How to Take a Structured Product Apart, Step by Step

Taking a packaged instrument apart is eight steps in a fixed order. Every movement of money the document provides for is listed. Each one is marked by whether its amount depends on the reference asset. The leg behind each group is named. The legs that can be priced are priced, on one date. The leg prices are added up. The total is subtracted from the price asked. Then the routine stops. The remainder is where the packaging is paid for.

Every figure below belongs to an invented instrument written on an invented reference asset. Three inputs generate the whole of it: a spot price of Rs 2,000.00/- for the reference asset, financing at 6.50 per cent a year for one year, and a call premium of Rs 180.00/- that is supplied rather than worked out. The reference asset pays nothing at all while it is held. The absence of a payout matters. A payout during the year would change the arithmetic at the fifth step, and this reference asset makes none.

The eight steps below are a routine rather than an explanation. A call obligation, a premium, present value, and the reason an amount due in a year is worth less today than the same amount now are all covered separately, and the steps below use them rather than rebuild them. The order is what the routine supplies instead, and the order is the whole of the value. A reader who prices before naming, or names before marking, produces a sheet that looks finished and is not.

Why does taking one of these apart work at all?

Because nothing inside a packaged instrument is new. To decomposeTo write an instrument out as the separate obligations inside it, so that each one can be named, priced and asked about on its own. one of these is not to discover anything. Every movementOne dated payment in or out that the document provides for. A movement is a single line item, not a summary of several. of money the document provides for is produced by an obligation that already carries a name, and that already has a price somebody quotes. Sorting the movements is therefore enough to recover the parts. The routine needs no model, no forecast and no view about anything at all.

Here is the everyday version, and it is closer than it looks. A restaurant bill arrives with one figure at the bottom. Nobody who wants to know what the evening cost invents a way of estimating it. The diner reads the lines above the total: four plates, two coffees, a service charge, a tax line. The total was never a mystery to be modelled. The total was a sum of items that already had prices, printed directly above it, and the only skill involved was the patience to read upward instead of glancing at the bottom.

Taking a packaged instrument apart is that, with two differences. The items are contracts rather than dishes, so they have to be named before they can be priced. And the prices are not printed on the same piece of paper, so they have to be obtained from whoever quotes them. Neither difference requires any modelling, and that is exactly what lets this routine say honestly which boxes it could not fill.

The second difference is where the routine earns its keep. On a restaurant bill, a smudged line can be checked with the person who brought it. Here, one of the prices may simply not be obtainable on the day the work is being done, and the most important instruction in this guide is about what to do at that moment. Everything else is bookkeeping. The instruction about the price nobody will quote is the reason the routine is worth running at all rather than being replaced by a rough estimate made in five minutes.

Step one: what has to be on the desk before anything is written down?

The document that sets out what the seller will pay and when. Not a brochure, not a one sheet summary, not a slide from a presentation, and not what somebody described over the telephone. A summary gives the name of the instrument, and this routine consumes what it obliges, and those are two different pieces of paper.

There is no clever way round this and there is no partial version of it. If the document is not available, the routine stops at the first step rather than starting on the summary. Stopping at the first step is a legitimate output rather than a failure to try. The stop records that the instrument could not be taken apart with what was supplied, and that is a fact about the supply rather than a fact about the instrument.

The two pieces of paper can be told apart in about ten seconds, and it is worth learning the tell. A summary uses adjectives and round numbers. A document uses dates, directions and formulas. Paper that says the instrument pays more when the reference asset does well is a summary. Paper that says an amount is payable on a stated date, equal to a stated formula applied to a stated level, is what this routine runs on.

Step two: what gets written down first, and in what form?

One row per movement of money, and each row carries three things: the date, the direction, and the amount or the formula that produces the amount. Three columns, and no fourth. A list is all this step produces, so nothing is sorted at it and nothing is named at it.

The instruction that matters here is about the third column, and it is one line long. The formula is copied rather than described. A formula put into somebody's own words is a formula that has already been interpreted, and the interpreter was the person running the routine, working quickly, before a single row had been marked. If the document says an amount equal to the level of the reference asset at the end date less Rs 2,000.00/-, and nil if that is negative, then that is what goes into the cell, in those terms, beside the date it falls on.

Run on the invented instrument, this step produces three rows and no more. One amount goes out at the start, and that amount is what somebody is asking for the whole thing. One amount of Rs 2,000.00/- comes back at the end of year one. And one further amount comes back at the end of year one, described by a formula applied to the level of the reference asset. Three rows are the entire document as far as this routine is concerned, and the shortness of the list is the point rather than a simplification made for teaching.

