A Rate View and a Credit View: Same Bond, Two Questions

A rate view is a position on what borrowing costs in general. A credit view is a position on the extra one borrower is charged over that. Both sit inside a single corporate bond yield, and that yield is the government rate for the matching maturity plus a spread. The price answers to a move in either part identically, so a price move on its own names neither.

Underneath that sits one fact about arithmetic that decides everything else here. A bond price is produced by discounting a list of dated amounts at a single rate. The single rate in that discounting was assembled out of two pieces that come from completely different places: what money costs when nobody is worried about being repaid, and what is charged on top because somebody might not be. Only the sum ever enters the discounting. The two pieces go in, one number comes out, and the price has no room anywhere in it to record which piece was which.

A view is always a view about a part, so the split has to be built with figures before either view can be named. Then comes the surprise: the two views are sized by the same number, produced by the same calculation, and the difference between them is entirely in which input is being watched.

Where does a 9.10 per cent yield actually come from?

Take a borrower. Palash Cements Limited, an invented cement maker, carries no grade of any kind here: what a grading scale means is set by the assessment firmsFirms that publish an opinion on a borrower's standing, placed on a scale each firm defines for itself. Every step on such a scale means whatever those firms and the authorities named further down have defined it to mean. and by the Securities and Exchange Board of India (SEBI). Palash Cements has sold five year debt at 9.10 per cent a year. The 9.10 per cent is the whole of what the borrower pays, expressed as a rate.

Now put the government beside it. On the invented curve used throughout, the government SPOT rate for that same stretch of five years reads 6.90 per cent a year. Annual compounding is the convention every price here is computed on. The government rate has no credit element in it at all. A lender charges that much when nobody at all doubts the money comes back.

Take the second away from the first and what is left is 2.20 percentage points, or 220 basis points, and that remainder is the spread. The spread is the whole of the extra Palash Cements is being charged for being Palash Cements rather than the government, at that maturity, on that day, on that invented curve.

Two things about that subtraction are worth slowing down on. The first is that both readings have to be taken at the same maturity, and here they both are: the issue is five years and the government SPOT rate is the five year one. Taking 9.10 per cent against the ten year government SPOT rate of 7.35 per cent would have given 1.75 percentage points. The 1.75 measures two completely different things at once, part borrower and part curve shape, and reports one. A wrong number of that kind looks exactly as much like a spread as the honest one does, and the resemblance is what makes the mistake worth naming.

The second is smaller and stranger. The 9.10 is one number and it has two parents. Nothing about the way a price is computed keeps them apart afterwards. Once 9.10 has been written into the discounting, the 6.90 and the 2.20 have gone, in the same way that stirring sugar into tea leaves a sweet cup and no separate sugar. Everything difficult in this guide follows from that one sentence.

What is a rate view, for a reader who has never had one explained?

A rate view is a position on the bottom bar. A rate view is an opinion about what borrowing costs in general, held without reference to any particular borrower. Somebody with a rate view thinks the general level is going to behave in some way, and they arrange what they hold so that they are exposed to that behaviour.

Try it at kitchen table scale, where it is the very same decision. Two households take home loans in the same month at the same lender. One of them thinks the general cost of borrowing across the whole economy is about to change, and picks a floating rate for that reason. That household has a rate view. The household has said nothing whatever about itself, about its own reliability, or about the lender. It has taken a position on the general level of borrowing costs, a level sitting above the household and the lender alike.

The instrument a rate view is expressed through is duration, not identity. Somebody who wants more exposure to the general level buys longer, and somebody who wants less buys shorter, and the choice of which name is on the bond is beside the point. Duration is why a rate view can be held perfectly well on government debt, where there is nobody to have an opinion about. Duration is also why two people with the same rate view can hold two completely different borrowers and be doing the same thing.

A rate view says nothing at all about who is borrowing. Silence about the borrower is the whole content of a rate view. A rate view is not a view that the borrower is good, or bad, or improving. On the split above, a rate view lives entirely in the 6.90 and has no opinion about the 2.20.

One more line, and it is the one that matters most. Naming what a view is is not the same as having one. Where the general level goes is set by, among a long list of other things, the policy rateThe rate a central bank sets for its own lending and borrowing. What moves it, and what it does to the rest of the curve, is settled in the economy material and is pointed at here rather than rebuilt., and how that gets set is covered separately. Nobody can call that level in advance, and the measuring is what can be taught.

And what is a credit view, built from nothing?

