How to analyse Default and Recovery Scenarios

A default and recovery scenario is a set of inputs written down and pushed through, not a view about what is going to happen. The analyst declares each input and labels it. Names the base every figure is struck on. Shows what was held still. Pushes the arithmetic forward, then pulls it back to where it started. Works an amount through the order rather than across it. Writes down what none of it can tell anybody.

Why write down something nobody is claiming is true?

Scenario work has an awkward property. An afternoon goes into producing five numbers, and not one of them can afterwards be called right. An afternoon that produces nothing right sounds like a wasted one. The afternoon was not wasted, and understanding why is most of what separates somebody who can use scenarios from somebody who merely knows the arithmetic in them.

A scenario earns its keep by being written down, not by being right. Its whole function is to make the effect of one assumption visible, and an effect is only visible if the assumption is visible too. The moment a scenario stops carrying its label it stops being a scenario. The scenario becomes a forecast that nobody remembers making, sitting in a spreadsheet cell that three people now quote and none of them can trace.

Think about how a caterer quotes for a wedding. The sensible quote has a line at the top that reads: this price assumes three hundred guests and a single sitting. Everything below that line is arithmetic, and the arithmetic is fine. The line at the top is what makes the quote usable six weeks later. When the guest list reaches four hundred, everybody knows exactly which number has to move and why. A quote with that line buried in a footnote at the bottom is the same arithmetic and a different document, and it is the one that produces an argument in the car park.

The whole method is an attempt to keep that line at the top. The order below exists so that every input is still wearing its label at step seven, exactly as it was at step one.

There is a second thing worth saying before any of the steps, and it is the sentence this whole sequence rests on. The document decided all of this before anything went wrong. The document fixed what counts as the event, who may say that it has happened, what becomes claimable and against whom, and in what sequence competing claims are met. All of it was put down in writing while the payments were still landing on their due dates, at a point when not one party had cause to give the subject a moment of attention.

Drafting habit does not explain the timing. The timing explains itself. Calm parties writing a rule produce a rule. Anxious parties proposing that very same rule produce a bargaining position instead, and bargaining positions held by people who need opposite outcomes settle nothing whatever. So the apparatus the scenarios below hang on was put together early, on purpose, by parties who fully intended never to open it.

Step one: what does it mean to declare an input rather than predict it?

A scenario is a sentence that starts with the word suppose. The word suppose is not a figure of speech, it is the specification. Suppose the recovery comes to 40 per cent of the amount owed. Suppose it comes to nothing at all. Suppose it comes to 80 per cent. Each of those is a legitimate opening, and not one of them carries a claim that the supposition is likely, or representative, or drawn from anything anybody counted.

Where the supposition is written matters as much as writing it. The supposition goes at the top of the output, in the same size type as the answer. The reason is entirely practical. An answer gets copied into a slide, then into an email, then into somebody's memory, and the footnote does not travel with it. An assumption in a footnote is an assumption that will be dropped. The top line travels with the answer.

The one assumed recovery figure, and what it exists to do

Exactly one assumed recovery figure runs through the whole sequence, and what it is has to be understood before it goes anywhere near a set of workings. The figure is 40 per cent of the amount owed. Its job is to invert a price, and it holds no second job of any kind.

Here is where it came from. Palash Cements Limited, an invented borrower, issues a five year bond at 9.10 per cent a year. Over that same stretch of five years the five year government SPOT rateMoney handed over today and paid back in one go on a single future date, priced as a rate. This material writes SPOT or FORWARD beside every rate, since the two land close together and are different objects. is 6.90 per cent a year. The gap between the two is 2.20 percentage pointsThe unit obtained by subtracting one per cent figure from another. Twenty two of them here, and a hundredth of one is a basis point, so the two units are never swapped about., or 220 basis points. Somebody wanted that gap turned into a rate of failure per year, and turning it needs a figure for how much survives a failure. The 40 per cent was picked so that the sum would run. Out of that comes an implied annual default rateA rate per year worked back from a market price once an assumption has been fixed. It says what the price is consistent with rather than what anybody expects, and it is settled elsewhere. of 3.6667 per cent a year, and that is the whole of its job.

