How to Read a Bond Term Sheet: Every Field in Order

A bond term sheet is the summary of an offered bond's terms, field by field: who is borrowing, how much, on what dates, at what coupon rate and in what form. Read in order, it fixes every rupee the holder will ever receive. The one thing it does not fix is the price. A price comes from the rates ruling on the day the bond is bought.

A reader has been handed a single sheet with about a dozen labelled rows on it and wants to know what to do with it. Not what it means in general. The question is what to do, in what order, so that the bottom of the sheet leaves the reader holding something that could not have been written down before starting. Seven steps answer it, run in order, each one producing what the next one needs.

A term sheetThe summary of an offered bond's terms, set out field by field rather than as prose, so each term can be read and checked on its own. is not a document read the way a letter is read. A term sheet is a form somebody has filled in, and the way to read a filled-in form is to use it. A term sheet has been read properly when the payments it describes have been written out on paper, and not one moment before. Everything below is built around that single discipline. Skipping it produces one specific and expensive error, worked through below.

Most readers have done this before without calling it anything. When a landlord hands over a rent agreement, the tenant does not summarise it. The tenant works out what leaves the bank account in month one, what leaves it in month thirteen after the stated increase, and what happens to the deposit at the end. Three numbers, and the agreement is now something that can be acted on. A term sheet is the same object with different labels, and the same move works on it.

What is a bond term sheet, and in what order is it read?

Seven steps. Each step consumes what the step above wrote down, so no step may begin before the one above it has produced its output. The constraint is what makes seven steps a procedure rather than a checklist. A checklist can be worked through in any order and still be complete. A procedure cannot.

1. Write out the cash flowsTake the fields that fix the payments, apply the coupon rate to the face amount, and write the resulting amounts against the dates they fall due. Nothing is summarised at this step. Every amount is written in full.
   Checking: is there one written amount for every payment date on the sheet?
2. Check the fields against each otherThree checks, each of which uses two fields at once. Dates against maturity, final flow against coupon plus face amount, and coupon rate against the stated coupon amount.
   Checking: did each check use two fields, and did all three agree?
3. Notice the field that is not thereGo looking for the price. It is not a term and it will not be on the sheet. Write down that it is absent and write down what it will depend on instead.
   Checking: is the reason the price is absent written down, rather than merely noticed?
4. Price the completed sheetDiscount each written flow at the rate for its own date, state the compounding convention inside the arithmetic, and add. The result is a number the sheet never gave.
   Checking: does every flow carry the rate for its own date, and is the convention stated?
5. Sort what the sheet cannot settleSeveral fields carry a meaning the issuer did not choose. Each one is routed to the authority that sets it, by name, and left blank on the working copy.
   Checking: does every blank row carry the name of an authority rather than a guess?
6. Change one field and price againMove exactly one field, hold every other field still, and reprice. The difference between the two prices is what that field is worth on this schedule.
   Checking: did only one field move, and can the difference between the two prices be stated?
7. Name what the sheet cannot be read forWrite down, in the working copy, the questions this document does not answer and the maturities it cannot be priced at here.
   Checking: is the list of limits written into the working copy rather than carried in memory?

Before step one there is a sorting move that costs thirty seconds and saves the rest of the reading. The fields on a term sheet are not all the same kind of thing, and a reader who gives every row the same weight has already lost. The rows fall into three kinds, and the sort is mechanical.

Which fields change what is paid, and which do not?

The first kind fixes the payments. The face amountThe amount the coupon rate is applied to, and the amount repaid when the bond matures. The face amount is a stated figure on the sheet, not a market value., the coupon rateA rate applied to the face amount to fix the size of each payment. A yield is struck on the price rather than on the face amount, so a coupon rate is not a yield., the payment datesThe dates on which the flows fall due. The sheet fixes them and nothing that happens later changes them. and the maturity date. Between them these four decide every rupee the holder will ever receive, and once the ink is dry no rate anywhere in the world alters a single one of them. The four payment fields are the only fields on the sheet that change what is paid, and they are therefore the only fields step one uses.

The second kind fixes the meaning of those payments rather than their size. The compounding convention, the day count convention and the quotation basisThe agreed way a price is expressed when it is quoted, set by an authority rather than by the issuer.. The three conventions decide how a calculation is performed and how a figure is expressed, not what falls due. One convention wrong makes every number computed from the sheet wrong. The payments themselves stay exactly what they always were.

