Collar and Protective Put: Two Different Obligations

A protective put is a holding of the reference asset together with a put on it. The holder ends with the higher of the price and the strike, and pays a premium for that. A collar adds a written call on the same holding, so the premium received funds the put and the holder gives up whatever lies above the call's level. The first keeps that part and pays for it. The second sells it.

Both arrangements start from the same place: one unit of the reference asset, sitting there, with contracts laid on top of it. The difference is not how many contracts there are but how many of those contracts point away from the person holding them. A bought leg leaves every choice with the holder, and a written leg hands one of those choices to somebody else and takes away the power to refuse it. Adding the second kind of leg is the whole of the difference between paying for a shape and selling one. Everything that follows comes out of that single sentence, including one finding in the middle of it that most readers do not expect.

What is a protective put, once it is spelled out in full?

Two things held at the same time. The first is the reference asset itself, one unit of it, bought and paid for and sitting in the holder's hands. The second is a put written on that same reference asset at a stated level, and the important word is that the put has been bought, so the right to use it belongs to the holder and the matching obligation belongs to whoever wrote it. A protective put costs money on the day it is put on for exactly that reason: a right that only one side holds has to be paid for, and the payment is the premium.

Take it out of the market for a moment. A stall holder has bought the whole season's stock, paid for it, and has it stacked at the back. Then they walk over to somebody with deeper pockets and pay a fixed sum for a promise: if the season goes badly, that person will take the entire lot off their hands at a price agreed today. The stock never stops being the stall holder's. The promise is the thing they paid for, and the fixed sum they handed over is gone whether or not the season goes badly. If the season is a good one, the promise is never called on and the fixed sum was simply the cost of not having to worry. A protective put is that stall and that promise, described without a line of notation.

The invented figures in this guide put numbers on the same picture. The reference asset has a price of Rs 2,000.00/- on the day the arrangement is put on. The put is struck at Rs 2,000.00/-, and the match is by construction rather than by accident: the pair of contracts used across this whole lesson is struck at the moneyUsed of a contract where the level written into it and what the referenced thing costs right now happen to land on one number.. The figure written into the contract and the figure the reference asset is changing hands at are one and the same. Financing runs at 6.50 per cent a year, both contracts have a year to go, and the reference asset returns not one paisa to whoever is holding it across that year. A payment coming off it would move every carried figure below, so that last condition earns its place.

The put premium in this working example is Rs 57.93/-. The premium is taken from the record rather than worked out here. The reason is plain: pricing an option from scratch needs a measure of how much the reference asset moves about, and no such measure exists anywhere in the record this lesson is built on. The two premiums here are consistent with each other, a different and smaller thing, and that consistency is all the arithmetic below leans on.

What does a protective put leave the holder with at each price?

Here is the sentence to hold on to, and it replaces the two case version most readers were taught. The payoff on a protective put is the higher of two numbers: whatever the reference asset is fetching when the contracts run out, and the strike. Not one rule for a fall and another rule for a rise. One rule, applied once. If the reference asset ends at Rs 1,600.00/-, the higher of Rs 1,600.00/- and Rs 2,000.00/- is Rs 2,000.00/-. If it ends at Rs 2,400.00/-, the higher of the two is Rs 2,400.00/-. The line is flat at Rs 2,000.00/- everywhere below the strike and rises one rupee for one rupee everywhere above it, and it never does anything else.

Now the second line, and the reason two lines are needed at all. A payoff counts nothing that changed hands at the start. The premium of Rs 57.93/- left on day one. Money left in the financing arrangement earns 6.50 per cent a year, so by the last day the premium is not worth Rs 57.93/- any more. Carried across the one year the contracts run, Rs 57.93/- becomes Rs 61.70/-. Take that off the payoff at each price and the profit line appears: Rs 1,938.30/- where the payoff is Rs 2,000.00/-, and Rs 2,338.30/- where the payoff is Rs 2,400.00/-.

Payoff line and profit line sit Rs 61.70/- apart, and it is the same Rs 61.70/- at every single price. A gap that never changes is exactly the kind a reader loses track of. A constant does not draw attention to itself. The two lines are parallel from one end of the diagram to the other, they never converge and they never cross, and a reader who reads the payoff line and calls the answer a profit is out by the same amount at every price rather than by an amount that would announce itself at one of them.

What is a collar, spelled out the same way?

Three things held at the same time, and the first two are the ones already met. The reference asset itself. A put bought on it at a stated level. And then the third: a call written on the same reference asset, meaning that the right under that contract belongs to somebody else and the obligation under it belongs to the person doing the holding. A right somebody else holds has to be paid for by them, so money comes in on day one, and the payment lands with the writer.

