Current Yield and Yield to Maturity: What Each Reads

The current yield divides one year of coupon by the price paid and stops there. The yield to maturity discounts every payment still to come, the face amount at the end included, back to that same price. Buy above the face amount and the current yield lands below the coupon rate but above the yield to maturity, because it never counts the loss back to face.

Two numbers, one bond, one instant in time, and they disagree. The disagreement is uncomfortable on first encounter, and the discomfort is worth sitting with. Neither noise nor a rounding artefact, the gap between the two numbers is the whole of what one measure counts and the other one does not.

Why do the price paid and the amount repaid have to be treated as two separate numbers?

Begin with something familiar that is rarely written down. A bond promises to repay a fixed sum on a fixed date. The repaid sum does not care what the buyer paid for the bond. A holder who paid more than it will be handed back less than they paid. A holder who paid less than it will be handed back more. The movement from the price paid to the amount repaid is real money on a known date, and only one of the two measures contains it.

Think about a shopkeeper who buys a delivery van for Rs 6,00,000/- knowing that a fleet operator has already agreed in writing to buy it back in four years for Rs 4,00,000/-. Whatever the van earns in those four years, Rs 2,00,000/- of the purchase price is gone by arrangement. A statement of what the van earns each year against what it cost is a true statement and a useful one. The yearly statement is also not the whole story, and nobody would confuse the two. Bonds are the same shape. Both numbers are printed as a percentage and both are called a yield, so the confusion happens anyway.

Every sum below follows one pattern, worth naming before the first of them arrives. Each sum is set up with every term visible, evaluated with the running total shown, and then evaluated again after exactly one input has changed. A total built line by line can be rebuilt from scratch. A total handed over whole has nothing in it to check.

Four words get used constantly below, and all four are built from scratch here before anything leans on them. A SPOT rate answers one narrow question: given a single lump arriving on one dated day ahead and nothing at all before it, what single annual rate carries that lump back to today? The word SPOT means nothing more than that here. A FORWARD rate answers a different narrow question: what annual rate applies across a stretch of time that has not begun yet? Both ends of that stretch, its start date and its end date, sit ahead of today. Two SPOT rates already imply a FORWARD rate. A FORWARD rate is therefore always derived from the pair rather than introduced by itself. Third, one basis point is a hundredth of one percentage point, so a hundred basis points make one percentage point, and the unit exists because 0.05 percentage points is easy to misread while five basis points is not. Fourth, and this one is load bearing on every sum below: annual compounding means the discounting clock ticks once a year and no oftener. On that convention a stated 8.50 per cent a year is an instruction rather than a description: divide by 1.085 once per year of travel, so a rupee due three years out meets the divisor three separate times.

One bond carries everything below. Bond A, an invented bond, runs ten years, carries Rs 1,000.00/- of face, and pays a coupon set at 8.50 per cent of that face on each of ten yearly dates. The bond has no issuer. Its coupon dates fall once a year for ten years, and it repays the whole face amount on the last of them. Repaying everything in one lump makes it a bulletA repayment shape where the whole principal comes back in one lump on the final date, with nothing repaid along the way. The opposite shape returns principal in slices across the life of the loan. rather than a bond that returns principal in slices. Annual compounding sits underneath every price below, and each of those prices is a chosen input.

What is the current yield, and what is the base of that ratio?

The current yield takes one year of coupon, divides it by the price paid, and reports the answer as a rate a year, with the price serving as the base and the face amount serving as nothing at all. That sentence has three parts and each one is doing work. One year of coupon, so a period is named. Divided by the price paid, so a base is named. Expressed as a rate a year, so the answer has units.

Run it on Bond A at a price of Rs 1,000.00/-. One year of coupon is 8.50 per cent of the Rs 1,000.00/- face, and 8.50 per cent of Rs 1,000.00/- is Rs 85/-. The price paid is Rs 1,000.00/-. Put Rs 85/- over Rs 1,000.00/- and the answer reads 8.5000 per cent a year, measured against the price. Nothing happened except one division.

The absences are the measure, so look hard at what is missing from that division. There is no date in it, no maturity, no face amount and no discounting of anything. The ten years Bond A has to run never entered the sum. The Rs 1,000.00/- that comes back at the end never entered the sum either, except through the back door, as the base the coupon rate was applied to when the coupon was worked out. The current yield is a ratio between two amounts standing side by side at one instant, and its honesty comes entirely from how little it claims.

The last point gets read as criticism, and it is not one, so it deserves a moment. A measure that claims less can be wrong in fewer ways. The current yield needs no view about what happens between today and the repayment date, needs no solving, and can be worked out by anybody with the price in front of them. The current yield answers a real question that nothing else answers as directly, and which question that is gets named further below.