Measurement did not produce it. No study underwrites it. The figure reports on no borrower, describes no instrument and records no outcome. Set against Rs 1,000.00/- owed it marks off Rs 400.00/- and leaves Rs 600.00/- standing, and that pair of rupee figures is the only one of its kind in the whole of this sequence. Both carry the assumption label wherever they turn up. No sum has reached anybody, so neither figure is ever tied to a sum that did.

So when the supposition is written at the top of the output, 40 per cent is not the sensible middle of a range. The 40 per cent is one entry in a declared ladder, and it sits on exactly the same footing as the nought and the eighty.

Step two: what is each figure a percentage of?

Naming the base is the step that catches the errors nobody notices, and it takes about forty seconds to do properly. Every figure in this exercise is a percentage, or a rate, or a share. Not one of them means anything until what it is a percentage of has been said, and the saying has to happen in the same sentence as the figure rather than in a heading somewhere above it.

There are four quantities in play here and they sit on four different bases. A recovery rate is a percentage of the amount owed. Never of the price somebody paid for the bond. The price is a different figure entirely, and often the one closest to hand. Never of the coupon. A loss given default is a percentage of that identical amount owed, so the two are complements and add up to a hundred. A default rate is not a percentage of anything at all, it is a rate per year, and a rate per year without the year attached is half a fact. And a rank's share is a percentage of what that rank was owed, not of the total owed to everybody.

Four quantities, four different bases, and any multiplication that joins them is meaningless until every one of them has been labelled. The reason this matters more here than almost anywhere else is that all four are printed as bare percentages that look interchangeable. Sixty per cent and forty per cent and 3.6667 per cent a year sit in the same column of the same table, in the same font, and a reader who has not been told which base each one belongs to has no way at all of telling them apart by looking.

Step three: how is a reader shown what did not move?

A scenario that moves one input is only readable if the person reading it can see that everything else stayed exactly where it was. Otherwise they are looking at five different answers with no way of attributing the difference to anything, and the honest response to five unattributed answers is to ignore all five.

The same difficulty turns up outside finance. A shopkeeper looking at a bill that has doubled wants to know whether the shop used more power or whether the tariff changed. More power and a higher tariff are completely different problems with completely different responses, and the bill only answers the question if the tariff schedule is printed on it. A bill with the units on it and no tariff is a number, not information.

So the fix is a frozen column: the figures that did not move, printed beside the one that did, at the same size and in the same output. Not described in a sentence underneath. Printed, in a column, where a sceptical reader can run their eye down it.

Here is what sits in the frozen column for everything below. Palash Cements Limited's five year bond carries Rs 1,000.00/- of face amountThe figure a borrower has written down as the sum it will hand back at the end. Interest is struck on it, and it is settled well before this guide picks it up.and pays Rs 91/- a year. The coupon is 9.10 per cent a year of the face amount. The five year government SPOT rate is 6.90 per cent a year over the same five years. The two rates stand 2.20 percentage points apart, and that same gap read in the other unit is 220 basis points. Not one of the three figures shifts in any reading below.

Two units for one quantity, and why the two are never swapped

Basis points are the smaller of the two units, and it takes a hundred of them to fill one percentage point. So the extra that Palash Cements pays over the government, for money of the same length, gets written both ways when it first appears: 2.20 percentage points, and 220 basis points. After that one unit is picked and kept. A figure in points sitting next to a figure in basis points is an invitation to subtract two numbers that are a hundred times apart, and somebody will accept the invitation.

A gap is also never written bare. A gap is written over a named reference, and for a named length of time. Strip either half away and nobody can check it, including the person who wrote it down.

One discounting period a year, said beside the price rather than under it

Every price above is struck on annual compoundingInterest reckoned once a year, so a rate is applied a single time in each twelve months rather than in smaller instalments. It is the convention every figure in this material runs on.. Compounding once a year means an amount is discountedCarried back from a future date to today by dividing by one plus the rate, once for each year in between. Settled well before this material and used here without being rebuilt. once by 1.0910 for each year standing between it and today, at a rate of 9.10 per cent a year. Drop that sentence and somebody redoing the sum twice a year arrives at a different price out of inputs that look exactly like the printed ones, then decides the slip must have been their own.

