The Iron Condor: Four Legs and Where the Payoff Is Flat

An iron condor is four legs at four levels, all ending on one date: a bought put lowest, a written put above it, a written call higher, and a bought call highest. Its payoff sits at Rs 0.00/- between the two inner levels, slopes away outside them, and settles at minus Rs 200.00/- past the outer pair. The payoff never rises above nil.

Four contracts, four levels, one end date, and a bird for a name. The name is the last thing that arrives and the first thing that misleads, so it can be set aside for a few minutes. Four rows of writing sit in front of the reader, each row a complete obligation on its own, and the only question worth asking of them is what the four together pay on the day they end. The question has an exact answer, worked from the rows at seven prices, with a marker that moves across every price in between.

Two habits carry everything below. The first is to read an assemblyThe legs held together and read as one position. An assembly is a stack of contracts written one under the other, not a new kind of contract with terms of its own. as its legs before reading its name, because four rows with the signs reversed carry the opposite obligation under the same name. The second is to keep the payoffWhat an assembly pays at the end date, before anything paid or received to put it on is counted. A payoff is arithmetic on the price and nothing else. and the profitThe payoff after every premium is counted and carried to the same date. A profit needs a price for each leg. A payoff does not. apart in every sentence. On this particular assembly the distance between the two pictures is the entire reason anyone finds the shape appealing, and that distance is a single figure none of these four levels supplies. The payoff of an iron condorFour legs at four levels ending on the same date: two written at the inner levels and two bought at the outer levels, one pair in puts below and one pair in calls above. is exact and never rises above nil, and everything above nil in the half-remembered drawing is a premium that has to come from somewhere else.

What is an iron condor, written out as its four legs?

Start with the thing the four legs are written on. One unit of the reference asset has a price today of Rs 2,000.00/-, it pays nothing at all to whoever holds it during the year, and money costs 6.50 per cent a year to borrow over the same period. The price, the absence of any payout and the cost of money are the whole of the setting. A payout during the holding period would change the carry arithmetic all over the place, so an asset that pays nothing while held matters more than it looks.

Now the four rows. A legOne contract held inside a larger assembly. A leg is complete on its own and keeps its own obligation however many other contracts sit beside it. is one contract inside the assembly, and it is written down as a signed primitiveOne leg written out as four fields: a plus or a minus, a call or a put, one level, and one end date. Primitive means it does not break down any further., which is four fields and never more: a plus or a minus, a call or a put, one level, one end date. In level order, lowest first, the iron condor worked here is these four rows.

Plus one put at Rs 1,600.00/- for one year. Minus one put at Rs 1,800.00/- for one year. Minus one call at Rs 2,200.00/- for one year. Plus one call at Rs 2,400.00/- for one year. Those four rows are the entire definition, and every reading of this assembly is arithmetic on them rather than a property of the name. A plus is bought, so the holder may walk away from it. A minus is written, so the holder must honour it and cannot walk away. Reverse all four signs and the position is a different one entirely, obliging the opposite thing, and nobody would be able to tell from the name alone.

One caution about the four levels before they become furniture. All four are declared levelsA level chosen here to draw a shape. A declared level carries no premium and is not read off any real venue., set at ten and twenty per cent either side of the price of Rs 2,000.00/-: ten per cent down is Rs 1,800.00/-, twenty per cent down is Rs 1,600.00/-, ten per cent up is Rs 2,200.00/-, twenty per cent up is Rs 2,400.00/-. The four were chosen to draw a shape cleanly, and not one of them carries a premium. The levels contracts are actually made available at, and how far apart those levels sit, are set by the Securities and Exchange Board of India (SEBI) at sebi.gov.in.

Why do three separate quantities here all read Rs 2,000.00/-?

Three different things in this guide are written Rs 2,000.00/-, and a reader who assumes one of them was copied into the other two will misread the rest. The three agree for three unrelated reasons, and separating them is worth a paragraph before any arithmetic starts.

The first is the price of the reference asset today. One unit is worth Rs 2,000.00/-, and that is a price, observed now, on the thing the four contracts point at. The second is the one level that carries premiums at all: a call at Rs 2,200.00/- and a put at Rs 1,800.00/- carry none, while a call and a put at Rs 2,000.00/- carry Rs 180.00/- and Rs 57.93/-, both of them stated figures rather than worked ones. The level reads Rs 2,000.00/- because the pair sitting there is struck at the money, and struck at the money is precisely what it means for the level and the price to be the same number. The third is the exposure carried by one unit of the reference asset. Exposure is the value of the thing referenced rather than any amount anybody paid, and the value of one unit is its price, so the exposure is Rs 2,000.00/- again.

