Extension Risk: When Repayment Slows and Money Stays Out

Extension risk is a pool’s principal turning up behind the dates its schedule assumed. No rupee goes missing. Whichever piece would meet a shortfall first is never called upon at all. Only the calendar shifts, so the weighted average life stretches, and the holder’s money is still tied up on the very day a rise in the SPOT rate would have paid best for having it free.

A repayment schedule is a plan about how other people will behave. Early repayment is that plan being beaten. Extension is that plan being missed. Early repayment is the easier half of the pair to see. The money actually arrives. Extension leaves nothing on the desk at all. The protection built into Sarvani Receivables Trust, an invented securitisation, is an order deciding who absorbs a shortfall, and a stretched tail never disturbs that order. The calendar is disturbed instead, and a calendar turns out to be quite enough.

If money coming back early costs something, does money coming back late pay something?

A pool where the borrowers repaid ahead of their dates has already been met, and the earliness cost the holder something real. So the mind does the tidy thing and draws the opposite picture. Principal arrives behind its dates instead of ahead of them, and the stretched shape gets booked as the good half. The two shapes really are opposites on a calendar, and they are not opposites in effect. Both lean the same way against the holder.

Look at what the two have in common before looking at what separates them. Neither is a loss. Neither one sends a single rupee into the order that decides who absorbs a shortfall. In both cases the pool hands back every rupee it was ever going to hand back. The only thing either event does is move dates, and in both directions the dates move to a place the holder did not choose and cannot undo.

Here are the three calendars this sequence now carries, drawn against one another. The middle one is the schedule declared at the outset. The upper one, three instalments of Rs 400 crore finishing in year three, is the front loaded shape settled under early repayment. The lower one is the stretched tail this guide is about. Every panel returns Rs 1,200 crore. Only the dates move, and the marker under each rule moves with them.

The reader who has just learned that 2.00 years cost something will look at 3.50 years and expect a refund. There is no refund. Both ends of that axis put the holder’s money in the wrong place at the wrong moment, and the rest of this guide is a slow explanation of why the wrong place is a different wrong place at each end.

Is a borrower who pays late the same as a borrower who has stopped?

Everything else here rests on this one separation, so it comes before the arithmetic rather than after it. Picture two collection months in the servicer’s ledger. In the first, an instalment that should have come in March comes in July. In the second, an instalment that should have come in March has not come, and nor has the one after it. On a bank statement for the month of March those two look identical, and they belong to two mechanisms that have almost nothing to do with each other.

A receivable paying behind its dates is a receivable that is still paying. The receivable has not shrunk. Nobody has written anything off. A date has moved, and a moving date is the whole of extension risk. A receivable that has ceased paying is different in kind: what is owed and not coming is a shortfall, and a shortfall has to land somewhere. In Sarvani Receivables Trust, invented, it meets the equity piece first, the mezzanine piece after that, and the senior piece last of all.

How long a receivable may run behind before it stops being treated as merely slow, and what has to be done about one once it has crossed that line, is set by the Reserve Bank of India at rbi.org.in. Those directions get revised.

From here on, every receivable in this pool is the slow kind. Nothing has stopped. Nothing has been written down. Hold that in place. The whole argument that follows would collapse into an ordinary credit argument the moment a rupee actually went missing, and an ordinary credit argument is settled somewhere else.

Why would a pool of receivables repay more slowly than it was expected to?

Nobody replaces a loan with a fresh one unless the fresh one is cheaper. Most of the answer sits in that one sentence. Let borrowing get dearer for ordinary households, meaning a rise in the SPOT rate they face, and the main reason anybody had to clear a balance early evaporates, leaving the pool to run its stated course. The borrower who was going to refinanceReplacing a loan already running with a fresh one, usually because the fresh one is cheaper. How a lender prices either of them is settled in a different subject area. does not refinance. The house that would have been sold and the loan cleared out of the proceeds is not sold. And somebody who would have thrown a spare bonus at the outstanding balance keeps the bonus instead. Holding cash has started to look sensible.

