The butterfly spread, and the cost of four legs

The answer

A butterfly spread uses 3 strikes and 4 contracts. You buy 1 option at a low strike, sell 2 at a middle strike, and buy 1 at a high strike, all in the same expiry. It pays the most if the price finishes exactly at the middle strike. It is cheap, its maximum loss is the amount you paid, and the reason it is cheap is that it usually pays nothing.

Why this costs you money

Two reasons, and the second one is the reason this article exists.

The first is the probability. A butterfly is advertised on its reward-to-risk ratio. Pay 25 to make 475 on a 500 wide structure sounds extraordinary. That ratio is not an opportunity. It is the market's estimate that the price finishes at exactly the middle strike, and it is roughly 5%.

You will be shown a picture of a tall thin peak. What the picture does not convey is that the peak has almost no width. Move 1% away from the middle strike and most of the profit is gone. Move to either outer strike and you lose everything.

The second is the transaction cost, and it is usually decisive. A butterfly has 4 legs. You cross the bid-ask spread on 4 legs to open it and 4 legs to close it. That is 8 crossings on a position that may have cost you 25 points in the first place.

Work it through with real numbers. If each leg has a bid-ask spread of 2 points, the round trip costs you 8 × 2 = 16 points, which is more than half the debit. On a thinly traded outer strike the spread can be 5 or 10 points, and then the cost of trading exceeds the cost of the position.

This is not a detail. On a 4 leg strategy, the bid-ask spread is frequently larger than the expected profit. Nobody puts that on the payoff diagram.

How it works

Three strikes, equally spaced, 1 expiry. Use all calls or all puts; the shapes are nearly identical.

1. Buy 1 at the lower strike.
2. Sell 2 at the middle strike.
3. Buy 1 at the upper strike.

You pay a small debit.

• Maximum loss = the debit. It occurs at or below the lower strike and at or above the upper strike.
• Maximum profit = the distance between adjacent strikes, minus the debit. It occurs at exactly the middle strike at expiry.
• Break-evens = lower strike + debit, and upper strike − debit.

One property matters more than the payoff diagram, and it is almost never mentioned.

A butterfly is worth almost nothing until expiry is close. With 3 weeks to go, even with the price sitting exactly at the middle strike, the position may show a small fraction of its maximum value. The profit is created by time value draining out of the 2 short options, and that happens in the final days.

So you can be exactly right, for weeks, and see nothing on your screen. Most people close the position before it has had a chance to work, because holding something that shows no progress is psychologically very difficult.

What it costs, and what it gives up

It costs the debit, and the debit is 100% at risk.

It costs 8 crossings of the bid-ask spread, which is the real cost and the one you can measure.

It gives up any tolerance for being approximately right. A directional trade that is roughly correct makes some money. A butterfly that is roughly correct makes nothing. The structure converts a range of outcomes into a point.

It gives up flexibility. Four legs cannot be adjusted cheaply. Every repair costs another set of spreads. Traders who "manage" butterflies usually spend more on adjustments than the original position could ever have paid.

It gives up certainty about what you own at expiry. With 2 short options in the middle, if the price finishes near that strike in a physically settled market, you do not know how many of them will be exercised against you. That is a real risk with a name, and it is covered below.

Who is on the other side, and why they are willing to be there

A market-making firm, and it is delighted to see your order.

Think about what you have asked them to do. You want 4 different options, in 4 different strikes, at once. Each of those has a bid and an ask. The firm earns part of that difference on every leg. Your 1 trade is 4 opportunities for them, and they will earn it again when you close.

That is why 4 leg structures are promoted so heavily by platforms that earn from order flow. The structure is genuinely defined-risk and genuinely low-cost in premium terms. It is also, per rupee of position, one of the most expensive things you can trade.

There is a second participant worth knowing about. The outer strikes are the thin ones. Those are the legs that cap your loss. The firm quoting them knows that few people want them, and quotes accordingly. When you enter, you pay up for protection. When you exit in a hurry, you sell it cheaply. The wings cost you twice.

The useful discipline: before you place a 4 leg order, price the exit. Look at the bid on the legs you would be selling and the ask on the legs you would be buying back, and work out what the position would fetch right now if you closed it immediately. On many butterflies that number is meaningfully below what you just paid, which means the trade starts underwater by construction.

The maximum loss, as a number

Take an index near 24,000 with a lot size of 75. the current lot size. Buy the 23,500 call, sell 2 of the 24,000 calls, buy the 24,500 call. Suppose the net debit is 90 points.

• Capital committed = 90 × 75 = 6,750 rupees.
• Maximum loss = 6,750 rupees = 100% of the capital committed.
• Maximum profit = (500 − 90) × 75 = 30,750 rupees.
• Break-evens = 23,590 and 24,410.

The ratio is about 4.5 to 1, which means the market thinks the odds of full success are roughly 1 in 5.5, and the odds of finishing anywhere inside the break-evens are perhaps 1 in 3. Now subtract 8 bid-ask crossings from the outcome, and the arithmetic gets worse than the diagram suggests.

The overnight gap. A butterfly handles gaps calmly in 1 sense: the loss is capped at the debit no matter how far the market moves. That is genuine, and it is the structure's main virtue.

Two things still go wrong.

You cannot close it at fair value on a violent day. During the market events of 24 August 2015 in the United States, quotes in many instruments were far from any sensible value for a period after the open. the Securities and Exchange Commission's research note on that day. A 4 leg position priced off 4 unreliable quotes is not a position you can exit.

