How to Review Prepayment and Extension Risk on a Bond

Seven steps run in one order. Step one establishes whether every payment date and amount is fixed by contract. Step two establishes who holds the choice about timing. Step three records the schedule's response in each rate direction. Step four asks whether a speed exists to size the exposure with. Step five tests whether the duration in the file still applies. Step six writes down every question the inputs could not answer. Step seven states what the review established.

Every sensitivity figure ever handed to an analyst was built on a list of dated amounts somebody took as given. Taking the dates as given is not a criticism of the figure. Discounting demands it, because a payment cannot be discounted until its arrival date has been decided. So the first job of this review is not to measure anything, it is to find out whether the assumption underneath the measurements is still true. And exactly one thing decides whether that assumption survives. Does the party on the far side of the contract get to pick the payment dates? Everything else in the sequence below follows from the answer to that single question.

A tenancy makes the point. Two households rent identical flats at identical rents for identical three year terms. In the first agreement, neither side can end it early. In the second, the tenant can walk out with one month's notice and the landlord cannot. On paper the two look like the same three year income. The two agreements are not the same thing at all, and no amount of studying the rent figure will tell which of them is being held. The notice clause has to be read. Reading the notice clause is the habit this review writes down and applies to a bond.

Why does the order of the seven steps matter?

A review is not a checklist that can be ticked in any sequence. The steps below are ordered because each one narrows what the next one is allowed to conclude. Step one settles whether the instrument's list of dated amounts is fixed. If it is not, then every figure already sitting in the file was computed on a set of dates that may no longer describe the instrument being held, and that is known before a single one of them has been quoted. Running the sequence out of order does not slow the review down, it lets a figure be used before the step that would have disqualified it has run.

Here is the whole of it in one picture, with what each step returns on the right. Notice how few of the seven produce a number. A step that returns no number is normal, and on some files the blank is the entire finding.

One more thing before the steps themselves. The seven steps are a sequence and nothing more. Early repayment's cost to a lender, and the effect of a stretched set of payment dates on the quantity a duration figure summarises, are covered where the two risks are set side by side. Here they are used rather than taught. A step that starts explaining a mechanism has stopped being a step.

Step one. Is every payment date and amount fixed by contract?

Step one reads the instrument's own terms. Not the summary sheet, not the file note somebody wrote when it was bought, and not the analytics screen: the terms. One thing only is being looked for, and it is whether the cash flow scheduleEach payment an instrument expects to make, written out with a calendar day beside it and a rupee amount beside that. is settled by the contract or left open by it. Read the redemption clause, read anything about early repayment, read anything that lets a date move, and read the definitions those clauses point at.

Step one comes first because a movable verdict here has already qualified every number in the file, and a fixed verdict is what allows the rest of the file to be used at all. The order is not a formality. A reviewer who starts at the sensitivity figures and works backwards will have quoted three of them before reaching the clause that makes them provisional.

The third of those three outcomes is the one people quietly drop. Where the terms could not be obtained, the honest verdict is not established, and it travels forward as a qualification on everything after it. Writing fixed because nothing in the summary sheet mentioned early repayment is not a reading of the contract. A summary sheet is somebody else's reading, and the principalThe amount the borrower has committed to repay, as distinct from the interest charged on it while it is outstanding. repayment terms are exactly where a summary sheet is thinnest.

Step two. Who holds the choice about timing?

If step one returned fixed, this step returns neither and takes ten seconds. If it returned movable, this is the most important question on the card and it decides the direction of everything downstream. Record who can move the dates: the borrower, the holder, or neither, with the timing depending on something outside anybody's choice at all.

A review that records only that the schedule can move, without recording who moves it, has stopped one question short of the one that decides which way the exposure runs. A timing choice sitting with the borrower is exercised when it suits the borrower, and that one sidedness is the whole of the disadvantage. A timing choice sitting with the holder is not a risk at all in the same sense; it is a right, and the instrument is a different object from the one the file thinks it is describing. A schedule can also move for reasons nobody controls, when the underlying payments simply arrive as they arrive. People most often mislabel that third case as the first.

Step three. What does the schedule do in each rate direction?