The third kind fixes nothing at all about the payments. The form the holding takes, where the holding is recorded, and who is eligible to hold the thing. A reader who has just learned the first two kinds is tempted to write this group off. Writing the third kind off would be a mistake, and the reason is worth stating plainly. The third kind decides whether a particular reader can hold the instrument at all. Eligibility is a completely different question from what the instrument pays, and it gets answered before the arithmetic ever matters. A perfect valuation of something the reader is not eligible to hold is an expensive way to spend an afternoon.

Here is the complete sheet worked from below, drawn up for an invented government issuer. Where an authority sets the meaning of a field, that row is drawn and left empty with the authority named inside it. An empty row with a name in it is a finding. A filled row with a guess in it is a liability.

How are the payment fields turned into cash flows?

Step one. Take the four payment fields and use them. Not summarise them, not restate them in a sentence beginning with the words this bond is a. Use them.

The face amount is Rs 1,000.00/-. The coupon rate is 6.5235176 per cent a year. There are three annual payment dates and the bond matures at the end of the third year. Those four fields are everything step one needs, and the multiplication is the whole of the work.

So the flows are Rs 65.235176/- at the end of year one, Rs 65.235176/- at the end of year two, and Rs 1,065.235176/- at the end of year three, the final coupon of Rs 65.235176/- together with the face amount of Rs 1,000.00/-. Three lines. Those three lines are the output of step one, and every later step consumes them.

A reader who cannot reproduce a figure has been given a figure to believe rather than a figure to check, so two things about that coupon rate are worth stopping on. First, why such an unusual rate. The rate was solved backwards rather than chosen: it is the coupon rate that makes this three year schedule price at exactly its face amount on the three recorded SPOT rates of the invented SPOT curve behind every price here. Second, the decimals are load bearing, and the reason is arithmetic rather than fussiness.

Now the decimals. Carried at seven decimal places the coupon rate reads 6.5235176 per cent a year, and 0.065235176 times Rs 1,000.00/- is Rs 65.235176/- exactly. Round the same rate to six decimal places and it reads 6.523518 per cent a year. Then 0.06523518 times Rs 1,000.00/- is Rs 65.23518/-, four ten thousandths of a paisa larger. The six decimal rate and the coupon amount printed beside it do not reproduce each other, so this sheet carries the coupon rate at seven decimals. A figure a reader cannot reproduce from the figures printed beside it teaches that reader to distrust their own arithmetic. Where this schedule appears elsewhere as 6.523518 per cent a year, that is the same rate rounded one place earlier, and the coupon amount that goes with it is Rs 65.23518/-.

How are the fields checked against one another?

Step two. Three checks, run in about a minute, each of which uses two fields at once. Using two fields at once is the entire point of the step, and the reason it cannot be replaced by reading more carefully. A single field read on its own has nothing to be inconsistent with, so it is always internally consistent. Every error that survives a careful reading is therefore an error between two fields.

Check one. Does the number of payment dates match the maturity and the stated frequency? Three annual dates over three years at one payment a year. Three against three, so this closes.

Check two. Does the last flow carry both the final coupon and the face amount? Rs 1,065.235176/- less Rs 65.235176/- is Rs 1,000.00/-, the stated face amount. Check two closes too. A sheet whose last flow is Rs 65.235176/- has either forgotten the repayment or is describing something other than a bond that repays at maturity, and either way that is worth knowing before the sheet is priced.

Check three. Does the coupon rate applied to the face amount give the stated coupon amount? 0.065235176 times Rs 1,000.00/- is Rs 65.235176/-, exactly what the sheet says. Check three is what the decimals above were preparing for: run at six decimals of rate it gives Rs 65.23518/- against a printed Rs 65.235176/-, and an analyst would be right to stop and ask which of the two the sheet was built on.

Why is the price the one field that is not on the sheet?

Step three produces a note and no arithmetic at all. Go looking for the price, fail to find it, and write down why.

The price is not a term. Every field on the sheet is fixed for the life of the bond, and being fixed for the life of the bond is exactly what a term means. A price depends instead on the rates ruling on the day somebody buys it, and rates move while terms do not. The one number a reader actually cares about on the day is the one number the document cannot carry, and understanding that reverses how most people approach the whole exercise. A reader who arrived hoping the sheet would tell them what the bond costs leaves knowing the sheet tells them what the bond pays, and that these are different questions with different answers.

