What is a butterfly spread, how is it constructed, and when would I use it?

A butterfly spread is a beautifully precise strategy for profiting when you expect the stock to stay near a specific price. It combines a bull spread and a bear spread sharing a common middle strike.

Long Butterfly with Calls:

1. Buy 1 call at K_1 (lowest strike)
2. Sell 2 calls at K_2 (middle strike)
3. Buy 1 call at K_3 (highest strike)

Where K_2 = (K_1 + K_3) / 2 (equally spaced strikes)

Alternatively: Think of it as:

• A bull call spread (buy K_1, sell K_2) PLUS
• A bear call spread (sell K_2, buy K_3)

Worked Example: Vortex Semiconductor trades at $100. You expect it to stay near$100 through expiration.

• Buy 1 $90 call at$12.40
• Sell 2 $100 calls at$6.20 each (receive $12.40)
• Buy 1 $110 call at$2.50

Net cost: $12.40 -$12.40 + $2.50 = **$2.50**

Payoff at Expiration:

Stock Price	K_1 Call	2x K_2 Calls	K_3 Call	Net Payoff	Net Profit
$85	$0	$0	$0	$0	-$2.50
$90	$0	$0	$0	$0	-$2.50
$95	$5	$0	$0	$5	+$2.50
$100	$10	-$0	$0	$10	+$7.50
$105	$15	-$10	$0	$5	+$2.50
$110	$20	-$20	$0	$0	-$2.50
$115	$25	-$30	$5	$0	-$2.50

Key Levels:

• Max gain: ($100 -$90) - $2.50 = **$7.50** (when stock = K_2 = $100 at expiry)
• Max loss: $2.50 (net premium — when stock is below K_1 or above K_3)
• Breakevens: $92.50 (K_1 + cost) and$107.50 (K_3 - cost)

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When to Use a Butterfly:

• You expect low volatility (stock staying in a tight range)
• You want a cheap, defined-risk position
• You have a specific price target (set K_2 at your target)
• Implied volatility is high (selling the middle strikes captures rich premium)

The Butterfly as a Volatility Bet:

• Long butterfly = Short volatility (profit from stability)
• Short butterfly = Long volatility (profit from large moves)

Exam Tip: Know the construction (buy-sell-sell-buy with 1-2-1 ratio), calculate max gain (K_2 - K_1 - net cost), max loss (net cost), and the two breakeven points.

Explore more strategies in our CFA Level I derivatives modules.