Two lines, always, and never one summary sentence. Line one records what happens to the payment dates when the yield falls. Line two records what happens when the yield rises. Against each line goes a note of whether that response helps or hurts the holder. The pair is what makes the pattern visible, so both lines get written even when the answer to both is the same, and even when the answer to both is nothing at all.

The step exists to catch a schedule that shortens on a fall in the yield and lengthens on a rise. The combination hurts the holder on both sides, and it has a name settled earlier in this sequence. The step does not ask for the name to be explained. The step asks for the two lines to be written down so that the pattern, if it is present, cannot be missed. A single summary line hides it. A reviewer writing one sentence about a moving schedule almost always writes the direction that worries them and leaves out the other.

Units get mixed at exactly this step, so here is a note on them. Rate moves in this sequence are quoted in basis pointsA percentage point cut into a hundred parts. Two hundred of them make 2.00 percentage points, and this sequence keeps the two names apart at every single mention. and price responses are quoted in per cent of the starting price. Basis points and per cent are two different scales, and a review that runs them together produces a card nobody downstream can check. Write the units into the line rather than leaving them to be inferred.

Step four. Is there a speed to size the exposure with?

Attaching a rupee figure or a percentage to either of these risks requires an assumed prepayment speedHow fast a group of borrowers is taken to be clearing their loans early. It is an assumption, normally quoted per period, and normally drawn from what similar borrowers did before.. There is no way round it. Without one the schedule cannot be built, and without the schedule there is nothing to discount. So this step does not ask for the number to be produced. Step four asks whether the number exists, and where it came from.

Record three things and then stop: whether a speed is available, its source, and the period it was estimated over. The estimation period matters more than reviewers expect. A speed estimated over a stretch when rates barely moved is not a speed at all. Such a speed is an average of a period in which nobody had a reason to act.

On a verdict of not available, this step stops, and stopping is the output. Stopping is the whole instruction, and it is the hardest one in the sequence to follow. A card with a blank on it looks like unfinished work. A card with a number on it looks like a review. The cost of filling the blank anyway is set out further down, in its own block.

Two things commonly get substituted for a real speed at this step, and both should be recorded as not available. The first is a speed borrowed from a different pool of loans on the grounds that the loans look similar. The second is a schedule reconstructed from what the borrower has done so far. Such a reconstruction describes the past rather than assuming anything about the future, and it quietly becomes a forecast the moment it is discounted. If either is used, it goes on the card as a stated assumption in its own row, never as an input.

Step five. Does the duration in the file still apply?

Now take whatever duration figure the file carries and interrogate it rather than using it. Three questions. Which kind is it, MACAULAY or MODIFIED? The two names have been kept apart all the way to here, and this is where the separation earns its keep. What schedule was it computed on. And when was it computed. Then issue one of three verdicts.

If step one returned movable and the figure was computed on a fixed schedule, the verdict is superseded, and superseded is a different finding from approximately right. Approximately right invites the number to be used with a mental discount that nobody can size and nobody writes down. Superseded says plainly that the figure is measuring an instrument which may no longer be the one being held, and that a replacement has to be computed rather than estimated in somebody's head.

Step six. Which questions could the inputs not answer?

This step is where the blanks collected on the way through get written out properly, as outputs of the review rather than as gaps in it. Each one gets three things: the question, the input that was missing, and the reason the question was not answered instead of estimated. The third of those is what makes the entry useful, and it tells the next reader what would have to arrive for the question to become answerable.

Because the next person can supply the missing input and finish the step, a refusal recorded this way is worth more than an estimate. An estimate has to be found and unpicked before it can be replaced. The asymmetry between a blank and an estimate is the entire argument for the step. Nobody is being asked to be scrupulous for its own sake. A blank costs the next reader one look, and a buried assumption costs them an afternoon, if they notice it at all.

