The Benchmark Yield: The Reference Everything Prices Against

A benchmark yield is whatever rate a market has settled on as its reference at one maturity. Every other borrower at that same maturity gets quoted as so much above it, never on its own. The reference earns the job by being the leg shared across all those comparisons, so it is the one that can be pinned while the other side moves.

Why does a comparison between two borrowers need something held still?

Start with the smallest arrangement in which the question even arises. Two borrowers want money for five years. One of them is the government. The other is Palash Cements Limited, invented throughout this sequence, and the only non-government borrower this record carries anywhere.

Quoted each on its own, the result is two rates. Two numbers sitting side by side with nothing joining them. Next month one of the two changes. Because nothing has been stated about what the two rates had in common, what the change means for the other cannot be said. Two quotes struck that way are measurements without a shared ruler.

Now quote one of them as an amount above the other. Something useful happens immediately: the quote has been separated into a part that both borrowers face and a part that attaches to only one of them. The shared part is the government legOne of the two rates inside a difference. Either of them can move on its own, which is why a difference can change without both of them changing.. The part that attaches to one borrower is the spreadThe amount a borrower pays above the benchmark for the same length of time. It is always over something and always for a stated horizon..

The government leg does that job because it turns up in every one of these comparisons in that market. Being in all of them makes it the only leg that can be held still while everything else moves. Being shared is a property of the arrangement, not a verdict on the borrower behind it. A government borrower can fail, and the arrangement would not change if it did. The leg is used because it is shared, never because it is safe.

The reasoning is already familiar under another name. The rate a wedding caterer in a locality charges means very little on its own. The amount that caterer charges above the going plate rate everybody in the locality quotes does mean something. The going rate is the part every caterer shares. When the price of vegetables rises for the whole locality, the going rate carries it and the difference stays where it was. Take the shared part away and every caterer looks like a separate mystery.

What does the subtraction need before it means anything?

Do it, and watch the conditions rather than the answer. The invented schedule of rates behind this sequence records a five year government SPOT rateThe rate for money placed today and returned at one stated future date. It is one of two kinds of rate used here; the other is a FORWARD rate. of 6.90 per cent a year. Palash Cements Limited borrows over the same five years at 9.10 per cent a year. Take one from the other and 2.20 percentage points is left. A basis point is a hundredth of a percentage point, so the same difference is 220 basis pointsOne hundredth of a percentage point. So 2.20 percentage points is the same quantity as 220 basis points, written in the other unit..

Two conditions sat inside that subtraction and neither of them was announced. The first is that both legs must cover the same horizon. Five years against five years is a difference between two borrowers; five years against two years is mostly a difference between two waiting times, and the borrower is buried somewhere inside it beyond reach. The second condition is the compounding conventionThe basis a rate is struck on, such as one discounting period a year or two. Two rates struck on different bases are not directly comparable.. Both rates in this guide are struck on annual compounding, one discounting period a year, so an amount due in three years at the three year SPOT rate of 6.55 per cent a year is divided by 1.0655 three times over.

Change either condition and the difference stops measuring the borrower and starts measuring how the two quotes were struck. The compounding convention is not housekeeping to be pushed into a footnote. Restated on a semi-annual basis, the same six rates change every price in this guide, along with every rate derived from them, and a reader who was never told which basis was in use cannot reproduce one line of it.

What does the same difference look like in rupees rather than in rate?

A rate difference is easy to shrug at. Two point two, against nine point one, sounds like a detail. So stop quoting it as a rate and buy something with it instead.

Take one promise of Rs 1,000.00/- payable in five years. At the five year government SPOT rate of 6.90 per cent a year, on annual compounding, that promise costs Rs 716.327252/- today. The identical promise of Rs 1,000.00/- in five years from Palash Cements Limited, discounted at 9.10 per cent a year on the same basis, costs Rs 646.958238/-. The two prices stand Rs 69.369015/- apart on every Rs 1,000.00/- of face.

Run the same formula twice, once at each rate, and subtract the answers. Running the formula twice is the whole of the next step, and the two divisions are worth watching rather than accepting the pair of prices.

