Maximum Loss: The Floor on an Assembly, If It Has One

Maximum loss is the lowest reading an assembly can produce, and which reading is meant has to be said out loud. One version counts only what the assembly hands over on the end date. The other counts that amount after every premium has been carried forward to the same date. And on a written leg standing by itself, the arithmetic sets no lowest reading at all.

A written leg with no lowest reading at all is the claim worth slowing down for. Every diagram most readers have ever seen had an axis that stopped somewhere, so they arrive expecting a number. A floor is a property of the rows written down, not of the picture somebody drew of them. Once the rows exist, the lowest reading is settled; the price only decides whether that reading is ever arrived at. The size of the floor is not what varies from one assembly to the next. The variable is whether a floor exists at all, and that turns on a count that can be done on the fingers.

The reference asset behind every figure below stands at Rs 2,000.00/-. Financing runs at 6.50 per cent for one year, and one year is how long everything here runs. The reference asset hands its holder nothing across those twelve months. The absence of any such payment does real work: the carry figure of Rs 130.00/- would be smaller if anything did arrive, and every profit floor in this guide is stacked on top of it.

Four words are doing four separate jobs below, and swapping any two of them changes the arithmetic. Say price and it means what the reference asset stands at. Say premium and it means money that moved on day one to put a leg on. Say payoff and it means the end date only, counting nothing that was paid to get there. Say profit and it means that same payoff with every premium taken forward to the end date and subtracted.

What is a maximum loss, and what exactly is it a floor on?

A room of people asked what the most that can be lost on a bought call is will give two answers that both sound right. One group says nothing at all. A buyer who does not want to exerciseChoosing to use the right a contract carries, rather than letting it lapse. That choice belongs to whoever bought the leg and to nobody else. simply walks away. The other group says the premium. The money left on day one and never came back. Both groups are correct, and they are answering two different questions.

The floor on the payoff is the smallest amount the assembly hands over on the end date, with everything paid or received to put it on left out of the sum. For a bought call at Rs 2,000.00/- that figure is Rs 0.00/-. The holder chooses whether to use a bought call and will not choose to use it at a loss, so no price makes it hand over a negative amount.

The floor on the profit is that same figure once every premium has been walked up to the end date, financing included. The call premium of Rs 180.00/- left on day one. Financing takes it to Rs 191.70/- by the end date. So the profit floor on that bought call is minus Rs 191.70/-, and it sits there at every price at or below Rs 2,000.00/-. Nothing is owed to anybody, and money has still gone.

The same split works on a bought put at that level, with a smaller number in it. The put premium is Rs 57.93/-. Taken forward twelve months it stands at Rs 61.70/-. So the payoff floor is Rs 0.00/- and the profit floor is minus Rs 61.70/-. The profit floor of minus Rs 61.70/- is rounded, and it is rounded because the premium it comes from was rounded beforehand. The relationship between the two premiums at this level holds to the paisa, not exactly.

How is the floor read off the legs instead of off a picture?

This is the part that removes any need for a diagram. Every signed primitive is written down as a row. The rows are sorted so that everything sharing a level and a date sits together. Then, standing at each end of the price range, one question is put to it: does the payoff keep falling as the walk continues?

At the top of the range the payoff falls without stopping wherever the written calls outnumber the bought calls. Think about why. Above the highest level in the assembly, every call in it is live. Every written call surrenders a rupee for each rupee added to the price; every bought call recovers one. If there are more of the first kind than the second, the net is a loss that grows with the price, and nothing in the rows caps how far the price can rise.

At the bottom of the range the same test runs on puts. Below the lowest level, every put is live. Every written put surrenders a rupee for each rupee taken off the price; every bought put recovers one. More written than bought, and the payoff keeps sliding until the price itself reaches Rs 0.00/-. A price cannot go below nothing, so the downward end does at least stop somewhere. The fall is steep but finite. The upward end has no such stopping point in it at all.

So the honest answer to whether an assembly has a floor is a count, not a drawing. Where the written legsRows sat on from the obliged side. Whoever bought one decides whether it happens, and where they decide it does, the writer performs. outnumber the bought ones at either end, there is no floor in the arithmetic, and the largest figure that happened to be drawn is no substitute for one.

Which assemblies have a floor, and which have none at all?

Four arrangements, and between them they give three different kinds of answer to the same question. The kind of answer matters far more than the size of any one figure. So the four are set out together.

