One bond, many yields

1Where bonds stop being simple

So far, this module has spoken only in rupees. You lend a thousand. Interest arrives. The thousand comes home. Every number could be held in your hand and counted.

That ends here.

From this chapter on, bonds speak in percentages, and percentages are where the trouble starts. Not because the arithmetic is hard. Because one bond, at one price, on one ordinary afternoon, can tell you several different things about what it earns, and every one of them can be true. Nothing on the screen warns you which one you are reading. Seasoned investors stumble here. So does software.

Here is the moment it happened to one reader. On a Tuesday in April, he looked up a single government bond on three different tools and wrote this:

Kite shows LTP for 833GS2026-GS as 102.9500 … I am assuming that 102.9500 is the dirty price of the bond. 1. TradingView shows YTM as -3.786% 2. My calculations show YTM as 5.0490% 3. Google Sheet's YIELDMAT(…) gives a result of 7.54068%. Which one of them is correct?

WideCalls, TradingQnA, 14 April 2026

Three tools. Three verdicts. One says he is losing money, one says five percent, one says seven and a half. Somebody is lying, surely.

Nobody was. The first reply he received is the line this whole chapter is built on:

Possibly all of them, based on what each of them is calculating.

cvs, TradingQnA, 14 April 2026

Hold on to that sentence. By the end of this chapter you will know which of those three numbers answered the question he meant to ask, and why the other two were not wrong so much as answering a different question altogether.

2The necklace that came back

In wedding season, some of the finest jewellery in the room does not belong to the person wearing it. It glitters through the pheras, poses for four hundred photographs, and is back in a jeweller's vault before breakfast. Rented for one night.

Keep that picture in mind. Now change one thing.

Scene one. Jaipur, the first week of the season. Mrs Kapoor needs ten lakh rupees, for one year, no longer. She will not sell her grandmother's necklace for good. She will not pawn it either. So she walks into Mr Shah's showroom with a proposal. She sells him the necklace, there and then, for ten lakh. And before the ink is dry on that, they sign a second line on the same sheet of paper: on this date next year, she will buy it back for ten lakh seventy thousand.

Not a rental. A sale with a return ticket.

Look hard at that extra seventy thousand, because it is the whole chapter in one number. When a jeweller rents out a necklace for a wedding, the fee is for wearing it. Here, nobody wears anything. The necklace just sits in Mr Shah's vault as security. The seventy thousand is what Mrs Kapoor pays for the use of his ten lakh for a year. A price paid for borrowing money has a name. It is called interest. And it is written on the paper. Let gold soar, and she pays ten lakh seventy thousand. Let gold collapse, and she pays ten lakh seventy thousand.

Scene two. Eight months later. Mr Shah needs his money back early. And the trading market has moved on. Deals like his are now being struck at a full lakh of interest, not seventy thousand. He carries the paper, and the necklace with it, to a younger dealer named Meera. She reads the paper twice. She looks out at the market. Then she offers nine and a half lakh. Why pay ten lakh for a promise of seventy thousand, when a fresh deal down the lane pays a lakh? They shake hands.

Scene three. The morning the year is up. Mrs Kapoor walks into Meera's shop, not Mr Shah's, with ten lakh seventy thousand rupees. Meera opens the vault. The necklace goes home. Mrs Kapoor has paid exactly what she promised, to whoever held the paper. She never needed to know it had changed hands.

Same promise. Now see what each dealer actually took away from it.

Mrs Kapoor's seventy thousand never moved an inch. What moved was the price each dealer paid to stand in line for it, and how long each of them stood there. And notice why Meera paid less: the moment newer deals started paying more, the old promise could only find a buyer by becoming cheaper.

A bond is that sheet of paper. Take the necklace away and what remains is a promise: a fixed number of rupees, on a fixed date. The rupees never change. The percentage you earn depends on what you paid for the promise, and it only matches the advertised rate if you hold it to the end.

Two things follow, and both will matter for the rest of this module. Most government bonds have no necklace behind them at all. The only security is the borrower's word, which is why who is borrowing matters so much. And the percentage worked out from the price you paid has a formal name, the yield to maturity. It describes your return only if you stay until the bond matures. Mr Shah left early, so it never described him at all. Chapter 5 is about exactly that gap.

3One bond, three honest numbers

Now leave that trading market for a real bond, and a real authority. In its own guide to government bonds, the Reserve Bank of India uses a ten year bond paying 8.24 percent a year, bought at ₹103 for every ₹100 of face value. Ask that bond what it earns, and it gives three honest answers.

