The Basis Point: Why Rates Are Quoted in Hundredths

A basis point is a hundredth part of one percentage point. Two hundred of them make two percentage points, a hundred make one, and twenty five make a quarter. Rates get quoted this way because the moves people act on are fractions of a point, and a fraction written as a decimal invites a lost decimal point. The unit kills that one error and leaves every other one standing.

Underneath that sits a combination that almost nothing else in money has. Rates are small numbers. The amounts riding on their small movements are enormous. When a figure goes from 8.50 to 8.51, everything interesting about the change is happening in the second place after the point, and the second place after a point is precisely where a number gets damaged: dropped in a retype, lost in a photocopy, misheard on a call, swallowed by a spreadsheet that reformatted a column. A quoting conventionAn agreed way of writing a number down. It carries no information of its own. It exists so that two people looking at the same figure take the same meaning from it. that moves the interesting part of the number into the units column, where it sits as a whole number with nothing fragile in it, has removed an entire class of accident before the accident can happen.

What exactly is one basis point?

One basis point is one hundredth of a percentage point. Written as a decimal fraction it is 0.0001. Written in percentage points it is 0.01. The three notations describe the identical quantity, and all three turn up in practice, sometimes in the same paragraph.

The whole of the trouble people have with this unit sits in one number, and the number is a hundred. A basis point and a percentage point are not two names for one thing: they are separated by a factor of a hundred, so writing one where the other belongs does not make a sentence loose, it makes it wrong by two orders of magnitude. Nobody would confuse a rupee with a hundred rupees. The same confusion in rate language happens constantly. Both words end in the word point. A percentage point already feels like a small quantity, so a reader assumes a basis point must be a slightly smaller version of it rather than a hundredfold smaller one.

The four rows below are the four sizes that actually come up. Read the ladder as a table rather than a rule. With familiarity the four sizes stop needing conversion at all.

Why does a rate need a unit of its own at all?

Ordinary life already handles small quantities this way. Nobody buys a quarter of a kilogram of sugar and then discusses it as 0.25 kilograms; the request is for two hundred and fifty grams. Nobody describes a fever as 0.6 degrees above normal in casual speech. Somebody long ago noticed that people handle whole numbers correctly and handle decimals badly, and invented a smaller unit so the everyday quantity could be spoken as a whole number.

Rates got the same treatment for the same reason, and the reason has teeth in this particular case because of what rides on the number. The unit exists because the interesting part of a rate move lives two places to the right of a decimal point, and moving it into the units column removes the single most commonly damaged character in a written number. Nothing deeper than that is going on. There is no theory in a basis point. The unit is plumbing, put there so that a figure survives being written down, read out, retyped and repeated.

Why hundredths, rather than tenths or thousandths?

A good unit is sized to the thing it measures, and the sizing is not a matter of taste. Ask what range of moves people actually talk about and act on. A supervising authority nudging its policy rate, a bond repricing after an announcement, a lender revising what it charges: those moves live roughly between a quarter of a percentage point and a couple of percentage points. Put that range into hundredths and it becomes 25 to 200.

Two or three digits, no decimal point, no leading zeros, no ambiguity about the scale. The alternatives show why nobody uses them. Tenths of a percentage point would put the same range at 2.5 to 20 and drag the decimal point straight back into the common cases. Thousandths would put it at 250 to 2,000, readable but wasteful, and a four digit number carries its own transcription risks. Hundredths win because they put the moves that people argue about into two or three whole digits, and two or three whole digits are what a human reads correctly at a glance and repeats correctly over a telephone.

The same sizing is why the unit does not scale up politely. Nobody says a rate moved by 850 basis points, even though it is perfectly legal arithmetic. Once a move is that big, the percentage point has become the readable unit again, and the convention quietly hands over. Units earn their place inside a range and give it back outside one.

Can one move in a rate be three different true numbers?

Yes, and this is where the real damage happens. Take a rate that goes from 5.00 per cent a year to 6.00 per cent a year. Now describe the move.

