The Policy Rate and the Bond Market: How the Link Works

A policy rate is an administered rate an authority sets by decision, and it acts on the very shortest borrowing in a market rather than across a whole schedule of government rates. Horizons further out are settled by what lenders will take for waiting longer, so a move at the near end need not reach the far end evenly, or reach it at all.

What is a policy rate, and which parts of it belong to an authority?

Start with the kind of object a policy rate is. Most of what follows is settled by that one fact. A policy rateA rate an authority sets by decision rather than one that emerges from borrowers and lenders meeting. Its level, and the process behind it, belong to the authority that publishes them. is decided. Somebody sits down, deliberates and announces a number. A rate decided that way is an administered rateAny rate that is set by decision. The opposite is a rate that emerges from what borrowers and lenders actually agree. Every rate on the schedule below is that second kind., and an administered rate is a different creature from a rate that emerges when a borrower and a lender agree terms and money changes hands.

The difference is familiar outside finance. The rent a household pays its landlord emerges: two people bargained and settled on a figure, and if either had wanted more or less the figure would have moved. The fare printed on a bus ticket does not emerge. Somebody sets it, publishes it, and it stays where it was set until it is set again. Nobody bargains with the conductor. An administered rate is the bus fare and the schedule of government rates below is the rent, and confusing the two is the source of almost every wrong sentence written about this subject.

The level at which a policy rate is set, the process by which it is decided, the corridor of administered rates that surrounds it, how each of those is used, and the operations through which any of it reaches the money market are all set and published by the Reserve Bank of India at rbi.org.in, with its data site at dbie.rbi.org.in as the route to any series.

Each of those items moves. A printed level would be correct on the morning it was written and wrong from the afternoon it changed, and a reader who trusted the printed figure would carry a stale number into arithmetic that then looks fine and is not. Naming a thing and routing it survives the change; printing it does not. So each item is named and routed to the authority that sets it.

Where on a schedule of government rates does an administered rate actually act?

On the shortest borrowing there is. Money lent for a night, or for a few days, has almost no alternative use in that window, so the administered rate available for exactly that stretch is close to the only rate in the room. The further out the horizon, the more alternatives a lender has and the less an administered rate is the whole story. The shortest horizons form the near endThe shortest horizons on a schedule of rates, where money is lent for very brief stretches and an administered rate is closest to being the only alternative. of the market, and contact happens there.

The record behind this walkthrough is narrow. The invented SPOT curve behind this material records six rates and six only: a one year SPOT rateThe rate for money placed today and returned at one stated future date. One rate for each date, and nothing said about the stretches in between. of 5.90 per cent a year, a two year SPOT rate of 6.25 per cent, a three year SPOT rate of 6.55 per cent, a five year SPOT rate of 6.90 per cent, a ten year SPOT rate of 7.35 per cent and a thirty year SPOT rate of 7.60 per cent.

The shortest horizon this record holds is one year, an administered rate acts on stretches far shorter, so the place where the two meet cannot be drawn on this schedule at all. That is worth sitting with rather than hurrying past. The most important part of the link, the exact place where a decision meets a market, lies off the left hand edge of everything this record holds. Saying so is more useful than sketching a plausible curve into the empty space and reading a number off it.

One convention belongs inside the arithmetic rather than in small print beneath it. Every rate in this guide is struck on annual compoundingOne discounting period a year. An amount due in three years is divided by one plus the three year rate, three times over., meaning one discounting period a year, so an amount due in three years at the three year SPOT rate of 6.55 per cent is divided by 1.0655 three times over. The convention is not housekeeping. The identical six numbers read on a semi annual convention would give different prices and a different set of derived rates entirely, and a reader who is not told which convention is running cannot reproduce a single line of what follows.

Why is the far end of the schedule not the near end moved along?

Because the two ends are not being charged for the same thing, and the record shows it plainly once division replaces subtraction. A raw subtraction between two recorded rates hides this. The gap from the one year SPOT rate to the two year SPOT rate is 0.35 percentage points and the gap from the ten year SPOT rate to the thirty year SPOT rate is 0.25 percentage points. The two gaps look like comparable quantities. The first gap covers one year of extra waiting and the second covers twenty, so the two are nothing of the kind.

Run it across the whole schedule and the shape arrives. From the one year to the two year horizon the schedule charges 0.3500 percentage points for each extra year of waiting. From two to three years, 0.3000. From three to five, 0.1750. From five to ten, 0.0900. From ten to thirty, 0.0125. Divide the first by the last and the ratio is exactly 28. Nobody had to soften that comparison.

