. So if we were to break it down into all the individual spreads, the scenario looks like this:

Buy 1 37.50 call
Sell 1 42.50 call

Sell 1 42.50 call
Buy 1 45 call

And then add one more short spread…

Sell 1 42.50
Buy 1 45 call

The result would be long one 37.50 call, short three 42.50 calls and long two 45 calls. So the potential loss on the two short spreads is offset by the potential gain on the one long call spread. This creates a profit and loss graph at expiration that has a wider sweet spot on the lower half of the trade compared to the upper half and creates a “lean” resembling a slightly lopsided (Charlie Brown) Christmas tree in the P&L graph.

The benefit of the lean is that it will be cheaper than doing a standard 5-point-wide butterfly - say, for example, buy 1 37.50, sell 2 42.50, and buy 1 47.50. So Christmas trees offer an interesting, often more affordable way to trade butterflies. The down side is if the stock rockets up on the upside (above 42.50) of the trade (between 42.50 and 45), there’s a much smaller range the stock can stay in and still be profitable.

Let’s talk about risk (and reward)

Where’s our break-even, max loss and max gain on this trade? Let’s review each in turn.

Break-even for Christmas trees happens at two different points: The 37.50 strike plus the net premium paid (37.50 + 0.65 = 38.15). The second point is the 45 strike minus one-half of the net premium paid (45 – 0.65/2 = 44.675 – call it 44.68 with rounding).

Your max potential profit is limited to the 42.50 strike minus the 37.50 strike, minus the debit paid (42.50 – 37.50  - 0.65 = +4.35).

Your max risk is limited to the net debit paid for the trade (65 cents) times the number of 1x3x2 ratios filled. So in this example, since we only entered one 1x3x2 ratio, the total risks in dollars would be .65 x 100 or $65 plus commission. Note: commissions are a non-negligible issue here because there are three legs to the trade, with a commission charged on each leg of the trade. That said, keep in mind that TradeKing sends your butterfly to the floor as a single unit, thus making sure your trade gets filled only if the net of all legs equals the limit debit you’re willing to pay. Without that assurance you could easily end up with a half-filled butterfly that’s not really what you were planning on.

Factoring in implied volatility

After you’ve established a Christmas tree, increasing implied volatility is your enemy. Your main concern is the options you've sold with the middle strike, or 42.50. An increase in implied volatility will increase the price of these options, so if you choose to close your position prior to expiration, it will be more expensive to buy them back.
 
In addition, you want the stock price to remain stable, but an increase in implied volatility suggests an increased possibility of a price swing.

You may want to consider running this play using index options rather than options on individual stocks. That's because historically, indexes have not been as volatile as individual stocks. Fluctuations in an index's component stock prices tend to cancel one another out, lessening the volatility of the index as a whole.

On the positive note, time decay is helping you out here. You’ve sold three calls at 42.50, so to achieve the maximum profit you hope to buy each of those calls for little to nothing at expiration and capture as much intrinsic value as possible in that long 37.50 call.

Check this space again next week to see how butterflies can be used to hedge a trade gone bad!

Regards,
Brian (Og)

[Image: Chicago: Daley Plaza Christmas Tree (2006) by Laffy4k on flickr]

Options involve risk and are not suitable for all investors. Please read Characteristics and Risks of Standardized Options.

While implied volatility represents the consensus of the marketplace as to the future level of stock price volatility or probability of reaching a specific price point there is no guarantee that this forecast will be correct.

Any strategies discussed or securities mentioned, are strictly for illustrative and educational purposes only and are not to be construed as an endorsement, recommendation, or solicitation to buy or sell securities. 
 

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