Run Palash Cements Limited's five dated payments back on that convention and they come to Rs 1,000.000000/- to six places. At par is the name for that condition. The document's rate and the discounting rate print as one number for a reason rather than by chance: they are a single rate doing two jobs.

Step four: how is the arithmetic run, and how is it run back?

Two directions, and the second one is not optional. Take them in turn.

Forward, from an assumed recovery to a rate per year. The loss given default is one hundred per cent less the assumed recovery, struck on that same base, the amount owed. Then the spread divided by that loss given default is the rate the price is consistent with. Suppose 40 per cent comes back. The loss given default is then 60 per cent of the amount owed, and 2.20 percentage points over 0.60 lands on 3.6667 per cent a year.

Backward, and this is the half people skip. Take 0.60 of that rate and see what appears. Sixty per cent of 3.6667 per cent a year is 2.2000 percentage points, precisely the figure the division set off from. An arithmetic only ever pushed forwards is something memorised; one pulled back to its own starting figure is something checked.

Where the decimals go, and why the cut is declared in advance

Dividing 2.20 percentage points by a loss given default of 60 per cent of the amount owed gives three and two thirds per cent a year, exactly. A repeating figure has to be cut somewhere, and where it is cut changes what the check returns.

The cut falls at four decimals inside every multiplication, so 3.6667 per cent a year is what the arithmetic carries. The two decimal reading, 3.67 per cent a year, is something to read and never something to compute with. Taking that two decimal reading back through the same 0.60 returns 2.2020 percentage points rather than 2.2000, a difference of 0.0020. Two ten-thousandths of a percentage point is nothing at all to the answer and everything to somebody checking it, who will otherwise assume they have slipped a digit. A display figure is not an input, and the cheapest way to teach that is to show the residual rather than to warn about it.

The ladder, five declared positions and nothing between them

Now hold the spread completely still at 2.20 percentage points and walk the assumed recovery across five declared positions. Every row below uses the same price, the same coupon, the same government SPOT rate and the same gap. Only the supposition at the top changes.

Read the last column downwards and something jumps out. The step from the first row to the second is 0.5500 percentage points. The step from the fourth row to the fifth is 5.5000, ten times as large, for an identical twenty point move in the supposition. Holding one price still and moving only the assumed recovery produces a curve rather than a line, and the curve runs away at the far end. End to end, 11.0000 per cent a year is five times 2.2000 per cent a year, and the price never moved by a paisa in between.

The reason is arithmetic rather than economics, and it is worth holding on to. A fixed number is being divided by a shrinking one. If more comes back each failure costs less, so an unmoved price needs failures to be more frequent to account for the same gap. Pushing the assumed recovery close enough to one hundred per cent takes the divisor towards nothing. The ladder stops at 80 for that reason, and the shape past that point is a statement about division rather than about any borrower.

Step five: why is an amount worked through an order and never across it?

A sentence cannot deliver this step, and a control is attached to it further down for that reason. The rule comes first, though. A control teaches nothing until there is something to be surprised about.

An order works like this. Each rank in turn receives the smaller of two figures: what is still left, and what that rank was owed. Whatever remains after it has been dealt with passes on to the next. Then the same test runs again. And again, until either the ranks run out or the money does, and it is nearly always the money.

An order is not a proportion. An order and a proportion are so different that they barely deserve the same verb. Almost everybody meeting the pair for the first time reaches for the proportion. Proportion is what a share normally means everywhere else in ordinary life.

Picture ten shops in one small mall paying into a single maintenance fund, and a written schedule that says which bill the fund settles first. A year comes when the fund is short. The fund does not pay each of the ten bills at ninety per cent. The fund settles the first bill completely, then the second completely, then the third completely, and then it reaches the fourth with only part of the money required, and the fifth to tenth are not reached at all. The shops may well have expected the shortfall to be spread evenly among them. The schedule they all signed says otherwise, and the schedule was written years before anybody was short of anything.

