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Debt Capital Markets · CoreTrack
1Fixed Income, Credit & Rates
iBond Fundamentals
The BondBond Price and YieldPrincipalRedemptionFace Value, Par and PrincipalThe CouponThe IndentureThe IssuerMaturityFixed Income and Debt Securities
iiBond Pricing and Yield
What a Bond Yield…The Policy Rate and a Bond YieldCurrent Yield and Yield to MaturityYield to Maturity and Yield to CallThe Coupon and the YieldReinvestment RiskCarrySpread Return and Price Return
iiiInterest Rate Risk
Duration and ConvexityDuration and Convexity Calculator,…Key-Rate Duration vs Modified DurationThe Basis PointAccrued InterestRecovery RateSpot Rate and Forward RatePrepayment Risk and Extension RiskA Rate View and a Credit ViewInterest-Rate Risk and Reinvestment RiskHow to Analyse a…How to Review Prepayment…How to Analyse a…
ivRates Markets
The Term Structure of Interest RatesThe Yield CurveThe Forward RateThe Term PremiumParallel Shift vs Steepening…
vCurve and Carry Strategies
Curve StrategySteepener, Flattener and ButterflyHow to Read a…How to analyse a Yield-Curve ScenarioThe Butterfly TradeCarry and Roll-Down
viSovereign Bonds
Sovereign BondsPar Bond and Premium BondGovernment SecuritiesHow to Compare Government…Inflation-Linked BondsBond Total ReturnBond LadderHow to Read a Bond Term SheetHow to Map the…How to Analyse a…Treasury BillsTreasury Bill vs Sovereign BondThe Benchmark YieldThe Policy Rate and the Bond Market
viiCredit Risk
Credit RiskCredit Risk and Interest Rate RiskG-Spread, Z-Spread and Option-Adjusted…Credit SpreadTerm Premium and Credit SpreadHow to Build an…Rating ActionsDefault Rate, Loss Given…Expected Credit LossWhat a Credit Rating…A Rating Watchlist EntryThe Fallen AngelThe Credit CurveInvestment Grade and High YieldCollateral vs Guarantee
viiiCredit Analysis
Credit AnalysisCollateral, Guarantee and Credit…How to analyse a…Seniority and SubordinationCovenantsLeverage RatiosGross Leverage and Net Leverage
ixCredit Events and Recovery
Credit EventsCredit Event vs Liquidity EventHow to update Credit…The Distressed ExchangeThe Default NoticeCovenant Breach vs Restructuring EventHow to analyse Default…
xSecuritisation
SecuritisationOriginator, Servicer and Trustee…How to map a…Mortgage-Backed SecuritiesThe TrancheAsset-Backed SecuritiesAsset-Backed Security vs Mortgage-Backed SecurityCredit EnhancementPrepaymentThe Cash Flow WaterfallExtension RiskWeighted Average Life
xiFixed Income Portfolios
Ladder, Barbell and BulletFixed Income Portfolio MeasuresBarbell vs BulletHow to Map the…Tracking Error in Fixed Income
xiiFixed Income Research
Fixed Income ResearchFixed-Charge CoverageHow to assess Fixed-Income…How to Write a…The Four Assumptions That…A Liquidity Assumption and…The Spread ThesisStating Limitations in Fixed…

Investment Grade and High Yield: What a Divide Does

Investment grade and high yield are two groupings produced by a single mark drawn across a rating scale, and where that mark sits is set by the rating agencies and by the Securities and Exchange Board of India (SEBI). The mark converts a ranking into a permission that is only ever on or off, so a crossing obliges certain holders to act while every payment written into the bond stays exactly where it was.

What actually makes a bond investment grade or high yield?

Almost everybody meets these two names and hears them as descriptions of borrowers: one kind of company is sturdy and one kind is shaky, and somebody with more information has sorted them. The sorting story feels natural and it is the wrong shape. Neither name describes a borrower at all. Each one describes a position.

