Reading Derivatives Data When the Number Is Missing

A reading arrives, and the figure a conclusion would stand on is not in it. The conclusion goes down first, the one quantity it depends on gets underlined, and only then does the looking begin. If that quantity is nowhere, the conclusion is not available and a shorter true sentence is. Five quantities go missing more often than the rest, and each leaves a different remainder.

Now the moment that matters. A readingA figure as it arrives on a screen or in a note, before anything at all has been concluded from it. lands in front of a reader. The arithmetic in it is right. Every figure says what it is. Nothing in it looks thin. And the sentence about to be written about it needs one number that is simply not there. Nobody notices the gap unless that number was looked for before the writing started. A reading and a conclusion are separated by specific quantities rather than by a general shortage of information, and because the gap is specific it can be named, and because it can be named the sentence that survives is something anybody can check.

The method is that, and there is nothing else to it. Everything below runs that one move five times, on five readings from the same invented record, and then sets out the general form. The general form runs on a reading nobody here has ever seen. The mechanisms being read, being where a forward price comes from, how a call sits against a put at one strike, what the two legs of an arrangement do and what is put down against an open position, are settled under those subjects. Each mechanism is used here rather than explained, and each is named in the sentence that uses it.

What comes first when a reading arrives without the number it was supposed to supply?

The conclusion goes down in one line, before anything else is written. Not the paragraph. Not the caveat. One line, in plain words, saying the thing the writer is hoping to be able to say. Then the quantity that line depends on is underlined. Then the search for that quantity begins, and what gets written down is whether it was found, where it was found, and as of when.

The first few times, that order feels backwards. Committing to a claim before it is clear whether the claim can be made is uncomfortable, and the discomfort is the mechanism working. A conclusion written down as one line has exactly one load-bearing quantityThe one number a written conclusion would fall over without. Remove it and the sentence stops being a statement. The sentence becomes a guess. most of the time, and a named quantity is one that can be looked for and not found. A conclusion still swimming around unwritten has no load-bearing quantity at all, because it has not yet been forced to say what it stands on, and a claim that never named its support can never be caught missing one.

Here is the everyday version, and it is worth holding on to because it travels further than the finance one. Somebody at home says the electricity bill this month looks high. Ask what that sentence stands on and the answer is a comparison: high against what, against last month, against the same month last year, against the neighbours, against what the meter reading implies. Now go and look for that comparison. If nobody in the house has last year's bill, the sentence about the bill being high is not available, and a shorter one is: the bill is Rs 4,200/- and nobody here has kept a record to set it beside. The second sentence is less satisfying and far more useful. The person hearing it now knows exactly what to go and fetch.

Every one of the five readings below produces the same three lines under this treatment. The first line is what may still be said. The second is what may not be said at all. The third is what somebody would have to hold before the second list could turn into the first. Three lines every time, so what follows is one move repeated rather than five separate lessons.

What can be said about a premium with no measure of how much the price moves about?

The reading is a pair of premiums on the invented reference asset. A call premium of Rs 180.00/- and a put premium of Rs 57.93/-, both struck at Rs 2,000.00/-, with a spot price of Rs 2,000.00/- and financing at 6.50 per cent a year on an asset that pays nothing at all while it is held. Three of those figures read Rs 2,000.00/-, and they agree for a reason worth stating rather than leaving to be guessed at. The spot price is the quote on the underlying and the strike is the price written into both options. The two match because the pair is struck at the money.

Plenty may still be said, more than most readers expect. The two premiums are consistent with one another and with the forward price, and that shows up in a subtraction. Rs 180.00/- less Rs 57.93/- is Rs 122.07/-. Separately, Rs 2,000.00/- discounted once at 6.50 per cent a year is Rs 1,877.9343/-, and the price of Rs 2,000.00/- less that present value of the strike is Rs 122.0657/-. The two results are the same relationship reached by two routes, and parityThe fixed relationship between a call, a put and a forward at one strike and one final date. Parity holds whatever the price later does. is what the relationship is called.

