Broken wing butterfly for UK investors: buying a discount by selling a tail

Prerequisite strategies: the long butterfly (the symmetric original), the bear call spread (the leg that carries the risk here) and the iron condor (managing a structure with two short strikes). Clear the Level 3 gate and position sizing first.

Why this structure exists

A symmetric long butterfly is a bet on a price, honest about its cost: the debit is the whole risk, and anywhere but your strike you lose most of it. The problem is the price of admission — the symmetric version below costs £288 to win at most £1,712, and 54% of the time it expires and takes the £288.

Breaking a wing changes the financing. Push one of the two longs further from the shorts and it costs less, so the structure costs less: £68 instead of £288, for a maximum profit that rises to £1,932 because there is less debit to subtract. The gap between the shorts and that far long is unhedged, and above it you are permanently short 100 index points — £1,000. You bought a £220 discount by selling a £1,000 tail.

Skew prices that swap, not your market view. On the surface modelled here the 10,800 call carries 13.81% implied volatility and the 11,300 call 12.00%, so the far call is cheap and skipping out to it saves real money. The same shape on the put side has skew against it — 16.89% at the far strike against 14.19% at the money — so an identical £1,000 of tail buys a discount of only £125.

The nearest simpler alternative is that symmetric butterfly, one tier down. Why not just do that? Because you pay four times as much for a slightly smaller payoff. Break the wing only when you can show arithmetically that skew has paid you enough for it.

Construction

• The skew gate: discount ≥ 20% of the tail accepted. The symmetric 10,800/11,000/11,200 fly costs £288; this one costs £68, a £220 discount against £1,000 of new risk — 22.0%, so it passes. The put mirror saves £125 on the same £1,000, 12.5%, and fails. This inequality, not your directional view, decides which side you break.
• Max loss = (wide − narrow) × multiplier + net debit. (300 − 200) × £10 + £68 = £1,068. Dropping the debit, as most published versions of this formula do, understates the risk on every debit butterfly ever built.
• Max loss ≤ 2% of account equity. £1,068 needs £53,400.
• Shorts on your target, not at the money. The peak is where the index must finish, so 11,000 is a forecast, not a convenience.

Max loss = (wide − narrow) × multiplier + net debit. Max profit = narrow × multiplier − net debit. Lower breakeven = lower long + net debit ÷ multiplier; upper breakeven = (lower long + 2 × narrow) − net debit ÷ multiplier. The mark cannot beat the expiry maximum either: over 9,000–13,500 index, 0.5–60 days and volatility shifts of −5 to +30, the worst mark modelled was −£1,068.

The tent is an expiry shape. With 60 days left the dashed line is almost flat, worth £67 at best and that at 10,420: everything you are trying to win lives in the final ten sessions, which is why this structure cannot use the tier's usual 21-day time stop.

Entry criteria

Do not enter if: the discount is under 20% of the tail; IV rank is below 30; the term structure is inverted; you cannot fund £4,068 against one structure; or you cannot name, in advance, the index level at which you will close rather than defend.

Greeks at entry and how they evolve

Modelled at 14% at-the-money implied volatility with a downside skew, 4% rates, 3.5% dividend yield. Gamma is pounds of delta gained per 100 index points.

Read the first column against the picture above; the mismatch is the lesson. The chart looks emphatically bullish, but delta is −£0.49 a point, theta +£4.44 a day and vega −£40.98. On the day you open it this is a short-volatility, positive-carry position with a mild bearish tilt, not a directional bet. It becomes the shape on the chart only in the final fortnight, and the flip shows in the 7-day column: with the tent out of reach, theta turns from +£8.08 to −£7.43 and vega from −£40.01 to +£4.49, because what you hold is now a lone out-of-the-money call. Vega decides the first month; gamma and strike selection decide the last two weeks.

Management and adjustment

ROLL WHEN: the index is inside 10,800–11,150 with 14 days or more and pulling the wide wing in from 11,300 to 11,200 costs less than half the £1,000 it removes. At 11,000 with 30 days that roll is £299 and the maximum loss falls from £1,068 to £367; at 11,200 with 14 days it is £458 and barely worth doing. ROLL TO: 11,200 — symmetry, nothing else. DO NOT ROLL: the wide wing further out to collect more premium, which doubles the tail to £2,000; and never the short strikes upward, because that is a debit paid to relocate risk rather than retire it. Be honest about what the wing roll is: £299 of certain money to remove a £1,000 loss the model puts at 22%, an expected cost of £216. It is a risk decision, not a value one, defensible only because the loss lands on one Friday morning. Where defence stops: at 11,300. Past that the roll costs more than the tail, every adjustment is fresh risk, and closing is the adjustment.