Three numbers, three questions, no contradiction. The coupon rate is simply the contract: ₹8.24 a year on ₹100, the bond's own version of Mrs Kapoor's seventy thousand. The current yield divides that ₹8.24 by the ₹103 you actually paid. Both figures are RBI's, printed on the same page as its definition of the third:

Figure 1

Current yield has a blind spot, and it is a slow one. You paid ₹103. At the end, you get back ₹100. Those three rupees leak away quietly over ten years, and current yield never notices. Yield to maturity does. It weighs every coupon, the final repayment and the price you paid, and finds the one rate that makes them balance. Work it out for this bond and it lands at 7.80 percent, below the coupon, because of that long, slow pull back down to ₹100.

Read RBI's wording again: the return "if it is held until its maturity." Inside that phrase sit three quiet assumptions.

1. You keep the bond to the end.No selling halfway.If it breaks: your return depends on the price you sell at.
2. Every payment arrives in full and on time.No default, no delay.If it breaks: you get less, or you get it later.
3. Every coupon goes back to work at the same rate.The moment it lands, it is reinvested at the same yield.If it breaks: reinvest at a lower rate and you earn less.

That list is standard in every bond textbook, and India's own market body, FIMMDA, states the third one plainly: the calculation assumes the payments along the way are reinvested at the yield to maturity itself. When any of the three breaks, the yield still describes the bond honestly. It just stops being a forecast of your money.

So which of the three does the market actually use? Not the current yield. SEBI makes every online bond platform show it, right beside the yield to maturity, for every bond on offer. Yet in the real market almost nobody prices, trades or compares a bond on it, because it cannot see the ending.

The number everyone uses is the yield to maturity, or its everyday cousin, XIRR. And yes, it leans on that slightly absurd assumption that every coupon is reinvested at exactly the same rate. It wins anyway, because every one of these calculations has its pros and cons:

Yield to maturity is not the perfect number. It is the common one. It puts every bond, whatever its coupon, price or maturity, on the same scale, and that is what you need when two bonds sit side by side on a screen.

4Twice a year, or once

This is where the screens start to argue. Feed that same RBI bond, at the same ₹103, into two respectable tools, and one answers 7.80 percent while the other answers about 7.95. The bond has not changed. Its price has not changed. The two tools simply disagree about how to count a year.

Indian government bonds pay interest twice a year, and the market quotes their yield the same way: it finds the half-yearly rate and doubles it. RBI's own instructions for working out a yield in a spreadsheet leave no room for doubt:

Figure 2

The other way, used by most spreadsheets and most retail tools, is called XIRR. It lays every payment out on its real date and compounds once a year. A half-year at 3.90 percent, earned and then earned on again, comes to a little more than double: 7.95 percent. Same bond. Same price. Same rupees. Two dialects. The gap here is about 15 basis points, roughly 12 at a 7 percent yield, and it widens as yields climb. It is why a 7 percent government bond, said the other way, is a 7.12 percent one.

When two screens show different yields for the same bond at the same price, check how often each one compounds before you suspect anything else. Nine times out of ten, that is the whole mystery.

Two smaller characters wait in the wings.

The first is the day count, the rule for counting the days between two dates. Indian government bonds pretend that every month has 30 days and every year has 360, the "30/360" you just saw in Figure 2. It decides, to the rupee, how much interest you hand a seller. It barely touches the yield.

The second is the interest that piles up quietly between payments. Say a bond pays ₹4 every six months and you buy it three months after the last payment. About ₹2 has built up, the seller earned it, and you pay it on top. That ₹2 is the accrued interest. The price without it is the clean price; with it folded in, the dirty price. A yield is worked out on the money that actually leaves your account, so if the price is off by those two rupees, the yield is off with it. Chapter 4 gives this its own stage.

5Working one out, step by step

Strip away the jargon and XIRR asks one plain question. If this much money leaves your account on the day you buy, and these exact amounts come back on these exact dates, what single, steady yearly rate makes the two sides balance? There is no choosing between a formula for bonds that pay twice a year and one for bonds that pay at the end. The list of payments already knows.

Now return to the reader from section 1, and solve his bond the way XIRR would. It was a government bond paying 8.33 percent a year, maturing on 9 July 2026. He was looking at it in the middle of April.

Four lines, and the mystery is over. About 5 percent, almost exactly the 5.05 percent he had worked out himself. The spreadsheet's 7.54 percent came from two numbers typed into each other's boxes, inside a function built for bonds that pay all their interest at the end. The negative figure came from a tool that added the built-up interest on top of a price that already contained it, so it believed he was paying about ₹105 to get back ₹104. The reader was right all along. He just had no way of knowing it.

Step 4 has a catch. Say you pay ₹99,500 for a bond that pays you back ₹1,00,000 in three days. You make ₹500, which is half a percent. Step 4 then asks a strange question: what if you could do this again every three days for a whole year, putting the money back in each time? A year has about 122 three-day stretches, and half a percent earned 122 times over comes to about 84 percent. The arithmetic is right. But you cannot do it again, because the bond is gone in three days. What you actually made is ₹500. Finding ₹500 over a long weekend is a lovely weekend. It is not an investment strategy.