Here is the apparatus, and it has exactly two parts. The first part is an ordering: a rating scale with many steps, running from a placement that is stronger to a placement that is weaker, with every assessed borrower standing on one of those steps. The second part is a single horizontal line drawn across that ordering at one chosen height. An ordering and one line are the whole machine. Everything standing above the line is then called investment gradeThe grouping on one side of a line drawn across a rating scale. The grouping is defined by the position of the line, not by any property a borrower carries., and everything standing below it is called high yieldThe grouping on the other side of that same line. The name marks a position, not a promise about what any holder will earn.. The two groupings are made by the line, so the line, and not any borrower, is the thing to understand.

The arrangement is a familiar one, met several times over in ordinary life. A school prints a pass mark. Two students sit the same paper, one scores a single mark above the pass mark and the other a single mark below it, and from that morning onward the two of them are in different rooms: one holds a certificate and one does not, one may sit the next paper and one may not. Nobody looking at the two scores would say the students differ by much. Everybody looking at the two certificates would say they differ completely. Both statements are true, and the reason they are both true is that a mark was drawn.

The same shape runs through a height requirement on a fairground ride, a minimum income on a rental application, and a cut-off date for a school year. In every one of those cases the underlying quantity moves smoothly and the consequence does not move smoothly at all. A rating scale with a line across it is that arrangement applied to lending, and once it is seen as an arrangement rather than as a fact about companies, everything that follows falls out of it without much effort.

Try it out

What produces the two groupings, investment grade and high yield?

One ordering. One mark. Two groupings. The steps are drawn blank on purpose. No scale is written out anywhere here. stronger placement everything above the mark is called investment grade THE MARK set by the rating agencies and by SEBI at sebi.gov.in, and revised from time to time everything below the mark is called high yield weaker placement Palash Cements Limited is invented and holds no rating, so it stands on no step of this drawing.
Blank steps and one horizontal mark are the entire apparatus: the two names sit either side of that mark, so what separates them is a position and not a property any borrower carries.
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Why does the scale have to be read from the source rather than recalled?

Because the scale, its steps, the meaning attached to every step and the height at which the line is drawn are all set by the rating agencies and by SEBI at sebi.gov.in, and all of them are revised. A text that reproduces a scale from memory is not merely stale on the day it changes. A scale recalled rather than read is already wrong on the day the ink dries. So the divideA mark drawn across an ordering, which converts a continuous ranking into a permission that is either on or off. is drawn below as an unlabelled mark across an unlabelled ordering. What the mark does stays true whatever the steps are called. What any step is called has to be read at the source.

Palash Cements Limited, an invented issuer, holds no credit rating, and none is assigned to it below. Not one claim about the divide needs an assessment of Palash Cements Limited in order to be true. Where an assessment would sit, the row stays empty and carries the reason inside it.

How often a borrower on either side of the mark actually fails is a measured question, and answering it needs three things: a counted default frequency, a recovery study and a run of past spreads. The arithmetic below has none of the three. So the arithmetic shows a shape and puts figures on an invented case, and what a real price did after a real crossing stays a separate question with a separate answer.

The snapshot, with one row that stays blank PALASH CEMENTS LIMITED, FIVE YEAR BOND, INVENTED What it is an invented issuer of one five year bond Face amount Rs 1,000.00/- Coupon 9.10 per cent a year, paid once a year Yield at issue 9.10 per cent a year, so the price is par Reference the five year government SPOT rate, 6.90 per cent a year Credit spread 2.20 percentage points, which is 220 basis points Compounding annual, one discounting period a year Credit rating Left empty on purpose. A rating scale, its steps and the meaning of each step are set by the rating agencies and by SEBI at sebi.gov.in, and all of them are revised. Every figure here is invented and illustrative. Annual compounding throughout.
The rating row in this snapshot stays blank and says why inside itself, so this issuer is placed on no scale.

Why draw a line across an ordering that already ranks everything?