The stall again. The stall holder still has the season's stock at the back and still has the promise they paid for. Now a second person walks up with an offer in the other direction: the right to take the whole lot off the stall at a set price if the season goes well, paid for today. The stall holder takes the money. The obligation they have taken on in exchange is not a bill and not a payment falling due later. The obligation is a standing instruction they cannot revoke: if the season goes well, the lot goes to that second person at the price agreed, and the stall holder gets no say in it at all on the day.

The direction of each leg is the whole of the difference, and it is worth counting them rather than adding them up. On a protective put, two legs, and both of them sit entirely inside the holder's control. On a collar, three legs, and the third one has been turned around to face the other way. Nothing about the first two has changed. The reference asset is still there, still bought and paid for. The put is still bought, still usable at the holder's discretion, still nobody else's decision. The arrangement has grown by exactly one contract, and that one contract is the only one on which somebody else gets to act.

What does the written leg actually hand over?

The written leg is the part most readers skim, and the reason they skim it is almost sympathetic: the written leg is the only one of the three that pays them anything at the start. Rs 180.00/- arrives. The money is real, it is countable, it is in hand on day one, and it does not have to be given back. Left in the financing arrangement at 6.50 per cent it would stand at Rs 191.70/- by the last day, and even that figure settles nothing about the leg it came from. Everything about it feels settled, and a settled item gets read once and filed.

Money is not what left in exchange. Out went every rupee of the reference asset above the level of the written call, for the whole life of the contract, permanently, whatever happens. If the reference asset ends at Rs 2,400.00/- and the call was written at Rs 2,000.00/-, then Rs 400.00/- of what the reference asset did belongs to the person who bought that call, and the holder has no route to any of it. Not a reduced share. None.

An amount and a shape are not the same kind of thing, so the premium received cannot be set against what was given up and called a net cost of anything. Rs 180.00/- is a number with a decimal point. The part given up is a region of a diagram whose size depends entirely on where the reference asset ends up, and where it ends up is the one thing nobody here knows. The two do not net. An amount and a shape do not even share a unit. A reader who notes down a receipt of Rs 180.00/-, then something given up, then a balance in their favour of Rs 180.00/- less something small has run a subtraction between an amount and a shape and come out with an answer that wears the clothes of arithmetic.

The asymmetry, in its plainest form. On the written leg the right belongs to somebody else and the obligation belongs to the holder. There is no event, no price, no market condition and no passage of time that flips those two back around. The person holding the right will exerciseTo use a right a contract carries, which turns the contract into the exchange of money and asset it describes. it when doing so suits them, and the moment that suits them is precisely the moment it does not suit the holder. The design produces that, not bad luck.

Set side by side, what does each one oblige?

Four rows, and one thing to be clear about before any of them are read. Obligations are what the four rows set against each other: what moves at the start, what the holder may do, what may be done to the holder, and what is left after a long rise. Results are a separate question and cannot be set side by side at all. Neither arrangement worked above has an outcome, a track record or a history of any kind behind it, so nothing above ranks them.

The third row generates all the others, so read it again. On a protective put, no leg of the arrangement faces away from the holder. Nobody can serve anything on them, nobody can require anything of them, and there is no last day on which somebody else's decision arrives uninvited. On a collar there is exactly one such leg, and its existence is what puts a lid on the fourth row and what puts money in on the first. One structural fact, three visible consequences, and the fact is simply that a leg was turned around.

What happens when both contracts sit at the same level?

Now the central point, and it is a finding rather than a definition. This lesson has a call premium and a put premium that agree with each other at one level and nowhere else, so the working example carries both contracts at Rs 2,000.00/-. Put together at that one level, a collar does something the word collar does not prepare anybody for.

Work it rather than assert it. Hold the reference asset. Buy the put at Rs 2,000.00/-. Write the call at Rs 2,000.00/-. Then take the four checkpoint prices this lesson uses throughout and add up what each leg pays at each of them.

The combined payoff comes out at Rs 2,000.00/- when the price finishes at Rs 1,600.00/-, comes out there again at Rs 2,000.00/-, again at Rs 2,130.00/- and again at Rs 2,400.00/-, which is not a floor with a rise above it but a flat line, and a collar built at one level is therefore not a collar at all. The put stops the line falling below Rs 2,000.00/-. The written call stops it rising above Rs 2,000.00/-. Between the two of them there is nothing left for the line to do in either direction, and what the holder has is not a holding with protection under it but a fixed amount wearing three legs.