First kind: a floor that exists and can be given in full, on both readings. A bought call at Rs 2,000.00/- floors at Rs 0.00/- on the payoff and at minus Rs 191.70/- on the profit, and both numbers are available because this record prices that level. The worst a unit of the reference asset held with a call written on it can hand over is nothing, so its payoff floors at Rs 0.00/-. Its profit floors at minus Rs 1,938.30/-, reached at a price of Rs 0.00/-.

The floor of minus Rs 1,938.30/- repays a second look. The same magnitude turns up as the bought put's profit ceiling at this level, and the agreement is not luck. The relationship between the two premiums at one level forces it: the financed cost of holding a unit less the financed call premium comes to the same amount as the level less the financed put premium. Rs 2,130.00/- less Rs 191.70/- is Rs 1,938.30/-. Rs 2,000.00/- less Rs 61.70/- is Rs 1,938.30/- as well. The two sides of one contract cannot disagree about how far down it goes, so the floor on one is the ceiling on the other with the sign turned over. The two agree to the paisa, and the last fraction of a paisa is missing because the put premium arrived here already rounded.

Second kind: a floor that exists on one reading and cannot be turned into the other. Consider the four-leg assembly built across the declared level set. Its payoff floor is minus Rs 200.00/-, and that can be checked by walking to either end: past the outer low level the inner written put and the outer bought put move together and leave a constant gap of Rs 200.00/- against the holder, and past the outer high level the two calls do the same. But no profit floor is available here. A premium is precisely what the record withholds at all four of those levels, and inventing one to close the sum would be inventing the answer.

Third kind: no floor anywhere in the arithmetic. A single call written at Rs 2,000.00/- with a year to run, and nothing at all beside it. Neither reading produces a number, and the reason sits in the written call's own arithmetic.

What does a written call actually look like at the far end?

Take one call written at Rs 2,000.00/-, twelve months to run, Rs 180.00/- taken in on day one. The short end of the story comes first. The most this leg can earn is Rs 191.70/-, the premium taken forward twelve months, and no price anywhere improves on that. Below the level the call is never used, the writer keeps what came in, and that is the end of the good news. There is nothing to add to it and no price at which more arrives.

Now the other end, stated plainly and without decoration. At Rs 2,130.00/- the leg owes Rs 130.00/-, and Rs 61.70/- still remains once the financed premium is counted. At Rs 2,400.00/- it owes Rs 400.00/-, and the profit is minus Rs 208.30/-. At Rs 2,600.00/- it owes Rs 600.00/-, and the profit is minus Rs 408.30/-. Keep walking and the pattern does not change: nothing written into the contract puts a stop on the owing, so there is no price at which it stops growing.

So there is no maximum loss figure for that leg. Not a large one, not a conservative one, not one with a note attached. The arithmetic does not produce a number, and writing one down would be manufacturing a comfort out of a drawing decision.

If the premium is the floor for a buyer, what is it for a writer?

This is the previous block read from the other side, and it deserves its own space because the sentence people carry away from learning to buy is the sentence that hurts them when they write.

For a bought leg the premium really is the floor on the profit. Pay Rs 180.00/-, decline to use the right, walk away having given up Rs 191.70/- once financing is counted, and no worse reading exists. The premium really is a genuine bound there, and it is the reason so many people describe an option position by its premium.

For a written leg the premium is the ceiling and not the floor. The premium is the most that can ever be received rather than the most that can ever be given up. Same number, opposite end of the range. Rs 191.70/- sits at the top of what the written call can produce. The bottom is a separate question with a different answer, and on that leg the answer is no answer at all.

There is a one-line test for this and it costs nothing. Find the sign on the row. A plus means the holder paid to get in, so the premium is the bottom of the range. A minus means the holder was paid to get in, so the premium is the top of it and the bottom has to be worked out separately. Somebody reading a position sheet quickly can run that check in about a second, and skipping it is what lets the rest of the sheet mislead them.

What does a floor at the end date leave out?

Everything about the route. A floor is a reading taken on one date, and the position has to survive every day between now and that date to collect it. The gap between the two is the difference between knowing where a road ends and knowing whether the car gets there.

Think about a household that has agreed to pay a fixed sum at the end of a year. Knowing the sum is not the same as having it every month along the way. A written leg is the same shape of problem, with one extra feature: while it is open, an amount is lodged against the obligation, and that amount is reworked as the price moves. Move the wrong way far enough and there is a call for further collateralA demand for more to be lodged while a position is still open, made because the price has moved against the side that lodged it. Meeting it is not optional.. A call for more has to be met in cash on a timetable somebody else sets. A position can be closed out on the way to a floor it would never have reached.