Which label every rate carries, and why

Since the price has to come from rates that are not on the sheet, rates are about to be written down, and one rule has to be in place first. Every rate written anywhere carries the word SPOT or the word FORWARD. Not sometimes. Every time.

A SPOT rateThe rate for money placed today and returned at one stated future date. A single dated amount is discounted at its own SPOT rate. is the rate for money placed today and returned at one stated future date. A FORWARD rate is the rate for money placed at one future date and returned at a later one. Two different objects. The reason the labels are compulsory rather than tidy is that on the invented SPOT curve this material carries, the two land close enough together to be merged by a reader who meets them without labels.

The one year one year FORWARD rate works out at 6.601157 per cent a year. The three year SPOT rate on the same invented curve reads 6.55 per cent a year. The two figures sit 0.051157 percentage points apart, or 5.1157 basis points. Forwards land near spots on any smooth curve, so nothing has been moved to separate them. Pulling them apart would make the curve a fiction. The label does the work instead, and it does it on every rate throughout this material.

One more thing about that FORWARD rate, the figure most often misread. The rate was not forecast. The rate was divided out of two SPOT rates already sitting on the curve, in the block above. A FORWARD rate is arithmetic pulled out of today's SPOT curve rather than anybody's opinion about the future, and that is why it is derived above rather than quoted.

How is the completed sheet priced?

Step four. Take the three flows from step one and discount each one at the SPOT rate for its own date. Not at one rate for all three. Each flow is a separate dated claim and each gets the rate for the date it falls due.

The rates come from the invented SPOT curve this material works from: one year 5.90 per cent, two years 6.25 per cent, three years 6.55 per cent, all on annual compoundingOne discounting period a year, so an amount due in three years is divided by one plus the rate three separate times. A different convention on the same numbers gives a different price..

The compounding convention sits inside that arithmetic rather than in a note beneath it. Annual compounding means one discounting period a year, so the amount due in three years is divided by 1.0655 three separate times. The convention is not housekeeping. The same six numbers on a semi annual convention give different prices and a different set of FORWARD rates, and a reader who is not told which convention is in use cannot reproduce a single sum of the arithmetic above.

The three printed present values add to Rs 1,000.000000/- exactly. Rs 65.235176/- is itself the par coupon rounded at the seventh decimal of the rate, so carried unrounded that coupon amount of exactly Rs 65.235176/- gives Rs 999.99999992/-, eight hundredths of a millionth of a rupee below the face amount. At the unrounded rate of 6.5235176030 per cent a year the three terms come to Rs 1,000.00000000/- exactly. Whichever rounding a reader carries, the sum lands on one of those three figures.

The arithmetic, and not a claim printed on the document, shows that this sheet describes a bond issued at parA price equal to the face amount. A bond issued at par is one whose price on the day equals the amount that will be repaid at maturity. on this schedule. The sheet was priced, and no field on it claimed par. No row on the sheet said at par. The arithmetic said it, and the arithmetic is reproducible by anybody holding the same four payment fields and the same three SPOT rates.

What is done with a field that cannot be checked from the sheet?

Step five. Several rows on any term sheet carry a meaning the issuer did not choose, and reading them off the sheet as though the issuer did is precisely the error this step exists to prevent. The temptation here is structural rather than occasional: a form with an empty row on it asks to be completed, and the instinct that completes it is the same instinct that completes it wrongly.

The procedure is three moves and it never varies. Name the authority that sets the field. Go to the source. Never fill the field in from memory. The reason for the third move is that every one of these fields moves over time, so a field filled in from memory is not merely old, it is wrong from the day it changed and carries no marker saying so.

The table does something to the sort made at the start. The four fields that fix the payments are all checkable on the sheet. Every field that fixes the meaning of the payments goes to an authority. The split is not a coincidence and it is worth carrying away as a rule of thumb: the issuer chooses what to pay, and somebody else decides how what it pays is computed, expressed and recorded.

Where a measured series would be needed rather than a rule, the route is the Reserve Bank of India's data site at dbie.rbi.org.in, and where the construction and publication of a benchmark government curve would be needed, the route is the Clearing Corporation of India Limited at ccilindia.com. Every rate used above is derived in the working itself rather than read off a market, and a reader who needs a measured series will find one at those two routes.

What happens when exactly one field changes?

Step six is the test that turns a reading into an understanding, and it is one move: change exactly one field, hold every other field completely still, and price again.

