Guide · Fixed income · Updated 2026-09-23

A yield curve is a list of prices for money on later dates, and an inverted one is arithmetic before it is a prophecy

Most explanations of the yield curve start with what it predicts, usually the American rule that an inverted curve comes before a recession, repeated for India with the ten year bond and the 91 day bill. The curve comes first. It is a price list, what the market pays today for a rupee in six months, five years or forty, and a forecast is an interpretation laid over it. This guide bootstraps the curve FBIL published, derives its forward rates, prices 119 bonds off it, and measures 102 month-end curves and eleven years of maturity bucket indices. It extends a bond's price and yield from one bond to the whole curve, and carries the forward price is not a forecast from index futures to interest rates.

The curve is published, and it is fitted before anyone reads it

Since 31 March 2018, following the RBI's policy statement of 7 February 2018, FBIL has administered the valuation of central government securities. Each business day it publishes every bond's price and yield, a par curve and a zero coupon curve at quarter year steps out to the longest bond. Under its methodology, version 4 of 8 August 2024, the zero curve is a cubic spline through selected yields from the last hour of trading on NDS-OM, the RBI's order matching system, and three choices shape every number read from it.

The first year is therefore a Treasury bill curve, moving with the corridor and with bill supply rather than with bond trading, and the par curve is generated from the zero curve by the standard formula, so the two carry the same information. On 23 September 2026 the public archive held 2,048 daily files, the latest dated 16 September 2026, which is the reference curve on this page.

Three yields, three different objects

A par yield is the coupon at which a bond would be priced at exactly 100 today, an average over all its payment dates. A spot rate prices one payment on one date: a rupee due in t years is worth D(t) = 1 / (1 + s/2)^2t today, s being compounded half-yearly as Indian bonds are. A forward rate prices a loan from one future date to a later one, and two discount factors fix it: from a to b, (1 + f/2)^{2(b − a)} = D(a) / D(b).

Their order is arithmetic. When par yields rise with maturity, a par bond's early coupons are discounted at the lower early rates, so its final payment must carry a higher one: spot sits above par. A rising average needs its newest additions above it: forward sits above spot. When the curve flattens or falls both orders reverse, and that reversal is all an inverted curve is.

At thirty years spot exceeds par by 51 basis points, and the forward for years twenty to thirty is 8.77. Beyond forty years the par curve is flat, and the last decade's forward, 7.31, falls below the forty year spot rate of 8.26: a small inversion made of nothing but that flattening.

Bootstrapping: one unknown at a time

A coupon bond's yield is not a spot rate. Spot rates are extracted from coupon bond prices one maturity at a time, each step reusing every factor already solved. A six month par bond at 5.73 per cent pays 102.865 at six months for 100 today, so D(0.5) = 100 / 102.865 = 0.972148. A one year par bond at 6.02 pays 3.010 at six months, worth 2.9262 at that factor, which leaves 97.0738 for its last payment of 103.010: D(1) = 0.942373, a spot rate of 6.0244 per cent.

The quarter year points need two conventions, found rather than assumed: the three month point is a money market rate, and a par bond at 0.75, 1.25 or 1.75 years has a short first coupon at three months. Under them the bootstrap reproduces FBIL's own zero curve within 0.84 basis points out to ten years, 2.22 to thirty and 4.40 to fifty. The residual is rounding, which each step inherits from every step before it: the files since February 2023 print par yields to two decimals. On three older files printed to full precision, 28 March 2018, 30 June 2020 and 30 December 2022, the same bootstrap reproduces every published zero rate to within a hundred-billionth of a basis point.

A forward rate is a loan priced today for a later date

Put 1,00,000 rupees to work for two years on the reference curve. A two year zero pays 1,13,054.11 at the end. A one year zero pays 1,06,115.10 in a year, to be lent again, and that path finishes level only if the second year earns 6.4356 per cent: the one year rate one year ahead, which is D(1) / D(2) turned into a rate.

