Straddle and Strangle: One Level Against Two Levels

A bought call, a bought put, both given the same end date, and where the two levels are placed decides which of these two has been built. Both at one level and it is a straddle, whose payoff drops to nil at a single price and stands above nil at every other. At two levels and it is a strangle, whose payoff is nil right across the distance between them.

Every leg in both assemblies is bought. The single fact that every leg was bought settles more than it looks like settling: both assemblies are paid for on day one, neither can ever be called upon afterwards, and the payoff of each is stuck at nil or above for the whole range of end prices. So the two are not separated by what they oblige, and they are not separated by their signs, and they are not separated by their end dates. One field separates the two assemblies, and one field only. The field is the place where the two legs sit.

Wherever a figure appears below it arrives carrying the word for what kind of figure it is. Two kinds move on day one, being the price the reference asset stands at and the premiumMoney handed over on day one to the side that sold the contract. It is gone whatever happens afterwards. somebody hands over. Two more land on the end date, being the payoff an assembly returns before anything is subtracted and the profit remaining after both premiums are added in and taken forward to that same date. Strip those words off and all four become interchangeable. A payoff then ends up being read as money made.

What is a straddle, once both of its rows are written out?

A straddle is two bought legs at one level: plus one call at Rs 2,000.00/- running one year, and plus one put at Rs 2,000.00/- running one year. The two rows are the whole of it. Nothing else varies between them. Same sign on both, one call and one put, one level, one end date.

Watch what that pair does on the end date. The reference asset finishes somewhere. If it finishes above Rs 2,000.00/-, the call is in the moneySaid of a contract whose holder would collect something if the end date fell today. A call needs the price above its level for that; a put needs it below. and pays the distance up from Rs 2,000.00/-. The put pays nothing at all. If it finishes below Rs 2,000.00/-, the put pays the distance down from Rs 2,000.00/- and the call is the one sitting silent. One leg works, one leg does not, and which of them works is settled by which side of Rs 2,000.00/- the price landed on. Put the two together and the payoff of the pair is simply the distance between the end price and Rs 2,000.00/-, measured in whichever direction the price went.

So finish at Rs 1,600.00/-. Rs 1,600.00/- is Rs 400.00/- below the level, so the pair pays Rs 400.00/-. Rs 2,400.00/- is Rs 400.00/- above the level, so finishing there pays Rs 400.00/- again. Finish at Rs 1,400.00/- and it pays Rs 600.00/-. Finish exactly at Rs 2,000.00/- and the distance is nothing, so the pair pays Rs 0.00/-. Drawn out, that is a V with its point sitting on the level.

Two figures in this guide read Rs 2,000.00/- and they are not the same quantity. One is where the reference asset stands today, its spot priceWhat the reference asset stands at today, before any contract is written against it. Every level named below is placed by measuring out from it.. The other is the level both straddle legs are written at. The record calls that level the strikeThe level written into a contract, at which its holder may buy or sell. Level is the word used below, because two of the four legs here sit where no premium is attached.. The two figures agree because whoever set this example up placed the pair right on top of the current price, and a pair placed there is what the words at the money describe.

The Rs 2,000.00/- these contracts reference is exposure. Multiplied out, it gives how much reference asset the legs are written over. Nobody handed it to anybody and nobody lodged it, and the only money that actually left a hand on day one is the premium. Nothing arrives from the reference asset between day one and the end date.

What is a strangle, once both of its rows are written out?

A strangle is two bought legs at two levels: plus one put at Rs 1,800.00/- running one year, and plus one call at Rs 2,200.00/- running one year. Look at the rows next to the straddle's rows and almost everything is identical. Both legs bought. One call, one put. One end date. The levels are what moved.

