Guide · Fixed income · Updated 2026-09-23

A bond's yield is its price restated, and whether the price includes the interest depends on where you trade

The usual explanation of bond yields is a formula plus the slogan that prices and rates move in opposite directions. Neither says which price the formula should be applied to. This page builds a price from one payment upward, finds the yield by the search every calculator runs, and follows the arithmetic to the two places it meets money: the accrued interest paid on top of a quoted price, and a pair of published indices that split a bond's price from its interest. Every figure is computed from stated terms or measured on the exchange's own files.

A yield is the price restated, not a second number

A 7 per cent government bond pays 3.50 rupees per 100 of face value every six months until it matures and then repays the 100, whatever interest rates do. The price is what the market pays today for that fixed stream. The yield is the same price translated into a rate, so that bonds with different coupons and maturities can be compared on one scale.

The RBI's primer on the government securities market defines it so (question 24): yield to maturity is the discount rate which equates the present value of a bond's future cash flows to its current market price. With the cash flows fixed, each price has exactly one yield and each yield exactly one price, because the price falls continuously as the yield rises. The RBI's draft Master Direction on secondary market transactions in government securities, released on 25 June 2026 for comment until 17 July, says at paragraph 4(4) that transactions "shall be undertaken on price basis or yield basis": two bases for one trade.

Two readings follow as errors. The coupon is not the yield; the two differ whenever the price is not 100. And the yield is not a promise; it is earned only under conditions set out below, which a holder rarely meets exactly.

One payment first: discounting is division by time

Take one payment of 100 rupees due in a year. At 7 per cent compounded half-yearly, money grows 3.5 per cent a half year, so the payment is worth 100 divided by 1.035 twice: 93.35 today. Due in ten years it is divided twenty times, 50.26; due in thirty years, sixty times, 12.69.

The last two columns hold the whole inverse relationship and the reason it steepens with maturity. A move from 7 to 8 per cent enlarges each divisor only slightly, but a payment divided twice loses 0.96 per cent and one divided sixty times loses 25.11. Sensitivity grows with distance, which is what duration measures, and the loss from a rise is smaller than the gain from an equal fall, 25.11 against 33.72 per cent at thirty years: convexity, which is nothing more than dividing by a power.

A bond is a bundle of such payments, each discounted on its own and then added. A five year 7 per cent bond is ten payments of 3.50 and one of 100.

Of its 97.95 at a 7.5 per cent yield, 69.20, or 70.7 per cent, is the discounted principal. The price is below 100 because the market rate exceeds the coupon: at 100 the bond would return 7 per cent, so the price falls until the same payments return 7.5. That is the whole mechanism of a bond trading away from its face value.

The yield is found by search, and the search cannot miss

From a price back to a yield there is no closed formula once a bond has more than a few payments, because the yield sits in the sum as a power many times over. It is found numerically, and bisection cannot fail: the price falls continuously as the yield rises, so a range of yields whose prices straddle the market price must contain the answer. Price the midpoint, keep the half that still straddles, and repeat.

By step 19 the midpoint is within a hundredth of a basis point of the answer (a basis point is a hundredth of one per cent), and after 39 steps the range is narrower than a trillionth: 7.5038 per cent. Newton's method, which follows the slope of the price curve instead, reaches the same yield in 5 iterations, and the build that produced this page refuses to write it unless the two agree to ten decimal places. Every bond calculator and trading screen runs a version of one of these two searches.

Yield to maturity is a statement about reinvestment

The primer also calls the yield the expected rate of return on a bond held until maturity, and that needs a condition the phrase leaves out: every coupon must be reinvested at the same rate until maturity. Buy a 7 per cent bond at 100, so that its yield is exactly 7 per cent, hold it to maturity, and reinvest each coupon at a fixed rate.

Only at 7 per cent does the realised return equal the yield. Over ten years, reinvesting at 5 or 9 per cent gives 6.49 or 7.55 per cent; over thirty years, 5.92 or 8.20. The long bond is more exposed because more of its outcome is interest on interest. Of the 198.98 a ten year holder has at maturity when coupons compound at 7 per cent, 28.98, or 14.6 per cent, is interest on reinvested coupons; for the thirty year holder it is 477.81 of 787.81, or 60.7 per cent. The yield of a long bond is mostly a claim about reinvestment rates that do not yet exist.

That makes a yield the same kind of object as a futures price, which the guide to the forward price shows is a statement about funding rather than a forecast: exact as arithmetic, conditional as a return. A sale before maturity adds another condition, the yield on the day of sale.

Why the price falls when the yield rises, and falls further for long bonds

Every curve passes through 100 at 7 per cent, because a bond whose coupon equals the market rate is worth its face value. A one point rise takes 0.94 per cent off the one year bond, 6.80 off the ten year and 11.31 off the thirty year; a one point fall adds 0.96, 7.44 and 13.84. Modified duration, the last column, is each curve's slope at 7 per cent expressed as a percentage change per point of yield: 0.95, 7.11 and 12.47.

