How Corporate Actions Can Affect Derivative Contracts

A corporate action can change the shape of the thing a contract references overnight. The contract’s own figures were written against the old shape. A rewriting puts those figures right. The position is worth what it was worth the moment before, and the exposure behind it has not moved. Holding the exposure still is what leaves the collateral standing against the position untouched.

Everything in this machinery is measured against the referenced thing. The exposure is a quantity of it. The collateral is struck as a proportion of that exposure. The settlement price each position is revalued at is a price of it. Let the referenced thing change shape while the contract's figures stay as they were, and every one of those measurements is being taken against something that has stopped existing. The arithmetic will keep running, and it will run perfectly, on figures that no longer describe anything.

Every figure below answers one of three questions. Was it agreed, quoted or determined by somebody? Then it is a PRICE, and Rs 2,000.00/- spot and Rs 2,130.00/- agreed are both of them prices. Did it leave an account or reach one? Then it is a PAYMENT. Is it what survived after obligations pointing both ways were set against one another? Then it is a NET. Quantities take a second pair of labels. Two units at Rs 1,000.00/- multiply out to Rs 2,000.00/-, and that product is what the word EXPOSURE means here. A NOTIONAL is the other sort of quantity altogether: a face figure a contract is written upon. No rewriting touches a NOTIONAL, and not one rupee of it ever moves.

What goes wrong when the thing a contract references changes shape?

A canteen has a standing order with its oil supplier for one carton a week, and a carton holds twelve tins. The supplier changes the packing to six tins a carton. The standing order still reads one carton, so what turns up on Monday is half the oil, and nobody wrote a single word of it down wrong. The order was accurate on the day it was placed. The order became inaccurate without being touched. The word carton had stopped meaning what it meant on the day the order was signed.

A contract that references something carries figures written against that thing as it was on the day the contract was struck, and the contract has no way of noticing when the thing stops being that. There are three such figures on the position worked through here. The quantity: one unit. The price a unit: Rs 2,000.00/- spot, a PRICE. The agreed price: Rs 2,130.00/-, also a PRICE, being Rs 2,000.00/- taken forward twelve months at 6.50 per cent a year. Every one of those three was correct the moment it was written down.

Now suppose an event changes the denominationThe size of unit a figure is quoted in. Change that and the figure changes while the amount behind it does not. the referenced thing comes in. A unit of it after the event is not the same object as a unit of it before. The three figures on the contract have not moved. The three figures cannot move on their own: a contract is a document, and a document does not read the news. The quantity still says one unit, and the word unit now means something smaller. The price a unit still says Rs 2,000.00/-, and no unit anywhere is worth that any more.

A change of denomination matters more here than it would for a shopping order. The units of a referenced thing are ordinarily fungibleOne of a kind where any unit does the job of any other unit, so nobody minds which particular one they are handed. and the whole arrangement leans on that. A contract does not name which unit it is written over. A contract names a count and a price a unit, and it trusts that a unit is a unit. Take that away for one night and the count and the price stop describing the same object.

So the problem is not that anybody made a mistake. Nobody did. The problem is that a correct record of a vanished object is a wrong record, and it goes wrong silently, without a single figure being altered by anyone. A rewriting exists to repair exactly that silent wrongness, and the repair has to be done by somebody, on a stated basis, rather than left to work itself out.

How is a correct rewriting recognised?

A rewriting has been done correctly when the position is worth what it was worth the moment before and the exposure standing behind it comes to the same figure on both mornings. The test is the whole of it, and it holds whatever any rulebook says. A test of that kind is not a rule but a definition: preserving the position is what the word rewriting has to mean if the word is to mean anything. A rewriting that left the position worth more would have handed one side of the contract money, and the money would have come out of the other side, and neither of them would have done anything to deserve it or to prevent it.

The consequence that matters in this part of the machinery follows in one step. The collateral behind the position is struck as a proportion of the exposure. Hold the exposure still and the proportion of it does not move either, so the total lodged is untouched. Hold both still and the relation between them is untouched as well. Both the total collateral and the multiple it implies are computed off the exposure, and neither has any other input. Get the exposure right and both of them come right on their own.