A credit view is a position on the top segment: on the 2.20, not on the 6.90. A credit view is an opinion about whether the extra being charged over the government rate is more or less than this borrower's situation warrants. A credit view has one subject, and that subject is a difference.

Same kitchen table, different question. A street vendor and a salaried office worker walk into the same lender on the same morning. The general cost of money is general, so it is identical for both of them. The extra each is asked to pay on top is what differs, and somebody who thinks the vendor is being charged more of an extra than the vendor's actual reliability calls for has a credit view about that vendor. Notice what has happened: the person holding that opinion may have no opinion whatsoever about what the lender's general rate is going to do. The two questions have come apart, and they came apart cleanly.

A credit view says nothing at all about the general level of borrowing costs. Somebody can hold the sharpest possible opinion about whether 220 basis points is generous or mean, and hold no opinion at all about what money costs in general. The two opinions are about different segments of the same bar and neither implies the other.

Now the boundary, and it matters more here than anywhere else. A credit view is not a grade, and a grade is a different kind of statement altogether. Palash Cements is unratedCarrying no published assessment from any grading firm. The absence of a published assessment is not a verdict: an unrated borrower may be reliable or unreliable. here, and being unrated is a fact about the paperwork rather than a judgement on the borrower. How a grading scale is laid out, what each step on it stands for, and what a firm publishing one has to do are set by those firms, and by SEBI, whose address is sebi.gov.in.

Nor is a credit view the same as an opinion about whether the borrower pays. The distinction is fine and it is easy to lose. A spread being priced too generously and a borrower being about to fail are different claims, and one can be true while the other is false: a borrower everybody expects to keep paying can still be charged an extra that somebody thinks is too small. A credit view sizes the exposure, not the borrower, and whether Palash Cements pays is covered separately.

What five questions will separate the two?

A comparison is only worth reading if the criteria were fixed before the answers were. So here are five, written out before either view is examined again, and every one of them separates the pair rather than merely describing it.

All five separate the two views, and the fifth one separates them in a way that costs money. Rows one to four describe the pair. Row five is where a holder who has answered rows one to four correctly still gets caught, and most of what follows is about row five.

How do the two views answer those five questions?

Run them in order, in the same order for both, and the shape of the pair falls out.

Row four is the row that should stop a reader, and the next part of this guide is entirely about it. The two measures are called different things, they are used to answer different questions, and on this bond they print the same six digits. The repeat is not a typing slip and not a coincidence, and understanding why is the single most useful thing here.

What does a holder end up carrying that they never chose?

Read the silent row across. A rate view is silent on the borrower. A credit view is silent on the general level. Both silences are perfectly honest as descriptions of an opinion. Neither of them is available as a description of a holding.

A bond bought for one of the two reasons carries the other exposure whether or not anybody wanted it. There is one instrument. Its price is discounted at 9.10 per cent, and that 9.10 has both parts in it, so both parts move the price. Buying it to express a position on the general level does not detach the spread from it. The spread came attached, it was never a decision, and it will be discovered the first time the two parts move in opposite directions and the total does something nobody's story predicted.

The household version is uncomfortably close. Somebody takes a floating rate home loan purely because they have a view on the general cost of money. The same household has also, without deciding anything, taken a position on its own funding costWhat it costs one particular borrower to raise money, expressed as a rate a year. It moves both with the general level and with how the lender views that borrower. being re-set by a lender entitled to reprice the extra it charges that household. One of those two positions was chosen. The other simply arrived, and it is the one that will surprise them.

The bond itself, worked from its five dated amounts

Everything from here on needs an actual instrument, so here is the one worked on throughout, with its assumption printed rather than hidden. The terms of the Palash Cements issue are assumed out loud rather than drawn from anywhere: a face amount of Rs 1,000.00/-, an annual coupon of 9.10 per cent, and a sale at par at primary issueThe first sale of a bond, straight from the borrower to whoever puts up the money, before any of it changes hands again., on annual compounding. Every figure below follows from those three lines and from nothing else, so a reader who disputes the assumption disputes the figures with it.

At par means the price equals the face amount and the yield equals the coupon rate, so the discounting runs at 9.10 per cent a year and lands back on Rs 1,000.00/-. Here are the five amounts and what each one is worth today.