Now run the same end-date walk. Finish below Rs 1,800.00/- and the put pays the distance down from Rs 1,800.00/-. The call has nothing to do. Finish above Rs 2,200.00/- and the call pays the distance up from Rs 2,200.00/-. The put has nothing to do. Finish anywhere between Rs 1,800.00/- and Rs 2,200.00/- and neither leg has anything to do, so the pair pays Rs 0.00/-. The flat stretch is the whole difference between the two assemblies, and every other difference below is downstream of it.

So finish at Rs 1,400.00/- and the strangle pays Rs 400.00/-. Finish at Rs 1,600.00/- and it pays Rs 200.00/-. Finish at Rs 1,800.00/-, at Rs 1,900.00/-, at Rs 2,000.00/-, at Rs 2,130.00/-, at Rs 2,200.00/-, and every single one of those pays Rs 0.00/-. Finish at Rs 2,400.00/- and it pays Rs 200.00/-. Drawn out, that is a flat floor with a slope rising off each end of it.

Rs 1,800.00/- and Rs 2,200.00/- are declared levels. Somebody picked those two figures in order to get a flat stretch onto the drawing. Neither carries a premium here, and which levels a venue actually offers is a separate matter.

If everything else on the four rows matches, what is left to differ?

One field, and it is the level. The four rows set beside each other read as follows. Plus one call and plus one put on the straddle; plus one put and plus one call on the strangle. Same signs. Same two types. Same one year to the end date on all four. Across the four rows, the only cell that moves is the one holding the level.

One cell is a smaller difference than the two names suggest, and it is worth pausing on. A reader who already knows both names will skim past that cell and lose the only thing that generates every other difference between them. Equal levels put the two slopes back to back, so the payoff leaves nil the instant the end price moves off the level in either direction. Unequal levels pull the two slopes apart and open a stretch between them where the payoff has nothing to do but sit at nil. Everything below is a consequence of that one cell.

Two households buy a cooling unit each in the same week. The first sets its thermostat to a single reading, twenty four degrees, so the unit begins working the instant the room is anything other than exactly twenty four, whether it has drifted up or drifted down. The second sets a band instead, twenty to twenty eight, so the unit stays completely idle right across four degrees of ordinary afternoon and only starts up once the room leaves the band at one end or the other. Both units cost money to install. Both do exactly nothing on a day the room sits where it was told to sit. The only thing that separates them is the pair of readings written on the dial, and every difference in how much electricity each burns comes out of that pair. In the two assemblies described here, the dial readings are the levels, the electricity is the payoff, and the thermostat set to one reading is the straddle.

Where does each of the two pay nothing at all?

The straddle's payoff reads Rs 0.00/- at exactly one end price, Rs 2,000.00/-, and stands above nil at every other price on the range. There is no second price where it reads nil. Move a single rupee off the level in either direction and the payoff is a rupee. A single nil reading is what a point at the bottom of a V means.

The strangle's payoff reads Rs 0.00/- at every end price from Rs 1,800.00/- to Rs 2,200.00/- inclusive, so its nil reading is a whole span and not a single spot. Four hundred rupees of end price, all of it paying the same nothing. Land on Rs 1,850.00/- and it is nil; land on Rs 2,199.00/- and it is nil; land on Rs 2,000.00/- and it is nil.

One has a point at the bottom and the other has a floor to walk along. The point and the floor are statements about two shapes, not statements about which shape anybody wants. How often an end price lands anywhere in particular is a matter of distribution. Distribution is covered separately.

Every leg here was bought. What can either holder be asked to do afterwards?

Nothing further, ever. The answer really is that short, and it is short because all four legs across the two assemblies are bought. Money left on day one, a right came back, and a right is something its holder may use or ignore. There is no later moment at which somebody knocks and asks for a performance.

Compare that with the position of a writerThe side that sold a contract and pocketed the premium for doing so. Whoever writes performs when asked; whoever buys never has to perform at all., who took the premium and therefore has to do whatever the contract says when the other side calls for it. Neither assembly described here puts anybody in that position. Because nobody here can be called upon, the payoff of both assemblies is stuck at nil or above at every end price: a holder who would otherwise owe something simply declines to use the right and walks away with nothing instead.