It can be bought today, which is what makes it a price. Buy 1,13,054.11 of face value of the two year zero for 1,00,000 and sell 1,06,115.10 of the one year zero for the same amount. Nothing changes hands now; 1,06,115.10 goes out in a year and 1,13,054.11 comes back a year later, a loan fixed at 6.44 per cent. No step asks what anyone expects. If a quoted forward drifted from D(1) / D(2), this zero cost trade would lock in a certain gain, and competition for that gain holds the forward in place.

A break-even, not an expectation

Because the two paths tie at the forward, the forward is the break-even between them, and the one year rate that actually prevails in a year decides the winner.

At 5.25 per cent, the repo rate on the reference date, rolling finishes 1,294.84 rupees behind; above 6.44 it wins. An expectation of falling rates has to be set against 6.44, not against today's 6.02: the curve has already charged for everything up to the forward.

Standard theory separates the forward from the expected rate by a term premium, the extra return demanded for holding the longer bond through its price risk, less a convexity effect that matters only at long maturities. One curve cannot show the premium. Forwards set against the rates that followed can.

The forwards ran high at every horizon: the three month rate three months ahead in 87 of 99 months, the one year rate a year ahead in 69 of 90, by 69 basis points on average. The table's split is an identity, the forward's lead over the rate of its day minus the change that followed, and it locates the error: the one year forward led by 50 basis points on average, and the rate then fell 19. Most of the error was in the curve on the day it was read.

The sample is one period, with the three month rate between 3.01 and 7.10 per cent and ending below where it began, and its windows overlap. A premium and a run of downward surprises push the error the same way, and one sample cannot separate them. It does not fit an unbiased forecast, which would not be too high in 87 months of 99. Money actually earned shows the same premium: holding to one year at the curve's one year rate beat rolling overnight tri-party money by 0.67 percentage points a year on average, in 79 of 90 one year windows. An RBI Bulletin article of June 2022, whose views are its authors', calls the empirical support for the expectations hypothesis, that long rates are averages of expected short rates, weak.

The front of the curve belongs to the corridor

The RBI steers the overnight rate, not the curve. Its revised liquidity framework of 30 September 2025 kept the weighted average call rate as the operating target inside a symmetric corridor, the standing deposit facility 25 basis points below the repo rate as floor and the marginal standing facility 25 above as ceiling, and made 7 day and other operations of up to 14 days its main tools in place of the 14 day variable rate repo and reverse repo. On 5 August 2026 the Monetary Policy Committee left the repo rate at 5.25 per cent, the floor at 5.00 and the ceiling at 5.50; it meets next on 5 to 7 October.

The reference curve starts on that corridor and leaves it within months. The three month par yield is 5.25, the repo rate. The tri-party overnight rate compounded by the exchange's Nifty 1D Rate Index averaged 5.01 per cent in August and 4.63 from 1 to 17 September; it is not the call rate the RBI targets, and it can sit below the floor. The three month rate three months ahead is 6.13, 63 basis points above the ceiling. As a forecast, it says the three month rate rises 88 basis points by mid December and takes the corridor with it. As a price, it says six month bills cost more than two three month bills in a row, which the front of the curve said in 87 of the 99 months tested. A front year built from bill rates answers to liquidity and bill supply as well as to policy, and the curve alone cannot apportion the gap.

An inverted curve is arithmetic before it is a prophecy

Across 102 month ends the one year par yield topped the ten year only twice, by 4 basis points on 29 February 2024 and by 1 on 31 May 2024; the ten year never fell below the three month, coming within 18 basis points on 31 May 2024. The February 2024 curve rose from 6.80 per cent at three months to 7.16 at nine, fell to 7.03 at two years and stayed near 7.07 out to ten.

The arithmetic is fixed: where par yields fall, spot rates fall faster and forwards fall below them, and the one year rate a year ahead was 6.95 against a one year spot rate of 7.11. As prophecy, the curve said rates would fall. As prices, it said one year money was dear, and the reason was public. The Governor's statement of 8 February 2024 reported system liquidity in deficit since September 2023, for the first time in four and a half years, averaging ₹1.61 lakh crore in December and January; the tri-party overnight rate averaged 6.74 per cent in those two months, at the 6.75 ceiling around a 6.50 repo rate. The front end was lifted by the price of overnight money before the long end had to forecast anything.