Three ranks, one amount, and what each of them reaches

Three ranks stand in an order, owed Rs 300.00/-, Rs 200.00/- and Rs 500.00/-. The three add to Rs 1,000.00/-, and nothing anywhere stands behind the sizes: they were chosen so that an amount has something to run through. Rs 400.00/- now runs through them, in that sequence.

The first rank takes the smaller of Rs 400.00/- and Rs 300.00/-, so it takes Rs 300.00/- and Rs 100.00/- passes on. The second takes the smaller of Rs 100.00/- and Rs 200.00/-, so it takes Rs 100.00/- and nothing passes on. The third takes the smaller of nothing and Rs 500.00/-, so it takes nothing at all. The three ranks therefore reach Rs 300.00/-, Rs 100.00/- and Rs 0/-: 100.00 per cent, 50.00 per cent and 0.00 per cent of what each was owed.

Look hard at that last line, the one worth carrying away. The amount handed out is Rs 400.00/- of Rs 1,000.00/- owed, or 40.00 per cent of the total. Not one of the three ranks receives 40.00 per cent. The average across an order describes none of the ranks inside it, and there is no setting of this arrangement at which it does.

Where the order comes from, and where it has to be read

Suppose two lenders, or twenty, are each owed something by one borrower. A sequence now has to exist. Everybody would simply ask first, so asking first cannot be the test that fixes it. So the sequence gets written down early. Some of it lives in the papers the two sides put their names to. The rest, past the point where the two sides can arrange anything privately, lives in law.

The contents of that sequence are settled elsewhere. Four things are missing from it. Where a class of claim stands. The papers that have to be produced before anything starts. Who has standing to start it. The time each stage is allowed. All four belong to the Insolvency and Bankruptcy Board of India, at ibbi.gov.in, and all four move. Copy any of them down from memory and the copy does not age gently. The copy turns false on the day the rule shifts, and it looks precisely as it looked the day before.

So the ranks in every drawing here are numbered and left unnamed, with the address sitting inside the frame. The teaching above is that an order exists, why it has to exist before anybody needs it, and what an amount meeting one actually does. The contents of that order sit with the Insolvency and Bankruptcy Board of India.

Drag it slowly and watch the upper block rather than the numbers. The first rank fills, and while it is filling the other two do not move at all. The first bar reaches the end of its track and stops. Then the second starts, entirely on its own, and finishes. Only then does the third begin. At every one of the twenty one settings there is at most one rank in the middle of filling, and at four of them there is none. Filling one rank at a time is the shape of an order, and a sentence cannot deliver it.

The lower block behaves differently as the control moves. All three bars move together, every time, and every one of them is part filled at every setting except the two ends. Nineteen settings out of twenty one show three part filled bars where the order shows one. The two blocks agree at exactly two settings: Rs 0/-, where nothing is handed out, and Rs 1,000.00/-, where everything is. Everywhere in between they disagree, and the disagreement is largest exactly where a reader is most likely to be quoting one of them.

Before any of this is put to work, one sentence about the people inside it

Nobody who lent money and was not repaid made an obvious mistake. Hindsight does that to a story: it takes an outcome and arranges everything before it into a trail that anybody could have followed. The trail was not there at the time. Every piece of machinery described above was assembled by parties who fully expected to be paid and who knew, quite calmly, that expecting is not knowing. The gap between expecting and knowing is the entire reason the machinery exists.

Nobody had to have spotted anything, and no borrower's conduct is what the arithmetic above turns on. Palash Cements Limited has no conduct to describe. The borrower is a promise with figures attached to it. The machinery is the subject, and the people are not the example.

Step six: what can the whole set of them not tell anybody?

Write this down as a list rather than as a caveat, because a caveat gets read as modesty and a list gets read as information. Three entries, and not one of them is a small omission.

The five scenarios carry no likelihood. Nothing about running five scenarios makes any one of them more probable than any other, and nothing above bears on which is nearer the truth. The ladder covers one axis completely, the axis of assumed inputs, and it is silent on the second axis a reader actually wants. Silent is different from cautious. There is no figure being withheld.