Change the coupon rate to 8.50 per cent a year, or Rs 85.00/- a year on the same Rs 1,000.00/- face amount. Every other field stays exactly where it was: same three annual dates, same maturity at the end of year three, same face amount, same conventions routed to the same authority. The flows become Rs 85.00/-, Rs 85.00/- and Rs 1,085.00/-.

Priced on the identical three SPOT rates, those three flows discount to Rs 80.264400/-, Rs 75.294118/- and Rs 896.952358/-, and they add to Rs 1,052.510876/-. The price now carries a premiumA price above the face amount. A premium is the present value of the extra coupon the sheet promises over and above what the rates of the day would call for. of Rs 52.510876/- over the face amount, produced by one field and nothing else.

One field moved a price by Rs 52.510876/- and left every date on the document untouched. The isolation is complete, and the coupon rate row can never again be read as a formality. And the premium is not mysterious once its source is traced: the second sheet pays Rs 85.00/- a year against the first sheet's Rs 65.235176/- a year, a difference of Rs 19.764824/- a year for three years. Discounted at the same three SPOT rates, that difference comes to Rs 52.510876/-. The premium is exactly the present value of the extra coupon, to the last paisa.

What can a term sheet never be read for?

Step seven, and it is written into the working copy rather than carried in memory. A term sheet says nothing about the bond's worth in any market, nothing about whether the issuer will pay, and nothing about how far the price would move for a given rise in the yield or fall in the yield. Worth, credit and price sensitivity are three separate questions with three separate methods, and none of them lives on this document.

There is a fourth limit here, and it is specific to the invented SPOT curve this material carries rather than general to term sheets. The curve holds six points and nothing between them: one, two, three, five, ten and thirty years. There is no four year SPOT rate here, no nine year SPOT rate, no twenty nine year SPOT rate, and nothing at all shorter than one year.

A straight line reading and a curved line reading disagree, so no line is drawn between the recorded points to read a value off. Two readings working from the same record would otherwise give two different figures for the same object. Where a reader expects a rate in between, the answer is that the rate is not in this record, and it stops there. Drawing a gap as a gap is more honest than filling it, and it is the thing most curve pictures get wrong.

The gaps decide which sheets can be priced here. Every flow of a one, two or three year sheet falls on a date the record carries, so such a sheet can be priced completely. A sheet written for a five year government bond paying once a year cannot. Its flows fall at one, two, three, four and five years, and the flow due at the end of year four has no SPOT rate in this record to be discounted at. One flow out of five, and one is enough to stop the sum. The missing four year point is also why the worked sheet above is a three year bond rather than the five year one a reader might have expected.

Who actually reads a sheet this way, and when?

Somebody runs these seven steps at the moment a document arrives and a decision has not yet been made. The moment before the decision is the only window in which the procedure is worth anything. Afterwards the arithmetic is being used to defend a position rather than to reach one.

A lending officer receiving a set of terms runs steps one and two before anything else, and does it for a reason that has nothing to do with pricing: the pair checks catch transcription errors, and a transcription error in a payment schedule is the kind of mistake that is cheap to find on day one and expensive to find in year three. Three checks, a minute, and the rest of the analysis is standing on a schedule somebody has verified rather than on a schedule somebody has read.

An analyst comparing two offered instruments runs step six as a matter of routine, and repeatedly. The two sheets are lined up field by field and every row that differs is identified. Then one differing row moves at a time and the sheet is repriced. At the end there is a rupee figure attached to each difference rather than a general impression that one sheet looks better. The discipline is exactly the one worked through above: the second price is only interpretable because everything except one row was held still.

Somebody reviewing a document for a committee lives in step five and step seven. Their output is not a price at all. The output is a note listing which rows were checked on the sheet, which rows were routed to an authority and to which one, and which questions the document cannot answer. The note travels further than the person who wrote it. Travelling that far is precisely why the empty rows have to carry the name of the authority inside them rather than being left blank.

The household version is the same shape and worth holding on to, and the instinct comes from there. Somebody offers a household a chit or a recurring deposit and hands over a small printed slip. The slip states the amount, the dates and the rate applied to the amount. The slip does not state the arrangement's worth to that household. Worth depends on what else the same money could do over the same period, and that changes month to month while the slip does not. So the payments are written out, the total on the slip is checked against the sum of the parts, and the comparison is then found elsewhere. The household has run steps one, two, three and four in a kitchen.