Butterfly spread
Also written Butterfly · Long butterfly · Butterfly strategy
A four-legged position — one option bought at a low strike, two sold at a middle strike and one bought at a high strike, all of the same expiry — that caps the unlimited loss of a short straddle.
In plain language
A short-straddle earns well when nothing happens and loses without limit when something does. A butterfly is the fix.
The workbook builds it exactly that way: take the short straddle, then buy one out-of-the-money call and one out-of-the-money put to cap each tail. The wings pay for themselves only in a crisis, and they cost a little of the profit — but they turn an unlimited-loss position into a limited-loss one.
Drawn out, the payoff rises to a peak at the middle strike and falls away flat on both sides, which is what earns it the name.
It can be constructed from calls only, from puts only, or from a mixture — the workbook gives the recipe for all three, and the payoff is the same shape whichever you use.
How it works
The call-only construction, which is the one the workbook works through:
Buy 1 call at the LOW strike
Sell 2 calls at the MIDDLE strike
Buy 1 call at the HIGH strike
The strikes are equally spaced and share an expiry. Note the 1 : 2 : 1 ratio — the two short calls are the short straddle's call leg doubled, and the two long wings cap each side.
The put-only version reverses the direction of travel: buy one at the highest strike, sell two at the middle, buy one at the lowest. The mixed version buys a call at the lowest strike, sells a call at the middle, buys a put at the highest and sells a put at the middle.
The economics are always the same:
- Maximum profit at the middle strike, where the two short calls expire worthless and the low-strike long call is in the money by the strike gap.
- Maximum loss = the net debit, suffered anywhere at or below the lowest strike and anywhere at or above the highest.
- Two break-evens, symmetric about the middle strike.
It is the low-conviction version of a short straddle: the same view — that the underlying will not move much — expressed with a known worst case.
The formula
Net cost = Premium(low) + Premium(high) − 2 × Premium(middle)
Max profit = (Middle strike − Low strike) − Net cost
Max loss = Net cost
Lower BEP = Low strike + Net cost
Upper BEP = High strike − Net cost
A worked example
A stock trades at Rs 6,100. The trader builds a call butterfly with a lot size of 100:
Buy 1 call @ 6,000, premium Rs 230 → −230
Sell 1 call @ 6,100, premium Rs 150 → +150
Sell 1 call @ 6,100, premium Rs 150 → +150
Buy 1 call @ 6,200, premium Rs 100 → −100
────
Net cost Rs 30 per unit → Rs 3,000 a lot
At 6,000 or below — every call worthless:
−230 + 150 + 150 − 100 = −Rs 30
At 6,100 — the low-strike call is worth 100, the rest are worthless:
(−230 + 100) + 150 + 150 − 100 = +Rs 70 ← maximum profit
At 6,200 or above — all the calls are live and the gains and losses lock:
(−230 + 200) + (150 − 100) + (150 − 100) + (−100) = −Rs 30
| Per unit | Per lot | |
|---|---|---|
| Maximum profit (at 6,100) | Rs 70 | Rs 7,000 |
| Maximum loss (outside 6,000–6,200) | Rs 30 | Rs 3,000 |
| Lower BEP | 6,000 + 30 = 6,030 | |
| Upper BEP | 6,200 − 30 = 6,170 |
Risk Rs 3,000 to make Rs 7,000 — better than two-to-one — but only if the stock finishes inside a 140-point window, from 6,030 to 6,170, on one particular day.
Compare the short straddle it was built from. That position would have collected the premiums and kept going down without a floor: a 10% move to 6,700 costs the short straddle Rs 30,700 a lot. The butterfly's answer to the same 10% move is Rs 3,000, and no more, forever. The wings cost Rs 40 a unit of profit; they bought an unlimited liability away.
Why NISM asks about it
Chapter 17.2 builds the butterfly explicitly as an extension of the short straddle and works the 6,000/6,100/6,200 call construction above, including the Rs 30 cost and the 6,030 and 6,170 break-evens. Expect an identification question — a four-leg, three-strike, same-expiry position is a butterfly — and a maximum-profit computation.
Common exam traps
- The middle strike carries two contracts, the wings one each. Getting the 1 : 2 : 1 ratio wrong wrecks every number.
- All four legs share one expiry. Different expiries make it a calendar structure, not a butterfly.
- Maximum profit sits at the middle strike, not beyond it. The payoff is a peak, not a plateau.
- It is limited profit and limited loss. The workbook says so in terms; neither side runs away.
- A butterfly can be built from puts only or from a mix of calls and puts — the shape does not change. "Butterfly means calls" is wrong.
- The four legs must go on together. With four contracts the execution risk the workbook warns about is at its worst.
Where this is taught
- Series VIII · Chapter 5: Strategies using Equity Futures and Equity Optionsintroduced here
- Series V-D · Chapter 17: Strategies using Equity Futures and Equity Optionsintroduced here
- Series IV · Chapter 5: Strategies using Interest Rate Derivativesintroduced here
- Series V-D · Chapter 22: Strategies using Interest Rate Derivatives
Related terms
- Break-even pointThe level of the underlying at which a position makes neither profit nor loss — for a bought call, strike plus premium; for a bought put, strike minus premium.
- Long straddleBuying a call and a put at the same strike and the same expiry — a bet that the underlying moves a long way in either direction, with two break-even points and a maximum loss equal to both premiums.
- Vertical spreadTwo options of the same type and the same expiry but different strikes, one bought and one sold — a limited-profit, limited-loss position that trades away part of the upside to cut the cost or cap the risk.
- Covered callHolding the underlying in the cash market and writing a call against it — a way of earning premium income from a holding, at the cost of capping the gain above the strike.
- Long strangleBuying an out-of-the-money call and an out-of-the-money put with the same expiry but different strikes — the cheaper cousin of the straddle, with a wider band of loss between two break-even points.