The relationship holds to the paisa, and never exactly. The two printed figures do not produce an exact equality, and writing that claims one has taught its reader to stop checking. The gap is about forty-three hundredths of a paisa, which is under half a paisa, and it is there for a dull reason: the put premium of Rs 57.93/- is a rounding of Rs 57.9343/-. Nothing is wrong. The rounding is visible, and saying so out loud costs one clause and buys the reader a reason to trust the next figure that appears.

Whether Rs 180.00/- is a lot or a little to pay for that call may not be said at all. Full, rich, cheap, generous, stretched: every one of those words is a size judgement, and a size judgement is a comparison in disguise. A measure of how much the referenced price moves about would have to be known. No measure of that kind appears anywhere in the reading. Pricing an option from scratch would need one, and both premiums arrive given rather than derived. The subtraction survives the absence completely. The adjective does not survive it at all.

What can be said about a price with nothing attaching a likelihood to it?

The reading is one row of a table of prices. A long forward on the invented reference asset, struck at Rs 2,130.00/-, standing at minus Rs 530.00/- at a price of Rs 1,600.00/- on the final date. The strike came from arithmetic and not from anybody's view: Rs 2,000.00/- carried for one year at 6.50 per cent a year is Rs 2,130.00/-, a carry of Rs 130.00/-, and the asset pays nothing while it is held so there is nothing to subtract from that carry.

The figure itself may still be said, exactly, at that price, with no estimate anywhere inside it. Rs 1,600.00/- less Rs 2,130.00/- is minus Rs 530.00/-. The same subtraction is exact at Rs 1,800.00/-, at Rs 2,400.00/-, and at any other price whatever, and it stays exact whether the price ever reaches any of them. The exactness is worth pausing on. A row of a table looks so much like a guess that readers routinely soften it. The row is not a guess. The row describes what the position owes at a price, and the price is a heading rather than a claim.

No price in that table may be called nearer than another, or likelier, or the one to plan around. Ranking prices needs a likelihood attached to each, and the reading attaches none to any. So no row carries a name the other rows do not have. Calling one of them the base case, the central case or the expected case does the ranking quietly, through a label rather than through a sentence, and a reader takes the label at face value.

A likelihood attached to each price would have to be known. Not a general feeling that some prices are more plausible than others, but a stated one, with a source and a method, open to a reader's disagreement. The reading carries no probability and no distribution of any kind. The table below can therefore go on for any number of rows without ever becoming a statement about what turns up.

What can be said about an arrangement with no spread around any of its figures?

The reading is an arrangement with two legs. A notionalThe amount the payments under an arrangement are multiplied by. A notional is a multiplier written into the agreement, not a sum anybody hands over. of Rs 1,000 crore. One side pays a fixed rate of 7.20 per cent a year and receives a floating benchmark. The other side pays the floating benchmark and receives the fixed rate. The floating benchmark reads 6.00 per cent a year for the first period, and this record contains no reading for any period after that one.

The whole of the first period may still be said, worked rather than quoted. The fixed leg over one full period is 7.20 per cent of Rs 1,000 crore, or Rs 72.00 crore gross. The floating leg is 6.00 per cent of Rs 1,000 crore, or Rs 60.00 crore gross. The two difference to a net of Rs 12.00 crore. The fixed payer hands that net to the floating payer, and the same figure comes out in one step from the gap of 1.20 percentage points on Rs 1,000 crore.

Now divide, in both directions. The two quotients teach opposite halves of the same fact. Rs 12.00 crore divided by Rs 1,000 crore is 1.2 per cent, so what actually moves is a bit over one hundredth of the headline. Rs 1,000 crore divided by Rs 12.00 crore is two hundred and fifty over three, or 83.33 to two places rather than exactly. The headline is roughly eighty-three times the cash. The notional never changes hands, and 98.8 per cent of it stays exactly where it is for the whole of the first period.

The worth of the arrangement today may not be said at all, nor the settlement of any later period, nor a typical net across periods, nor the worst period. Every one of those needs a reading of the floating benchmark for periods that have not happened yet. Such a reading is a curveA reading of a rate for every future period rather than only the first one. Without it there is nothing to discount later periods against., and the arrangement above comes with none. So the arrangement cannot be valued at all, and the reason is a missing curve rather than a reluctance to say a number.