Rs 69.369015/- is nearly seven per cent of the face amount. Five years of compounding is what turns 220 basis points into a gap that size. The rate difference sounded like a rounding error. The price difference is a sum anybody would notice going missing. Nothing was added between the two readings; the second one simply lets the difference act for five years before it is read.

What is actually sitting inside the amount above the benchmark?

Everything that differs between the two legs except the waiting time. The first condition matched the waiting time away. The difference includes what a lender wants for the possibility of not being paid. The difference also includes what a lender wants for the possibility of not being able to sell the holding easily when it wants to. And it includes whatever else the two sides settled between themselves when the terms were struck.

The shape of that list matters. The spread is a list of ingredients with no recipe. The 2.20 points arrive already mixed, and nothing in this record says how much of them belongs to each ingredient. The ingredients can be named. How much of each went in cannot be read off.

The 220 basis points therefore cannot be turned into a default rate, a recovery figure or a probability of any kind, and the obstacle is arithmetic rather than modesty. Making that conversion needs an assumption about how much comes back when a borrower stops paying. The schedule of rates behind this sequence supplies no such assumption. Worse, it needs the whole difference treated as payment for one ingredient out of three, when the list above says plainly that it is not. Running it would produce a confident number built on a step the list above has already contradicted. The arithmetic that turns a difference into a probability is covered separately, where the assumption it needs can be stated, moved and argued with.

What moves a spread when nothing has happened to the borrower?

A spread is a subtraction. A subtraction moves whenever either of its two numbers moves, and the published figure records only the answer.

There are several ways a wider figure can arrive. The borrower rate may have risen while the benchmark leg stood still, and this is the case everybody assumes. The benchmark leg may have fallen while the borrower rate stood still, in which case the widening is a fact about the government cost of money and says nothing whatever about the borrower. The security treated as the reference at that maturity may have been replaced by a different one. A replacement changes the benchmark leg by construction and by decision rather than by anything the borrower did. Or both legs may have moved by different amounts. The result is a mixture that cannot be attributed to either until it is separated.

A spread is a statement about two things, so every change in one has to be traced back to which leg moved before a single word is said about the borrower. Tracing the move is a habit rather than a calculation, and it costs about thirty seconds: write the two legs down before, write the two legs down after, and only then reach for a conclusion.

A note on wording that this sequence enforces harder than it might look. No rate in this guide goes up or down. In one sentence up would mean the price and in the next it would mean the yield, so a move is always written as a rise in the yield or a fall in the yield. An account that lets the two mix will state the reverse of its own arithmetic without anybody catching it.

One limitation belongs here rather than in the small print. The schedule behind this sequence carries a single spread at a single moment, the 2.20 percentage points at the five year point. One spread at one moment cannot show a spread moving at all, so the figure below draws the four routes as structure rather than inventing rate levels for a movement nobody recorded.

What happens at a maturity where no benchmark exists?

Nothing can be quoted, and that answer is more useful than it sounds.

The invented schedule behind this sequence records six horizons and not one point between them: one year at 5.90 per cent a year, two years at 6.25, three years at 6.55, five years at 6.90, ten years at 7.35 and thirty years at 7.60, all SPOT rates on annual compounding. There is no four year SPOT rate here. No nine year, no twenty nine year, and nothing at all shorter than a year. Each recorded horizon is a nodeA horizon at which a rate is actually recorded. Between two nodes the record holds nothing, and a value read there would be a product of the method used to read it., and between the nodes there is empty space.

The tempting move is to lay a line across the six points and read a value off it wherever one is needed. The line is not drawn here, and the reason is reproducibility rather than fastidiousness. A straight line between the three year point and the five year point gives one answer for four years. A curve fitted through all six gives another. Neither is in the record, so two writers working honestly from the same six numbers would publish two different four year rates and both would be entitled to theirs. Drawing the gaps as gaps is the only reading of this record that two people can arrive at independently, and it is the thing most pictures of a curve quietly get wrong.

The consequence lands hard, and it is taken rather than worked around. A spread needs a same-maturity referenceA benchmark at exactly the horizon being quoted. Without one, there is nothing to subtract, so no spread can be struck at all., so a spread can be struck here only where the government rate for that same horizon is recorded. On this record that is one place. Palash Cements Limited borrows for five years, the five year SPOT rate of 6.90 per cent a year exists, and the subtraction goes through. Had the same issuer borrowed for four years, no spread could be quoted at all.