The ladder carries no ranking. A scenario producing a larger number is not a worse scenario. A larger number is a different input. The habit of calling the highest figure the prudent one smuggles a probability judgement in under a word that sounds like temperament, and once it is in, the ladder has quietly turned into a forecast with an opinion attached.

The scenarios carry no history. No claimant at any rank has been paid a single rupee out of any of them. Every figure above dropped out of arithmetic worked on declared inputs, and arithmetic worked on a declared input tells the reader about the input.

An absence, named here rather than worked around

No payment has been missed here by anyone. Behind the name Palash Cements Limited there is a promise. There are figures attached to it. After that there is nothing at all. Nothing failed. No promise was ever rewritten. No sum came back to anyone. There is no account of events. No events took place. The absence is a choice rather than a gap somebody forgot to fill.

The reason is worth stating, and it explains the shape of everything above. The machinery here exists whether or not anybody ever needs it. Stories travel and structures do not. One instance of the machinery written up in use is what a reader walks off with, and the structure stays lying where it was written. So the account of events a reader expects turns out to be a document. The sum that came back turns out to be an order with empty rows. And the length of time the whole thing takes turns out to be an address.

Step seven: which rules is the whole exercise standing on?

Step seven happens before the output leaves the desk, not after somebody has queried it. Everything above is arithmetic, and arithmetic is portable. The rules underneath it are not, and they move.

Six of them belong to the Insolvency and Bankruptcy Board of India at ibbi.gov.in, and here they are. The route an unpaid claim runs. Which claim is reached before which, once several of them compete, and the place each kind holds in that queue. Standing to begin the route, the basis it is begun on, and what has to be produced first. The time each stage is allowed. How a body of lenders is constituted and who speaks for it. And the paperwork a claim goes in on, together with where it is lodged.

Two belong to the Reserve Bank of India at rbi.org.in: the valuation rule fixing the figure a credit holding is shown at inside a lender's books, and how much of its funds a regulated lender ties up behind a credit exposure. One belongs to the Institute of Chartered Accountants of India at icai.org: the standard an expected credit lossA loss recognised in a set of accounts before anything has gone wrong, on a basis the accounting standard sets. It is a reporting measure and it is settled outside this material. is measured under and shown within. And two belong to the Securities and Exchange Board of India (SEBI) at sebi.gov.in: what a corporate borrower puts on the record about assets pledged behind a bond, and what it puts on the record about a third party standing behind one.

Every one of those eleven is revised, and a scenario built on a remembered version of any of them was wrong from the moment it moved rather than gradually out of date afterwards. The failure is sharper than staleness. A stale number usually announces itself and a wrong rule does not. The table further down carries all eleven as blanks with their addresses in them.

What no scenario can settle

Asked what to do when a payment fails to arrive, the method has nothing to offer. Declare, or hold on? Take an offer, or refuse it? Move alongside the others, or alone? Each of those is decided under documents nobody here has read, with consequences nobody here can see, and handing out a course of action on that footing stops being teaching and becomes something else. So the sequence names the machinery, names whichever party the document names, and gives the address where the rest of it is kept. The naming and the address are the whole of what can honestly be offered.

What has the order produced, and what has it not?

Run once, all seven steps produce an output worth taking stock of. There is a set of labelled inputs. There is an arithmetic that closes on itself in both directions. There is a picture of what an amount does when it meets an order, and a short list of things the exercise is structurally unable to say. And sitting underneath all of it there is a set of blanks with addresses in them.

The missing item is an answer to the question the reader arrived with. How much comes back, and how long does it take? Neither of those appears anywhere above, and neither absence is a shortcoming of the method. The method was never able to produce them. The method produces instead a set of workings somebody else can pick up, disagree with, change one input in, and rerun: a different kind of useful, and the only kind available.

There is one last thing worth noticing about the whole exercise. Every step above is about presentation except two. Steps four and five carry arithmetic; the other five are entirely about how the arithmetic is written down and what is written down beside it. The ratio of five presentation steps to two arithmetic ones is not an accident. Presentation is what the work actually is.