Pin risk. If the price finishes very close to the middle strike in a physically settled market, you are short 2 options that may or may not be exercised against you, and you will not know until after the market has closed. You can end the weekend holding an unhedged stock position you never chose. In cash settled index options this does not happen, which is a real advantage of the Indian index market.

When it is genuinely reasonable to use

The list is short and every item is a condition, not a preference.

1. You have a precise price target and a date. Not a direction. A number and a day. Very few people have this, and the ones who do usually have it because of a corporate event with a fixed price, such as a buyback or an announced acquisition.
2. All 4 strikes are liquid. Check the outer strikes specifically. If either wing shows a handful of contracts of open interest, the position is a trap.
3. Your broker executes the 4 legs as a single order at a net price. If the legs go to market separately, you will be filled on some and not others, and a partial butterfly is an entirely different and much riskier position.
4. The total bid-ask cost is a small fraction of the maximum profit. Measure it. If it is more than about 10%, the structure is not worth trading at that size.

There is 1 more legitimate use, and it belongs to professionals. A butterfly is a clean way to express a view that the market's implied distribution is the wrong shape, because it isolates a narrow range of outcomes. That is a real trade and it requires a model of the distribution. It is not what most retail butterflies are.

The decision rule. Add the bid-ask spread of all 4 legs, double it for the round trip, and divide by the maximum profit. If that fraction is above 10%, the structure has already taken a large share of your edge before the market has moved. Do not place it, whatever the payoff diagram shows.

Try this now

Five minutes in your broker's strategy builder. This is the single most useful exercise in the whole cluster, because almost nobody does it.

1. Open the strategy or basket window. Choose a liquid index and the nearest monthly expiry.
2. Build a butterfly: buy 1 call about 2% below the current level, sell 2 calls at the current level, buy 1 call about 2% above. 1 lot per contract, so 4 lots in total.
3. Read the maximum profit, the maximum loss and the net debit the platform shows.
4. Now go to the options chain and, for each of the 3 strikes, write down the bid price and the ask price. Subtract to get the spread on each. Remember the middle strike is traded twice.
5. Add the 4 spreads together. Multiply by the lot size. Then double the result, because you must cross all 4 spreads again to close.
6. Divide that total by the maximum profit.

What you should see. On a very liquid index at the money, the answer might be 5% to 10%, which is tolerable. On a single stock, on a distant strike, or in a week when the market is nervous, the answer is often 30%, 50%, or more than 100% of the maximum profit.

When that fraction goes above 100%, you have found a position where trading it costs more than the best possible outcome. Platforms display these positions cheerfully, with a diagram of a tall peak, and never show you this number.

Do the same exercise on a 4 leg structure in a single stock, and the difference between an index and a stock will be immediately obvious.

Three real cases

1. Option expiration pinning, documented in 2005 — the effect the strategy relies on Research published in the Journal of Financial Economics found that on expiration dates, share prices cluster at strike prices more often than chance would explain, and linked the effect to the hedging activity of option market makers and to the positions of large traders. the paper by Ni, Pearson and Poteshman and any later work. This is the real phenomenon that makes expiry butterflies attractive. It is a statistical tendency measured across many thousands of observations. It is not a prediction about the strike you chose this month.

2. SEBI's interim order on expiry-day index activity, 2025 — who else is trading that strike SEBI passed an interim order concerning a large international firm's strategies in index options and their underlying components around expiry. the order, the amounts and its current status. Read it for the description of scale. A butterfly placed on an expiry day is a bet about where the index settles, and the order describes participants whose activity is measured in thousands of crores of rupees of notional in the same session. Their positioning is a fact about your trade whether or not you know it.

3. The United States market open, 24 August 2015 — the day quotes stopped meaning anything In the opening minutes, hundreds of listed instruments traded at prices far from any reasonable valuation, and a large number of trades were later cancelled. the Securities and Exchange Commission's research note on the day. A 4 leg position depends on 4 simultaneous fair quotes to be closed at all. On days like that one, those quotes did not exist. A defined-risk position is only defined if you can hold it to expiry, and holding it to expiry is exactly what a margin call prevents.

The question that resolves it

A novice asks: what is the maximum profit? An expert asks: what does it cost to get in and out, as a share of that maximum profit? For most retail butterflies, the second number is the trade.

What would make this wrong

If transaction costs did not matter, then structures with high reward-to-risk ratios would be worth trading in volume, and systematic butterfly buying would produce a profit over many trades. Measure the bid-ask cost using the exercise above and the arithmetic answers itself.

The honest limits.

Butterflies are a real professional tool. On very liquid index products, executed as a single net order, with narrow spreads and a genuine view about where a market will settle, they are an efficient way to buy a narrow range of outcomes with a small, known amount of capital. That is why desks use them.

And the loss really is capped. In a portfolio where you want a small bet on a specific level without any tail risk, the structure does what it says. The problem is not the shape of the payoff. The problem is that the payoff is small, the probability is low, and the cost of trading it is large, so all 3 have to be measured together.

Carry this

• The reward-to-risk ratio is the probability, restated. It is never a bargain.
• Add the bid-ask on all 4 legs, double it, and compare with the maximum profit. Do this every time.
• A butterfly is worth almost nothing until the last few days, even when you are exactly right.
• Check the wings. The legs that cap your loss are the ones nobody trades.

Knowledge check

Related

• The iron condor
• The bull call spread
• The calendar spread
• Gamma, and why options near expiry get wild
• ← Options and derivatives