Here is the shape of that arithmetic, and every number in it rests on a level set for teaching. On an exposure of Rs 2,000.00/-, a collateral level of 8.0 per cent, set for teaching and not a requirement of any kind, is Rs 160.00/- a unit. An adverse move of 4.0 per cent of that exposure is Rs 80.00/-, or 50.0 per cent of what was lodged. And Rs 2,000.00/- of exposure standing on Rs 160.00/- of collateral is 12.50 times, the leverageHow much reference asset a position stands over, set against the far smaller amount lodged to keep it open. It works in both directions. carried here. The two halves belong on the same line: a four per cent move taking half of what was lodged is the same fact as twelve and a half times, and reading either one alone gives the wrong impression of the other.

Rs 2,000.00/- turns up three times above doing three unrelated jobs, and the agreement is worth explaining rather than leaving a reader to suspect a typing slip. Rs 2,000.00/- is what the reference asset stands at. The same figure is where the pair is struck, and the pair sits exactly there because that is the one level this record puts premiums against. One unit of contract is written over one unit of the thing itself, so Rs 2,000.00/- is the exposure as well. Three quantities, three separate reasons, one figure.

What is a floor still silent on, however carefully it is worked?

Two things, and both of them matter more than the arithmetic does.

A floor with no likelihood beside it is a number and not a comfort. The size of a floor comes out of the rows, while how often it is reached comes out of a spread of outcomes, and no spread of outcomes has been assumed anywhere in this arithmetic. A floor of minus Rs 1,938.30/- that is reached once in a lifetime and a floor of minus Rs 1,938.30/- that is reached most years are the same figure here and are not remotely the same thing to hold. Telling them apart takes a likelihood, and no likelihood is available.

The second thing is closer to home. A floor that is small in the arithmetic can still be more than a particular person could carry. Minus Rs 191.70/- against one unit sounds like nothing. Multiply it by whatever quantity somebody actually put on, set it against what they earn in a month, and the same figure can be either trivial or the end of their year. A floor has a size and it has a survivabilityWhether a particular person could absorb a given outcome, given what else they hold and what they would have to sell to meet it. It varies from one person to the next and is not a property of the contract., and only the first of those two is anywhere in this guide.

Which is why three words mislead. Calling an assembly limited in its risk, defined in its risk, or secure converts a bound in the arithmetic into a reassurance the arithmetic does not support, and readers hear those words as permission.

At what moment does anybody actually reach for this number?

Not at one moment, and that is what makes the two readings worth keeping apart. The same figure gets pulled out at four different points, and at each point a different one of the two readings is the useful one.

The second row is the one people skip, and it is the row that ends positions. A household reading its own sheet the morning after a sharp move does not need to know where the line eventually stops. The household needs to know what has to be found by close of business, and no floor in this guide answers that. The collateral arithmetic therefore sits on a timeline above rather than in the same picture as the payoff.

The third row is the one that changes the reading. The holder's premiums are not the lender's, so somebody lending against a position does not net them into the assessment. A lender wants the obligation as it stands. The obligation as it stands is the payoff reading, and the profit reading is a courtesy to the holder rather than a description of what is owed.

Should the size of a floor decide which assembly is held?

The count above is a way to tell whether an obligation has a bottom, and where it sits when it does. Reading that off the rows is a skill, and a reading skill is not a reason to take on any of the arrangements it reads.

Which assembly to hold is not a matter the arithmetic can settle. Three things sit between the arithmetic and an answer, and this record supplies none of them. Where the reference asset could end up, and how likely each ending is: no spread of outcomes and no run of past results exist here to build that from. The holder's own circumstances: whether a floor of minus Rs 1,938.30/- is survivable turns on what else they hold and what they would have to sell to meet it, and none of that reaches this guide. The cost of the assembly to put on, to keep on and to unwindTo end a position before its date arrives, by taking the opposite side of the same rows rather than waiting for the end date to settle them.: every one of those costs is real and not one of them is priced above, including every call for further collateral along the way.

The count in the second block does one thing and not another. The count sorts assemblies into those with a bottom and those without one. Because a bottom that exists is not automatically better to hold than one that does not, the count does not rank them. An assembly with a floor of minus Rs 1,938.30/- and an assembly with no floor at all are not in an order until somebody supplies the three things above, and none of the three is supplied here.

So the closing line is a small one. Knowing exactly how far down an obligation goes, or that it goes down without stopping, is a skill in reading a sheet. Reading a sheet well is not a reason to sign one.

The reference asset, its price, the financing cost, the two premiums and the collateral level are invented.
Educational material. Not advice on any investment, tax, budget or market position.