The diagram makes it look tidier than it is, so say what it means in ordinary words. The holding has been neutralised rather than protected. Whatever the reference asset does between now and the last day, right or wrong, up or down, by a little or by a great deal, the payoff is the same figure. A reference asset that hands its holder nothing along the way and then finishes anywhere at all still leaves the same Rs 2,000.00/- at the end.

Now the tie back, and every part of it is already in place. The net premium on this arrangement is received rather than paid: Rs 180.00/- comes in on the written call and Rs 57.93/- goes out on the bought put, leaving Rs 122.07/- in hand on day one. Carry that at 6.50 per cent across the year the contracts run and it becomes Rs 130.00/-. Set that on top of the flat Rs 2,000.00/- and the holder finishes at Rs 2,130.00/-. The closing Rs 2,130.00/- is the forward priceWhat buying the thing today and borrowing the money to do it works out to by a stated later date. It is a cost worked forward rather than an opinion about where a price is going. on this reference asset, settled by the earlier part of this subject long before options were mentioned.

Two things about that agreement, and the second matters more than the first. The agreement is forced arithmetic rather than a happy coincidence. Take the difference between the two premiums forward a year and what drops out is the reference asset taken forward a year, less the level the contracts are struck at: Rs 2,130.00/- take away Rs 2,000.00/-, being Rs 130.00/-. Nothing was fitted to make that work. The parity relationshipThe arithmetic tie between a call and a put sharing one level and one date, which fixes what one of them must cost once the other is known. the reader has already checked between a call and a put has turned up here from a third direction. And it lands to the paisa and not on the nose. Bringing Rs 2,000.00/- back to today at 6.50 per cent gives Rs 1,877.9343/-. The true gap is therefore Rs 122.0657/- and the rounded put leaves Rs 122.07/-, a distance of 0.43 paise. Asserting an exact equality that rounded inputs cannot deliver quietly tells the reader that checking is not worth their time.

Why is the two level collar not worked out here?

A collar as it is usually built does not put both contracts at one level. The bought put sits below the current price of the reference asset and the written call sits above it, and the combined payoff is then a band: flat at the put's level while the reference asset is below it, following the reference asset rupee for rupee between the two levels, and flat again at the call's level above that. A floor under it and a ceiling over it, with live ground in between.

That band can be drawn exactly, and it is drawn below, but the cost of putting it on cannot be stated here at all. The two things are not equally knowable and the difference between them is worth being precise about. The shape needs only the two levels, and levels are inputs the reader chooses, along with the expiryThe date written into a contract after which no right under it can be used at all, whatever the thing it references then does. both contracts share. The cost needs the premium on the second contract, and this working example carries a premium at one level only.

Name what would have to be known to produce it. The premium on a call written at any level other than Rs 2,000.00/- depends on the range the reference asset could cover before the contracts run out, and on the weight sitting on each part of that range. Neither of those exists anywhere in the record behind this lesson. There is no history for the reference asset, no spread of endings, no weighting across them and no measure of how much it moves about, and that absence is deliberate rather than an oversight.

Putting a made up second premium here would leave a plausible wrong figure in place. A named absence can be checked. A plausible wrong figure invites being used, and that makes it the worse of the two. A third premium invented to fill a hole would also disagree with the other two, breaking every treatment that leans on the pair agreeing. So the shape below is exact and the box inside it is empty, and the box says why on its own face.

Which figures are payoffs, and which are profits?

Both arrangements make this easy to get wrong, so it gets its own heading rather than a parenthesis. A payoff is what the combination pays on the last day and it counts nothing that was paid or received at the start; a profit takes the premium into account as well, brought up to that same last day at the same financing rate. The distinction is not pedantry and it is not a rounding matter. On the protective put it is worth Rs 61.70/-, and on the collar it is worth Rs 130.00/- in the other direction.

Take the protective put first, on its own terms, with nothing else in the picture.

Every row of the third column is the second column less Rs 61.70/-, which is what Rs 57.93/- of put premium grows to over twelve months at 6.50 per cent a year. Now the collar built at one level, on its own terms too.

Here the profit column sits above the payoff column rather than below it, by Rs 130.00/-, because the premium on this arrangement came in rather than went out. The two tables are descriptions of what each arrangement owes at each price and nothing more. Neither is a forecast, neither is a claim about which arrangement is worth putting on, and lining the two profit columns up next to each other and pointing at the larger figure would be answering a question there is no information to answer.