A price, a level struck at the money, and an exposure per unit are three different quantities that happen to read the same because the level was placed at the price and the exposure is the value of one unit. None of the three was copied from another. The missing entry matters too: not one of the four legs sits at Rs 2,000.00/-, so the one level with premiums attached is a level this assembly does not use. The absence of any leg at the one priced level shapes everything that can and cannot be said about what this assembly costs.

How do the four legs group into two pairs, and what does each pair do?

Sort the four rows by level and something falls out immediately. Two of them are puts and both sit below the price of Rs 2,000.00/-. Two of them are calls and both sit above it. A put needs a price beneath its level to do anything and a call needs a price above its level, and Rs 1,800.00/- is beneath Rs 2,200.00/-. The puts and the calls therefore never both work at the same price. So the assembly is two pairs that never meet, one working at the low end of the price scale and one at the high end.

The put pair sits below: written at Rs 1,800.00/-, bought at Rs 1,600.00/-. The call pair sits above: written at Rs 2,200.00/-, bought at Rs 2,400.00/-. In both pairs the written leg is the one nearer the price today and the bought leg is the one further out, and that arrangement is the whole architecture. The two levels nearest the price, Rs 1,800.00/- and Rs 2,200.00/-, are the inner levelsThe two levels at which the legs are written, one below the price today and one above it. In this assembly they are Rs 1,800.00/- and Rs 2,200.00/-.. The two further out, Rs 1,600.00/- and Rs 2,400.00/-, are the outer levelsThe two levels at which the legs are bought, sitting further from the price today than the written legs. In this assembly they are Rs 1,600.00/- and Rs 2,400.00/-..

Each pair does exactly the same job at its own end of the price scale: the written leg is the one that can owe, and the bought leg beyond it takes over so that the owing stops growing. Walk the put pair down and watch it. At Rs 1,700.00/- the written put owes Rs 100.00/-. Rs 1,700.00/- is above Rs 1,600.00/-, so the bought put is still silent. At Rs 1,600.00/- the written put owes Rs 200.00/- and the bought put has just reached the point where it starts paying. Below that, every rupee the written put owes is a rupee the bought put pays, so the pair stops moving. The call pair does the identical thing upside down, starting at Rs 2,200.00/- and finishing at Rs 2,400.00/-.

Consider a shop on a lane with a shutter at each end. Nothing happens while the traffic stays on the lane. Far enough one way there is a shutter, far enough the other way there is the second one, and both shutters were fitted before anything moved. A shutter at each end is the shape of the arrangement, and everything else about this assembly follows from it. The joinWhat happens where two legs meet, either at the same level or at the same date. The join is where a group of legs starts behaving differently from any of them alone. in each pair, that is, the point where the second leg starts working, is what fits the shutter, and the assembly contains nothing that is not already contained in two ordinary pairs pointing in opposite directions.

Where is the payoff flat, and what is it flat at?

Take a price of Rs 2,000.00/- on the end date and read the four rows one at a time. The bought put at Rs 1,600.00/- needs a price below Rs 1,600.00/- before it pays anything, and Rs 2,000.00/- is not below it, so it pays Rs 0.00/-. The written put at Rs 1,800.00/- needs a price below Rs 1,800.00/- before it owes anything, so it owes Rs 0.00/-. The written call at Rs 2,200.00/- needs a price above Rs 2,200.00/-, so it owes Rs 0.00/-. The bought call at Rs 2,400.00/- needs a price above Rs 2,400.00/-, so it pays Rs 0.00/-. Four rows, four nils, and the assembly pays Rs 0.00/-.

Now do the same at Rs 1,850.00/- and at Rs 2,150.00/- and nothing changes: every one of the four is still silent, and the answer is still Rs 0.00/-. The flat stretchThe range of prices over which the payoff does not change at all, because no leg in the assembly is doing anything across it. runs from Rs 1,800.00/- to Rs 2,200.00/- including both ends, and the figure it is flat at is Rs 0.00/-. Not a small positive amount. Not a modest amount that grows as the end date approaches. Nothing at all.

The flat figure of Rs 0.00/- is a definition doing its work rather than an accident of these particular levels. A payoff counts what the contracts pay and owe at the end date and counts nothing else. Whatever was received for writing the two inner legs was received at the start, so it is not in this picture anywhere, and no amount of staring at the flat stretch will reveal it. A street vendor counts the day's takings at dusk and forgets the money handed over at dawn for the vegetables. The takings are real. The takings are simply not the answer to what the contracts pay at the end.