There are four figures worth checking, and the fourth is the agreed price read across the new quantity rather than a unit. The agreed price is the only figure on the position that was never derived from the spot price on the day: it was fixed when the contract was struck and has been sitting there ever since. The fourth check therefore catches something the other three can miss. If the rewriting scaled it by the wrong ratio, the position would owe or be owed a different amount at the end date, and the exposure alone would not reveal it.

What actually changes on the position, and what does not?

Take the position as it stood the evening before. One unit. The price a unit is Rs 2,000.00/- spot. One times Rs 2,000.00/- makes an EXPOSURE of Rs 2,000.00/-. The agreed price is Rs 2,130.00/-. Take Rs 2,000.00/- forward twelve months at 6.50 per cent a year of financingWhat it costs to borrow the money for something being held. Here it is the reason Rs 2,000.00/- turns into Rs 2,130.00/- by the end of a year.. Across those twelve months the reference asset returns its holder not one rupee. Had a payment come off it, the agreed price would sit below Rs 2,130.00/- instead of at it.

Rs 160.00/- of collateral sits behind that one unit. The figure is 8.0 per cent of the exposure, a percentage invented for teaching. The exposure runs to 12.50 times what has been lodged behind it, Rs 2,000.00/- standing over Rs 160.00/-. And a 4.0 per cent slip in the reference asset removes Rs 80.00/- of value. Set beside the Rs 160.00/- lodged, that comes to one half of it.

Now apply an invented ratio that turns one unit into two. The quantity becomes two units. The price a unit becomes Rs 2,000.00/- over 2, or Rs 1,000.00/-. The agreed price a unit becomes Rs 2,130.00/- over 2, or Rs 1,065.00/-, and the two units together therefore still carry Rs 2,130.00/-. The collateral becomes Rs 160.00/- over 2, or Rs 80.00/- a unit, and the two units together still lodge Rs 160.00/-.

Every figure written a unit has halved, and not one figure describing the position as a whole has moved at all. The exposure is two times Rs 1,000.00/-, or Rs 2,000.00/-. Divide the exposure by what was lodged and 12.50 falls out, exactly as it did the evening before. A 4.0 per cent slip in the reference asset still costs Rs 80.00/- across the position and still amounts to half of everything lodged. The position holder has done nothing, has been asked for nothing, and stands precisely where they stood.

The two halves behave differently for a precise reason, and the reason is not that one set of figures is more important than the other. The upper four are all divided by the ratio, or multiplied by it in the case of the quantity. The lower three are all products or ratios in which the ratio appears once on top and once underneath, so it cancels before it reaches the answer. Nothing is being protected. The cancellation is arithmetic and nothing else.

Why do two different figures here both read Rs 80.00/-?

Rs 80.00/- turns up twice in the paragraphs above and the two are not the same quantity. Collateral of Rs 80.00/- a unit is what Rs 160.00/- becomes once it is spread over two units, and it is a proportion of an exposure. The other Rs 80.00/- is what a 4.0 per cent slip in the reference asset takes off the position, and it is a movement in value. The two figures agree because the invented margin percentage, 8.0, happens to be exactly twice that 4.0 per cent, and because the ratio worked here happens to be two. The agreement is forced arithmetic and not a signal of any kind.

Step to a ratio of one into four and the agreement disappears. The collateral a unit falls to Rs 160.00/- over 4, or Rs 40.00/-. The 4.0 per cent slip is struck on the exposure and the exposure has not moved, so the slip stays at Rs 80.00/-. Watch that separation happen in the simulation below: the collateral marker slides down past a level line that stays exactly where it is.

The same warning applies one step earlier. Two figures above read Rs 2,000.00/- and they are not the same quantity either. One is the price of a single unit, a PRICE. The other is the exposure of the whole position, a quantity of referenced thing, and it agrees with the first only because the position holds exactly one unit. The first rewriting worked above pulls the pair apart. Two units at Rs 1,000.00/- still make Rs 2,000.00/- of exposure, and the price a unit has become something else entirely.

Why does any of this sit beside the collateral machinery?

