Mortgage-Backed Securities: Prepayment as the Defining Risk
A mortgage-backed security is a claim on a pool of home loans, paid for by pieces that take their money in a fixed order. A pool of home loans differs from every other pooled claim in one respect: the borrower may hand principal back before it falls due. So a holder carries an open question about WHEN the money returns, not only whether it returns. Timing is the part most readers underestimate.
Every claim on a pool of loans carries the first question. Will the money come back? A pool of home loans then adds a second one, and the second has no counterpart in a plain bond. The borrower is holding a right to finish the loan early. The borrower may use that right at a moment nobody else picks, and using it returns the principal in full on a date the holder had planned around differently.
What is a mortgage-backed security, and what is actually inside it?
The box matters more than the label. The structure worked through this whole sequence is Sarvani Receivables Trust, an invented trust that exists only to supply arithmetic somebody can check. The trust holds a pool of receivablesMoney contracted to arrive from somebody else. A lender's loan book is a stack of them, each one a promise carrying a date. worth Rs 1,200 crore. Three pieces paid for that pool between them. The senior piece put in Rs 960 crore. The mezzanine piece put in Rs 180 crore. The equity piece put in the last Rs 60 crore.
Reading Sarvani Receivables Trust as a mortgage-backed security changes exactly one thing, and it is not any of those amounts. The change is in what the receivables are. Every rupee stays where it was. The three pieces added together return the Rs 1,200 crore of the pool, with the senior piece still at 80.0 per cent of it, the mezzanine piece at 15.0 per cent and the equity piece at 5.0 per cent. The contents are what is new. The receivables are now home loans, and a home loan is a particular animal: it runs for a long time, it is securedThe lender has a claim over a named asset, here the house, that it can fall back on if payment stops. Security changes what is recovered, not when. on the house it paid for, and the person repaying it holds a right that the writer of a plain bond does not hand out.
What is the one feature of a home loan that changes everything downstream?
A home loan repays in slices. The loan is amortisingThe amount owed is paid off in pieces across the life of the loan instead of arriving in one lump at the end. Each payment kills a little of the balance., so principal keeps coming back through the years rather than waiting for one date at the end. Repaying in slices is already unlike a plain bond, and it is not the interesting part.
The interesting part is that the borrower may hand the principal back before it is due, in part or in full, and generally does not need anybody's agreement to do it. Somebody sells a flat. Somebody gets a lump of money and would rather not owe anything. Somebody finds a cheaper loan and closes this one with the proceeds. In every case the lender gets the money. Nothing is lost, nothing is written off, and no default has occurred anywhere.
The calendar has changed. The documents described a set of dates on which principal would arrive; some of that principal now arrives sooner. Every difficulty that follows grows out of that one change and out of nothing else. The pool is not smaller. The order is not disturbed. The dates moved.
What is the one feature of a home loan that makes this instrument behave unlike a plain bond?
Does the money come back, or when does it come back?
Those are two questions, and a reader who has met only the first is holding half the instrument. Take them one at a time.
The first question is about loss. Will the pool deliver what it promised? The order is what answers that one, and it was settled earlier in this sequence. The equity piece takes the first rupee of any shortfall. Only once that piece has gone does the mezzanine piece begin giving anything up. The senior piece is touched last of the three. Add the two lower pieces and Rs 240 crore is the total, a 20.0 per cent share of everything in the pool, and every rupee of it has to be consumed before the senior piece parts with anything. A pool shortfall of 5.0 per cent comes to Rs 60 crore, and Rs 60 crore wipes the equity piece exactly and reaches nothing above it.
The second question is about the calendar. On what dates does the money actually arrive? The order has no opinion about this at all, and no rearrangement of the order could produce one. Ranking who absorbs a loss before whom says nothing about which year a rupee lands in. The two questions have different answers, run on different mechanisms and carry different costs when either is got wrong. Both answers arrive in the same monthly statement, and arriving together is exactly why they get merged.
What single number captures when the money comes back?