Now the sentence that keeps a reader honest, and it is the one most easily skipped. A payoff that never falls below nil is a completely different statement from a profit that never falls below nil, and the gap between the two statements is exactly what was handed over on day one. A payoff ignores the premiums; a profit counts them. The straddle’s payoff at Rs 2,000.00/- is Rs 0.00/-, and a reading of Rs 0.00/- sounds like nothing happened. Its profit at the same price is a loss of everything paid. Both readings are correct and they describe different things.

A second question hides underneath. Joining two legs must do something neither leg did alone. Two rights added together are still two rights, so the join adds no obligation whatsoever. The join produces instead a payoff shaped in both directions at once, and no single bought leg can manage that: a lone call ignores everything below its level and a lone put ignores everything above its own.

Which of these two can be costed from what is here, and why only one?

The straddle costs Rs 237.93/- on day one, being a call premium of Rs 180.00/- and a put premium of Rs 57.93/-, and both figures exist because both of its legs sit at Rs 2,000.00/-, the one level these notes carry premiums for. Add them and the outlay closes. Carry each forward twelve months at 6.50 per cent a year. Rs 180.00/- becomes Rs 191.70/- and Rs 57.93/- becomes Rs 61.70/-. Add those and the financed cost is Rs 253.40/-.

The put premium in these notes has already been rounded, to Rs 57.93/-. Carry that a year and the exact result is Rs 61.69545/-, printed above as Rs 61.70/-. So Rs 253.40/- and both nil-profit prices below hold to the paisa and no further. Push any of them to a fourth decimal place and they stop agreeing. The disagreement is a fact about the rounding rather than about either assembly.

The strangle cannot be costed here at all. Its two legs sit at declared levels, and no premium is attached to either of them anywhere in this guide. A missing premium is not a shortcoming in the strangle. The gap is a statement about what these notes hold. Any level other than Rs 2,000.00/- comes without a premium in these notes, and attaching one would take a measure of how far the reference asset can travel before the end date, and no measure of that kind is held in any form. There is no volatilityA measure of how much a price has moved about already, or is expected to move about over some stretch of time. A model needs one before it can put a figure on a contract, and no measure of the kind is stored behind these notes. figure to feed in, so nothing legitimate comes out.

So one of these two closes and one refuses, and the reason is the record rather than the assembly. On a real venue's screen both would carry premiums; in this guide only one does. The temptation at exactly this moment is to reach for a figure from somewhere else and let the arithmetic finish, so which is which is worth stating plainly.

At which end prices does the straddle come out level, and why is there no matching pair?

The straddle's profit is nil at Rs 1,746.60/- and at Rs 2,253.40/-, being Rs 253.40/- measured out below and above Rs 2,000.00/-. The logic is one step. Profit is payoff less the financed cost, so profit reaches nil exactly where payoff reaches Rs 253.40/-. And the straddle’s payoff is the distance from Rs 2,000.00/-, so a payoff of Rs 253.40/- means an end price Rs 253.40/- away from the level. Two end prices sit that far out, one below and one above.

Two prices, both of them arithmetic, both reproducible from figures printed above. Between them the profit is below nil, and at Rs 2,000.00/- itself it reaches its worst reading of minus Rs 253.40/-, the whole financed outlay and not a paisa more. Outside them the profit is above nil and keeps climbing a rupee for every rupee further out.

The strangle has no such pair, and the reason is arithmetic rather than modesty. Its profit would be nil where its payoff met its financed cost, its financed cost needs a premium at each of two declared levels, and a premium at a level these notes do not price needs a measure of travel that these notes do not hold. The chain runs out, so the cells stay blank rather than being filled with something that looks like arithmetic.

The whole worked instance sits below, both assemblies at the same seven end prices, with the strangle's cost row and nil-profit row drawn empty on purpose.