For a bond with less than a year left, look at the plain return in rupees over the time you will actually hold it. The yearly percentage is correct arithmetic and almost no use.

6Why nobody agreed on one formula

If one bond can honestly carry 7.80 and 7.95 percent at the same price, why did the world never simply pick one? It is tempting to imagine regulators from every country at one long table, arguing late into the night and failing. The truth is simpler. For most of history, there was nobody at the table at all.

First came the books. A century ago, nobody calculated a yield. Bond dealers looked it up in thick printed tables, with a price for every bond and every yield. Different markets printed different tables. Some assumed interest twice a year, some once, some four times. Each market grew up on its own books, and learned its own habit.

Here is a real page, printed in 1907. Find the bond's coupon along the top, 5 percent. Find the yield you want down the side, 4 percent. Where they meet is the price: 113.68 for every 100. Notice the line under the title, too. This page only works for bonds that pay twice a year. For any other kind, you needed a different book.

Figure 3

Then came the machines. Calculators that could work out a bond's yield arrived in the 1970s, and spreadsheets in the 1980s. They did not replace the old habits. They copied them. The twice-a-year markets kept their twice-a-year sums, the once-a-year markets kept theirs, and spreadsheets put XIRR in front of everyone, which is why so many everyday tools use it.

Then came the attempts to tidy up. When Europe prepared to share one currency, its banks tried to line up their bond markets, and could not even agree on how often a bond should pay interest. Britain changed its own convention as late as 1998. Each time, the rulebooks wrote down the habits markets already had instead of choosing one.

Even the reinvestment assumption was argued over. A Boston bond dealer called it absurd back in 1907, and admitted in the same breath that custom had already settled it. More than a century later, it is still there, and still the standard.

India's own central bank says it plainly, in the very primer this chapter has been quoting:

Figure 4

Nobody failed to agree on one formula. Each market settled into its own habit long before anyone could coordinate, and by the time anyone could, every desk, every table and every contract was built around the old one. So read a yield the way you would read a price in a foreign currency: first, ask what it is quoted in.

7One bond, every number

Before you go, here is the whole chapter on a single table. It is the RBI bond from section 3: 8.24 percent a year, bought at a clean price of ₹103, maturing on 15 January 2037. One thing changes. You buy it on 2 October 2026, partway between two interest dates, so the day count has something to count. Now imagine four versions of this bond that differ only in how often they pay interest, and work each one out under the two day counts you will meet most often: 30/360, which treats every month as 30 days and is what Indian government bonds use, and Actual/Actual, which counts the real days over a 365 day year, 366 in a leap year, and is what Indian corporate bonds use. Under Actual/Actual each interest payment is also worked out on the real days in its own period, so a coupon for a 184 day half year comes out a little bigger than one for 181 days. Every figure is per ₹100 of face value, to four decimals.

Every number on that table is true. A few things are worth noticing.

The coupon and the current yield never move. The coupon is the contract, 8.2400 percent. The current yield is that coupon divided by your price, 8.24 ÷ 103, exactly 8.0000 percent. Neither one cares when the money arrives, or how the days are counted.

The day count changes the cheque. On the twice-a-year bond, the last payment was on 15 July. 30/360 counts 77 days since then out of a 180-day half year, and charges you ₹1.7624 of accrued interest. Actual/Actual counts the 79 real days over a 365 day year, and charges ₹1.7835. On the once-a-year bond the gap runs the other way: 257 days out of 360 against 260 out of 365. And on the monthly bond both rules count the same 17 days, because September really does have 30, yet they still differ, because one divides by 360 and the other by 365. Neither rule is always the cheaper one.

The day count barely touches the yield. On the twice-a-year bond the XIRR is 7.9530 percent on 30/360 and 7.9568 percent on Actual/Actual, a gap of under four thousandths of a percent. Actual/Actual charges a little more accrued interest, but it also pays each coupon on the real days in its period, which over the life of the bond comes to slightly more. That is the day count's whole effect. It decides what you pay and what each payment is. It hardly moves what you earn.

The simple yield hardly moves either. It is a rough shortcut: the yearly coupon, plus the ₹3 premium you lose spread evenly over the years left, divided by your price. It ignores timing completely, which is why it sits below the real figure. The Actual/Actual rows show 7.7169 instead of 7.7168. That is not a typo: the two day counts measure the years left very slightly differently.

The last column climbs. Interest that reaches you sooner can start earning sooner, so a bond that pays every month is genuinely worth a little more each year than one that pays once. XIRR shows it: from 7.7881 percent up to 8.0936. The day count moves the yield in the fourth decimal. How often the bond pays moves it in the first. That is why, to compare two bonds that pay on different schedules, you want them both on the same footing, and compounding once a year, the XIRR way, puts them there.

Day count decides what you pay. How often a bond pays decides what you earn. Before you compare any two yields, make sure they are answering the same question.