Underneath all three of those is one shared cause, and it is the same cause that stops the holder placing money elsewhere: borrowing has become dearer for everybody at once. The overlap is not a coincidence. The shared cause is why extension and the holder’s own disappointment tend to arrive together rather than separately, and why the pair is a lean rather than a run of bad luck.

There is a fourth reason and it is more ordinary than any of those. A household can be slow without being in trouble at all. A salary lands on the ninth rather than the first, a wedding empties a month, a hospital bill takes precedence, and the instalment goes in three weeks behind its date and then keeps going in three weeks behind its date. The household running three weeks late is the slow receivable separated out a moment ago, and a slow receivable never becomes a shortfall.

The third column is empty in every row and it stays empty. Putting those four in order of importance would take a tally, drawn from a body of pools nobody here has examined, of how frequently each turns up. No tally of that kind exists in this material, so the four reasons stand set out and unranked.

How far does a stretched tail actually move the average wait?

The calendar this sequence already carries is declared rather than reported, and it is worth saying so plainly. The pool hands back Rs 300 crore a year for four years, one instalment at each year end. Four of those add to the whole Rs 1,200 crore. Year four carries the last of it. The weighted average lifeTake every principal amount a pool will hand back, note how many years away each one is, and average those waits with the larger amounts counting for more. of that arrangement works out at 2.50 years.

Now declare the stretched version. The first three instalments turn up exactly as before. The fourth instalment changes. Instead of closing the pool in year four, that Rs 300 crore stays out until the end of year eight. Nothing has been lost, nothing has been forgiven and the pool still returns Rs 1,200 crore in total. One date moved, and it moved four years.

Rs 4,200 crore-years of waiting, spread over Rs 1,200 crore of principal, gives an average wait of 3.50 years. The schedule declared at the outset carried Rs 3,000 crore-years over the same Rs 1,200 crore, and that is where the 2.50 years came from. The plan has lengthened by 1.00 year and the holder agreed to none of it.

Look at the size of that movement. The size of it is the part readers get wrong. The date moved four years. The average moved one. Nothing accidental is going on there, and no rounding either. The instalment that shifted is one quarter of the pool by value, so it carries one quarter of the weight in the average, and one quarter of a four year delay is 1.00 year. Shift a quarter of the money by four years and a quarter of four years is what shows up in the answer.

Can two calendars that look nothing alike give the same answer?

Two calendars can share an answer, and seeing that once shows what an average wait measures and what it leaves out. Consider the stretched tail above: three instalments on time and a quarter of the pool sitting out in year eight. Against it stands a completely different arrangement, six instalments of Rs 200 crore arriving one a year and finishing in year six, already worked out under early repayment. Both of them average 3.50 years, and no reader looking at the two pictures would guess it.

The reason is arithmetic rather than chance. Both calendars pile up Rs 4,200 crore-years of waiting and both spread it over Rs 1,200 crore of principal, so the ratio has to come out the same. The match is forced, not lucky. The arithmetic teaches something wider. An average wait is a summary, and the shape that produced it does not survive the summarising. One of those pictures has a quarter of the pool still outstanding four years after the other has finished paying, and the single number cannot see the difference.

The blindness to shape is a limit worth carrying, not a defect in the measure. Drawing the bars beside the average is the remedy. A lengthening average on its own never says which part of the calendar stretched.

Why is waiting a cost when every single rupee still arrives?

Under early repayment, principal arrived back exactly when there was least to be earned by putting it anywhere. Extension is the identical lean seen from the far side. The principal stays out on the day placing it again would have paid most, and the reason the two line up is the one already given. The same climb in the SPOT rate those households face is precisely what takes away their reason to repay early.

Set the two side by side and the sentence that comes out is uncomfortable and exact. The holder is short of money at the moment money is worth most, and holding it at the moment it is worth least. The pairing is not a run of bad luck across two events. One mechanism produces both. Filing early repayment as a cost and late repayment as a gain puts the sign wrong on half of the pair.