The rate moved by 100 basis points. The rate moved by 1.00 percentage point. The rate moved by 20.00 per cent. Every one of those three sentences is true, and no two of them are the same sentence. The first two are the same statement wearing different units, related by the factor of a hundred established above. The third is a different kind of object altogether: it is a ratio, and it got its answer by dividing the move by where the rate started.

Now put it on a shelf. Most people meet the same arithmetic there long before they ever meet a bond. A shopkeeper who sells a packet of tea at Rs 5.00/- puts the price up to Rs 6.00/-. The price went up by Rs 1.00/-. The price also went up by 20.00 per cent. Both sentences are correct, neither is a rewording of the other, and a customer who hears only the second one and knows nothing about the first has learned nothing about how much more money to bring.

What is a base, and why does it decide the answer?

A ratio is a division, and every division has something underneath it. The number underneath is the baseThe number a ratio is divided by. Change it and the same difference reports a completely different percentage, which is why it has to be named in the same breath as the answer.. In the move above, the base was the 5.00 per cent the rate started from, and that base is why the answer came out at 20.00 per cent. Start the same one point move from 10.00 per cent instead and the identical move reports as 10 per cent. Start it from 2.00 per cent and it reports as 50 per cent. Nothing about the move changed. Only the number underneath the division did.

The rule that follows is short enough to memorise and worth memorising: name the base in the same sentence as any ratio. A rate change quoted as a percentage without its base is not imprecise, it is unreadable. A basis point figure needs no such protection. Nothing is underneath it. A basis point is a count of hundredths of a point, and a hundredth of a point is a hundredth of a point whether the rate started at 2.00 per cent or at 12.00 per cent. The absence of a base, and not brevity, is why the unit is the professional one.

What is one basis point actually worth on a bond?

A unit nobody can price is a unit nobody respects, so price it. The ten year bullet bond has Rs 1,000.00/- of face amount. Ten annual dates. A contracted rate of 8.50 per cent struck on that face amount. The bond sits at par, so its yield to maturity is 8.50 per cent too and its price Rs 1,000.00/-. Its MODIFIED duration is 6.5613, and everything here compounds once a year.

One basis point put through it: 6.5613 multiplied by 0.0001 is 0.00065613, or 0.0656 per cent of the price. On Rs 1,000.00/- of face amount that is Rs 0.65613/-, printing as Rs 0.6561/-. Sixty five paise and a bit, for the smallest unit anybody quotes.

Now stop estimating. Discount all ten dated amounts again, this time at 8.51 per cent a year, and the ten year bullet bond comes to Rs 999.3442/-, or Rs 0.6558/- below where it began. Run the same discounting at 8.49 per cent a year and it comes to Rs 1,000.6564/-, Rs 0.6564/- above where it began.

How close did the straight line actually get?

Compare the three numbers in the third column. The estimate says Rs 0.6561/-. After a rise in the yield the truth came to Rs 0.6558/-. After a fall in it, Rs 0.6564/-. At one basis point the straight line and the full repricing differ by Rs 0.0003/- on each side. Three hundredths of one paiseOne hundredth of a rupee. A hundred of them make Rs 1.00/-, and Indian coinage stopped bothering with most of them long ago. on Rs 1,000.00/- of face amount is a difference nobody can spend, so at this size the estimate is exact for any purpose at hand.

Two small things in that picture are worth naming. Both grow into something later. The first is that the estimate misses by the same Rs 0.0003/- in both directions, and that symmetry is not a coincidence of rounding. The bend in the price response is a squared term, and a squared term does not care which way the yield went, so at one basis point it lands on the same size of error on each side. The published convexity of 58.4702 reproduces exactly that Rs 0.0003/- when it is worked through. Working it through is a satisfying check, and convexity is covered separately.

The second is the asymmetry hiding inside those two truths. The rise of Rs 0.6564/- is larger than the fall of Rs 0.6558/- by Rs 0.0006/-. Six ten thousandths of a rupee. Utterly ignorable here, and it is the same property that turns into rupees nobody can ignore once the move grows.

What is the same unit worth on something the size of a large holding?