The answer to that question is about writing rather than about credit. An ordering establishes that one borrower stands ahead of another, and that is genuinely useful information. But obedience needs a test, and a test needs an answer that two people reading it separately will agree on, so an ordering cannot be written into a sentence that somebody else has to obey.

Consider the difference between two instructions given to a person managing money for somebody else. The first reads: hold only reasonably strong borrowers. The second reads: hold only what sits above the mark. Reasonably strong is an opinion, and every person reading it will draw the boundary somewhere slightly different, so the first instruction is an invitation to an argument. The second is settled by looking. A line is drawn because a rule needs a switch, and an ordering on its own does not supply one.

The written instruction has a name in practice: the mandateThe written instruction a holder operates under, which sets out what it may hold and what it may not. A mandate may be worded against a credit assessment. the holder operates under. Some mandates are worded against a credit assessment and some are not, and how an assessment may be used inside a rule about who may hold what, along with which categories of holder may hold which categories of debt, is set by SEBI at sebi.gov.in and by the Reserve Bank of India at rbi.org.in. Both rule sets move, and both are named below with the regulator that sets them. The shape of the arrangement needs no rule set at all in order to be true.

Notice what the line has done to the ordering it was drawn across. Before the line, every step counted for the same thing: one place further along. After the line, one particular step between two adjacent positions is the only place where a sentence in a mandate begins to read differently, and that step counts for something no other step counts for. The scale did not change. The consequence of standing on one part of it did.

What a crossing edits, and what it leaves alone while the mandate reads one way the set of holders whose mandate permits this bond a crossing after it reads the other way still permitted under the same wording no longer permitted size not drawn to any scale The bond is the same object in both panels: Rs 91/- at the end of each of five years, and Rs 1,000.00/- of face at the end of the fifth. Not one of those amounts is touched here. Illustrative. This platform holds no measure of how many holders are permitted before or after anything.
One rectangle, drawn twice, with part of the second removed and no size claimed for the removed part: a crossing edits who may hold the bond, never what the bond pays.
Try it out

Why would anybody draw a line across an ordering that already ranks everything?

Try it out

Two borrowers move by the same small amount on an ordering. One crosses the mark and one does not. How different are the changes in what is permitted?

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How can a very small movement change everything that is permitted?

Two objects are stacked on top of each other here and they behave in completely different ways. Underneath sits a quantity that flows: how strongly a borrower is placed relative to others. The placement can shift by a hair or by a mile, and it takes every value in between. On top sits a permission with exactly two positions and nothing between them. The permission is on, or the permission is off.

Put those two together and the consequence is immediate. A movement of almost nothing in the quantity underneath can flip the permission completely, provided it happens to straddle the mark. A movement of a great deal can flip nothing at all, provided it stays on one side. The size of the change in what is permitted therefore carries no information whatsoever about the size of the change underneath it. That sentence is the whole argument compressed, and it is worth reading twice, because almost every misreading further on comes from forgetting it.

The examination hall shows the same thing. The last mark that lifts a candidate past the pass mark is worth exactly one mark, and it is also worth the entire result. Neither of those sentences is an exaggeration and neither cancels the other. Both sentences are true because the certificate is a switch and the score is a flow, and no amount of staring at the certificate reveals whether the candidate scraped through or sailed through.

The permission, written as a function of the placement
$$ \Pi(q) = \begin{cases} 1 & \text{if } q \ge q^{*} \\ 0 & \text{if } q < q^{*} \end{cases} $$
qwhere a borrower stands on the ordering, a quantity that moves continuously
q*the height at which the mark is drawn, set by the rating agencies and by SEBI
Π(q)the permission, which takes the value one or the value zero and nothing else
What it says in wordsThe permission takes the value one whenever the placement reaches the mark and the value zero whenever it does not, so the permission has no intermediate values at all however finely the placement itself is measured.

Of the symbols in the term table above, one carries the trouble. The trouble is not in the placement and not in the permission. The star on the mark carries it: that one figure is set elsewhere, it is revised, and every consequence traced above and below hangs from it.