What is the yield to maturity, and what does it carry that the current yield does not?

The yield to maturity is the single rate that discounts every payment still to come, all the coupons and the face amount together, back to the price being paid. The yield to maturity is not a division but a rate to be searched for, and it has been found when the discounted amounts add up to the price exactly.

Take Bond A at a price of Rs 1,000.00/- again. Try 8.50 per cent a year on annual compounding. Divide the first Rs 85/- by 1.085 once, the second by 1.085 twice, and so on out to year ten, where Rs 85/- of coupon and Rs 1,000.00/- of face arrive together and both get divided by 1.085 ten times over. Add the eleven results. The eleven results come to Rs 1,000.000000/-, and Rs 1,000.000000/- is the price. So 8.50 per cent a year is the yield to maturity, found by trying rather than by dividing.

So the second measure has two things the first one lacks, and they are worth saying plainly. The yield to maturity contains every date, and it contains the face amount as an amount rather than only as the base a coupon was struck on. That is the entire difference between them. Everything else below is a consequence of those two inclusions.

Why does every price need its compounding convention written beside it?

Because the same figures on a different clock give a different price, and the difference is not small enough to shrug at. The convention is not housekeeping and it does not belong in a footnote.

Bond B, an invented zero coupon bond with no coupons at all, matures in 7.1191 years. Priced at an 8.50 per cent annual yield the way this guide prices everything, dividing by 1.085 once for each year, Rs 1,000.00/- of face comes back to Rs 559.4640/- today. Taking the identical 8.50 per cent and the identical 7.1191 years and running the clock twice a year instead, dividing by 1.0425 fourteen and a bit times, the same bond prices at Rs 552.8781/-. The two prices sit Rs 6.5859/- apart on a Rs 1,000.00/- face, and the two sets of figures behind them look identical when printed.

One more line on Bond B before leaving it. Its price is usually written Rs 559.47/- and the figure just computed is Rs 559.4640/-. The stated maturity of 7.1191 years is itself a rounding of 7.119062643353 years, and pricing at the unrounded maturity gives Rs 559.4657/-, the source of the Rs 559.47/- figure. The two annual prices sit Rs 0.0017/- apart. Set that against the Rs 6.5859/- the convention change produced and the ranking is obvious: a rounded maturity moves the price by less than a fifth of a paisa, and a changed compounding clock moves it by more than six and a half rupees.

The rule that falls out of this is short. Put the convention next to the price and a reader can rebuild the sum from nothing. Omit it and the sum turns unrepeatable, however precisely everything around it is written. A sum nobody can rerun has taught nobody anything, so the one tick a year underneath every price here gets repeated inside the sums themselves rather than filed in a footnote.

Why do all three measures read the same number at par?

At a price of Rs 1,000.00/- something happens that is worth stopping for. The coupon rate on Bond A is 8.50 per cent a year of the Rs 1,000.00/- face. The current yield is 8.5000 per cent a year of the price. The yield to maturity is 8.5000 per cent a year. Three measures built three different ways, and one number comes out of all of them.

A reader who files that away as a coincidence has thrown away the cleanest illustration of the difference between the three. The three agree because at a price of Rs 1,000.00/- nothing moves at all between the price paid and the amount repaid, so the only cash a holder ever receives beyond their own money coming back is the coupon, and every honest way of turning that cash into a rate has to give the same answer.

Work the logic once slowly. The holder pays Rs 1,000.00/-. Over ten years they receive Rs 85/- ten times. At the end they receive Rs 1,000.00/- back, exactly what they put in. The redemption amountThe sum the issuer hands back on the final date. The amount is fixed by the terms of the bond at the time it is issued and does not move afterwards, whatever anybody later pays for the bond. and the amount paid are the same figure, so the principal contributes nothing to the return in either direction. All that is left is the coupon stream. The price and the face are the same number, so one year of it divided by the price gives 8.5000 per cent a year. A stream that pays 8.50 per cent of its own principal every year and then repays that principal in full is, by construction, worth its principal at 8.50 per cent, so the rate that discounts the whole stream back to the price is 8.50 per cent a year. The equality of those three readings is precisely what the words at par mean.

Anywhere else on the price scale, the three numbers come apart. The two sections below move the price above the face amount and then below it.

What happens to each measure when the price rises above the face amount?

Keep every term of Bond A exactly where it is and move only the price. The coupon is still Rs 85/- a year, the face amount is still Rs 1,000.00/-, there are still ten yearly dates, and the discounting clock still ticks once a year. One input moves and nothing else does.

