Butterfly Spread Strategy¶

Overview¶

A butterfly spread is a defined-risk strategy that profits when the underlying stays near a specific price at expiration. It combines bull and bear spreads around a central "body" strike.

Difficulty intermediate Market Outlook: Neutral (pin risk at center strike) Risk Level: Low to moderate (defined risk, defined reward)

Long Call Butterfly¶

Construction¶

Buy 1 lower strike call (K1)
Sell 2 middle strike calls (K2)
Buy 1 higher strike call (K3)

All options have same expiration.
K2 - K1 = K3 - K2 (equidistant strikes)

Payoff Formula¶

Net Debit = Premium(K1) - 2 × Premium(K2) + Premium(K3)
Max Profit = (K2 - K1) - Net Debit (at price = K2)
Max Loss = Net Debit (at price ≤ K1 or ≥ K3)
Breakeven (Lower) = K1 + Net Debit
Breakeven (Upper) = K3 - Net Debit

where: K1 < K2 < K3 equidistant strikes · Premium(·) market call premium at each strike · Net Debit total cost to enter (always positive for long butterfly). does: maps the four corners of the payoff: cost in, peak at body, wings define risk, breakevens flank the body. Neutral / pin-the-strike trade — ideal in a tight range-bound market with low IV so debit is cheap; max payoff if spot lands exactly on K2 at expiry.

Payoff Diagram¶

Profit/Loss
  |           /\
  |          /  \
  |         /    \
  |        /      \
  |       /        \
  |      /          \
  |     /            \
  |    /              \
  |   /                \
  |  /                  \
  | /                    \
  |/                      \
--+--K1----K2----K3--------\-- Stock Price
  |                        \
  |                         \
  v                          \
                              (Max Loss)

Long Put Butterfly¶

Construction¶

Buy 1 lower strike put (K1)
Sell 2 middle strike puts (K2)
Buy 1 higher strike put (K3)

Same equidistant strikes, same expiration.
Identical payoff to long call butterfly (put-call parity).

Iron Butterfly¶

Construction¶

Buy 1 OTM Put (K1)
Sell 1 ATM Put (K2)
Sell 1 ATM Call (K2)
Buy 1 OTM Call (K3)

Net Credit strategy (vs. debit for standard butterfly)
Max Profit = Net Credit (at price = K2)
Max Loss = (K2 - K1) - Net Credit = (K3 - K2) - Net Credit

where: K1 < K2 < K3 equidistant strikes · Net Credit premium collected at entry · max loss bounded by the wing width minus credit. does: identical pinning payoff as long butterfly but built from short ATM straddle hedged by long OTM wings. Neutral / range-bound trade for elevated-IV regimes — you sell rich vol at the body and collect theta; ideal high IV crush trade when implied is above realized and a catalyst won't move spot far from K2.

Comparison¶

Feature	Long Butterfly	Iron Butterfly
Entry Cost	Debit	Credit
Max Profit	(Width - Debit)	Credit
Best When	Low IV (cheap options)	High IV (expensive options)
Vega	Positive (long vol)	Negative (short vol)
Theta	Negative	Positive

Entry Rules¶

Market Conditions:
Range-bound market with defined pivot point
Low IV for long butterfly (options cheap)
High IV for iron butterfly (options expensive)
No catalysts expected near center strike
Strike Selection:
Center strike (K2): At expected price at expiration
Wing width: \(2.50-\)10 typical for equities
Delta approach: Center strike ≈ 0.50 delta
Wings ≈ 0.15-0.25 delta
Expiration:
30-45 days (optimal theta)
Avoid through earnings/events
Shorter expirations increase gamma risk
Debit/Credit Target:
Long butterfly: Debit < 1/3 of spread width
Iron butterfly: Credit > 1/3 of spread width

Exit Rules¶

Scenario	Action
50-75% of max profit reached	Close position
Price moves beyond breakeven	Close at loss
14 days to expiry	Close (gamma risk increases)
IV changes significantly	Re-evaluate and possibly close
One side becomes worthless	Consider rolling wings

Position Sizing¶

Example: Long Call Butterfly
Stock: $100
K1 = $95, K2 = $100, K3 = $105
Debit: $9 - 2×$5 + $2.50 = $1.50
Max Profit: $5 - $1.50 = $3.50 × 100 = $350
Max Loss: $1.50 × 100 = $150
Return on Risk: 233%

Position sizing:
- Risk 1-2% per trade
- With $100k: can buy 6-13 butterflies

Expected Performance¶

Metric	Value
Win Rate	40-60% (depends on strike placement)
Risk-Reward	1:2 to 1:3 (favorable)
Best Market	Low vol, price stays near center
Worst Market	Large directional move
Theta	Negative (long), Positive (iron)
Vega	Positive (long), Negative (iron)

Variations¶

1. Broken Wing Butterfly¶

Skip buying one wing to reduce cost. Creates undefined risk on one side but higher probability.

2. Reverse (Short) Butterfly¶

Sell the body, buy the wings. Profits from large moves. Negative theta.

3. Ratio Butterfly¶

Sell more body options than wings bought. Generates net credit but increases risk.

4. Diagonal Butterfly¶

Different expirations for body vs. wings. Combines time spread with butterfly.

Checklist¶

[ ] Price expected to be near center strike at expiration
[ ] IV conditions match strategy (low for long, high for iron)
[ ] Strikes are equidistant (for standard butterfly)
[ ] Debit/credit ratio favorable (> 1:3 risk-reward for long)
[ ] No earnings/events expected
[ ] Exit targets defined before entry
[ ] Position size within portfolio limits

Assumptions & Limitations¶

Narrow profit zone — requires precise price prediction
Low win rate, but favorable risk-reward compensates
Commissions matter (3-4 legs per trade)
Early assignment risk on short options
Illiquid options can make entry/exit expensive
Pin risk if price lands exactly at center strike

References¶

McMillan, L.G. (2013). Options as a Strategic Investment (5th ed.). NYIF.
Hull, J.C. (2022). Options, Futures, and Other Derivatives (11th ed.). Pearson.
Rehl, R. (2020). "The Butterfly Spread: Theory and Practice." Derivatives Quarterly, 26(4).