Which parts of this are set by an authority rather than by arithmetic?

More of them than a first reading suggests, and the sorting is mechanical once it is seen. Everything above this line was arithmetic performed in the open on invented inputs. Several things this guide has leaned on are not arithmetic at all.

How a benchmark government yield curve is constructed and published is set by the Reserve Bank of India at rbi.org.in, with the Clearing Corporation of India Limited at ccilindia.com as the route to how such a curve is built and made public. Which security is treated as the reference at a given maturity, and how that is decided, sits in the same place. So does how a government security is issued, and so does the valuation norm deciding the price at which a holding is carried. The scale a credit assessmentAn opinion about a borrower expressed on a scale that an authority governs. Nobody in this record carries one, and none may be invented. is expressed on, and what an issuer of corporate debt must disclose, sit with the Securities and Exchange Board of India (SEBI) at sebi.gov.in. Palash Cements Limited carries no credit assessment here, and an invented one would be an invented opinion.

One more rule belongs in this block, and this guide could not have been written without it. Every rate here carries the word SPOT or the word FORWARD. A SPOT rate is for money placed today and returned at one stated future date. A FORWARD rateThe rate for money placed at one future date and returned at a later one. It is arithmetic pulled out of the SPOT rates already recorded, not an opinion about what will happen. is for money placed at one future date and returned at a later one. Different objects, and on this schedule they land close enough to be merged by a reader who is not watching.

Watch it happen. Take the one year SPOT rate of 5.90 per cent a year and the two year SPOT rate of 6.25 per cent a year, and pull the one year rate one year FORWARD out of them.

The derived FORWARD rate reads 6.601157 per cent a year. The three year SPOT rate reads 6.55 per cent a year. The two rates sit 0.051157 percentage points apart, or 5.1157 basis points, and they are entirely different objects: one covers a single year beginning twelve months from now, the other covers three years beginning today. Nothing was moved to separate them and nothing will be. The label does the whole of the work, and that is exactly why it is never dropped.

What is a benchmark yield not?

Four things, and each of them is a reading somebody has made and paid for.

A benchmark yield is not a claim that the reference borrower is unable to fail. The government leg earns its position by being shared, and a shared leg would still be shared if it were riskier than every other leg in the market. Safety was never part of the argument.

A benchmark yield is not a floor under any other rate. Nothing in this record stops a borrower being quoted below the reference in circumstances the record does not describe, and any promise otherwise would be a promise about something the record cannot see.

A benchmark yield is not a fixed object. Which security serves as the reference at a maturity is decided by an authority, and it changes. Replacement is not a flaw in the idea; it is the third route on the failure figure above, and it is why the benchmark leg has to be written down alongside the borrower leg every time.

And it is not a measure of anything on its own. A benchmark yield only does work inside a subtraction, and quoted bare it is the cost to one borrower at one horizon and not a syllable more. Somebody quoting the reference rate at ten years has said that the government pays the ten year SPOT rate of 7.35 per cent a year on this invented schedule, and nothing at all about anybody else.

Which points at the thing worth carrying away. The six recorded rates describe neither six borrowers nor six markets. The schedule is one borrower quoted at six different lengths of waiting: 5.90 at one year, 6.25 at two, 6.55 at three, 6.90 at five, 7.35 at ten and 7.60 at thirty, all SPOT rates on annual compounding. Nothing about the borrower differs between the one year point and the thirty year point. Only the length of the wait differs, and the shape of that schedule is to be read before any single level on it.

How is this read in practice, and by whom?

So what does a benchmark yield give, and what does it withhold?

A benchmark yield gives a shared leg. Nothing else makes two borrowings at the same horizon comparable at all. The benchmark also gives a difference that can be written in two units, priced in rupees and repeated by anybody holding the same two rates. And it gives a discipline: match the horizon, match the compounding convention, then subtract.

A benchmark yield withholds more than most readers expect. The reference withholds every statement about the safety of the borrower standing behind it. Nor does it supply any split of the difference into named parts, or any probability, for anybody, at any horizon. And where no rate is recorded at the maturity in question, the benchmark withholds a spread entirely. Refusing is not the same as omitting.