Here is the reason this belongs next to margin and settlement rather than next to the events themselves. Suppose a rewriting got the exposure wrong. Nothing would break, nothing would complain, and no figure anywhere would come out looking odd. The settlement price for the day would still be determined. The position would still be priced again against it. A call would still be worked out and collateral would still move. Every one of those steps takes the exposure as an input and none of them has any means of asking whether the input is the right size.

Work it through on a deliberately wrong rewriting, one nobody would publish, put here only to see what fails to object. Say the quantity is doubled to two units and the price a unit is left at Rs 2,000.00/-. The exposure now reads Rs 4,000.00/-. The collateral, struck at the invented 8.0 per cent, reads Rs 320.00/-. The agreed price across two units reads Rs 4,260.00/-. Three of the four checks catch it immediately. The fourth does not: Rs 4,000.00/- over Rs 320.00/- is 12.50 times, exactly what it read the evening before.

Scaling the top and the bottom by the same factor leaves a ratio alone, so a ratio survives a scaling error. The blind spot is not a defect in the four part test and the row stays in it, but it is worth knowing which of the four is doing the work. The multiple is there to show what the position feels like to hold. The multiple is not there to show whether the position has been described correctly, and a reader who checks only the multiple will find every scaling error looking perfectly normal.

A silent error of that kind is why the test above is worth carrying in mind, and why the method behind a rewriting is settled beforehand by somebody other than the two sides of the contract. A rule fixed in advance is a rule fixed while nobody yet knows which side of it they will be standing on. Fixed on the morning instead, one side is arguing for the arithmetic that suits it. The machinery could not survive that negotiation twice.

Which events cause an adjustment, and who decides the method?

Not every corporate action leads to a contract being rewritten, and which ones do is not decided by anybody exercising judgement on the day it happens. Both halves of that sentence carry weight and they carry different weight. The first says the reader should not expect a rewriting every time something happens to the referenced thing. The second says that where one does happen, the arithmetic behind it was written down before the event was announced, and the person applying it is applying rather than deciding.

The second half is the more important one for a reader trying to understand why the machinery works. A rewriting is applied by a conventionA way of doing something that was settled once and is followed thereafter, rather than argued out afresh every time it comes up. and not by discretionRoom to decide a thing case by case at the moment it happens, instead of following something written down beforehand.. If it were the second, the two sides of every contract would have an argument to have on the morning of every event, and each of them would know which answer they wanted before the discussion started.

Which events, and by what arithmetic, the Securities and Exchange Board of India (SEBI) settles at sebi.gov.in. Neither half of that has been written into the paragraphs above. The venue publishes an announcementA notice put out to say that a change is coming and what will happen to what. Who publishes one, and what has to be inside it, is covered separately. naming what is being rewritten and how, and that notice is the document a position holder reads.

What does an adjustment deliberately not do?

Readers expect more of a rewriting than a rewriting offers, and the over-expectation is understandable. The word rewriting sounds like a word for putting somebody back where they were. A rewriting keeps the arithmetic lined up with the new shape of the thing, and it pays nobody anything for what the event did to the worth of the thing. Lining up the arithmetic and paying for lost worth are two entirely separate matters, and only the first of them is being attended to.

Put it in the canteen again. When the supplier repacks twelve tins into cartons of six, correcting the standing order to two cartons a week restores the oil. The correction does nothing whatever about the price of oil. If oil got dearer that week, the canteen pays more, and no amount of rewriting the order changes that. The order never set the price of oil.

So if the referenced thing is worth less after an event than before, on its own merits, the position holder carries that in exactly the way they carry every other movement in the referenced thing, through the daily revaluation and through whatever call follows from it. The rewriting concerns the units the contract is written in, and the worth of what is inside those units is somebody else's department entirely. A reader who expects otherwise will read every rewriting as a compensation that has been mysteriously withheld.

What does a position holder see on the morning after one?

Every figure on the statement written a unit has changed, and the position holder did nothing to bring any of it about. The quantity reads two units where it read one. The price a unit reads Rs 1,000.00/- where it read Rs 2,000.00/-. The agreed price a unit reads Rs 1,065.00/- where it read Rs 2,130.00/-. The collateral a unit reads Rs 80.00/- where it read Rs 160.00/-. Four rows, four changes, and no instruction given by anybody holding the position.