The schedule does nearly all of its work in its first few years and almost none in its last twenty. Whatever is happening at the far endThe longest horizons on a schedule, where what is being priced is the willingness to wait a very long time rather than anything happening soon. is being decided by something other than pressure arriving from the near end. A household stall that charges a lot for the first hour of storage and almost nothing for the twentieth is the same shape: the first hour and the twentieth are priced by different considerations, and a change in the first hour rate says very little about the twentieth. The honest reading of the shape stops there. One schedule at one moment lets nobody go further.

What does today's schedule already fix about later stretches of time?

More than most readers expect, and none of it by opinion. Between any two recorded horizons there is a windowThe stretch of time lying between two recorded horizons. A rate priced for that stretch alone is what a FORWARD rate is., and that window already has a rate attached to it. Nobody has to be consulted to find it. The rate comes out of a division.

Start with what a SPOT rate does to money over its own horizon. One rupee placed at the one year SPOT rate of 5.90 per cent a year becomes 1.0590000000 after a year. Because 1.0625 is applied twice, one rupee placed at the two year SPOT rate of 6.25 per cent a year becomes 1.1289062500 after two years. The two totals are the growth factors, and the whole of what follows is one division between them.

Now the division. Growing for two years is the same as growing for one year and then growing again for the second year alone. So the second year alone must supply exactly the amount by which the two year growth factor exceeds the one year growth factor, as a ratio. 1.1289062500 divided by 1.0590000000 is 1.0660115675. Subtract one and read it as a rate, and the second year alone is priced at 6.601157 per cent a year. Nobody was asked what they thought. Two recorded numbers were divided.

Do that for every window and the whole path appears. The FORWARD rateThe rate for money placed at one future date and returned at a later one. A FORWARD rate is already inside the SPOT curve rather than a separate opinion about the future. for the second year alone is 6.601157 per cent a year, from the one year SPOT rate of 5.90 per cent and the two year SPOT rate of 6.25 per cent. For the third year alone it is 7.152544 per cent a year, from the two year SPOT rate of 6.25 per cent and the three year SPOT rate of 6.55 per cent. Across the fourth and fifth years together it is 7.427157 per cent a year, from the three year SPOT rate of 6.55 per cent and the five year SPOT rate of 6.90 per cent. Across the sixth to tenth years it is 7.801894 per cent a year, from the five year SPOT rate of 6.90 per cent and the ten year SPOT rate of 7.35 per cent. And across the last twenty years it is 7.725218 per cent a year, from the ten year SPOT rate of 7.35 per cent and the thirty year SPOT rate of 7.60 per cent.

Does the derived path close back on the recorded schedule?

The derived path does close back. Five separate divisions could each be wrong in a way no single one of them reveals, so the check is worth running. Take one rupee. Grow it for a year at the one year SPOT rate of 5.90 per cent a year and it stands at 1.0590000000. Carry it through the second year at the derived 6.601157 per cent and it stands at 1.1289062500. Carry it through the third at 7.152544 per cent and it stands at 1.2096517614. Carry it through the fourth and fifth at 7.427157 per cent a year and it stands at 1.3960099896. Carry it through the sixth to tenth at 7.801894 per cent a year and it stands at 2.0324528891.

Now take one rupee again and do nothing clever with it: grow it for ten years at the ten year SPOT rate of 7.35 per cent a year and stop. The rupee stands at 2.0324528891. Two routes, one landing figure, digit for digit. Five separate derivations are one identity read five ways.

Why is a FORWARD rate not a forecast of an administered rate?

Two reasons, and they are independent. The second matters most, and survives even for a reader who has accepted the first and then quietly gone back to old habits.

The first reason is the one the arithmetic above has already made. A FORWARD rate is a quotient. The quotient came out of dividing one recorded growth factor by another and taking a root. Every FORWARD rate in this guide could be reconstructed by somebody who has never held a single view about the future, has never met an authority and does not know what a policy rate is. Nothing demonstrates more plainly that no opinion went into the figure.

The second reason is that the two figures are not even about the same object. A FORWARD rate here is a rate for government borrowing across a stated future stretch of time. An administered rate is a rate an authority sets, for a different purpose, on different borrowing, at the very short end. Different thing, different setter, different stretch. A correct answer to one question is not an answer to a different question, so even a perfect forecast of an administered rate would still not be a statement about a FORWARD rate for government borrowing.