One more distinction travels with the payoff and profit one, and both tables are still in view. A received premium is not a profit, for exactly the same reason a paid premium is not a loss: neither of them has met the end of the contract yet. The Rs 122.07/- in hand on day one is a premium sitting in the holder's pocket with a year of obligation still to run against it. Once that year has run and the premium has been carried to Rs 130.00/-, it is the amount that turns a flat Rs 2,000.00/- into Rs 2,130.00/-. Counting it as money made on day one and then counting the Rs 2,130.00/- at the end counts the same rupees twice.

And one line on what each figure here actually is. The premiums of Rs 180.00/- and Rs 57.93/- are amounts that genuinely move between two parties. The Rs 2,000.00/- of reference asset sitting underneath both arrangements is exposure in the technical sense, the value the contracts are written on, and on these two arrangements it is also something the reader has actually bought and paid for. The figure a contract is sized against is not always bought and paid for. Where a contract's payments are sized against a figure that never changes hands at all, that figure is a notionalA figure a contract's payments are sized against, used as a multiplier, which does not itself move between the parties at any point. and it is a different animal, settled elsewhere.

How does anybody use this outside a lesson?

Somebody hands over a single sheet describing an arrangement on something a business already holds. The sheet has a name at the top, some levels, a premium figure and a diagram. So what does a person actually do with it, if they are a lender looking at a borrower's hedging, an analyst reading a disclosure, or a household head who has been shown something at a bank counter?

The direction of the legs decides the shape, and the figures only decide where the bends sit. So the first move is to count the legs and sort them by direction, before reading a single figure. How many contracts are described? On how many of them does somebody other than the holder get to act? A sheet describing two legs both facing inward has a floor under it and its cost is a number. A sheet describing three legs where one faces outward has a lid on it, and the lid is the part the sheet will describe last and briefly.

The second move follows from the first. For every leg that faces outward, ask what region it removed rather than what premium it brought in. This is the discipline that stops an arrangement being read off its premium line. The premium is on the sheet in a box with a rupee sign. The region removed cannot be written as a single figure, so it is nowhere on the sheet at all. A lender reading a borrower's hedging arrangement is asking whether the borrower can still benefit from a recovery in the thing they hold, and the answer to that question lives in the legs facing outward and never in the premium box.

The third move is the one demonstrated throughout: check whether the levels are the same. An arrangement whose put and whose written call sit at the same level has no live ground between them and no participation at all. Building that is legitimate, in the sense that somebody may have wanted precisely that outcome, but it is a different thing from what the word collar suggests, and anybody reading a sheet needs to know which of the two they are looking at. Reading the two levels off the sheet takes four seconds and settles it.

The fourth move is knowing what the sheet cannot tell anybody. The cost of holding the arrangement to the end and the cost of unwinding it early are separate from the premium. What has to be placed as collateralValue placed with the system by whoever carries an obligation under a contract, held against the chance that the obligation is not met. where one leg is written against a leg held is separate again and is set by an authority rather than by the sheet. And what the reference asset is capable of doing between now and the last day, expressed as more than a single number, is not on the sheet either and is the input everything else would need. A reader who has these four moves has more than a definition. The four moves are a way of reading the next sheet that is handed over.

Should either of these be held?

Whether either arrangement should be held has no answer above, and the silence is a matter of missing inputs rather than caution. Answering it would take three separate things, and not one of them exists in the record this lesson is built on.

The first is some view of where the reference asset could get to by the last day and how much of that view rests on each ending. The record behind this lesson contains no history for the reference asset, no spread of endings and no weight across them, so the question cannot be answered here rather than merely being left unanswered. Second, the circumstances of whoever is asking, never visible to any written account: what is already held, what has already been promised elsewhere, and what a bad year would really mean inside that particular household or business. Third, the cost of entering each arrangement, carrying it through to the last day and closing it out early, and this working example cannot even hand over the premium on a second contract, never mind the rest of that.

Draw either arrangement and what sits on the paper is a statement of who owes what at every price the reference asset could reach, carrying no claim at all about which of those prices turns up. That sentence is the whole of the boundary between a lesson and a suggestion, and it is worth carrying away more than any of the figures. The shapes above are exact, checkable and complete. The shapes are also silent on the only question that would decide anything.

The reference asset, its price of Rs 2,000.00/-, the Rs 2,000.00/- level both contracts are struck at, the 6.50 per cent a year financing cost and the two premiums of Rs 180.00/- and Rs 57.93/- are invented.
Educational material. Not advice on any investment, tax, budget or market position.