The same statement read the narrowing gap between the ten year yield and the 91 day bill, 24 basis points in December and January against 40 in October and November, as better anchored inflation expectations. Both readings fit the same prices; a shape alone cannot choose between a view and a squeeze. The June 2022 Bulletin article found that in India, unlike advanced economies, the curve's level and curvature carry the useful information about growth and inflation expectations, and its slope, the number the recession rule reads, does not.

The far end is a few bonds and a spline

Beyond fourteen years the curve rests on six buckets with as little as one bond in each, and the grid follows issuance: about forty years until the file for 30 November 2023, when a fifty year bond joined the list, and fifty since. Forwards, being differences of long products of rates, magnify every wiggle in so thin a curve. FBIL's zero rate peaks at 8.45 per cent at 36 years and falls to 8.11 at fifty, so forwards past the peak sit below spot. Six month forwards computed from the two decimal par yields run from 0.25 to 12.80 per cent, neighbours up to 745 basis points apart: one basis point of rounding in a forty year yield becomes about eighty in the six month forward after it.

Trading pulls the middle too. In 69 of 102 month ends the ten year par yield sat at least two basis points below the highest yield between seven and ten years, by up to 37 on 29 May 2020. A dip exactly where trading concentrates is what a price for liquidity looks like, not a view that money for year ten is cheaper than money for year nine.

Measured: the long bucket against the short, 2015 to 2026

The index provider's 4 to 8 year and 15 year and above G-Sec indices each hold the three most traded central government bonds in their band, weighted 40 per cent by turnover and 60 per cent by amount outstanding, reviewed monthly and computed on a total return basis (methodology of April 2022). Both run in the exchange's daily index files from 13 October 2015.

In the 10.9 years to 18 September 2026 they returned almost the same, 121.4 and 123.7 per cent, or 7.54 and 7.64 a year, the long bucket at 1.9 times the volatility, 5.35 per cent a year against 2.87. Month by month it moved 11.55 per cent per point on FBIL's thirty year par yield, and the short bucket 4.05 per point on the six year, fits that explain 92 and 94 per cent of the variation. The gap between the two buckets therefore reads the curve's level and slope together.

When yields fell across the curve, the long bucket's sensitivity carried it ahead even as the curve steepened: in 2020 the thirty-over-five spread widened from 0.49 to 1.34 points, but the five year yield fell 145 basis points and the long bucket gained 2.59 points more. In 2025 the five year fell only 32 while the spread widened from 0.29 to 0.87, and the long bucket trailed by 4.75. From its high on 26 September 2024 it lost 9.2 per cent against the short by 2 April 2026 and ended 7.1 below that high, as the curve steepened from both ends: from 30 September 2024 to the reference date the three month par yield fell 110 basis points while the repo rate was cut from 6.50 to 5.25 per cent, and the five year rose 11, the ten year 29 and the thirty year 75. None of this says where the slope goes next; it says what a change in level and slope did to each bucket.

What the curve is actually for

Its first use is pricing. FBIL values a bond with enough trades at its own traded yield and any other at the curve plus an adjustment factor, and the bootstrapped curve reproduces that split. Priced off its spot rates for settlement on 17 September 2026, the 22 bonds FBIL used as inputs sit within 2.6 basis points of their published yields, a median 4 paise per 100 of face value. The 81 bonds with no qualifying trade and over a year to run sit a median 2.4 basis points cheaper than the curve, and the 8 with under a year scatter from −18 to +29, because the front of the curve came from bill rates.

Its second use is reading what is already priced. On the reference date the curve charged 6.44 per cent for one year money a year out, 7.47 for five year money five years out and 8.53 for ten year money ten years out. A borrower fixing a rate or a lender choosing between bills and a bond is comparing a belief with those numbers, and a belief that matches them is already in the price. The split of each forward into expectation and premium is not in the curve; it takes judgement about the corridor, supply and demand, and a check of forwards against what followed. Reading the curve as prices first, and each forecast laid over it as a hypothesis to test, is how fixed income is taught here.