Exit rules

• Profit target: +£483, 25% of maximum profit. The best mark available is £256 at 21 days and £366 at 14, so the target is unreachable until roughly 8 days out, with the index between 10,825 and 11,049. A butterfly pays late or not at all.
• Stop: a mark of −£400, which is the index touching 11,300 at almost any point in the trade's life — 11,296 at 30 days, 11,306 at 21, 11,300 at 10. Mechanical, checked on the close.
• Time stop: 3 days to expiry, Tuesday 13 October 2026, unconditional. Not the tier's usual 21 days, because at 21 days this structure has not yet earned anything; the risk avoided is settlement, not decay.
• Settlement exit: be flat before the October series stops trading shortly after 10:15 on Friday 16 October. Cash settlement means no assignment, but at 11,000 the payoff swings £10 a point either side of the peak, so a 20-point surprise in the auction is £200 you cannot trade against.

If all four are silent, do nothing.

Margin and broker reality

A margin account is mandatory — a cash account cannot hold a written index call — and spread permission is the minimum. Uncovered-option permission is not needed, because every short is covered by a long. Send all four legs as one combination order and never leg in.

Initial and maintenance. Interactive Brokers' published combination definitions recognise a butterfly only where the intervals between exercise prices are equal. A broken wing is by construction unequal, so it is not margined as a butterfly at all. IBKR's optimiser pairs what it can instead: a long 10,800/short 11,000 spread, paid in full and requiring nothing, plus a short 11,000/long 11,300 spread charged at the strike differential times the multiplier, credit applied to cash rather than netted off. That is 300 × £10 = £3,000 initial and £3,000 maintenance, against a structure whose true worst case is £1,068. IBKR's own guidance is that the optimiser cannot guarantee the best combination, so check the figure in a paper account first.

After a 2 SD adverse move the requirement is still £3,000, and after a 20% gap to 12,900 it is still £3,000, because strike differentials do not move when the index does. That is what defined risk buys, and this is the last page in the tier where the sentence is true.

Your equity moves, and that is what liquidates you. IBKR liquidates when net liquidation value falls below maintenance margin. Funded with £3,500 you have a £500 cushion, gone at 11,358 with 21 days left — a 5.7% rally, inside one standard deviation. Fund it with £4,068, the requirement plus the whole maximum loss, and nothing can force you out. Portfolio margin would charge less, but IBKR requires USD 110,000 of net liquidation value to upgrade an existing account and restricts margin-increasing trades below USD 100,000. Away from front-month round strikes the chain trades wide, and across four legs the bid-ask beats the commission.

Stress test

One standard deviation over the 60 days is 610 points, 5.68%. Volatility responses are modelled, not observed.

The table is unusual for this tier, and that is the point: a 1987 or March 2020 crash costs you £68, the requirement never moves, and nobody rings you up. Which is why the row to fear is not a tail row. +1 SD is already the maximum loss — 11,300 sits only 5.1% above spot, inside one standard deviation, at odds the model puts at 15.1%. In a short strangle the worst case is a disaster that rarely happens; here it is an ordinary autumn rally, roughly one time in seven.

The same row shows how this structure hurts people. At 11,360 with 30 days left the mark is −£507, which reads as recoverable, while settlement at that level is −£1,068. That £561 gap is time value on the long wing flattering a position that has already lost. Traders hold because the screen looks survivable. The screen is not the payoff.

What to trade instead

Simpler, from the tier below: the symmetric long butterfly — same tent, same target, no tail, no margin beyond the debit, a £288 maximum loss you can hold through anything. You pay four times as much for a payoff 11% smaller. For direction without precision, a bull call spread says it in two legs.

More precise, from inside this tier: the backspread is this page inverted — long the convexity, loss in the middle rather than the tail. The jade lizard expresses the same "no risk on one side" ambition using a genuine credit. And the ratio spread is what this becomes if you drop the far wing to save the £435: the same shape with the ceiling removed.

Risk statement

Listed options are complex instruments, and this tier assumes a margin account, a written risk process and capital that can absorb the maximum loss without liquidation. This is educational material, not a recommendation to trade the FTSE 100 or anything else, and it takes no account of your circumstances. Every premium here is modelled, not quoted.