At par means the third column adds to Rs 1,000.0000/- with nothing left over, and that addition is worth checking rather than assuming. The fourth column divided by the price is the MACAULAY duration: 4,232.6216 divided by 1,000 is 4.2326 years. Dividing that by 1.091 gives the MODIFIED duration, 3.8796. The convexity of the same five amounts comes out at 20.1011. The MACAULAY duration, the MODIFIED duration and the convexity are settled separately and are used here rather than rebuilt. Only two things matter below: the MODIFIED duration of this bond is 3.8796, and it was computed from the five amounts in the table above rather than taken from anywhere.

Why does the SPREAD duration come out at exactly the MODIFIED duration?

Look at what each measure is actually asking. MODIFIED duration asks: if the yield moves by one percentage point, what percentage does the price move? SPREAD duration asks: if the spread moves by one percentage point, what percentage does the price move? Two different questions, plainly.

Now look at what each one has to do to answer. The price is computed by discounting five fixed amounts at 9.10 per cent. Push the government SPOT rate to 7.90 per cent and the discount rate becomes 10.10 per cent. Push the spread to 3.20 percentage points instead and the discount rate becomes 10.10 per cent. The two questions arrive at the same discount rate, hand it to the same five amounts, and get the same price. SPREAD duration and MODIFIED duration on a fixed rate bond are the same calculation asked a different question, so this bond prints 3.8796 for both.

The difference between a rate view and a credit view is therefore not in the arithmetic at all; it is entirely in which input is being watched. The equality is worth sitting with. A reader who expected the two measures to be different numbers has quietly misunderstood why the two labels exist. The pair is not two measurements of two things. One measurement carries two labels, and a holder uses the labels to say which of the two stories is being sized.

An identity that holds on this bond is not a law of the universe, so the condition matters. The equality survives only because the coupon is fixed and the discount rate is the plain sum of the two parts. Change either of those and it stops. On an instrument whose coupon is itself re-set from the general level, a move in the general level changes both the discounting and the amounts being discounted, so the two measures come apart and the equality goes. No such instrument is worked here. The condition is what can honestly be stated: fixed amounts, one discount rate, two labelled inputs, and the equality follows.

Can the price say which part moved?

Run both moves properly, one at a time, with the other part held exactly still, and print them beside each other.

The two rows run the same calculation, so they print the same figure to every digit shown. A fall of 3.7811 per cent in both rows. Not similar, not close enough, not the same to two decimals and different underneath. The same, because 7.90 plus 2.20 and 6.90 plus 3.20 are both 10.10, and 10.10 is the only thing the discounting ever receives.

Here is the discounting itself at the new rate, so the Rs 962.1888/- is not asked for on trust.

The column total needs a word. Its Rs 962.1887/- disagrees with the Rs 962.1888/- printed above it, and the disagreement is real rather than a slip. The five rounded amounts add to Rs 962.1887/-. The unrounded discounting comes to Rs 962.18877569/- and rounds to Rs 962.1888/-. The parts and the total round in opposite directions across one ten thousandth of a rupee, so the column footing and the true price differ in the last place shown, and the check runs on the unrounded figure. The gap is worth saying rather than tidying away. Otherwise a reader recomputes the column, lands on a different last digit, and concludes that the mistake is theirs. In ordinary use the price is Rs 962.19/-, and the fourth decimal exists here only so that two calculations can be shown to agree exactly.

The price change is the sum of the two, always, and a sum cannot be unadded. Carry that sentence away. A corporate bond price move handed over with nothing else cannot be attributed. Not because the tools are weak, but because the information was never in the number. The effect is one measurement; the attribution needs a second one, taken somewhere else entirely.

The second measurement is the government SPOT rate for the same maturity on the same day, observed separately. Subtracted from the bond's own yield it gives the spread, and only then can the move be split between the two parts. Two observations, two parts, one sentence. One observation gives a fact about the price and a guess about the cause.

What does the straight line get wrong here, and by how much?

One correction before the desk work, because it applies to both views equally and it is easy to forget when the two measures agree so neatly. A MODIFIED duration is a straight line held up against something that bends. The straight line always overstates the loss where the yield rises and understates the gain where the yield falls, and that error is not a defect to be apologised for so much as a known lean to be allowed for.

On this bond, with the yield 100 basis points higher, the line predicts a fall of 3.8796 per cent while the true fall is 3.7811 per cent. The line overstates the loss by 0.0985 percentage points, and it leans the same way on this corporate bond as it does on every other fixed coupon bond. Add the convexity term and the estimate moves to 3.7791 per cent, within two thousandths of a percentage point of the truth, and the remaining gap is what the third order would have caught.