Set the price at Rs 1,079.4804/-. At that price the yield to maturity works out to 7.35 per cent a year on annual compounding. Now read the three measures off, one at a time.

Read them in the order they came out: 8.5000, then 7.8742, then 7.3500. A descent, and not an even one. The descent happens because the holder paid Rs 1,079.4804/- and will be handed back Rs 1,000.00/-, so Rs 79.4804/- of what they paid never returns as principal at all, and the yield to maturity is the only one of the three measures that has subtracted it.

The coupon rate did not move because it never could. The coupon rate is fixed at issue, applied to the face amount, and completely blind to what anybody pays. Its base moved, so the current yield moved a little: the same Rs 85/- divided by a larger number is a smaller ratio. But the current yield has no dates in it and no face amount in it, so it still has no idea that Rs 79.4804/- is going missing. Only the third measure feels the loss, discounting an actual Rs 1,000.00/- arriving on an actual final date back against a price of Rs 1,079.4804/-.

The sum that produced that price is worth seeing on its own, and it also shows where the two parts of the promise sit. With the clock at one tick a year and the rate at 7.35 per cent, the ten coupons come back to Rs 587.4641/- between them while the Rs 1,000.00/- face comes back to Rs 492.0163/-. The two discounted amounts add to Rs 1,079.4804/-. Printing the ten dated amounts to four places and adding the printed figures instead gives Rs 1,079.4806/-, two paise over. The two paise are a rounding artefact and nothing else: the parts round independently and nine of them rounded upward. Where a total matters it is taken from the unrounded amounts, and the printed parts are printed as they round rather than nudged to close.

What happens to each measure when the price falls below the face amount?

Now push the price the other way and the whole thing runs in reverse. Running in reverse is what makes it a rule rather than an observation. Set the price at Rs 931.2325/-. At that price the yield to maturity works out to 9.60 per cent a year on the same annual clock.

Read them in order again: 8.5000, then 9.1277, then 9.6000. Climbing, where the premium case descended, and climbing in the same order. The current yield always sits between the coupon rate and the yield to maturity, and which of the two is above and which is below is decided entirely by whether the price sits above or below the face amount. That is a checkable rule, not a generalisation. Given any two of the three readings, the side of the face amount the price sits on can be named without the price being shown at all.

Here the holder paid Rs 931.2325/- and will be handed back Rs 1,000.00/-, so Rs 68.7675/- arrives as principal beyond what was put in. The current yield does not know about that either. Its base shrank, and that alone is why the current yield went up. The yield to maturity went up further because it counted both things: the same Rs 85/- a year against a smaller outlay, and a dated principal gain on top.

What does the worked grid show when it is read across rather than down?

With the three prices side by side, the teaching moves from the columns into the rows. One bond carries all three columns: Bond A, Rs 1,000.00/- of face, a coupon set at 8.50 per cent of it each year, ten yearly dates, one discounting tick a year, at three chosen prices.

Now read across. The coupon row never moves at any price, the current yield row moves a little, and the yield to maturity row moves most, and the space that opens between the last two rows is exactly the principal movement the current yield cannot see. Three rows, three different amounts of sensitivity to the one input that changed, and the ordering of that sensitivity is the whole difference between the three.

The bottom row is the one to carry away. Above par it reads 0.5242 percentage points, taken from 7.8742 less 7.3500. Below par it reads minus 0.4723 percentage points, taken from 9.1277 less 9.6000. At par it reads nothing at all. There is nothing to read. The sign of that bottom row names which side of the face amount the price sits on, and it does so without the price being shown at all.

The two gaps are also not the same size. Rs 79.4804/- above the face amount opened a gap of 0.5242 points. Rs 68.7675/- below it opened one of 0.4723 points. The premium was the bigger movement in rupees and produced the bigger gap in points. The ordering is unsurprising and is not a rule worth leaning on: the relationship between a rupee of price and a point of yield is not a straight line, and putting a number on that curvature is covered separately.

What is the pull back to the face amount, and why can the current yield not see it?

Here is the mechanism underneath everything above, stated on its own because it is the mechanism and not merely an observation. Whatever a bond costs today, the issuer repays the face amount on the final date and not one rupee more or less, so a price above the face amount has to come down to it and a price below it has to come up. The movement is not optional and nobody has to predict it. The terms of the bond write it in.

Give it the everyday shape first. A household buys a fixed deposit receipt from a neighbour who needs cash now. The receipt will pay Rs 1,00,000/- on a stated date and nothing before it. Whatever the neighbour is paid for it today, the bank will hand over Rs 1,00,000/- and no other figure. Pay Rs 1,05,000/- for it and Rs 5,000/- is gone by the terms of the thing. The receipt has one payment and the arithmetic is impossible to hide, so nobody would call that a surprise. Bonds have eleven payments instead of one, and the same certainty hides behind the coupons.