The unit stops looking fussy on a large holding. Take a Rs 5,000 crore fixed income holding, carrying a MODIFIED duration of 5.20, measured against a benchmark whose MODIFIED duration is 4.80. One basis point of parallel moveA change in which every point on a set of rates shifts by the same amount at the same moment, so the shape of the curve is untouched and only its level changes. across the whole curve costs 5.20 times 0.0001 of the holding, or 0.052 per cent of it.

On Rs 5,000 croreOne hundred lakh, written as 1,00,00,000 in the Indian digit grouping. Rs 5,000 crore is therefore Rs 50,00,00,00,000/-. that is Rs 2.60 crore. The smallest unit anybody quotes is worth Rs 2.60 crore on this holding, and that is the entire practical reason the unit is cut as fine as it is: a coarser one would round away amounts nobody can afford to round away. A holder discussing moves in quarter percentage point steps on this base would be working in Rs 65 crore chunks and would have no vocabulary at all for anything smaller.

Which of those two numbers does a report actually mean?

There is a second figure in the same picture and it is thirteen times smaller. The difference between the holding's MODIFIED duration of 5.20 and the benchmark's 4.80 is 0.40, and that 0.40 is a difference between two sensitivities rather than a stretch of time. Run that 0.40 through the same multiplication and one basis point against it comes to 0.004 per cent, or Rs 0.20 crore on the same Rs 5,000 crore base.

The remaining 0.048 per cent, Rs 2.40 crore, is the part of the exposure that simply comes with matching the benchmark. No decision produced that part. Anybody holding this kind of thing would carry it. Add the two and they close on the whole: Rs 2.40 crore plus Rs 0.20 crore is Rs 2.60 crore, on a base of Rs 5,000 crore, for one basis point, measured instantaneousMeasured as though the change happened with no time passing at all, so nothing else in the arrangement has had a chance to move in response.ly and with every point on the curve moving together.

One of those two numbers is the whole exposure and the other is the part somebody chose, they differ by thirteen times, and a report leaving its reader to guess which of the two was meant has published a figure nobody can use. The objection is not a stylistic one. A reader who takes Rs 0.20 crore for the whole exposure is understating by Rs 2.40 crore, and a reader who takes Rs 2.60 crore for the decision has attributed twelve parts of somebody else's benchmark to a choice that was never made.

The last picture is the quiet argument for the unit. The rupee answers are fifty million apart. A basis point is a statement about a rate and carries no size in it, so the share is the same 0.052 per cent in all three rows. Which is exactly why the base has to travel alongside it in every sentence, in the same way and for the same reason that a ratio has to.

Does the rupee value scale when the move gets bigger?

A basis point is a unit of the input. The unit measures what was done to the rate. A unit means exactly this: two hundred basis points really is two hundred times one basis point, exactly and with no argument. The temptation is to assume the output follows, and it does not.

Two hundred times Rs 0.65613/- is Rs 131.2270/-, and that is what the straight line says the ten year bullet bond should give up on a rise in the yield of 200 basis points, or pick up on a fall of the same size, symmetrically. Reprice it properly instead. Discount the ten dated amounts at 10.50 per cent a year and the bond comes to Rs 879.7045/-, having given up Rs 120.2955/-, or 12.030 per cent of where it started. Discount them at 6.50 per cent a year and the bond comes to Rs 1,143.7766/-, having picked up Rs 143.7766/-, or 14.378 per cent.

Basis points scale exactly and prices do not, so multiplying a one basis point value by the number of basis points is an approximation that degrades in a known direction, always overstating what is given up on a rise in the yield and always understating what is picked up on a fall in it. Notice what has happened to the size of the error. At one basis point the line missed by Rs 0.0003/-. At two hundred it misses by Rs 10.9315/- one way and Rs 12.5496/- the other. The move grew by a factor of two hundred and the error grew by roughly forty thousand.

None of this is a fault in the unit. The unit did its job perfectly: it counted the input, and the input really was two hundred of them. The assumption smuggled in alongside it is what went wrong: a quantity which is proportionalTwo quantities are proportional when doubling one doubles the other, so the relationship between them draws as a straight line through nought. Most relationships in money are not. on one side of a relationship must be proportional on the other. The bend that breaks the assumption is measured separately and is not rebuilt here.

How many decimal places actually have to be carried?