Three kinds of question turn up here more than any other. The first is the size of the exposure, and it needs a speed. The second is the curvature of a movable schedule instrument, needing the same speed and then a rebuilt schedule on top of it. The third only appears where the instrument sits over a pool of receivablesAmounts owed to a lender by many separate borrowers, gathered together so that the payments they make can fund a single instrument., and it asks how likely a loss of any particular size is. The third question needs a loss distributionA description of how likely each possible size of loss is across a pool, rather than merely which piece of the funding meets a loss first., and often a cash flow waterfallThe written order in which money coming into a pool is paid out, period by period, to the pieces that funded it. period by period as well. Where those are absent, the order in which losses are met is knowable from the structure and the odds are not, and the card must say which of the two it is reporting.

Step seven. What has the review established?

One paragraph, and it separates three things that a reader will otherwise merge. The findings. The assumptions, with the word assumed written against each. The refusals, each with its reason. Findings, assumptions and refusals get three different labels because the moment a card is quoted onward, whichever of the three is unlabelled becomes a finding by default.

If the findings section reads longer than the inputs could possibly justify, one of the steps above has been filled in rather than answered, and the run should be read backwards until the invented input turns up. The backwards read takes a minute, and it catches the thing no gate downstream will. The read works because a review is arithmetic in reverse: three real inputs cannot produce seven substantive findings, and a card that shows seven has manufactured four of them somewhere between step one and here.

What does the sequence look like run end to end?

Run it on the instruments this platform teaches with, and something useful happens: the review comes back mostly empty in the places people expect numbers, and it is a stronger demonstration than a full card would have been. There are two instruments here. A ten year bullet bond carrying an 8.50 per cent annual coupon, priced at par at Rs 1,000.00/-, and a zero coupon bond struck at that same 8.50 per cent yield, whose maturity was chosen to match the bullet's MACAULAY duration exactly. Both compound annually, and neither has a borrower behind it.

Step one, on both instruments

Read the terms of each. On the bullet, ten dated amounts, nine coupons and a tenth date carrying the last coupon together with the face amount, every one of them set by the contract. On the zero, a single payment at a single stated date. Neither document contains a clause that lets any date move. Verdict on both: FIXED. Evidence: the coupon and redemption terms, read in full.

Step two, on both instruments

No clause on either instrument grants anybody the choice to move a date. Verdict on both: NEITHER. And the review records the consequence in one line. The risk under review does not arise on either of these two bonds at all. A verdict of neither is a finding, not an absence of one, and it is what lets everything downstream stand.

Step three, on the bullet bond

Two lines, as always. On a fall in the yield, the schedule does nothing. On a rise in the yield, the schedule does nothing. The two responses point the same way, and that way is no way at all. Here is what a settled schedule buys the holder, in figures the file already contains. Move the yield 200 basis points either side of 8.50 per cent, on the annual compounding convention this whole sequence uses, and the price does not move symmetrically. On a rise in the yield to 10.50 per cent, the price falls 12.030 per cent. On a fall in the yield to 6.50 per cent, it gains 14.378 per cent. The MODIFIED duration of 6.5613 predicts 13.123 per cent in both directions, being twice 6.5613 rounded to three places.

Read that carefully. The wrong lesson is easy to take from it. The bond is not beating anything. A MODIFIED duration draws a straight line where the true relationship bends, and a relationship bending in this direction stays above that line on either side of where it started. The bend belongs to any instrument whose amounts and dates are all fixed and all positive, and that is exactly the condition step one just confirmed. The advantage is a property of the arithmetic, and the condition that produces it is the fixed schedule the review established at step one. Both of these bonds are priced off one and the same yield, and that makes the extra bend look like something obtained for nothing. In a market where curvature is wanted it would be charged for, and a bond with more of it would ordinarily be priced to yield less. The two yields are set equal here for the comparison, so the extra bend is not a reason to prefer one schedule to the other.

Step four, on both instruments

Not available, and the blank carries its reason. Neither bond amortisesDescribing a schedule in which the amount owed is paid down in slices across the life of the instrument rather than all at the end., neither has a payment date that can shift, and neither has a borrower who could repay early. So no speed exists to be quoted, and the step stops here with the reason written into the space where a number would have gone.

Step five, on the bullet bond

The file carries a MODIFIED duration of 6.5613. The figure was computed on the ten dated amounts of a fixed schedule, on annual compounding, and step one returned FIXED for that same instrument. Verdict: STILL APPLIES. The card records the figure, records that it is the MODIFIED one and not the MACAULAY one, and records the schedule it was built on. A later reader can then run step five again rather than having to trust that somebody did.