What can be said about a position with nothing that came after it?

The reading is a position somebody took. A long forward on the invented reference asset, struck at Rs 2,130.00/-, entered on a spot price of Rs 2,000.00/- with financing at 6.50 per cent a year, on an asset that pays nothing while it is held. The record is the position itself and the four figures it was built from. Nothing follows it.

Plenty may still be said, enough to fill a section on its own, and the amount surprises people. Known: the spot price and the financing rate, both as of the moment the position was entered. Computed: the forward price of Rs 2,130.00/-, the spot price plus a carry of Rs 130.00/-. Assumed: that the underlying pays nothing during the holding period. Checked: that the carry accounts for the entire gap between Rs 2,000.00/- and Rs 2,130.00/-, leaving no room for a view about direction to be hiding inside the figure.

Then one more sentence that costs nothing and does most of the work: which of the assumptions was load-bearing. Here it is the third one. If the asset paid something out during the year, that payout would subtract from the carry and the forward price could sit below the spot price rather than above it. No payout appears in the reading, so the case is named here rather than worked.

Whether the position worked, whether the decision was a good one, or what anybody learned from the way it went may not be said at all. A result would have to be known, and no result was recorded for this position. Now the twist that makes this step behave unlike the other four. Hand over the result and the second sentence still does not become available. Reading the quality of a decision off the way it turned out is a separate error, and a result cannot repair it. Supplying the missing number moves one obstacle out of the way and leaves another standing exactly where it was.

What can be said about a figure with nothing that came before it?

The reading is two figures with no history behind either of them. A count of contracts still outstanding, arriving on its own with no series and no dates. And Rs 160.00/- put down against Rs 2,000.00/- of exposureThe amount of the underlying a position actually stands against, which is a different quantity from the notional and from the amount put down., at an initial margin of 8.0 per cent of the exposure, a rate chosen for teaching rather than one anybody set.

Plenty may still be said about the count, and all of it is structural rather than numerical. Every contract has a long side and a short side, so a change of one in the count means one new long side and one new short side arriving together, and the count records each contract once rather than twice. The statement needs no history at all, and it is true of the first count anybody ever sees.

Plenty may still be said about the two rupee figures, all of it arithmetic on the figures themselves. A 4.0 per cent adverse move on Rs 2,000.00/- of exposure is Rs 80.00/-. The same Rs 80.00/- is 50.0 per cent of the Rs 160.00/- put down. And the same two figures make the exposure 12.50 times what was put down. Name the base out loud every single time. A move of 4.0 per cent and a loss of half of what was posted are the same event described against two different bases, and they sound nothing alike.

No level, no series, no trend and nothing whatever about either figure being high or low may be said at all. High is a comparison, and the reading carries nothing to compare against. A series with its source and its dates would have to be known. And for the count of contracts specifically, there is a second missing number: the contract sizeThe number of units of the underlying that one contract stands for. Without it a count of contracts cannot be turned into an amount of anything. in units, without which a count cannot be turned into money at all. The contract size is set by the Securities and Exchange Board of India (SEBI) at sebi.gov.in, it varies by contract, and it moves, so the address stands here in place of the number.

What do the five readings look like when they are set side by side?

Each of the five above was worked on its own, one at a time, and working them that way is how they are learned rather than how they are best seen. Set side by side they stop being five lessons and become one shape. The left column carries the reading with every figure in place, exactly as it arrived. The middle column names the one quantity a conclusion about it would stand on. The right column is where that quantity's value would go.

The right column is empty in all five rows, and it is empty because this record holds none of those five numbers, not because there was no space for them. Nothing has been left out for tidiness and nothing has been abbreviated. Read the layout across rather than down: reading, missing quantity, blank. Five times, with no exception and no case where a plausible figure has been quietly slipped in to make a row look finished.

The third column repays a moment's attention rather than a glance on the way past. The blankness is doing the teaching. Writing that filled those cells with plausible figures would be more satisfying to read and would have handed over five numbers nobody measured. Writing that filled them with a range would be worse. A range looks like a measurement that has been carefully qualified, and inventing a spread for a quantity nobody holds is exactly the move the whole procedure exists to catch.