Step three: how is each row marked, and what happens to a row that will not take a mark?

Two marks, and only two. A row is a fixed rowA movement whose amount does not depend on the reference asset. It pays the same whatever the reference asset has done. if its amount is the same whatever the reference asset does. A row is a moving rowA movement whose amount depends on the level of the reference asset at a stated date. Its size is written as a formula rather than as a figure. if its amount depends on the level of the reference asset. One pass down the list puts one of those two marks beside each row. The marking step decides nothing about what anything is. Marking records only what each amount depends on, and that is a smaller question with a shorter answer.

Then comes the instruction most people skip, and it is the reason this step exists as a step of its own rather than being folded into the next one. A row that will not take either mark is left unmarked and carried forward. An unmarked row is not forced into the nearer group and it is not quietly dropped off the bottom of the sheet. An unmarked row is information, and a wrongly marked row is not, and the difference between them stops being visible about four steps later.

Run on the invented instrument, the marking pass goes like this. The second row takes the FIXED mark. Rs 2,000.00/- at the end of year one is Rs 2,000.00/- whether the reference asset has doubled, halved or sat exactly where it started. The third row takes the MOVING mark. Its amount is written as a formula on the level of the reference asset and cannot be settled until that level is known. And the first row takes neither mark at all.

The first row is worth a sentence on its own. A reader who forces it into a group has broken the routine at its third step and will not find out until the seventh. The amount going out at the start is not produced by an obligation the seller has taken on. The amount is a price somebody is asking for the whole instrument. So the row is left unmarked and carried forward. The seventh step brings it back as the other half of the final subtraction, and that is exactly the job it was being kept for.

Step four: what is each group called once it has been sorted?

The fixed rows are produced by a promise legA promise to pay a stated amount at a stated date. What it is worth to a holder depends on who made the promise, which is a separate question from what it costs., which is a promise to pay a stated amount at a stated date. The moving rows are produced by an option legThe contract inside a packaged instrument whose value comes from the reference asset. Here it is a call, identified by its strike and its end date., a contract on the reference asset. The name of the leg is written beside its group, and beside the moving group the strike and the end date are written as well. Naming a thing is not the same act as explaining it, so this is the entire step and the shortest one in this guide.

Each leg, what it obliges each side to do, and why it behaves the way it does are covered separately and used here rather than repeated. The naming step does not need any of it. One name per group, plus the two figures that identify the option leg, is the whole requirement. A step that paused to explain what a call obliges would turn a routine into a lesson at the exact moment when the reader is holding a document and wants to keep moving down it.

Run on the invented instrument, the two names come out as follows. The fixed group is a promise to pay Rs 2,000.00/- at the end of year one. The moving group is a call on the reference asset, struck at Rs 2,000.00/-, ending at the end of year one. Two lines of writing, no arithmetic, and the sheet now has names on it where it previously had marks.

There is something a careful reader will already have noticed, and leaving it alone is how a text loses somebody who was paying attention. Three figures here are all Rs 2,000.00/-, and they agree for three separate reasons rather than because one was copied into another. The spot price of the reference asset is Rs 2,000.00/-, simply what one unit of it is worth. The strike is Rs 2,000.00/- because this option leg is struck at the money, and matching the spot is precisely what at the money means. And the third is the scale this worked instance is written on. The routine is being run against one unit of the reference asset, worth Rs 2,000.00/-, and that scale keeps the leg prices below comparable with something rather than floating free. Two of the three are exposure, meaning the value of the thing a contract references rather than an amount anybody has handed over, and a repeated figure that nobody explains gets read as an error.

Step five: where does a price for each leg come from, and what happens when there is none?

A price for each leg is obtained, on one date, from somebody who quotes it. The two legs on this sheet get their prices by routes that share no step, and saying which route each one took is not pedantry. The price of a promise to pay a stated amount at a stated date is arithmetic on a financing rate: Rs 2,000.00/- due in one year, at 6.50 per cent a year, divides by 1.065 and comes to Rs 1,877.9343/-. The price of an option leg is a premium, and a premium is obtained rather than worked out. Computing a call premium from scratch needs a figure for how far the reference asset might move, and no such figure exists behind the worked instance, so the call premium of Rs 180.00/- is supplied rather than computed.

So beside every price goes a note of where it came from. Two marks are enough: arithmetic, or obtained. A sheet that carries a number and cannot say which of the two it is has not finished the work, and the reason will be obvious two steps from here. A mark has now done more work than a figure for the second time, and the repetition is not a coincidence.