One question settles the lot of it, and it is: has the exposure changed. If the answer is no, the position is where it was. Then three follow ups, in the order that makes them quickest to ask. Is the total collateral the same figure it was. Is the exposure for each rupee lodged the same multiple. Does the agreed price read across the new quantity come to what it came to before. On the worked instance those answers are Rs 2,000.00/-, Rs 160.00/-, 12.50 times and Rs 2,130.00/-, and every one of them matches the evening before.

A reader who can ask those four questions needs to know nothing whatever about the method. Knowing nothing about the method is precisely what makes the test more useful to that reader than any formula could be. The arithmetic behind a rewriting is somebody else's job and is published by somebody else. Checking that the arithmetic left the position alone is a job that takes four glances and belongs to whoever holds it.

Where do the rewritten figures actually land?

Follow the rewritten figures out of the contract and they come to rest in four separate places, and the four places do not check the same thing. A risk desk pulls the exposure into a total, so a wrong exposure on one position quietly moves a firm level figure that nobody is looking at position by position. A lender holding the position as security copies the collateral figure onto a schedule of what it is holding. The total is what such a lender can call on, so the lender wants the total rather than the figure a unit.

A household reads the same rewriting off an account statement over breakfast and sees only the price a unit. The price a unit is the row printed largest, and the row that means something in ordinary speech. The household reading is the one the failure below is built on. An analyst files the sheet beside last week’s and cares mainly about the fourth check, the agreed price read across the new quantity. The agreed price decides what the position settles for at the end date, and it is the one figure a casual glance never reaches.

Four destinations, four different rows examined, and only one of them naturally looks at the exposure that all four depend on. The narrowness is not a criticism of any of them. The split is the reason the four part test is stated as four parts rather than one, and the reason a position holder who checks only the row printed largest is checking the row least likely to tell them anything.

What cannot be shown without a real corporate action

There is no corporate action anywhere in the material behind these notes. No issuerWhoever brought the thing into existence in the first place and answers for it afterwards. What an issuer does, and why, is covered separately. either, and no method of rewriting. The ratio worked above is therefore invented, and what can be shown is what a rewriting has to preserve rather than what any real one did.

The four ratios were chosen because one into two, one into four and one into five all divide Rs 2,000.00/-, Rs 2,130.00/- and Rs 160.00/- into whole paise. Whole paise keep every figure checkable by hand, and the convenience is a teaching one and nothing more. Nothing about the choice of ratios carries information about what ratios occur, how often anything is rewritten, or what any rewriting looked like when it was done.

Where the body in the middle gets its capital is covered separately. All that is borrowed from it here is that the body is there at all, and that it prices every position again each evening. A reader who wants what a real rewriting did reads the venue's own notice, published under SEBI at sebi.gov.in, and what they will find there is a document rather than a principle.

Does a position holder have to act when one is announced?

A reader who has followed all of that will want to know whether they ought to be carrying one of these positions. Answering that takes not one thing but several, and none of them is available here. The job the position is there to do. The exposures that already stand against it. The collateral lodged already, and whatever else could be turned into cash quickly if a call landed. And beyond all of those, the size of the call that arrives on the single worst morning. A worst morning call is a different figure from the one that arrives on a typical morning, and it decides whether the position can be carried at all.

The arithmetic above establishes what a rewriting preserves, and preserving a position is not the same as commending one. A rewriting says nothing about whether the position was worth holding the day before the event, and nothing about how any position turned out. Whether such a position belongs anywhere near a particular reader is settled by that reader’s own circumstances.

None of this is a method. The four figures are simply what to look for on a morning when everything else on the sheet has moved, and the looking takes about as long as reading this sentence.

The reference asset, the position holder, the clearing member and the body the clearing member faces are invented, along with the financing cost of 6.50 per cent a year, the margin percentage of 8.0 and the four ratios.
Educational material. Not advice on any investment, tax, budget or market position.