A switch sitting on top of a flow on top, a permission with exactly two positions permitted not permitted underneath, a quantity that moves by any amount at all stronger weaker the mark this small move flips the permission this one flips nothing two movements of identical length Illustrative shapes only. No scale, no step of any scale and no borrower is placed on this drawing.
Two movements of identical length arrive at opposite results, because a step function sits above a quantity that flows, and only one of the two movements meets the mark.
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Who has to act when something crosses, and what does having to act mean?

Some holders operate under a mandate worded against a credit assessment. When the thing they hold crosses the mark, those holders must act. The word must is doing real work here and is not a figure of speech, so read it carefully. Such a holder has no discretion about whether. There is usually a date by which the selling has to be done. The wording of such mandates is not a private matter, so the position such a holder stands in is no secret from the people on the other side of the transaction.

A holder in that position becomes a forced sellerA seller with no discretion about whether to sell, and usually a date by which the selling must be finished., and a forced seller is not a nervous version of an ordinary seller. A forced seller is a different object. A willing sellerA seller with discretion about whether to sell, about when to sell, and about the price at which it stops selling. holds three things the forced seller does not hold: discretion about whether to sell at all, discretion about when, and a price at which it simply stops and keeps the bond instead. Remove all three and what is left is a party that must complete a transaction inside a window, whatever the other side offers.

An everyday version, and it is uncomfortably close. A household that has decided to move house next year is one kind of seller: if the offers on the table are poor, it stays put and tries again later. A household whose posting begins on the first of next month is a different kind of seller entirely, and every buyer walking through the door can see the packed boxes. Same house, same street, same roof. The two households are not in the same negotiation.

A price produced by a seller who could not walk away is a different kind of evidence from a price produced by one who could, and nothing printed beside the price reveals which it was. That is not a criticism of anybody. A holder acting under a mandate is doing exactly what it undertook to do, and doing it on time. The point is narrower and stranger: the number that comes out of the transaction records the constraint as well as the borrower, and the two arrive fused together with no seam to pull apart.

Two sellers, the same bond, three structural differences A FORCED SELLER A WILLING SELLER Whether to sell When to sell Where to stop No discretion. The wording decides, not the holder. Usually a date by which it must be done. No stopping price of its own to fall back on. Discretion about whether to sell at all. Discretion about when, including not yet. Discretion about the price at which it stops. Two sellers, the same bond, and only one of them is able to walk away from the table. Illustrative. A mandated holder is not acting carelessly; it acts exactly as it undertook to.
Three ruled rows separate the two sellers structurally rather than by degree, and the row about where each one stops is where the difference turns into a difference in price.
Try it out

Which three things does a willing seller hold that a forced seller does not?

What do the same unchanged payments fetch at a wider spread?

Enough shapes. A difference stated in adjectives can be nodded at, and a difference stated in rupees has to be reckoned with, so put rupees on the table. Palash Cements Limited pays Rs 91/- at the end of each of five years, and a further Rs 1,000.00/- of face amountThe amount a bond repays at maturity. The face amount is fixed by the contract and does not move for any price reason. at the end of the fifth. Six amounts in total. Not one of them is touched by anything in this guide, at any point, in any direction.

Every price below is struck on annual compounding, one discounting period a year, and that is stated inside the arithmetic rather than in a note beneath it. The convention is not housekeeping. The six amounts discount to Rs 1,000.000000/- exactly at 9.10 per cent a year, and that is what at par means. The identical coupon, maturity and yield on a semi-annual convention would produce a different price from figures that look the same in print. With the convention written beside the price, a reader can reproduce the sum. Without it, no amount of surrounding detail makes the sum reproducible.

Step one, the supposed yield
$$ y = r_{5} + \frac{s}{100} $$
ythe supposed yield on this bond, in per cent a year
r5the five year government SPOT rate, 6.90 per cent a year on the invented curve
sthe supposed credit spread, in basis points over that same five year rate
What it says in wordsThe supposed yield is the five year government SPOT rate plus the supposed spread converted from basis points into percentage points, so a supposed spread of 320 basis points is 3.20 percentage points and gives a supposed yield of 10.10 per cent a year.