A principal scheduleA list of principal amounts set against the dates they are expected on. It says how much and when, and nothing about interest. is a list: so much principal on this date, so much on that one. The list is honest and the list is unusable in a sentence. Nobody compares two instruments by reading two lists aloud. One number that carries the shape of the list would serve, and there is a plain one.
Multiply each principal amount by the number of years until it arrives, add the results, then divide by the total principal. The result is an average of TIME, weighted by MONEY. Big amounts arriving early pull it towards the present; small amounts arriving late barely tug at it. The measure is called the weighted average life, and it is the plainest summary there is of when a pool's principal comes home.
| Pt | the principal amount expected on one date, in rupees, taken from the schedule |
| t | how many years away that date is, counted from today |
| the divisor | every principal amount added together, which is the whole principal owed |
| the answer | a number of years, always between the first date and the last one |
Rs 1,200 crore of principal returns in four equal annual instalments, at the end of years one to four. Before any computation: is the weighted average life closer to two years or to four?
What does the weighted average life of this pool work out to?
Working anything out requires a schedule, and this record does not contain one. The record fixes the sizes of the pieces and the order they absorb in, and it stops there. The schedule below is therefore DECLARED, purely so that the arithmetic has something to bite on. Nobody measured it, nobody modelled it, and no pool anywhere was watched to produce it.
The declaration: the Rs 1,200 crore of principal returns in four equal annual instalments of Rs 300 crore, at the end of years one, two, three and four. The sum is short enough to do by hand. Each instalment is weighted by the year it lands in, so 300 goes in once, then twice, then three times, then four times. The four weights add to ten, so the total is 300 multiplied by ten, or 3,000 crore-years. Divided by the Rs 1,200 crore of principal, the weighted average life is 2.50 years.
| Date the principal arrives | Principal | Years away | Principal x years |
|---|---|---|---|
| End of year one | Rs 300 crore | 1 | 300 |
| End of year two | Rs 300 crore | 2 | 600 |
| End of year three | Rs 300 crore | 3 | 900 |
| End of year four | Rs 300 crore | 4 | 1,200 |
| Whole declared schedule | Rs 1,200 crore | 3,000 |
The right-hand column is in crore-years, which is a slightly odd unit and the reason the divide is needed. 3,000 crore-years over Rs 1,200 crore of principal leaves years, and the years are 2.50. Both columns close on their totals with nothing left over, so either one can be added by hand and lands on the same figure.
For the special case of equal annual instalments there is a shortcut that is the whole of this arithmetic: the answer is the count of instalments plus one, all over two. Four instalments give five over two, and five over two is 2.50 years. The shortcut works only when the instalments are equal and annual, and it is a check rather than a substitute for the schedule.
Now do it. Four equal annual instalments of Rs 300 crore, at the end of years one to four, against Rs 1,200 crore of principal. What is the weighted average life?
The figure of 2.50 years already says something before a single borrower has done anything unusual. The last instalment lands at the end of year four, and the summary number is 2.50 years, so there is a gap of 1.50 years between the two. The gap is not a warning about prepayment. The gap is just what happens when money arrives in slices instead of in a lump: 50.0 per cent of the principal is already back by the end of year two, and 75.0 per cent by the end of year three. An instrument that repays in slices is shorter than its last date, and it was shorter before anybody prepaid anything. The reader who quotes the final date as the life of the pool has already overstated it by a year and a half, without help from any borrower.
Why is money arriving early and in full still a cost?
Change the declaration and hold everything else still. Suppose the same Rs 1,200 crore comes back in three equal annual instalments of Rs 400 crore, at the end of years one, two and three. The name for that change is front loadingMore of the total arriving in the earlier years than the later ones. The same money, pushed towards the near end of the calendar.: nothing has been added or taken away, the pile has simply been shoved towards the near end of the calendar.
Work it the same way. 400 goes in once, twice and three times. The three weights add to six, so the total is 400 multiplied by six, or 2,400 crore-years. Over Rs 1,200 crore that is 2.00 years. The weighted average life has moved from 2.50 years to 2.00 years, a difference of 0.50 years, and the shortcut agrees: three instalments give four over two. Meanwhile 66.67 per cent of the principal is back by the end of year two, against 50.0 per cent under the first declaration.