Now the honest limit. Costing that lean in rupees would take a future path for the SPOT rate, and no such path has been established anywhere in this sequence. So the direction of the lean can be stated and the size of it in rupees cannot. A rupee figure in that row would be a forecast wearing the clothes of arithmetic, and once printed the two would be impossible to tell apart.

There is a second thing worth naming while the two sit together. Neither event is a credit event. Nobody has to be assessed, nothing has to be written down, and the loss given defaultWhen a borrower stops paying altogether, the share of what was owed that never comes back. Estimating it is covered separately, under credit. of anything in the pool is untouched by both. Leaving the loss order alone is what makes this pair so easy to miss in practice. A loss leaves a mark somewhere. A calendar moving leaves none.

Why is there no MODIFIED duration for any piece?

Elsewhere, this subject is described as a holding’s duration lengthening. The phrase does not fit this arrangement, and saying why teaches more than borrowing it would have done. A MODIFIED durationA measure of how far a price shifts when the rate used to value it shifts. It only exists once the thing being measured has a price attached to it. reports a price moving when a rate moves. So the thing being measured has to carry a price before the measurement means anything, and forming a price takes a rate. Not one of the three pieces has a rate written against it anywhere here, so no MODIFIED duration exists for any of them and none is quoted.

The same goes for its companion. A MACAULAY durationThe other duration in this material: an average wait for a bond’s payments in years, with each date weighted by what it is worth today rather than by its face amount. weights each date by what that date is worth today. Weighting a date that way means running every amount back through a discount rateThe rate used to charge for waiting when a future amount is pulled back to what it is worth in the present.. No such rate exists in this arrangement either, so the measurement is out of reach for the same reason and by the same route.

The weighted average life can be moved honestly and to the last decimal. The measure averages time using money as the weight, and needs no discounting whatsoever. Amounts and dates are the entire input list. So 3.50 years stands above with no hedging attached to it, while the box beside it stays blank.

One habit is worth taking away. Whenever either measurement moves, which one moved has to be said. The two are different objects that happen to be quoted in years. Letting the two run together reads a rupee sensitivity into a number that has no rupees anywhere in its construction. An average wait says when money arrives. An average wait does not say what anything is worth.

Which piece ends up doing the waiting?

The sequence has already declared a queue for paying out what a period collects, and exactly one line from it is borrowed here under a label. In that queue, principal returned to the senior piece stands at the fourth step. So principal that arrives at the pool later reaches the fourth step later. Read that for precisely what it is: a reading of one declared queue in one declared period, and not a general rule about how structures behave.

No schedule of collection periods has been declared, so how a stretched tail gets shared out across the three holdings over time cannot be worked out honestly. The stopping point that is defensible is the plain one. The pool’s calendar moved, and everything downstream of the pool’s calendar waits.

Meanwhile the sizes are exactly where they were. Sarvani Receivables Trust, invented, still funds a Rs 1,200 crore pool of receivables with three pieces. The senior piece is still Rs 960 crore. Below it sits the mezzanine piece at Rs 180 crore. Below that again sits the equity piece at Rs 60 crore. Add the lower two together and the senior piece still has Rs 240 crore underneath it, and set against the pool that reads 20.0 per cent. Extension is not a loss and never enters the order at all.

What does this look like between two people who know each other?

Somebody lends a cousin money in January against a promise to have it back before a school fee falls due in June. June arrives. The cousin has not paid. The fee does not care, so the lender borrows for a few months at whatever that cost that week and pays the school. The following February the cousin turns up and pays every rupee, with nothing missing and nothing forgiven, and thanks them warmly.

Nobody defaulted here. Nobody was cheated. Asked afterwards whether anything had gone wrong, both would say no, and both would be right about the money. The lender is still out of pocket, and the amount they are out of pocket is written nowhere in the arrangement. An amount written nowhere is easy for both of them to miss.

The cousin and the school fee are the whole mechanism at household scale. The rupees are complete. The dates are not. The cost lives in the gap between the two, and no document created by either party records it. Scale it up to Rs 1,200 crore of receivables and the only thing that changes is how many people are involved.

What does somebody holding one of these pieces actually do about it?