The 320 basis points in that sentence is a suppositionA figure introduced on the face of the text in order to work an argument through, supported by nothing in the underlying record., carried across from the decomposition of a widened spread rather than invented afresh here, and labelled as a supposition every single time it appears. Nothing measured stands behind the 320 basis points, and no spread anywhere in this sequence ever moved. The supposition buys one thing: the arithmetic can be run, and the size of the answer seen in rupees.

Step two, what the six amounts are worth at any yield
$$ P = \sum_{t=1}^{5} \frac{91}{(1+y)^{t}} + \frac{1000}{(1+y)^{5}} $$
Pthe price today, in rupees per Rs 1,000.00/- of face amount
91the coupon amount in rupees, paid at the end of each of five years
1000the face amount in rupees, repaid at the end of the fifth year
ythe yield as a decimal, on annual compounding, one discounting period a year
What it says in wordsThe price is each of the five coupon amounts divided by one plus the yield raised to the number of years until it arrives, added to the face amount divided by the same figure raised to five, so the only thing that can move the price is the yield.

Run it at the yield the bond was issued at and the six amounts come to Rs 1,000.000000/- exactly, par to the last digit, and par is where the whole sequence starts. Now run it again at the supposed yield of 10.10 per cent a year. The same Rs 91/-, the same Rs 91/-, the same Rs 91/-, the same Rs 91/-, the same Rs 91/-, the same Rs 1,000.00/-. The six amounts now come to Rs 962.188776/-, or Rs 962.19/- as it would be printed. The difference is Rs 37.811224/- on Rs 1,000.00/- of face amount.

The same six amounts, discounted three waysSupposed spreadPresent valueAgainst par
At the yield the bond was issued at, 9.10 per cent a year220 basis pointsRs 1,000.000000/-Rs 0.000000/-
At a supposed yield of 9.60 per cent a year270 basis pointsRs 980.850782/-Rs 19.149218/-
At a supposed yield of 10.10 per cent a year320 basis pointsRs 962.188776/-Rs 37.811224/-

Every rupee of that Rs 37.811224/- is a difference in the price somebody accepted, and none of it is a difference in what the bond has promised to pay. The contract is a sheet of paper with six dated amounts written on it, and no arithmetic performed on the far side of the market rubs out a single digit of it. The price is what somebody would hand over today to stand in line for those six amounts, and that is a separate object with a separate life.

Six amounts that never move, and a total that does bar height is the amount promised, on one scale for all six The six heights below are the contract. They are identical at every yield in this guide, at every position of the control further down, and in every sum this sequence performs on this bond. Only the total underneath them moves. Rs 91/- Rs 91/- Rs 91/- Rs 91/- Rs 91/- Rs 1,000.00/- year 1 year 2 year 3 year 4 year 5 year 5, face The same six amounts, discounted twice Discounted at 9.10 per cent a year, the yield at issue Rs 1,000.000000/- Discounted at a supposed 10.10 per cent a year Rs 962.188776/- The difference, all of it price and none of it payment Rs 37.811224/- Annual compounding, one discounting period a year. The 320 basis point spread is a supposition of this guide.
Five bars of Rs 91/- and one of Rs 1,000.00/- keep identical heights while the total beneath them travels Rs 37.811224/-, which locates the entire change in the discount rate.
Try it out

Between the sum at 9.10 per cent a year and the sum at a supposed 10.10 per cent a year, how many of the six payment amounts changed?

Try it out

The difference between the two totals is Rs 37.811224/- on Rs 1,000.00/- of face. What is that a difference in?

Play with it

Slide the supposed spread. Watch the six amounts refuse to move.