So where is the harm? Every rupee arrived. Nothing was written off. Not one of the three pieces absorbed anything. And yet the holder is worse off in one specific, nameable way, and it is worth being precise about it rather than waving at it.
The holder has been handed a decision they did not ask for, on a date they did not choose. Money that comes back has to go somewhere. Putting the money back to work is reinvestmentPutting returned money back to work. Whatever it earns next is settled by the terms available on the day it is placed, not by the terms of the loan it came out of., and what the money can earn next is whatever the SPOT rateMoney handed over today, one stated date on which it comes back, and the rate that pairs those two moments. Every rate in this material compounds once a year. happens to be on the day it is placed. Nobody can state that rate in advance. The rate is fixed on the day the money is placed, by the terms available that day, and not by the loan the money came out of.
The same Rs 1,200 crore comes back in three instalments of Rs 400 crore instead of four instalments of Rs 300 crore. What has changed, and what has not?
A holder receives principal a full year earlier than the declared schedule promised. What is the honest thing to say about what that money now earns?
Two declarations give two points, and two points are not yet a shape. Pushing the same Rs 1,200 crore across more years makes the shape appear: five equal instalments of Rs 240 crore give 3.00 years, six of Rs 200 crore give 3.50 years. Every extra instalment adds exactly half a year, every time, with no curvature anywhere. The half-year step is not a property of this pool; it falls straight out of the count plus one over two, and it holds for any total split into equal annual instalments.
Rearrange the same principal along the calendar
The control moves one thing. The pool is Rs 1,200 crore at every setting. Every rupee of principal comes back at every setting. The senior piece keeps its Rs 960 crore. So does the mezzanine piece keep its Rs 180 crore, and the equity piece its Rs 60 crore. The control rearranges the calendar, and the calendar alone.
One setting on that control needs a warning label, and it is worth stopping for. At five instalments each one works out to Rs 240 crore, and Rs 240 crore is also the amount standing beneath the senior piece. The two have nothing to do with each other, and the only defence against confusing them is to name the base every time. One is a yearly slice of principal, measured against the calendar. The other is other people's money sitting below a piece, measured against a shortfall. Same digits, different question, and the base is named each time both appear.
Set the control to five instalments. Each one is Rs 240 crore, and Rs 240 crore also happens to be the amount standing beneath the senior piece. What is the relationship between those two figures?
Borrowers across the pool repay faster than the declared schedule. Predict, before reading on, what happens to the Rs 240 crore standing beneath the senior piece.
Does early repayment move the loss order at all?
The last section, read again with attention on the pieces instead of the bars, holds four figures. The equity piece reads Rs 60 crore. The mezzanine piece reads Rs 180 crore. The two smaller pieces together put Rs 240 crore below the senior piece, being 20.0 per cent of everything in the pool. The senior piece itself reads Rs 960 crore. Switching from the four instalment declaration to the three instalment one and reading the same four figures again: not one of them has moved.
Early repayment rearranges the calendar and leaves who absorbs before whom exactly where it was. The match is not a coincidence and it is not a feature of this particular structure. The order is a statement about rank: which piece gives up money first when the pool falls short. A schedule is a statement about dates: which year the money lands in. Neither statement contains a term of the other, so neither can move the other, however hard a reader squints at the monthly statement where both are reported.
Keeping the two apart is most of the discipline of reading this instrument. Merging them produces the two classic errors in one move: treating a fast pool as a safe pool, and treating a slow pool as a risky one. Speed is a statement about the calendar. Safety, to whatever extent this material can speak to it at all, is a statement about rank. How the money actually gets shared out period by period, once it has arrived, is a mechanism of its own and it is covered separately.
What does this look like on an ordinary street?
A shopkeeper lends a neighbour some money against a written promise of twelve monthly instalments. She is not being reckless. She knows the neighbour, she has the promise in writing, and she plans the year around those twelve arrivals: stock in one month, a wedding contribution in another, the shutter repaired in a third.