The pool is not theirs to change, so the realistic answer is that they work on the calendar instead. Somebody running a treasury has dated obligations of their own: a payout falling due, a settlement to meet, a commitment already made against money expected back in year four. The first thing a stretched tail does is put a hole in that, and the hole is a dating problem long before it is anything else.

So the work looks like this. Line the pool’s expected dates up against the dates the holder is committed to. Ask what happens to each of those commitments if the pool’s average wait moves by half a year, and then by a full year, without any rupee going missing anywhere. Note which commitments survive that and which ones would have to be met by borrowing instead. The exposure worth measuring is not the pool, it is the gap between the pool’s dates and the holder’s own.

A lender looking at the same structure from the other end asks a different question, and both questions are worth seeing. The tail stretches in the collections long before it shows up in anybody’s average, so the lender wants the servicer’s month by month report on how the underlying households are actually paying. Whether the servicer has to report any of that, to whom, and how often, is set by the Securities and Exchange Board of India (SEBI) at sebi.gov.in and by the Reserve Bank of India at rbi.org.in.

Both readings measure what a stretched tail would cost the person asking. The worth of a holding is a different quantity altogether, settled separately, and neither reading produces it.

Whose job would it be to write any of this down?

Five rows follow and each one is deliberately hollow. The wording that belongs inside is kept elsewhere, it gets revised on somebody else's timetable, and a copy pasted in today would only ever be a copy of one version of it. Read the obligation, then read who holds the pen.

None of the five is written out above and none is written out below either. Neither absence is an oversight, and neither is modesty. A requirement pasted into teaching material goes stale without announcing it. Whoever trusted the paste is then holding an old rule and believing it current. An address never goes stale that way.

What can nobody here say about how long a tail gets?

About here a reader starts expecting a line grading how probable a stretched tail is. No such grade appears, and why it is missing teaches more than the grade itself would have done. Grading one takes a spread of repayment paths with weights set against them. The record carries instead a handful of calendars declared outright and no weights of any description.

The pieces go ungraded on exactly the same ground. Four amounts are fixed in this record. One order is fixed. A spread of possible losses is not, and neither is any correlationA figure describing how far two things tend to move together. Nothing in this material supplies one for the households behind these receivables. among the households behind the receivables. A schedule of collection periods is missing too. How likely any of that is goes unstated, and so does any grade for a holding. Calling anything safe would take a frequency of loss, and a frequency of loss is exactly what is missing.

The slip is easy to make at exactly this point, so being blunt about where the gap bites is worth the space. Learning that the senior piece is reached last reads like a statement about safety, and from safety it is one short step to a decision about holding. Neither step is supported by anything above. The order gives a sequence, in which one holding is reached before another. The order withholds a frequency, and no figure in the record could supply one.

The control above stops at the end of year eight because a range has to stop somewhere. The stopping point is a decision, not a finding, and reading it as an outer bound on how far a tail can stretch would be reading a setting of the illustration as evidence about the world.

Where did the two calendars above come from?

Two repayment calendars appear above and both were written here. Neither one was measured off a pool, lifted from a servicer’s report or produced by a repayment model. The control adds three more calendars and they have the same standing: every position it reaches is a shape a reader has chosen by dragging, and dragging is not evidence. Which calendar a pool actually follows is settled by the borrowers inside it, not by a drawing.

The worth of the pool on any of those calendars goes unwritten as well. The sizes themselves were chosen for arithmetic rather than measured anywhere. Rs 1,200 crore sits in the pool because a round pool divides cleanly into four instalments, Rs 960 crore funds the top of it, Rs 180 crore sits below that and Rs 60 crore below that again. There is no rate against the pool, no rate against the senior piece, no rate against the mezzanine piece and no rate against the equity piece, so no price can be formed for any of them, and a MODIFIED duration cannot exist without a price to be sensitive about. A spread of possible outcomes is absent from this material as well. So is any statement that the households behind the receivables behave alike. So is a schedule of collection periods. Each of those absences is stated at the point a reader would start expecting the number.