One control, and it moves the supposed credit spread over the five year government SPOT rate of 6.90 per cent a year. The control moves nothing about the borrower, nothing about the bond and nothing about any scale. The six amounts along the top stay exactly where they are at every position; only the shading underneath them, showing how much of each amount survives discounting, and the two totals at the foot respond.

The control starts at 220 basis points because that is the spread this bond was issued at, and nothing in this sequence supports a narrower one. The control stops at 320 basis points because that is the only supposed spread anywhere in this sequence, and beyond it there is nothing to appeal to.

The contract stands still. The price walks. each tile is one dated amount; the shaded bar inside it is the share of that amount surviving discounting These six amounts never move. Only the shading under them does. end of year 1 Rs 91/- Rs 83.409716/- end of year 2 Rs 91/- Rs 76.452535/- end of year 3 Rs 91/- Rs 70.075651/- end of year 4 Rs 91/- Rs 64.230661/- end of year 5 Rs 91/- Rs 58.873200/- end of year 5, face Rs 1,000.00/- Rs 646.958238/- Present value of all six together, on a scale running from zero to Rs 1,000.00/- Rs 1,000.000000/- 0 250 500 750 1,000 rupees per Rs 1,000.00/- of face amount The same figure read as a shortfall against par, on its own scale from zero to Rs 40.00/- Rs 0.000000/- 0 10 20 30 40 rupees per Rs 1,000.00/- of face amount, magnified so the movement can be seen Educational illustration. Palash Cements Limited and the SPOT curve behind it are both invented. Palash Cements Limited holds no credit rating, so it sits on no scale and on no side of any divide. Any supposed spread wider than 220 basis points is a supposition of this guide; no spread here ever moved. Annual compounding, one discounting period a year. No forecast, and no claim that anyone would trade here.
Supposed spread
220 bp
Supposed yield
9.10%
Price today
1,000.000000
Against par
0.000000

At a supposed spread of 220 basis points over the five year government SPOT rate of 6.90 per cent a year, the supposed yield is 9.10 per cent a year and the same five payments of Rs 91/- and Rs 1,000.00/- of face are worth Rs 1,000.000000/- today, and not one of those payment amounts has changed at any position of this control.

The three positions, in plain text. At 220 basis points of supposed spread the supposed yield is 9.10 per cent a year and the price is Rs 1,000.000000/-, which is par. At 270 basis points the supposed yield is 9.60 per cent a year and the price is Rs 980.850782/-, a shortfall against par of Rs 19.149218/-. At 320 basis points the supposed yield is 10.10 per cent a year and the price is Rs 962.188776/-, a shortfall against par of Rs 37.811224/-. Annual compounding throughout.

Try it out

A price is reached during a week in which some holders had to sell by a date. How much of that price is a statement about the borrower?

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What may honestly be read off a price reached like that?

Less than the price appears to offer, and the shortfall is worth being precise about. The number may be read as a price. Somebody transacted at that level, on that day, in that bond, and the number is a genuine record of that event. Nobody is disputing the transaction.

The number may not be read as a measurement of how likely the borrower is to fail. At least one of the parties who produced that number was acting under a constraint that has nothing to do with the borrower at all, and the number arrives as a single figure with no breakdown attached to it. There is no line in the record that separates the part contributed by an opinion about repayment from the part contributed by a date in a mandate. The two are welded together at the moment of the transaction, and no amount of subsequent staring will separate them.

The mechanism runs in both directions, and saying so is part of stating it honestly. Something can cross the mark the other way, and when it does the set of permitted holders enlarges rather than shrinks. A seller facing more permitted buyers stands in a different position from one facing fewer, and that is as far as the shape carries. Which way a price moves after a crossing is a separate question, and answering it would need a series of past spreads, a case in which some spread actually moved, and a count of the permitted holders before and after. No such record stands behind anything above, so no direction is claimed for any price.

One comparison a reader will reach for is simply unavailable here. No second issuer appears anywhere in this sequence, so no bond on one side of a divide can be set beside a bond on the other and the difference read off. The arithmetic instead discounts one unchanged set of payments at two different rates, a comparison of rates rather than a comparison of borrowers.