In month four the neighbour sells a scooter and clears the entire balance in one go. Not one rupee is lost, nobody has broken a promise, and the shopkeeper is still not where she planned to be. She is holding a lump of cash eight months early with nothing arranged for it, and the eight arrivals she had spent against on paper have quietly stopped existing. Her next move depends entirely on what she can find to do with the money in month four. Nobody could have answered that question for her in month one.
Scaled up by several powers of ten, that shop is the pool. The structure holds thousands of borrowers, each with a promise and each with the same right to end it early. The holder receives the sum of thousands of private decisions about scooters, job moves, inheritances and cheaper loans down the road, and not one of those decisions was in anybody's schedule.
How does somebody holding this actually work with the schedule?
The practical answer is smaller and duller than the concept, and that is usually the sign it is the right one. Somebody carrying a claim on a pool keeps two columns rather than one. The holder writes down when the money is expected as well as how much, and treats a change in the when as an event even when the how much is untouched.
The second column is the whole repair, and it shows up in four ordinary habits.
| What gets done | Why it is done that way |
|---|---|
| The expected dates are written down beside the amounts, in the same place | A schedule kept only in the head of whoever bought the thing cannot be compared with what actually arrived |
| The realised arrivals are set against the declared schedule, period by period | The difference between the two IS the prepayment showing itself, and it shows nowhere else |
| The summary number is recomputed when the shape changes, rather than quoted from the offer | A weighted average life computed once at issue describes a schedule that may already have stopped being true |
| Any figure describing repayment speed is labelled with where it came from | A declared assumption and a measured behaviour look identical in print and are worth entirely different amounts |
Notice what is not on that list. What the returned money will earn is settled on the day it is placed and not before, so no step tries to work it out in advance. No step assesses any of the three pieces. And no step predicts the speed. Prediction is the one thing a reader most wants handed over, and the one thing that would need a measurement nobody has taken.
The error that gets made, and what it costs
Filing early repayment under good news. Capable people make that reading, and every visible signal points that way: the money came back, it came back whole, and it came back sooner. On one loan held against no plan, that reading might even be right.
The cost shows up on the calendar rather than in the total. A holder who planned around a stated schedule finds the plan shortened by 0.50 years and has to place the money again at whatever rate the day offers. Nothing went wrong, so no claim lies against anybody. Every rupee arrived.
The repair is one line long. Write down when the money is expected as well as how much, and treat a change in the when as an event even when the how much is untouched.
Which sources carry the parts left blank here?
Everything above came out of arithmetic on invented amounts, so nothing above needed a rule. With a real structure in front of the reader that stops being true, and seven separate items arrive whose wording is set at a source rather than computed. Each one is maintained by somebody and revised on a timetable nobody here controls, so a remembered version of any of them would state something false rather than something merely old.
| Left blank here | Decided by, and where | Why it stays blank |
|---|---|---|
| Which receivables may go into a pool at all | Reserve Bank of India, rbi.org.in | Eligibility is redrawn as lending practice changes, so a list here would go quietly out of date |
| How long an originator keeps a receivable on its own books before moving it | Reserve Bank of India, rbi.org.in | A holding period is a bare number, and the number in force is revised on its own timetable |
| What buyers must be told about a pool before the pieces are sold, and who counts as a buyer | Securities and Exchange Board of India (SEBI), sebi.gov.in | Disclosure attaches to the offer rather than to the arithmetic, and it differs by how the pieces are sold |
| What the originator and the servicer must report about the pool afterwards, and how often | SEBI, sebi.gov.in | Reporting is a live obligation with dates attached, and a wrong frequency sends a reader to the wrong calendar |
| The valuation norm fixing the price at which a holding is carried | Reserve Bank of India, rbi.org.in | A carrying price sits inside a wider measurement framework, and one line lifted out of it misleads |
| The treatment applying to a receivable in the pool once it has stopped paying | Reserve Bank of India, rbi.org.in | What matters here is the definition rather than the label, and definitions get revised without the label changing |
| How prepayment on the underlying loans reaches the holders | SEBI, sebi.gov.in | Of the seven this one sits closest to prepayment itself, and the wording that governs it is set at the source |
Four more addresses sit behind this structure without appearing in the arithmetic. The charge over the receivables is registered with the central registry at cersai.org.in. Whether the transfer takes the receivables off the originator's own books is settled by the test the Institute of Chartered Accountants of India maintains at icai.org. The tax treatment of a pass-through certificateThe form in which a holder's claim on a pool is issued, so that collections reach the holder rather than staying with the lender who made the loans., and tax on whoever holds one, is written at incometaxindia.gov.in. Should the originator itself collapse into insolvencyThe legal process that opens when a person or a business cannot pay what it owes, and which decides who gets what out of whatever is left., where the pool's receivables stand in the queue is decided at ibbi.gov.in. Every one of them is named here and left unwritten.