Sensitivity rises with maturity but less than in proportion, because a long bond's coupons arrive long before its principal: the thirty year bond moves about 12 times as much as the one year bond, not thirty. And the curves bend: a two point rise costs the thirty year bond 20.64 per cent, less than twice 11.31. Applied to every bond a bank holds at once, this is the arithmetic behind the bond book being marked up or down that the guide to RBI policy days describes.

Half-yearly, 30/360, next day: the Indian conventions

The RBI's primer states the four conventions that turn this arithmetic into a settlement amount for a central government bond. Coupons are paid half-yearly on the face value, so a yield is twice a half-yearly rate. The bond market counts days on 30/360, every month 30 days and every year 360, while treasury bills count actual days over 365 (question 25), so a bill yield and a bond yield are not on one basis until converted. All outright secondary market transactions settle T+1, on the next working day (question 16). And accrued interest runs from the last coupon date to the day before settlement (question 22).

The day count makes small calendar effects that no quote screen shows. The 31st of a month earns nothing, the end of February earns two or three days in one calendar day, and a purchase settling on a Monday usually carries three days more accrued interest than one settling on the Friday before.

The accrued interest function behind every figure here was first run on the primer's own illustration: an 8.83 per cent coupon last paid on 25 November 2013, settling on 30 January 2014 at a clean price of 100.50. It returns the primer's 65 days, 1.5943 per 100, a dirty price of 102.0943 and a consideration of Rs 5,10,47,150 on 5 crore of face value, to the rupee.

Clean price, dirty price, and what leaves the account

The clean price is the price with accrued interest taken out; the dirty price puts it back. A coupon is paid in full to the holder of record however briefly the bond has been held, so a buyer three months into a coupon period pays the seller three months' interest at settlement, and the next coupon repays it. Quoting clean keeps the quote from lurching at every coupon; settling dirty keeps the transfer fair. The primer's worked example does exactly this: the quoted price is clean, and accrued interest is added to reach the dirty price on which the consideration is computed.

The bond is constructed, with its terms stated; the dates are real. Settlement fell on Friday 18 September 2026, a day on which the exchange's government bond indices were published and moved. Accrued interest runs 103 days on 30/360 from 5 June, and the buyer of the minimum 10,000 rupees of face value pays Rs 10,026.57, of which Rs 200.28 is interest the seller had earned. Settling on the following Monday would carry 106 days, 2.0611 per 100.

At a constant 7.25 per cent yield the dirty price climbs from 98.24 to 101.78 through the first coupon period and drops by the 3.50 coupon on 5 December, while the clean price barely moves. Its small drift is the pull toward 100 as maturity nears, plus a quirk of the convention: accrued interest is linear in days while discounting compounds, so between coupon dates a bond yielding exactly its coupon has a clean price just below 100, 99.9853 on the example's settlement date.

The exchange shows the other price

The folk version of all this is that Indian government bonds are quoted clean and paid dirty. On NDS-OM, which the primer describes as an order driven electronic system where participants trade anonymously (question 8), that is right. It is not what a buyer sees on the National Stock Exchange's cash segment, where central government bonds trade in the GS series beside shares, through the same broker and demat account. There the traded price already contains the accrued interest. The exchange's own handbook for its retail debt market, dated May 2003, says accrued interest "is added to the price of the security while entering the quote on the system", on the same 30/360 count, and the function used here reproduces its example too: 133 days, 2.76 per 100, a dirty price of 115.26. A handbook from 2003 is weak evidence about today, so the claim was tested on the exchange's daily files for 2022 to 2026.

Of the 149 central government securities in the GS series of the exchange's daily bhavcopy over that period, the most traded changed hands 1,70,733 times in 1,051 sessions. It is a long-dated bond with a 7.54 per cent coupon paid in halves each May and November, not named because nothing here turns on which bond it is. A clean price would ignore a coupon date. A dirty price should rise by about 7.54/360 of a rupee a day between coupons and fall by about the half-yearly coupon, 3.77, in the session in which a buyer stops being entitled to it.

All eight coupon dates show the fall, 86 to 101 per cent of the half-yearly coupon, on the session whose trades settle on or after the coupon date, too late to be on the record: the session before it, and in November 2022 two sessions before, which is where the fall lands if trades then took two working days to settle. Across the other 1,033 single-session moves the median move, up or down, was 0.13 rupees, and only one, on 14 September 2022, was a fall as large as three fifths of the half-yearly coupon. Between coupons the price rose 3.5 paise a session on average, against 3.1 paise of accrual. Remove the accrued interest to each trade's settlement date and the falls vanish: the implied clean price moved a median 0.13 on the eight sessions, against 0.12 on ordinary ones.

On Thursday 17 September 2026 the bond closed at 105.30, for settlement on Friday 18 September 2026, 115 days of 30/360 accrual after the May coupon: 2.4086 per 100. The clean price is 102.8914 and the yield 7.12 per cent. Read 105.30 as a clean price and the yield comes out at 6.78 per cent, 33.7 basis points too low. The error grows with the interest accrued and shrinks with maturity:

A two year bond 179 days after a coupon, misread this way, appears to yield 2.42 percentage points less than it does. A quote from the exchange and one from NDS-OM for the same bond on the same day differ by the accrued interest before any difference in market level, so comparing them unconverted reads the interest as a premium. And a holder watching the exchange price will see it drop by about a half-year's coupon one session before each payment. Nothing has been lost: the coupon itself arrives on the payment date.