What the number will carry, and what it will not MAY BE READ OFF IT MAY NOT BE READ OFF IT A price at which somebody transacted, on that day, in that bond. One entry. The column ends here, and its shortness is the finding. How likely the borrower is to fail. Whether anything about the borrower changed at all. What any spread does when anything crosses a mark. How a price on one side compares with one on the other. A price arrives as one number, and no seam runs through it separating the two contributions. Illustrative. No series of past spreads, no default study and no second issuer exists on this platform.
One entry on the left against four on the right measures how narrow an honest reading of such a price turns out to be once a constraint is admitted into it.

The error that gets made, and what it costs

A reader opens a holding record. One line: Palash Cements Limited, five year bond, Rs 962.19/-, and beside it the words current value. Nothing else on the line. A price is the best available summary of what everybody knows, and this one has moved, so the reader concludes, quite reasonably, that something has happened to the borrower.

Who makes that error? Anybody who was taught correctly and was not taught one further thing. The reader was told that a price aggregates what the market knows, and that lesson is true and useful. Nobody told the reader that this particular price was produced in a room where at least one participant had no option to decline. A holding record has one column for a price and no column for the circumstances of the people who set it, so nothing on the record hints at the constraint.

Put a size on the misreading rather than leaving it as a caution. Run that price back through the arithmetic this sequence uses. Read the supposed spread of 320 basis points as entirely compensation for credit and divide by a loss given default of 0.60: the implied default rate is 5.3333 per cent a year. The same unchanged contract at issue, run the same way on 220 basis points, implies 3.6667 per cent a year. The gap is 1.6667 percentage points a year, and no measurement of anything produced a single point of it.

The repair is one line: before reading a price as an opinion, ask who had to be in the room to make it, and whether any of them had the option of leaving.

What the holder actually sees Palash Cements Limited, five year bond Rs 962.19/- one line, one number, and nothing else current value What the record does not carry Rs 91/- at the end of year one, unchanged Rs 91/- at the end of each of years two, three and four, unchanged Rs 91/- at the end of year five, unchanged Rs 1,000.00/- of face amount at the end of year five, unchanged Who else was in the room, and whether any of them was able to decline Illustrative record for an invented issuer. Annual compounding, one discounting period a year.
A record showing Rs 962.19/- beside the words current value, with every unchanged payment drawn as a ghost row, is the exact artefact that manufactures the misreading.

How does anybody actually use a divide in practice?

A lending desk uses it as a planning fact rather than as a judgement. If part of the eventual demand for a bond comes from holders whose mandate is worded against a credit assessment, then the position of that bond relative to the mark is a fact about the size of the eventual audience, quite separately from any view about the borrower. Nothing about that reasoning requires an opinion on whether the borrower will pay. The reasoning requires only an accurate reading of who is permitted to be in the room.

An analyst reading somebody else's price uses it as a question to ask before drawing a conclusion. The question is simple and it is almost never asked: were the sellers in this transaction able to decline? If the answer is no, or is unknown, the analyst records the price and refuses to convert it into a statement about repayment. The refusal is the entire professional contribution, and it is worth more than a confident number.

A household holding a corporate deposit or a bond has the plainest use of the three. When a statement shows a value that has moved and nothing else has been explained, the first thing to check is whether the payments written into the contract have changed. Very often they have not moved at all, and the number on the statement is describing what somebody would pay today for a set of amounts that are exactly where they were last month. Knowing which of the two moved is the difference between reacting to news and reacting to a discount rate.

A constrained sale records a price and nothing more. See what the grade permits.

What are the three limits that travel with any of this?

Three limits ride along with every implied figure this sequence produces, and none of them is optional. Each of the three moves the implied figure, and none of the three is visible in the figure itself.

First, the 40 per cent recovery used to turn a spread into an implied default rate is an assumption, and no measurement stands behind it. Move it and the answer moves with it. Hold the 220 basis point spread perfectly still and the implied default rate walks from 3.1429 to 7.3333 per cent a year purely on the strength of a figure nobody measured.