Then the instruction the whole routine depends on, and it is one sentence long. A leg with no obtainable price stays empty. The leg is not estimated, it is not interpolated, and it is not filled with a figure that looks about right. The empty boxA step the routine could not complete. It is an output of the routine, carrying the name of what would fill it, rather than a gap somebody forgot about. is an output of the routine and not a hole in it. Every step after this one is arithmetic, so a figure invented here comes out at the end looking exactly like a figure that was obtained.

Look at the shape of that last sentence. The shape is the only justification the step needs, and it contains no mechanism whatsoever. The instruction does not say the invented figure would be wrong, and it does not say by how much it would be wrong. The instruction says that nothing downstream can distinguish an invented figure from a real one. The sameness is a property of arithmetic rather than a property of any instrument, so the instruction is absolute rather than a matter of judgement on the day.

Step six: what does adding the leg prices together give?

Adding them gives the assembled costThe prices of the legs added up, on one stated date. The date belongs to the name, because both prices were taken on it. of the parts on that date, and the words on that date belong to the name rather than hanging off the end of it as a qualification. Run on the invented instrument: Rs 1,877.9343/- plus Rs 180.00/- is Rs 2,057.9343/-. Both prices were taken on one date, so the total is a fact about that date and about nothing else, and a total that has lost its date invites a reader to treat it as what the parts cost rather than what they cost then.

The other half of this step is the part people find uncomfortable, and it follows directly from the fifth step rather than being a new rule. If any leg was left empty at the fifth step, this total is not produced at all. The prices that happen to be available are not added up with the gap noted underneath. INCOMPLETE is written across the box, and that is where it ends.

The reason is about how numbers travel rather than about arithmetic. A partial total is a number, and numbers get copied into messages, forwarded, and read out in meetings by people who never saw the sheet. So a partial total is worse than no total. The footnote does not travel with it. The word INCOMPLETE does travel with it. Nothing else is in the box to copy.

Step seven: what does the last subtraction give, and what does it not give?

The assembled cost is subtracted from the price askedThe amount somebody is offering the whole instrument for. It comes off an offer document that the person running the routine holds., the amount somebody is offering the whole instrument for. The price asked is the row left unmarked at the third step, coming back to do the job it was kept for. The difference between those two figures is where the packaging is paid for.

Now the three things that difference is not, and every one of them is a place a reader arrives at without noticing they have moved. The difference is not a verdict on the instrument. The difference is not a verdict on whoever is selling it. And the difference is not a figure the worked instance can supply.

The last of the three comes first, because it is the concrete one. The price asked comes off an offer document held by whoever runs the routine. An invented instrument has no seller, no offer and no fee, so the first term of the subtraction is simply absent, and the box for the answer is absent with it. The routine produces the shape of the subtraction, and the reader supplies both terms from the day in front of them.

The other two are subtler and matter more. A difference between a price asked and a cost of parts is a located quantity rather than a measured one, and a located quantity says nothing about whether it is large, whether it is reasonable, or whether anybody has been treated badly. A located quantity also says nothing in the other direction, and the second direction is the half a reader who has just finished the arithmetic tends to skip. The subtraction locates the figure, and a place on a sheet is not a judgement about a person.

The routine stops here rather than pressing on. Everything up to this point was description: what the document obliges, what those obligations are called, what they cost on a date. The next question after this one is a question about a price somebody set for reasons the routine cannot see, and answering it would need what those reasons were. The routine therefore hands over a shape and steps back. The shape is genuinely useful. A reader who knows what to subtract from what can go and get both terms in an afternoon.

Step eight: when does the routine stop, and what does the sheet look like when it has?

The routine stops at the eighth step, whether or not every box on the sheet is filled. Every box the routine could not fill is written down, what would fill it and who would have it is named, and the sheet ends there.

The sheet at the end of the worked instance carries five boxes. Three of them are filled: the promise leg at Rs 1,877.9343/-, the option leg premium at Rs 180.00/-, and the assembled cost of the parts at Rs 2,057.9343/- on that date. Two of them are empty. The price asked sits with whoever holds the offer document, and the difference cannot exist until the price asked does. Each empty box carries a line beside it naming what would fill it and who would have that figure.

A decomposition that has been completed by guessing is worse than one that stops honestly. A reader can act on the second and cannot tell the difference in the first. Acting on the second means going and asking a question of somebody who can answer it, and that is a small, ordinary, obtainable thing. Acting on the first means acting on a number whose parentage nobody can now establish, including the person who wrote it down, who by then has forgotten which of the five figures was the one they were unsure about.