The labelling rule earns its strictness on this subject. Every rate carries the word SPOT or the word FORWARD, and an administered rate is named as an administered rate and never given a level. The reason is arithmetic rather than pedantry. On this schedule the FORWARD rate for the second year alone works out at 6.601157 per cent a year, from the two year SPOT rate of 6.25 per cent and the one year SPOT rate of 5.90 per cent. The three year SPOT rate reads 6.55 per cent. The two figures sit 0.051157 percentage points apart, or 5.1157 basis pointsOne hundredth of a percentage point, so 170 basis points is 1.70 percentage points and 5.1157 basis points is 0.051157 percentage points..

Nothing should be moved to separate them. Rates for windows land near rates for horizons on any smooth schedule, and pulling the numbers apart to make a tidier table would make the schedule a fiction. The label does the work instead. Stripped of their labels, these figures let a careful reader merge two completely different objects without noticing, and no arithmetic anywhere will complain.

Which claims about the link cannot be made from one schedule?

Three things, and each refusal is drawn as an empty cell with the reason written inside it rather than hedged in a sentence somewhere at the bottom. A refusal that hides is not a refusal.

One schedule does not say how much of a change at the near end reaches the far end. Answering that would need at least two schedules to compare, one before and one after, and this record holds a single schedule at a single moment. The schedule does not say the far end is independent of the near end either. Independence would be exactly as unsupported as the opposite claim, and it is the more tempting mistake. The arithmetic on the shape sounds like it is heading there. And no movement appears anywhere in this record, so nothing can be said about what happens to a holding when a schedule moves.

A reader can see the shape of what is missing and check that nothing was quietly filled in, so drawing a refusal as an empty cell with its reason inside is stronger than writing a careful sentence. One wording rule follows from the same discipline. A rate does not go up or down. Up and down mean the price in one sentence and the yield in the next, so a movement is a rise in the yield or a fall in the yield, every single time. Mixing them ends in saying the opposite of the arithmetic while nobody notices.

What can be said from one schedule, which is more than it looks?

Three things, each of them carried by arithmetic on the record rather than by assertion.

First, the far end of a schedule is a price for waiting a very long time, and per year of waiting it is charged at 0.0125 percentage points against 0.3500 at the near end. Two quantities that differ by a factor of 28 are not the same kind of number, whatever they look like sitting in adjacent rows of a table.

Second, every stretch of time between the recorded horizons already carries a rate, and each one falls out of today's recorded SPOT rates by division. So the schedule is not silent about later stretches of time even though nobody forecast anything. Arithmetic that predicts nothing says more than most readers expect.

Third, the thirty year SPOT rate of 7.60 per cent a year stands 1.70 percentage points above the one year SPOT rate of 5.90 per cent a year. In the other unit that distance is 170 basis points. A lender is charged the whole of it for waiting twenty nine years longer. Nobody decided the 170 basis points. A price is what emerges when people who want money and people who have it settle terms, and an administered rate is precisely not that.

Where does this schedule stop, and what is missing from it?

The record carries six horizons and nothing between them: one, two, three, five, ten and thirty years. There is no four year SPOT rate here. There is no nine year SPOT rate and no twenty nine year SPOT rate. And there is nothing at all shorter than a year. Each of those is a nodeA horizon at which a rate is actually recorded. Six of them exist here, and the space between two nodes holds no recorded rate. the record does not carry, and no line is drawn between the recorded points to read a value off.

The reason is reproducibility rather than fastidiousness. Filling a gap means choosing a method, and a straight line reading and a curved reading disagree. Two readings working from one record would then give two different numbers for the same object, and anybody checking one against the other would find a contradiction that neither reading created. So where a reader expects a rate in between, the answer is that the rate is not in this record, and it stops there.

The entire region where an administered rate acts lies shorter than the record's shortest node, so the sharpest consequence of that rule lands on this subject rather than any other. So the shape of the schedule is described from one year outwards, what that shape already fixes about later stretches is derived, and the near end where a decision actually lands is left undrawn, since drawing it would mean inventing every point on it.

One last thing worth saying before the routing, and it is the organising idea underneath everything above. The record does not hold six rates so much as one borrower at six different horizons. Nothing about the borrower changes between the one year point and the thirty year point: same promise, same payer, same everything. Only the lender's waiting time changes. So the shape of the schedule is read first, and any single level on it second.

Every row above is either arithmetic on the record or the property of an authority, and nothing sits in between. The division is a useful test to carry away. Most confused writing about rates comes from a sentence that quietly moved a figure from the second kind of row into the first.