Put a size on it for Bond A at the premium price. The holder pays Rs 1,079.4804/- and will be handed Rs 1,000.00/-, so Rs 79.4804/- of principal disappears across ten years by arrangement. Spread that evenly and it is about Rs 7.94804/- a year, and Rs 7.94804/- against a price of Rs 1,079.4804/- is about 0.7363 per cent a year of the price.

Now the honest part. The spread-evenly figure illustrates the size of the pull and is not the arithmetic the yield to maturity does. The yield to maturity discounts, so it does not spread anything evenly, and the two routes do not reconcile. The rough route gives 7.8742 less 0.7363, or 7.1379 per cent a year, against a true yield to maturity of 7.3500 per cent a year. The two figures are 0.2121 percentage points apart. A reader who tries to make them agree and cannot might otherwise conclude that the arithmetic is wrong. The approximation is what fails, and it is labelled an approximation for exactly that reason.

The shape of that line says something the numbers alone do not, so look at it for a second. The price does not fall in equal steps. The price drifts down slowly at first and drops faster near the end, and it lands on Rs 1,000.00/- exactly, not approximately. The landing is not a prediction, it is a term of the bond. Everything else on the chart is arithmetic; the last point is a promise.

Where is the current yield still the right number to use?

The current yield is not a broken version of the yield to maturity, and the other half of the account is owed. The two are different measures answering different questions, and there is a question the current yield answers that nothing else does.

If the question is about cash arriving in a period, the current yield is the correct number; if the question is about the whole of what is owed and on what dates, the yield to maturity is the correct number. That is the whole test, and it is decided by the question rather than by which measure is more sophisticated.

Take a retired household living on the coupons from a set of bonds and paying the electricity bill out of them. The household needs to know how much cash lands in the account this year against the money that went out to buy the holding. The question is a current yield question from top to bottom. The yield to maturity cannot answer it, and not because it is inaccurate: it blends cash arriving with a dated principal movement into one figure, so it simply cannot be read as cash in any particular year. Asking it how much money arrives in March is asking a question it was never built to answer.

The everyday version to run beside that: the rent a shop pays this month and the total cost of a ten year lease on the same shop are both true numbers about the same arrangement. Neither answers the other's question, and a shopkeeper who used the monthly rent to judge the whole lease, or the whole lease to judge whether this month is affordable, would be making the same kind of mistake in opposite directions.

Who reaches for which measure, and what do they do with it?

The split shows up in real desks, and seeing where each measure lives makes the distinction stick better than any definition.

A lender assessing whether a borrower can service a loan is running a cash question. The lender needs to know whether money arrives in each period, in what amount, against what was laid out. If a holding of bonds is being counted as a source of that money, the number the lender wants is the cash per period against the outlay, and cash per period against outlay is a current yield in everything but name. A yield to maturity dropped into that calculation would overstate or understate the cash by exactly the amount of the coming principal movement, in whichever direction the price happens to sit.

An analyst comparing two holdings for what they are worth is running the other question and reaches for the yield to maturity. The whole of what is owed and when is precisely what is being compared. But even there the analyst has to know the compounding convention behind each published figure before comparing them, and the routing table below matters more than it looks for exactly that reason.

A treasury team inside a company sitting on cash it will need in three years asks both questions in sequence. First, the current yield: does this holding throw off enough cash each year to cover what the company has committed to pay out? Second, the yield to maturity: what is the whole holding worth to the company if it runs to the end? Two questions, two measures, and no conflict at all between them.

A household is the simplest case and the one most often got wrong. Somebody with savings placed in bonds hears one number quoted by whoever sold the holding to them. The higher number sells better, so the quoted one is nearly always the higher of the two. Ask which of the two measures a quoted yield is, and then ask whether the price sits above or below the face amount. Those two questions together reveal what the number left out.

None of this touches the plumbing. The registrarThe party that keeps the list of who holds a security at any moment. The registrar keeps the record of ownership and decides nothing about the value of the security. keeping the holder list and the paying agentThe party that actually sends out the interest and repayment amounts on the dates they fall due, on behalf of the issuer. The paying agent moves the money and does not decide the amounts. sending out the money have nothing to say about which yield is read, and neither does the principal outstandingThe amount of borrowed money still owed at a given moment, before any interest. On a bullet bond it stays at the full face amount for the whole life and then drops to nothing on the final date., which on Bond A stays at the full Rs 1,000.00/- until the last date and then goes to nothing. The registrar, the paying agent and the principal outstanding are facts about the instrument. The two yields are two different questions asked about the same facts.