Down the two payoff columns something falls out that is worth naming. At every end price on this range the straddle's payoff is either Rs 200.00/- above the strangle's or closer than that, and it is never below it. Outside the stretch the two lines run parallel with exactly Rs 200.00/- between them. Rs 200.00/- is the distance chosen when the levels were placed. Inside the stretch the gap narrows to the distance from Rs 2,000.00/-, closing to nothing at Rs 2,000.00/- itself. The relationship is forced by where the levels sit and by nothing else. One column of costs is missing, and a payoff comparison with a cost missing is half a comparison, so the two columns say nothing whatsoever about which assembly anybody should want.

What is deliberately left uncompared here, and why does that matter?

Neither of the two has been ranked above the other, and the list of what was left out is longer than the list of what was compared. A reader holding both shapes will otherwise finish the comparison in their own head, so the boundary follows.

Neither assembly is described as more likely to pay than the other. Nothing behind this guide measures that. There is no past run of prices for the reference asset, no distributionA statement of which end prices are reachable and how much weight each one carries. Producing one is a separate subject. over where it might finish, and no record of what happened to anybody who held either. Neither is called cheap or dear. Cheap and dear are judgements about a price against a value, and only one of the two prices can be produced here. And neither is called safe, or limited in its risk. What was handed over on day one is gone in every case, and how likely any end price is remains a separate question.

The comparison actually made is smaller and it is checkable. Where the legs sit. Where each payoff falls to nil, and whether that is one price or a stretch of them. The obligation each assembly creates, which came out at nothing for either. And which of the two a cost can be put against here, which came out at one.

Somebody says they hold two bought legs. How is it worked out which of these two it is?

The difference stops being a definition here and starts being a question asked out loud, and answering it takes two questions rather than one.

The first question is whether the two levels match, and it settles the name on its own. The question is the level on each leg. Equal levels, and what is being described is a straddle. Unequal levels, and it is a strangle. Nothing has been asked about what it is called, what it cost, when it ends or who sold it, and the shape of the payoff and where it touches nil are already known. All of that comes out of reading one cell.

The second question is which levels, and that one settles whether any of the money can be checked. A level where a premium is available is a level where an outlay closes, a financed cost closes, and two nil-profit prices fall out of the arithmetic without anybody supplying anything. A level where no premium is available is a level where the payoff still closes perfectly and the money does not close at all. Asking which levels first, before asking anything about cost, saves the whole conversation from arriving at a number nobody can source.

There is a third move, and it is the one that most often gets skipped: which of the figures on the table were worked out and which were supplied. On a payoff column the question is usually unnecessary. A payoff at a stated end price is arithmetic anybody can redo in their head. On a cost column it is the only question that matters, and the case worked above is one where the answer is available for one assembly and simply is not available for the other. A person who asks it habitually will spot the missing provenance in tables that have nothing to do with options at all.

The two can now be told apart. Does that settle whether to hold either?

A straddle can now be separated from a strangle in about four seconds, and that is a reading skill answering a different question from the one a reader is likely holding. Whether to hold either is not answered here, and no modesty is involved in saying so.

Three things stand between that question and any answer to it. How far the reference asset might travel by the end date, with some weight attached to each place it could finish, is missing, and estimating it is a separate subject. A holder’s existing holdings, that holder’s existing obligations, and what losing the whole outlay would do to the rest of the year are missing too, and all of that belongs to the circumstances of the holder. The cost of placing either assembly, keeping it open and closing it out is missing as well, and for one of the two that figure could not even be produced above.

A shape that can be read is a shape that can be read. Reading it gives what somebody would collect and what somebody would owe at each end price, and it stops there. A readable shape hands over no reason to put money behind either one.

The reference asset in these notes, its price, the rate financing it and the two premiums quoted against it are invented.
Educational material. Not advice on any investment, tax, budget or market position.