Honesty about the empty boxes is the whole argument for the eighth step existing at all. The routine's only value is that it separates what is known from what is not, on one sheet, in a form somebody else can check. A sheet with no empty boxes on it has traded that value away in exchange for looking finished, and looking finished is worth nothing to anybody who has to rely on it.

What does the routine look like run end to end on one instrument?

Here is the whole of it in one table. The output is visible in it rather than the instruction. The third column read downward shows the sheet filling, and then stopping.

A reader will do this arithmetic themselves within a minute of finishing the table, so one reading belongs beside the output rather than hidden underneath it. The assembled cost of the parts is Rs 2,057.9343/-. The scale this worked instance runs against is Rs 2,000.00/-, being the value of one unit of the reference asset. So the parts as the document specifies them cost Rs 57.9343/- more than the scale they were specified against.

The gap of Rs 57.9343/- is a statement about the specification and not about any price anybody has asked. In practice, an instrument written to be bought for the value of one unit could not pass on one whole call at these figures. A whole call and a whole promise together come to more than that. How much less than a whole call it could pass on is a quantity with a name of its own. Working it out is a different routine with a different output, and it is covered separately.

How does somebody with a document in front of them actually run this?

The eight steps above are the routine. A reader arriving at this point is more likely to be using the routine than reading about it, so what follows is how the routine survives contact with a real afternoon, a real document and a real conversation. None of these five is a step. The five are habits that keep the eight steps from collapsing into a scribble.

1. Ask for the document before the meeting rather than during it Give yourself an hour alone with the terms rather than reading dates aloud across a table while somebody waits. If only a summary arrives, say so in writing and wait for the rest. A request in writing is also a record that the request was made.
2. Rule the sheet before reading a word of it Three columns for the list, two more for the mark and the leg name, one for the price and one for where the price came from. A sheet ruled in advance is a sheet that cannot be quietly extended when a figure will not fit, and the discipline is in the ruling rather than in the filling.
3. Finish the whole marking pass before naming anything at all Every row gets FIXED or MOVING or nothing beside it, and only then does the pass return to the top to name the groups. The urge to name a leg the moment one is recognised is the single habit that puts rows in the wrong group, and it feels like efficiency while it is happening.
4. Ask for the leg prices by name, on one stated date Two questions, put to whoever quotes them. What does a promise to pay this amount on this date cost today, and what is the premium on this option leg. Both answers carry a date or they are not answers, and a price without a date cannot be added to another one.
5. Take the empty boxes to the person who can fill them An empty box is a question with a known addressee, which is what makes it useful rather than embarrassing. The price asked sits in an offer document. The terms of leaving before the end date sit in the same document. Who owes the promise leg sits there too. None of those is a hard question; they are just questions somebody else holds the answer to.

The sequence produces a description of what is owed and what it cost to assemble on a date, and it is not a verdict on anything. The distinction between a description and a verdict is worth holding on to. The sheet at the end looks authoritative, and looking authoritative is exactly how a description gets read as a judgement by the third person who sees it.

Should the result of this routine change what anybody does?

No. Running the routine establishes what is owed and what the parts cost on a date, and nothing more. Deciding whether to hold something needs four other things, and the routine produces none of them.

1. Who owes each amount, and what stands behind that undertaking A promise leg is a promise by somebody in particular. The arithmetic that prices it is identical whoever that somebody is, and that is precisely why the arithmetic cannot answer this.
2. What the parts cost on the day the instrument is actually offered Not at the figures in this record. An invented example worked on one date supplies illustrations rather than quotations.
3. What leaving before the end date would cost Every figure in this guide assumes the year runs to its end. What it would take to get out halfway through is a separate term in a separate part of a document.
4. The circumstances of the person asking Which this guide cannot see, and which no text written for everybody ever can.

A reader who has just watched the parts add up to more than the scale they were written against will feel a pull toward a conclusion, so the second direction of the refusal is the one worth naming. Knowing how something is put together is not a reason to hold it, and it is not a reason to refuse it either. The sheet contains what it contains, and the routine stops where the sheet stops.

Who sets the parts of this that are not arithmetic?

Everything above is arithmetic and description, and it holds wherever the arithmetic is carried out. The set of requirements attaching to instruments of this kind does not travel, and this routine touches five of them without stating any. Each is set by an authority, each changes, and any figure written out here would be wrong rather than merely out of date on the day it changed.

The packaged instrument and the reference asset are invented.
Educational material. Not advice on any investment, tax, budget or market position.