The obvious guess about what follows is wrong, and that is what makes it worth a drawing. The ten year bullet bond has a MODIFIED duration of 6.5613, or 1.6913 times this bond's 3.8796. With the yield 100 basis points higher, its own straight line error is 0.2826 percentage points. An error scaling in step with the MODIFIED duration would come to 0.1665. The actual error is 0.2826, or 2.8698 times the five year bond's error. The lean grows faster than the MODIFIED duration does, so a longer holding is not merely more sensitive, it is also worse served by the straight line that measures it.

Who actually does this in the morning, and what do they write down?

The split is not a classroom distinction. The split is a two column entry that somebody makes before the market opens, and the discipline of making it is the whole of the practical content here.

Take a treasury deskThe team inside a bank or a large company that manages its cash, its borrowing and the securities it holds against both. holding a corporate bond. Each morning the price is refreshed. Somebody has to say what changed. The honest routine has three steps and it takes about a minute. Read the bond's own yield. Read the government SPOT rate at the matching maturity from the published curve, separately. Subtract, and record all three: the total, the government part and the spread. The next morning, the change in each is available by subtraction, and the price move has an attribution rather than a story.

The whole practice reduces to one rule: never record a corporate bond's total without recording both of its parts in the same line. A book kept that way answers the attribution question automatically on every future day. A book kept as a column of total yields never answers it at all, and no amount of later analysis recovers what was not written down.

The same routine serves three different readers. A lender deciding whether to keep lending to this borrower cares about the spread column and can ignore the government column entirely. Somebody managing the sensitivity of a whole book cares about the government column and about how much MODIFIED duration is riding on it. The explanation is exactly the split, so somebody explaining last month's result to whoever paid for it needs both columns. One entry, three uses.

There is a fourth use, and it is the one households meet. A home loan rate goes up by half a percentage point. Was that because the general cost of money moved, or because the lender re-priced the extra it charges that borrower in particular? The instalment does not say. The answer is the lender's published benchmark for the same day, read separately and subtracted, and that is the identical routine with the identical logic. A single instalment, like a single bond price, is a fact about an outcome and silent about its cause.

One caution to go with it. Whether a holder must restate what it holds at a current price, and at which price, is not a matter of preference: mark to marketRestating something held at a current price rather than at what was paid for it. Which prices a supervised holder must use, and when, is set by the authorities named in the block above. requirements and the curve they run against are set by the authorities named in the block above. The routine described here is a discipline of record keeping, not a statement of what any rule requires.

Why the two calculations are printed in full

A subject built out of two moving inputs looks like it is asking for something to drag. The reason nothing moves here is the finding itself. A control earns its place where moving one input traces out a relationship worth watching, and what sits at the centre of this subject is an equality instead: pushing the government part and pushing the spread reach one price by two routes that turn out to be the same route. A slider would show two paths onto a single number and would teach less than the two rows already printed beside each other. Where the finding is an identity rather than a relationship, printing both calculations in full beats animating either one. The ninth question below stands in its place, and it asks the reader to perform that refusal rather than watch a needle move.

What does neither view say?

Three things, and each of them is a different subject rather than a harder version of this one.

Neither view says whether the borrower actually pays. Whether the borrower pays is not the same question as whether the spread is fairly priced, and the two can point in opposite directions on the same borrower on the same day. The link between a spread and a default rate, and what a recovery assumption does to that link, is covered separately.

Neither measure carries convexity. Both MODIFIED duration and SPREAD duration are first order, both are straight lines, and both lean in the same known direction: overstating the loss where the yield rises and understating the gain where it falls. The two measures being equal does not make either of them complete, and a holder who trusts a 3.8796 across a large move has taken the sensitivity and left the curvature behind.

And neither view says where either part goes. There is no second borrower to set Palash Cements against, no series of spreads over time and no grade for anybody, so whether 220 basis points is generous or mean cannot be settled here. Where a comparison would have gone, there is an absence.

How much of this matters to any particular reader depends on the holding periodThe stretch of time between buying something and selling it, which decides which price moves the holder actually lives through rather than merely reads about.. Somebody who will hold to maturity and be repaid the face amount lives through every one of these price moves on paper and none of them in cash, provided the borrower pays. Somebody who may have to sell lives through all of them in cash. The arithmetic is identical for both; what differs is which of them has to care, and that is a fact about the holder rather than about the bond.

Two questions have been separated and the measurement that sizes each has been given. Neither has been answered.

Palash Cements Limited and the curve its issue is measured against are invented.
Educational material. Not advice on any investment, tax, budget or market position.