Assumed recovery, of the amount owedLoss given defaultSpread held completely stillImplied default rate, per cent a year
30 per cent0.70220 basis points3.1429
40 per cent0.60220 basis points3.6667
50 per cent0.50220 basis points4.4000
70 per cent0.30220 basis points7.3333

Second, the whole spread has been treated as compensation for credit. In a real market some part of a spread pays for the difficulty of selling the bond when the holder wants to, and every basis point of that read as credit pushes the implied default rate too high. Carve 0.40 percentage points out of the 2.20 and call them payment for something else: 1.80 points of credit remain, and the implied rate falls from 3.6667 to 3.0000 per cent a year. Nothing in the price separates the two.

Third, an implied default rate is what a price says. An implied default rate is not a forecast and not a measured frequency of anything. Nobody counted a default to produce 3.6667 per cent a year; the figure was solved backwards out of one spread and one assumption. A reader who carries it away as the chance that Palash Cements Limited fails has misread the arithmetic that produced it, and the word implied was attached to every use of it precisely to stop that happening.

So what is a divide actually good for?

A divide is good for exactly one thing, and that one thing is real: it makes a written instruction testable. Everything else attributed to it is borrowed. A divide does not measure a borrower, does not rank two borrowers against each other, and does not say what will be paid. A divide converts a position on an ordering into an answer of yes or no, and it does that reliably enough that instructions can be written against it and checked afterwards by people who were not there.

From that one function everything else follows. Because the answer is yes or no, a tiny movement can flip it. Because the flip changes who may hold something, some holders must act. Because those holders must act, part of a price is produced by a constraint. And because a price arrives as one number, the constraint and the opinion cannot be told apart afterwards. Read a price as a price, ask who had to be present to make it, and keep the six unchanged amounts of the contract in view.

Try it out

Something crosses the mark in the other direction, so the set of permitted holders enlarges. What can be said about the price?

India

Where the rules behind all of this actually live

Every arithmetic step above is free of any rule set except the compounding convention, and that convention is stated inside the arithmetic itself. A sum cannot be reproduced without it. The rows below are the rule-set items this guide touches. All of them are set elsewhere and all of them are revised.

  • The rating scale a credit assessment is expressed on, and what each step of it means. SEBI, sebi.gov.in.
  • The definition a rating agency attaches to each step of its own scale. SEBI, sebi.gov.in.
  • What an issuer of corporate debt must disclose, and to whom. SEBI, sebi.gov.in.
  • Which categories of holder may hold which categories of debt. SEBI, sebi.gov.in.
  • How a credit assessment may be used inside a rule about who may hold what. SEBI, sebi.gov.in.
  • The capital treatment that applies to holding a credit exposure. The Reserve Bank of India, rbi.org.in.
  • The valuation norm that decides the price at which a credit holding is carried. The Reserve Bank of India, rbi.org.in.
What a crossing costs in implied default terms, and how a widened spread splits between default and everything else, are covered under the decomposition of a widened spread. What a credit assessment claims, and what a change to one announces, are covered separately. How a spread is computed, and on which measure, is settled earlier in this sequence. What happens to a claim after a borrower stops paying is covered separately. The rating scale, its steps, the definition of any step and either side of the divide are set by the rating agencies and by SEBI.

References

SourceNamed forWhere
SEBIThe scale a credit assessment is expressed on and what each step of it means, the definition a rating agency attaches to each step, how an assessment may be used inside a rule about who may hold what, which categories of holder may hold which categories of debt, and what an issuer of corporate debt must disclosesebi.gov.in
The Reserve Bank of IndiaThe capital treatment of a credit exposure and the valuation norm that decides the carrying price of a credit holdingrbi.org.in

Palash Cements Limited and the five year government SPOT curve behind every figure are invented.
Educational material. Not advice on any investment, tax, budget or market position.

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