Outside the flat stretch the shape is easy to state precisely, and precision here is worth more than a shape word. Over the whole stretch from Rs 1,800.00/- to Rs 2,200.00/- the payoff equals Rs 0.00/-, at every price including both endpoints. At every single price outside that stretch, in either direction, the payoff is strictly below Rs 0.00/-. Between Rs 1,600.00/- and Rs 1,800.00/- it falls away one rupee for every rupee the price falls. Between Rs 2,200.00/- and Rs 2,400.00/- it falls away one rupee for every rupee the price rises. Below Rs 1,600.00/- and above Rs 2,400.00/- it does not move at all and sits at minus Rs 200.00/-. Checked on a dense grid of prices across the whole span from Rs 1,400.00/- to Rs 2,600.00/-, the highest reading anywhere is Rs 0.00/- and the lowest is minus Rs 200.00/-.

What does the whole assembly oblige that no single leg obliged?

Read the written put at Rs 1,800.00/- entirely on its own for a moment, with the other three rows covered up. At Rs 1,700.00/- it owes Rs 100.00/-. At Rs 1,400.00/- it owes Rs 400.00/-. At Rs 1,000.00/- it owes Rs 800.00/-. Nothing in that row stops it, and the only thing that ever does stop it is the price reaching nil, at which point it owes the full Rs 1,800.00/-. One row, one obligation, no floor of any kind written into it.

Now uncover the bought put at Rs 1,600.00/- and read the two together. At Rs 1,400.00/- the written put owes Rs 400.00/- and the bought put pays Rs 200.00/-, so the pair is at minus Rs 200.00/-. At Rs 1,000.00/- the written put owes Rs 800.00/- and the bought put pays Rs 600.00/-, so the pair is at minus Rs 200.00/- again. At a price of Rs 1.00/- the written put owes Rs 1,799.00/- and the bought put pays Rs 1,599.00/-, and the pair is still at minus Rs 200.00/-. Something exists in the pair that existed in neither row: the amount owed stops growing, and where it stops is the distance between the two levels, Rs 200.00/-.

Everybody has met this arrangement outside a contract. Agreeing to cover a friend's shortfall with no figure written on the paper is one thing. Agreeing to cover it while holding a second paper from somebody else that repays everything past a stated point is a different thing, and the difference is not in either paper. The difference is in holding both. The call pair above does exactly the same: the written call at Rs 2,200.00/- owes more as the price rises with nothing in that row to stop it, and the bought call at Rs 2,400.00/- takes over from it rupee for rupee, so the owing settles at Rs 200.00/-.

Put the two pairs back together and the assembly carries a property that belongs to the four rows held together and to no contract among them: its payoff cannot fall below minus Rs 200.00/- at any price whatsoever, including prices far outside anything drawn here. A floor of minus Rs 200.00/- is a fact about a shape, and what a shape is not is worth naming plainly. The floor says nothing about how much money a holder can be called on to find, or when, or against what collateral. A bounded shape is not a bounded risk.

What does this assembly pay at seven stated prices, worked row by row?

Here is the whole thing worked rather than drawn. Seven prices: the four declared levels themselves, the price today between them, and one price beyond each end so that both shelves show up. At each price all four rows are read separately and then added with their signs. No premium is available at any of these four levels. Every figure below is therefore a payoff, and not one of them is a profit.

At Rs 1,400.00/- the bought put pays Rs 200.00/-, the written put owes Rs 400.00/-, both calls are silent, and the assembly pays minus Rs 200.00/-. At Rs 1,600.00/- the bought put has just reached its level and pays Rs 0.00/-, the written put owes Rs 200.00/-, and the assembly pays minus Rs 200.00/-. At Rs 1,800.00/-, at Rs 2,000.00/- and at Rs 2,200.00/- every one of the four is silent and the assembly pays Rs 0.00/-. At Rs 2,400.00/- the written call owes Rs 200.00/-, the bought call has just reached its level and pays Rs 0.00/-, and the assembly pays minus Rs 200.00/-. At Rs 2,600.00/- the written call owes Rs 400.00/-, the bought call pays Rs 200.00/-, and the assembly pays minus Rs 200.00/- once more.

The last column, read downwards, states the sentence most readers of this assembly never quite say out loud. The best this payoff ever does is nothing, and the worst it does is minus Rs 200.00/-. There is no price on the axis, and no price off the axis either, at which these four rows pay a positive amount. A reader meeting that for the first time usually assumes something has been left out, and something has, but not from the arithmetic: what has been left out is the money that changed hands at the start, and that money belongs to a different quantity with a different name.

