# Christmas Tree Spread: A Skewed, Limited-Risk Butterfly

Define a 1-by-3-by-2 long call Christmas tree, derive its piecewise payoff and two breakevens, and distinguish its asymmetric tail losses from a standard butterfly.

Canonical: https://wiki.fcontext.com/options/christmas-tree-spread/
Fact checked: 2026-07-22

> For educational purposes only; not investment advice.

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## Direct answer

“**Christmas tree spread**” is not a perfectly standardized name. One common long call version uses one expiration and three ascending strikes: buy one call at `K₁`, sell three calls at `K₂`, and buy two calls at `K₃`, with `K₁ < K₂ < K₃`.

This 1-by-3-by-2 structure concentrates its best expiration result near the middle strike. Unlike a symmetric 1-by-2-by-1 butterfly, it has unequal low-side and high-side outcomes. When all legs share an expiration, the total call quantity above `K₃` is zero (`1−3+2=0`), so both tails are bounded, but the upper-tail loss can be materially larger.

Other brokers may call different call, put, short, or four-leg structures a Christmas tree. The name alone never establishes the payoff; quantities, strikes, expirations, and buy/sell directions do.

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## Piecewise payoff

For a net debit `D`, expiration profit per share is:

`Π(S_T)=max(S_T−K₁,0)−3max(S_T−K₂,0)+2max(S_T−K₃,0)−D`

The slope changes at every strike:

- `S_T ≤ K₁`: all calls expire worthless; profit is `−D`.
- `K₁ < S_T ≤ K₂`: profit rises with slope `+1`; lower breakeven is `K₁+D`.
- `K₂ < S_T ≤ K₃`: profit falls with slope `−2`; if the root lies in this interval, upper breakeven is `(3K₂−K₁−D)/2`.
- `S_T > K₃`: all legs are active and slope becomes zero; high-tail profit is `−K₁+3K₂−2K₃−D`.

At `K₂`, expiration profit is `K₂−K₁−D`, commonly the maximum for this long version. Unequal strike spacing changes the high-tail amount and may move or remove a breakeven, so the formulas must be evaluated using the actual strikes.

Before expiration, the position's Delta, Gamma, Theta, Vega, and skew exposure vary sharply around the three strikes. A bounded expiration graph does not imply stable mark-to-market risk.

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## A 100/105/110 call Christmas tree

Use one expiration:

- Buy one `100` call.
- Sell three `105` calls.
- Buy two `110` calls.
- Pay a `1.00` net debit.

Below `100`, loss is the `1.00` debit. The lower breakeven is `101`. At `105`, the long `100` call is worth `5`, the other calls have no intrinsic value, and profit is `5−1=4.00`, or `400` dollars with a 100-share multiplier.

Between `105` and `110`, profit falls twice as fast as spot rises. The upper breakeven is `(3×105−100−1)/2=107`. At and above `110`, intrinsic payoff before premium is `−5`, so total loss is fixed at `6.00` per share, or `600` dollars before fees.

The position therefore risks `100` dollars on the low side and `600` dollars on the high side to target a narrow maximum of `400` dollars near `105`. That asymmetry is the central feature, not the decorative strategy name.

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## Risk and execution checklist

- Write every leg, signed quantity, strike, expiration, multiplier, and exercise style; verify that the broker's template matches this exact variant.
- Calculate both tail results, both breakevens, maximum profit, and maximum loss using the actual net fill.
- Stress spot at every strike and far beyond both tails, then reprice before expiration under IV and skew changes.
- Use a multi-leg limit order. Six contracts create multiple partial-fill and bid-ask costs even though there are only three strikes.
- Monitor early assignment of the three American-style short calls, especially near ex-dividend dates and when extrinsic value is small.
- Do not assume the two higher long calls cover every operational outcome; assignment timing can temporarily create stock and mismatched option positions.
- Plan expiration around the two short/long strike regions, broker cutoffs, pin risk, exercise notices, and cash or share capacity.
- Compare the structure with a standard butterfly or broken-wing butterfly; fewer legs or clearer tails may better express the same view.

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## Common misconceptions

- “Christmas tree always means one payoff.” Multiple variants use the name.
- “All butterflies have equal tail loss.” The 1-by-3-by-2 ratio produces asymmetric tails.
- “Limited risk means small risk.” The upper-tail loss can be several times the lower-tail debit.
- “More short options make it a credit strategy.” Actual premiums determine debit or credit.
- “Maximum profit occurs across a wide range.” This version peaks at one middle strike and loses value quickly on either side.
- “A six-contract package is easy to fill at midpoint.” Each leg's liquidity and partial execution matter.

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## Related topics

- [Butterfly Spread](/options/butterfly-spread/)
- [Broken-Wing Butterfly](/options/broken-wing-butterfly/)
- [Vertical Spread](/options/vertical-spread/)
- [Assignment Risk](/options/assignment-risk/)

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## Authoritative sources

- [Characteristics and Risks of Standardized Options](https://www.theocc.com/company-information/documents-and-archives/options-disclosure-document) - Options Clearing Corporation
- [Options](https://www.finra.org/investors/investing/investment-products/options) - FINRA
- [Options Institute](https://www.cboe.com/optionsinstitute/) - Cboe