What is the general form of the check, in four lines?

Five worked cases are only worth having if they generalise. Here is the form, in four lines, ready to run on any reading at all.

1. Write the conclusion in one sentence. Not the paragraph and not the hedged version. The plain sentence the writer would like to be able to publish, written down where it can be looked at.
2. Underline the quantity that sentence stands on. Usually there is exactly one. Where there are two, the sentence is doing two jobs and should be split before anything else happens.
3. Look for that quantity, and record what turns up. Whether it was found, where it was found, and as of when. All three, because a figure without a date is a figure whose vintage the reader has to guess at.
4. If it is not there, write the longest true sentence that does not need it, and name the missing quantity in the same breath. Not in a footnote and not at the end of the note. In the same breath, so that the two arrive together and a reader cannot take the first without the second.

The fourth line is the one people skip, and it is the one that does the work. Lines one to three are ordinary care, and plenty of careful writers already do something close to them. Line four is the departure, and it asks the writer to publish an absence rather than to quietly work around one. A sentence with its missing quantity named beside it is worth more to a reader than a longer sentence resting on something nobody ever went and looked for.

Why is naming an absence a stronger move than hedging?

Because the two look alike in print and do opposite things, and only one of them can be checked by the person reading it.

A hedgeA sentence that avoids committing to anything without saying what is unknown. A hedge reports the writer's uncertainty and leaves the reader with nothing to act on. avoids a commitment. A closing line saying that a figure may go either way costs the writer nothing to write, cannot be wrong, and gives the reader nothing whatever. Such a line is a sentence about the writer's state of mind wearing the clothes of a sentence about the subject.

A named absenceA stated account of which number is missing and what it would settle. A named absence is a claim about the text carrying it, so a reader can test it against that text. is a commitment, and a testable one. A closing line saying that no likelihood is attached to any of these prices, and that nothing therefore ranks them, makes a claim about the note carrying it. Anybody can go back through the note and look for a ranking. If they find one, the writer is caught. A hedge tells a reader that the writer is uncertain; a named absence tells a reader exactly what the writer does not have. One is a mood and the other is a fact.

Then there is the second-order effect, and it is the reason this way of writing is worth the trouble. A reader who has watched a writer decline five specific numbers, naming each one, has a reason to believe the sixth number when it does appear. A reader who has watched a writer hedge five times has no such reason and no way of getting one. Refusals are the only currency a writer has for buying credibility, and a hedge is not a refusal, it is an avoidance.

What does this procedure not do?

A stretch of writing that has just gone well is exactly where a reader is most likely to draw the wrong conclusion, so the limit gets said plainly here. Five readings have now survived their missing numbers. Overestimating what that leaves in hand is very easy at this point.

The procedure improves what gets written and what gets believed, and it does nothing else at all. It does not supply any of the five numbers. The procedure does not change what a position obliges: the Rs 80.00/- still moves on a 4.0 per cent adverse move, the net of Rs 12.00 crore still passes from the fixed payer to the floating payer, and the long forward struck at Rs 2,130.00/- still stands at minus Rs 530.00/- at a price of Rs 1,600.00/-. Running a check catches a misreading, and a misreading was never part of what any of those contracts required of anybody.

So somebody who runs all four lines on every reading they meet is better at reading and no better protected, and those are genuinely different things. Treating them as the same thing is how a method turns into a talisman.

One more thing belongs here. Somebody who drew a conclusion from a reading that could not support it was doing what almost every commentary they had ever seen was doing. The mistake is not carelessness and should never be written up as carelessness. The default way of writing about these figures skips straight from arithmetic to judgement, so a person who follows the default has copied the room rather than failed at something. A guide that treats it as a personal failing has taught blame instead of reading.

What does a reader who will never publish a line do with this?

Most people who need these four lines will never write a note for anybody. Most are on the receiving end, and the receiving end is where the procedure earns its keep, converting a passive reading problem into a small active one.