Two indices on one bond, and a gap made of interest

The exchange's index provider publishes two indices on one bond, the current ten year benchmark central government security. Its methodology document of April 2022 builds the Nifty 10 yr Benchmark G-Sec index as a total return index, each day's return being the change in clean price plus the change in 30/360 accrued interest plus any coupon, over the previous day's price including accrued interest; the clean price variant uses the change in clean price alone. The bond is replaced when a new ten year security qualifies, which since 17 October 2019 means at least 15,000 crore rupees outstanding or a three day average traded volume above the incumbent's, with five working days' notice. The only difference between the two indices is the interest, accrued and paid.

If so, their daily gap should behave like accrued interest and not like the market, and it does. Across 2,795 sessions from 18 March 2015 to 18 September 2026, excluding 7 steps that span a missing session and the 38 sessions of the 2024 window and its correction, described below, the total return index beat the clean index on 98.6 per cent of sessions, while the clean index itself rose on 48.4. The gap's standard deviation was 1.79 basis points, against 26.42 for the clean index's daily return, and it follows the 30/360 day count:

A Monday carries the weekend's interest: its median gap, 5.67 basis points, is 3.01 times a weekday's 1.88. On the 41 sessions whose accrual date moved from a 30th to a 31st, where 30/360 pays nothing, the median gap was 0.04 basis points below zero; on the 7 sessions in which one calendar day crossed the end of February, carrying two or three days of interest, it was 5.56. The 30/360 count and the clean return explain 95.6 per cent of the gap's variance, calendar days 91.3 per cent. The slope, 1.89 basis points a day, is 6.80 per cent a year on 360 days, the average running interest on the benchmark bond. The small negative coefficient on the price return, 0.015, is accrued interest too: a fixed rupee amount whose share of the price shrinks when the price rises.

Two more fingerprints are in the files. The total return index is computed for every calendar day: after a three day gap its own reported change starts from a value that already includes 1.99 days of accrual, so that column cannot flag a missing file after a weekend, as it can for a price index. And the accrual date moved in late 2016. On the sessions where the two possible accrual dates give different day counts, the index accrued to the valuation date in 17 of 18 up to 1 November 2016, and to the following day, where next-day settlement puts it, in all 108 from 30 December 2016.

One stretch is a defect in the published series. From 16 April 2024 to 7 June 2024, 37 sessions, the published total return index moved exactly with the clean index, as if the bond had stopped earning interest. On 10 June 2024 it jumped 106 basis points relative to it, and its change column shows the previous value restated by 24.02 points, 1.05 per cent, close to the 52 days of accrual, about 0.99 per cent, that the window omitted. Year-end levels are unaffected, but a daily or weekly return taken across those weeks from the published files is wrong by up to about one per cent, and every daily statistic here excludes them.

From 31 December 2015 to 18 September 2026, 10.7 years, the total return index rose 90.3 per cent and the clean price index fell 7.6 per cent; their ratio, the interest alone, rose 106.0 per cent, 6.98 a year. In no full calendar year did the interest earn less than 6.13 per cent or more than 7.55, while the clean index ran from a 6.31 per cent loss to a 7.11 per cent gain. In 2017 and 2022 the clean price fell by more than 6 per cent and the total return index still ended slightly ahead, 0.34 and 0.40 per cent.

The clean price index is chained across every change of benchmark bond, so its level is no bond's price. The total return index credits interest daily and coupons on payment, with no tax, cost or delay, so it is a ceiling for a holder, not the record of one: the fixed income counterpart of the gap that the guide to total return and price indices measures on equities, except that a bond's interest accrues every calendar day and its gap is close to a straight line.

What a yield does not tell you

It is not the return from a sale. A bond sold before maturity returns the price on the day of sale, set by the yield then, which nobody knows today.

It is not comparable across conventions. A half-yearly 30/360 bond yield, a treasury bill yield on actual days over 365, and a yield computed from an exchange price that still contains accrued interest are three numbers for three things. Convert them to one basis before comparing.

It leaves out costs and tax. Brokerage and exchange charges sit in neither price, and coupons and gains are taxed under their own rules, which this page does not cover.

It is not a forecast of rates. A yield is today's price in another unit, not a view on where the rate will be next year.

What the yield is for

A yield is a unit of account for bond prices. It puts a 6 per cent bond with five years to run and an 8 per cent bond with twenty on one scale, and it states a price move in the language monetary policy is set in. Used that way it is exact, and price and yield convert into each other to any number of decimal places. Used as a statement of what a holder will earn, it carries every assumption in the reinvestment table.

In practice the arithmetic goes wrong most often at the first step: knowing whether a screen shows a clean or a dirty price, and converting before comparing. That takes the coupon, the last coupon date, the settlement date and a minute. Treating price and yield as one quantity in two units, and redoing the conversion rather than trusting a screen, is how fixed income is taught here: as arithmetic you can rebuild, not vocabulary to memorise.