Two rows in the table repay a second look. The Rs 1,600.00/- row and the Rs 2,400.00/- row are the two places where a bought leg has arrived at its own level and is paying Rs 0.00/-. Paying nothing looks like nothing happening, and is in fact the moment the shelf begins. One rupee further out in either direction and that leg starts paying rupee for rupee against the written leg beside it. The shelf does not begin where the payoff stops falling in the table; it begins where the second leg of the pair wakes up, and those are the same price.

The order in which things happen is the lesson. Drag the marker slowly down from the middle and watch that order. Nothing at all changes until the marker touches Rs 1,800.00/-. One rupee below that the written put alone starts owing, and the payoff begins sliding away from nil at one rupee per rupee while the other three rows sit still. At Rs 1,600.00/- the bought put wakes up, and from there the two put rows move together in opposite directions, so the line stops sliding and runs flat at minus Rs 200.00/-. Drag on to Rs 1,400.00/- and the two rows are both large, Rs 400.00/- owed against Rs 200.00/- paid, and the answer has not changed at all.

Every bend in the line is a row waking up, and every flat stretch is either no rows working or two rows cancelling, so what is worth watching is which rows are lit rather than the number in the corner. There are exactly four bends, at the four levels, and they are the only four places the shape can change direction. Having only four bends is why an assembly like this can be read completely from its rows without ever looking at a picture, and why the picture is worth having anyway: four bends are easy to check and hard to hold in the head at once.

What does this assembly cost, and can that be worked out here?

One fact makes this assembly worth a full treatment rather than a paragraph. The payoff never rises above nil at any price, so if there is anything at all on the positive side of this position, every last rupee of it is the net premiumWhat is taken in for the written legs less what is paid out for the bought legs, settled at the start rather than at the end.: what is taken in for writing the two inner legs, less what is paid out for buying the two outer ones. Nothing else is available. The whole of the attraction anyone has ever felt looking at this shape sits in a figure none of these four levels supplies.

None of these four levels carries a premium, so that figure cannot be worked out at all. The one level with premiums attached is Rs 2,000.00/-, and not one of the four legs sits there. Producing a premium at Rs 1,600.00/- or at Rs 2,400.00/- would need a figure for how far the reference asset might move, and no figure of that kind exists behind these four levels. So no net premium is printed, and no profitThe payoff after every premium is counted and carried to the same date. Where no premium is available, no profit can be stated either. line is drawn for this assembly anywhere. A profit line drawn without a premium would carry a made-up number inside it, and every reading taken off such a line would be a reading of that number.

More than nothing can still be said, and what is said is honest arithmetic rather than a consolation prize. Two bounds hold whatever the missing premium turns out to be. The first: the net premium must be above nil. Nobody takes on a set of obligations whose payoff is Rs 0.00/- at best and minus Rs 200.00/- at worst without receiving something at the start, so the figure is on the receiving side rather than the paying side. The second: it cannot be above Rs 187.79/-. The bound of Rs 187.79/- is Rs 200.00/-, the most the payoff can ever owe, brought back one year at 6.50 per cent, and anyone taking in more than that could set the money aside at that same rate for the year and end with more than the assembly could possibly be called on to pay.

The second figure is a rounded one and needs care. Rs 200.00/- divided by 1.065 is Rs 187.7934/- and the digits keep going, so the bound is carried here as Rs 187.79/-, true to the paisa rather than exactly. The gap is about a third of a paisa. Run in the other direction, the rounding shows itself plainly: Rs 187.79/- carried forward a year at 6.50 per cent comes to Rs 199.99635/-, which is not Rs 200.00/- and was never going to be. Those two figures are bounds and not a price, and no arithmetic available at these four levels brings them any closer together.

What does the word range in the name actually describe?

People describe this assembly as having a range, and the word does most of the damage in this corner of the subject. So say exactly what it points at. The range is the stretch of prices from Rs 1,800.00/- to Rs 2,200.00/- over which the payoff does not change, and it is a fact about where the four legs were placed rather than a statement about where the price will be. Move the two written legs to Rs 1,700.00/- and Rs 2,300.00/- and the range widens by Rs 200.00/-, while nothing whatever has happened to the reference asset.