Step six, on this file

Three questions go down as unanswered, each with its reason.

Step seven, the statement

The review establishes three things and refuses four. The first is that no party holds a choice over the timing of any payment on either instrument, so neither bond is exposed to either risk. The second is that the MODIFIED duration of 6.5613 in the file still applies to the bullet bond, on the schedule and convention it was computed with. And the third is that no speed of early repayment reached this file, so no figure for either risk can stand on any other instrument either. Everything else on the card is a refusal with its reason attached.

Count what the finished card holds. The count itself is the teaching. Six of the seven steps returned a verdict. One step, the fourth, returned a blank. And the card carries four recorded refusals altogether: the one at step four, plus the three written out at step six. A run that had produced seven substantive answers from these inputs would have manufactured most of them, so the blanks are not the weakness of this card, they are the part that makes the rest of it trustworthy.

The pooled structure, recorded for what it can carry

One structure sits behind this guide as well, and step six's third refusal is about it, so it is worth setting out exactly. The thing being funded is Rs 1,200 crore of receivables. Three pieces put up that money between them. The senior one contributes Rs 960 crore. The mezzanine one contributes Rs 180 crore. The equity one contributes Rs 60 crore. The three contributions add back to the pool exactly. Measured against the Rs 1,200 crore base, they read 80.0, 15.0 and 5.0 per cent, and those three close on 100.0 as well.

The three pieces are not slices of the pool that each take their share of whatever arrives. The three pieces establish an order. Losses meet the equity piece first, then the mezzanine, then the senior. So Rs 240 crore, or 20.0 per cent of that same base, has to be used up before the senior piece is reached at all. Now take a pool loss of exactly 5.0 per cent, which on that base is Rs 60 crore. The equity piece absorbs the whole of it, and nothing further up the order gets reached.

An order is not a probability, and the gap between the two is the single most useful thing to carry away from this structure. The equity piece meets a loss before the mezzanine does, and that much is certain. Whether a loss arrives, or how large it is likely to be, cannot be said at all without a description of how losses are distributed, and no such description sits behind this guide. An order of loss is not a grade, and it makes none of the three pieces safe. Step six's third entry says exactly that, in the place where a probability would otherwise have been written.

Who actually runs this, and when?

Three people run some version of this sequence, and it is worth seeing all three, because the same seven questions look very different depending on which side of the contract the person stands on.

A desk that buys bonds for a balance sheet runs it before the instrument is added to the book, and step one decides where the instrument goes. A fixed schedule instrument can be handed to the ordinary sensitivity arithmetic and its MODIFIED duration means what the arithmetic says it means. An instrument whose dates can move cannot, and putting one into the same process produces a number that looks identical on the screen and is describing something else. The step one verdict is a routing decision before it is anything else, and routing an instrument wrongly is a mistake that never announces itself.

An analyst covering a lender runs it from the other side of the table entirely. The lender's borrowers hold the timing choices, so the lender is the party carrying the consequence, and the analyst's step two is really a question about the lender's book. Step two matters most where the servicerThe firm that collects payments from borrowers on a pool of loans and passes the money on to whoever funded them. is a different firm from the one that made the loans. The information about who is repaying early then flows through the collecting firm rather than the lending one.

And a household runs it without ever calling it a review. A household with a home loan repayable ahead of schedule at no cost holds a timing choice, and will use it when cheaper borrowing appears. The lender is on the other end of that. Nothing about that arrangement is unfair or unusual. The ordinary domestic decision to clear a loan early is simply the same object that step two exists to find, seen from the side that benefits.

In all three cases the practical value is the same and it is not the numbers. The value is that the sequence forces a question to be asked before a figure is used, and that it leaves a written record of which questions could not be answered. Six months later, when somebody asks why the file has no figure for this, the card already says why, and it says which input would produce one.

Who settles the rows left empty here?

The ten year bullet bond, the zero coupon bond standing beside it, the pool of receivables and the three pieces funding it are invented.
Educational material. Not advice on any investment, tax, budget or market position.