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Christmas Tree Spread: A Skewed, Limited-Risk Butterfly

For educational purposes only; not investment advice.

Direct answer

Section titled “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.

Piecewise payoff

Section titled “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.

A 100/105/110 call Christmas tree

Section titled “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.

Risk and execution checklist

Section titled “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.

Common misconceptions

Section titled “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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Authoritative sources

Section titled “Authoritative sources”