Consider what it would take for the word to mean the other thing. Saying a price is likely to stay inside a stretch requires something that measures how far the thing might move and how often it moves that far. No measure of that kind sits behind these four levels: no past run of prices, no distribution, no probability, not one figure. How likely any stretch is, how often the price stays inside it, and how frequently an assembly like this settles at nil rather than at minus Rs 200.00/- are all unanswerable without one. The stretch is marked on the price axis; the axis of likelihood is empty and is drawn empty below.

A bus route board states where the bus goes. The board does not state whether the bus will be full, whether it will arrive, or whether anybody should be on it, and nobody confuses the two because the board obviously has nothing to say about them. A payoff diagram is the same kind of object: a complete description of an obligation across every price, and a complete silence about which price will happen.

There is a second slide packed into the same word, shorter and worse. A bound in a payoff is not a bound on what a reader can carry, so the words limited-risk and defined-risk do not follow from this shape. Knowing the payoff cannot fall below minus Rs 200.00/- for one unit gives the shape of one unit. The bound gives nothing about how many units somebody holds, what collateral has to be found while the position runs, what happens if that collateral has to be found on a bad day, or whether the household behind the position can meet it. Each of those questions has a separate answer, and a bounded diagram answers none of them.

How does somebody reading a four leg position statement work through it?

A statement showing four rows under one name is exactly the artefact where the habits above either hold or fail. Somebody analysing a position, or lending against one, or checking a household member's account, does the same four things in the same order, and each of them is a direct consequence of something above rather than general good sense. The name arrives last and misleads first, so the most useful move on a four leg position is to refuse to name it until all four rows have been written out and sorted.

1. Write all four rows out in four fields, in level order, before reading the nameSign, call or put, level, end date, on every row without exception. A statement that gives a name and four levels has given half the information, and the missing half is the four signs. Reconstructing the signs from the name is guessing. Reading them off the contract is not, and the two positions that share this name with the signs swapped oblige opposite things.
2. Sort by level and check that the bought legs are the outer twoThe whole architecture is written legs inside, bought legs outside. If the sort comes back with a bought leg inside a written one, the position is a different assembly whose shape runs the other way up, whatever it is called on the statement. Two minutes with a sorted list settles this, and no shape needs to be drawn to do it.
3. Work the payoff at the four levels and at one price beyond each endSix evaluations settle the shape completely, because four bends is all there is. For the assembly worked here those are minus Rs 200.00/- at Rs 1,600.00/-, Rs 0.00/- at Rs 1,800.00/-, Rs 0.00/- at Rs 2,200.00/-, minus Rs 200.00/- at Rs 2,400.00/-, and minus Rs 200.00/- again at Rs 1,400.00/- and at Rs 2,600.00/-. The two beyond the ends are the real test: if the reading has not stopped moving out there, the shape is not the one assumed.
4. Write unknown in the cost cell rather than filling it with something plausibleA payoff worked from the rows is exact. A cost needs a premium for every leg in the assembly, and a missing premium cannot be replaced with an estimate without the whole line becoming an estimate wearing the clothes of a calculation. A household budgeting around a figure it made up is in exactly the same position as a position sheet doing it, and both find out on the same day.

None of those four steps is a view about where the price is going, and not one of them produces a reason to hold or not hold anything. The four steps are reading habits. Every misreading described above survives right up until somebody performs them, and stops surviving immediately afterwards.

Should a reader who can now read this assembly hold one?

Being able to read an obligation does not answer that question, and the reason is stated rather than a matter of caution. Reading an obligation and deciding to take it on are separate acts, and only the first has been done here. Three things would have to be known before anyone could answer the second, and not one of them is available here.

The first is a view on how far the reference asset might move and how likely each move is. No probability, distribution or past run of prices sits behind these four levels, so there is no material from which such a view could be built. The second is the reader's own circumstances: what else is held, what the collateral would have to come out of, what happens if it has to be found on a bad week, and what the consequence of the worst reading actually is for that particular household or institution. None of that is visible here. The third is what the assembly costs to place, to hold and to unwind, and not even the first of those three figures is available, for the reason set out above.

Clarity is exactly where that caution has to be loudest. Every part of this assembly is drawn clearly, and clarity feels like an invitation. The shape is memorable, the arithmetic is exact, the worst reading is a small round number, and all of that together makes the thing feel available in a way that plain prose about risk never does. None of it is a reason. Four legs are four obligations, and being able to read all four is not a reason to take any of them on.

The reference asset, its price of Rs 2,000.00/-, the financing cost of 6.50 per cent a year and all four declared levels are invented.
Educational material. Not advice on any investment, tax, budget or market position.