A trap sits inside the arithmetic of the unit itself. The ten year bullet bond reports its MODIFIED duration as 6.5613 nearly everywhere it appears. The 6.5613 is a display figure. Behind it the MACAULAY duration runs unrounded to 7.119062643353, making the MODIFIED duration 6.5613481, and the printed 6.5613 is its four place version.

Take one basis point by all three routes. The unrounded duration gives Rs 0.65613481/-. The printed 6.5613 gives Rs 0.65613/-. The printed rupee figure is Rs 0.6561/-. All three agree perfectly, to four decimal places, and a reader could be forgiven for concluding the difference is not there at all.

One step of that spread is Rs 0.0010/-, and the whole spread from top to bottom is Rs 0.0070/-. Rounding that is completely invisible at one basis point turns into seven paise when the answer is multiplied two hundred times. A figure printed for display is not a figure fit to be used as an input.

Seven paise on Rs 1,000.00/- is nothing to anybody. The same discipline applied to the Rs 5,000 crore holding, where every basis point is Rs 2.60 crore, turns the arithmetic that produced seven paise here into figures with commas in them. The rule is not about size: the unrounded value is carried through every multiplication and rounded once, at the end, when the answer is printed.

What does this cost when somebody gets it wrong?

What does quoting in basis points still not settle?

The unit removes one error. A figure that arrives in a respectable unit borrows an air of completeness it has not earned, so how little else the unit does is worth stating precisely.

The unit does not say which rate moved. A move of 50 basis points in a government SPOT rate and a move of 50 basis points in what a riskier borrower pays over that rate are the same count and completely different events, and separating those two is covered separately. The unit does not say over what stretch of time the rate applies, so a rate still has to carry its period and its compounding convention: everything here compounds once a year, and the same figures on a different convention would price differently. The unit does not say whether every point on the curve moved together or one part of it moved alone. And it says nothing whatever about how likely any of it was, or about what happens next.

Quoting in basis points removes exactly one error, the misplaced decimal point, and it removes nothing else at all. The contribution is real and it is small. A figure quoted in the unit is still a figure that needs a rate named, a period named, a shape of move named and a base named beside it before anybody can act on it.

Who actually has to get this right, and when?

Four kinds of reader meet this unit in a form where getting it wrong has a cost, and they meet it differently.

Somebody responsible for a large fixed income holding uses it as a working currency. The question they ask is never what a rate did in the abstract. One basis point on their own base is the question, and that number turns a curve move into an amount they have to explain. With 5.20 of MODIFIED duration sitting on a Rs 5,000 crore base, that number is Rs 2.60 crore, and they carry it in their head the way a shopkeeper carries the margin on a packet of tea. When a rate moves 12 basis points, they are not converting anything; they already know the answer is around Rs 31 crore.

An analyst writing about that holding has the harder job. They have to choose between two numbers thirteen times apart, and their reader cannot see which one was chosen. The discipline that survives contact with a deadline is to write the base into the sentence rather than into a footnote: Rs 2.60 crore per basis point on the Rs 5,000 crore holding, of which Rs 0.20 crore is the part attributable to the 0.40 difference in MODIFIED duration.

A lender pricing a loan meets the unit at the other end of the size range, where it is the granularity of a negotiation rather than a measurement. The gap between two competing quotes is often 10 or 15 basis points. On a Rs 40 crore facility 10 basis points is Rs 4 lakh a year, a real number to a borrower and a small one to a lender. The unit exists at that scale so that a difference which matters can be discussed without either party writing a decimal that the other party misreads.

And a household meets it without ever hearing the word. A home loan rate revised by 25 basis points is a rate revised by a quarter of a percentage point, and on Rs 30 lakh outstanding that is Rs 7,500/- of interest a year from the date of revision. The unit is not professional decoration but the smallest step at which the price of borrowed money is actually negotiated, and that is why it exists at exactly the size it does. The household is being quoted in it whether or not anybody uses the word.

The ten year bullet bond, the Rs 5,000 crore fixed income holding, the benchmark reading 4.80 and the shopkeeper with the packet of tea are invented.
Educational material. Not advice on any investment, tax, budget or market position.