What cannot be stated here about how fast a pool repays?
How quickly a set of home loans is actually repaid is a measurement, and somebody would have had to take it. Nobody took it for this material. The three repayment shapes in this guide were chosen because they make arithmetic visible on a screen, not because one of them is expected, and ranking them by likelihood would need behaviour this platform does not hold.
The absence goes further than that, and it is the harder half. The record fixes sizes and it fixes an order. A distribution of losses, a correlation between the receivables and a schedule of periods are all measurements, and no measurement stands behind these amounts, so the timing of repayment carries no distribution either. Any treatment of prepayment is under constant pressure to say how fast pools usually repay, and the pressure has to be refused until somebody has done the measuring.
So no likelihood attaches to any of the three pieces, and none of them is assessed or called safe. There is a specific temptation to guard against: somebody meeting the order for the first time turns absorbing last into being safest, and from being safest it is one short step to a holding decision. Neither move is supported by anything above. The order says who absorbs before whom. The order says nothing about how often anything is absorbed, and that frequency is a measurement nobody has taken.
Three repayment schedules have appeared in this guide. Which of them is the one this pool will actually follow?
What is behind the numbers, and what is not?
Arithmetic, and one invented structure. The four amounts of Sarvani Receivables Trust were checked against each other before a single bar was drawn. The three pieces added together return the Rs 1,200 crore of the pool exactly. The smaller two combined give Rs 240 crore, and Rs 240 crore is the whole of the support figure quoted above.
The repayment schedules are a different kind of object and the difference matters. The schedules were DECLARED so that the arithmetic has something to run on. Nobody measured them. No pool anywhere was watched to see how fast it repaid. No prepayment model stands behind them. No schedule of periods sits behind the drawings. No future rate curve stands behind them either, and that is why the box asking what returned money earns is drawn with nothing in it.
The missing rate curve is the absence to sit with. Filling the empty box would mean inventing precisely the input the answer turns on.
References
Seven addresses carry the parts of this subject that are set rather than computed. None of them supplied a figure above. Each one maintains its own wording and revises it on its own timetable.
| Who maintains it | What they decide for this subject | Where |
|---|---|---|
| Reserve Bank of India | Which receivables may be pooled, the period an originator keeps one first, how much of a structure it must retain, the capital treatment of a holding, the carrying price, support given after issue, and a clean-up call | rbi.org.in |
| SEBI | Disclosure before the pieces are sold, reporting afterwards, listing and dealing, trustee duties, an assessment of a structured note, what counts as a default for reporting, and how prepayment reaches holders | sebi.gov.in |
| Central registry of security interests | Registration of the charge over the receivables | cersai.org.in |
| Institute of Chartered Accountants of India | The test deciding whether a transfer takes the receivables off the originator's own books | icai.org |
| Insolvency authority | Where a pool's receivables stand in the queue should the originator collapse | ibbi.gov.in |
| Income tax authority | The treatment of a pass-through certificate and of whoever holds one | incometaxindia.gov.in |
| Working paper repositories | The class of document in which a named idea about repayment speed would be found, checked before a name is written rather than after | ideas.repec.org, ssrn.com, nber.org |
Sarvani Receivables Trust and Palash Cements Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.