The household case comes first, and it matters most and gets written about least. A message arrives on a phone with a screenshot in it and a sentence underneath. The screenshot is real enough: figures, a strike, a premium. The sentence underneath says the premium looks full, or that the arrangement is a huge one, or that a small move barely matters. Line two, run on that sentence, asks what quantity it stands on. Full needs a measure of how much the price moves about. Huge needs to know what actually changes hands, not the headline. Barely matters needs a base named out loud. The same Rs 80.00/- is 4.0 per cent of one thing and 50.0 per cent of another. Nobody is being argued with. One question is being asked, and the question is what the sentence needs rather than whether the sentence is right.

An analyst uses the same four lines as a filter on writing rather than on figures. Given twenty notes on the same subject, the fastest sort is not by who is right. Nobody can tell that in advance. The fastest sort is by which notes name what they do not hold. A note that says plainly that it holds no series behind a figure, and prints the figure anyway with that stated beside it, has said where its edge is. A note that hedges its closing paragraph and prints the same figure has said nothing usable.

A lender looking at a borrower who is party to one of these arrangements runs line two on the credit note itself. The sentence being written is usually about size, and size is the exact place a notional gets read as an amount at risk. Ask of every headline quantity what sum would actually change hands in the period, then divide the headline by that sum, and a Rs 1,000 crore arrangement producing a first period net of Rs 12.00 crore stops looking like a Rs 1,000 crore problem. The habit is worth more than the fact that produced it, and it works on any figure ever presented as a size, in this subject and well outside it.

And somebody holding a position uses the fourth line on themselves, the hardest of the four. The quantity needed to say the position is going well gets written down, then looked for, and whatever does not turn up gets noticed. Nothing about the position changes. The sentence the holder tells themselves about it changes, and that sentence had been doing more work than it could carry.

Who sets the four requirements, and where is each one published?

Four requirements are touched by everything above. Each one has a body that sets it and a site where its current value is published.

Every row is drawn blank for a reason that sits in the reader's interest. Each of those four is set by the authority printed inside its row, each of them changes, and a guide that wrote one of them out would be handing the reader something wrong rather than something merely old. Wrong is worse than old. Old announces itself and wrong does not.

The initial margin of 8.0 per cent of the exposure, which gives Rs 160.00/- against Rs 2,000.00/-, was chosen for teaching and set by nobody. The 8.0 per cent is not a floor, a norm or a typical level, and it was picked so the arithmetic would come out in round figures rather than because it resembles anything. The amount actually required against an open position is worked out under the framework of SEBI at sebi.gov.in by the clearing corporations operating within it, it varies by contract and by day, and it moves. The same goes for every contract size, lot size, expiry, position limit and exposure limit anywhere near this subject: none of them is stated here, and the address is named instead.

Should a reader who can do all of this enter into one of these contracts?

The question arrives here and is answered here rather than in small print at the foot. Running those same four lines on it produces the answer, and a limit that comes out of a procedure is worth more than one announced as a policy.

Line one, the conclusion in one sentence: this reader belongs inside one of these contracts. Line two, the quantities that sentence stands on. There are four. The first is what the reader already carries. A position means something different beside one holding than beside another. The second is the sum whose loss would change something for them, a fact about their circumstances and not about the contract. The third is a likelihood attached to every price rather than a list of prices. Without it the list describes obligations rather than supplying a basis for choosing. The fourth is whether the position is open to this particular reader at all, a permission question.

Line three, the search, and the record of what turns up. Three of the four are facts about a person, and no reference work anywhere can hold those. The fourth sits with SEBI at sebi.gov.in, an address rather than a value, and it moves.

Line four, write the longest true sentence that does not need them, and name the missing quantities in the same breath. Understanding a mechanism completely is not a reason to use it. Whether anybody belongs inside one of these contracts turns on those four quantities, and somebody would have to hold all four before the question could be answered at all. The limit is not modesty and it is not a disclaimer. The limit is the output of the same four lines run above on premiums, prices, arrangements, positions and margin.

The reference asset, the option pair, the two legged arrangement, both of its sides, the note quoted in the failure block, the initial margin of 8.0 per cent of the exposure and every figure in this guide are invented for teaching.
Educational material. Not advice on any investment, tax, budget or market position.