The Tranche: How One Pool Becomes Pieces of Different Risk

A tranche is a place in a queue. Each piece funding the same pool differs from its neighbours in one respect only: how soon a shortfall reaches it. Cutting a pool into pieces takes nothing off the total that can go wrong. The cutting settles the sequence instead: the bottom piece has to be used up completely before the tranche above it gives up a rupee.

One pool throws off one stream of money, and when things go wrong it throws off one total of losses. Sell claims on that pool as a single instrument and every buyer receives the identical thing. Sell them as an ordered set of claims and the buyers receive different things out of the same unchanged pool. Nothing was added to the pool to make one claim safer than another; what was added was a queue. The queue is the whole of the device, and everything below is the arithmetic that comes with it.

What makes the senior piece different from the equity piece?

Start with a structure. Sarvani Receivables Trust, an invented issuer, holds a pool of receivables worth Rs 1,200 crore. Three pieces of funding paid for that pool. The table below is the whole of the structure, and there is nothing else in it.

Now ask the question the structure exists to answer: what separates the largest piece from the smallest? The obvious reply is the amount, and the obvious reply is wrong. The separation is that a shortfall arrives at the equity piece before it arrives anywhere else, and reaches the senior piece only once both of the pieces below it have nothing left to give. Without that sequence there are not three instruments carrying three risks. There is one instrument sold in three denominationsThe size a single unit of an instrument is issued in. Denomination is a matter of packaging, and it says nothing about where the unit stands in any order., and one instrument in three denominations is a completely different product.

The distinction is why the word tranche is worth the trouble of learning. The word does not mean a slice in the sense of a slice of cake, where every slice is the same substance in a smaller amount. A tranche means a rung. A reader who hears slice will reach for the shares column of the table above, and the shares column is the one column that will not tell them what they want to know.

Does slicing take any risk out of the pool?

A reader who gets the answer the wrong way round will misread everything that follows. The question is therefore worth settling before anything else. Suppose the pool loses Rs 144 crore. The loss is 12.0 per cent of the pool. Then Rs 144 crore has been lost, whether the pool was funded by one instrument, by three, or by thirty. The receivables have no idea how the money that bought them was raised, and no arrangement of the funding reaches back into them.

The pieces decide where those Rs 144 crore land. The equity piece is where a shortfall arrives, and Rs 60 crore is all it has, so the whole of it goes. Rs 84 crore of the loss is still unplaced, and the mezzanine piece is next in line, so it absorbs that. The loss ran out before it got to the senior piece, so the senior piece absorbs nothing at all. The three absorptions add back to Rs 144 crore. Adding back exactly is the arithmetic proof that the slicing moved the loss rather than shrinking it.

Where does each piece start absorbing, and where does it stop?

Everything so far has been about one particular loss. Lay the whole range out instead, from a pool that loses nothing to a pool that loses everything, and each piece turns into a band on a single line. The equity piece begins absorbing the moment the first rupee is lost and has nothing left once 5.0 per cent of the pool has gone. The mezzanine piece does nothing until that point and is finished at 20.0 per cent. The senior piece takes its first rupee at 20.0 per cent and absorbs everything from there to 100.0.

The three bands sit end to end. The bands do not overlap, they leave no gaps, and there is a reason the arithmetic works out that tidily: the width of each band is exactly that piece's share of the pool, so the shares column is not useless, it simply measures something other than what most readers reach for it to measure. Widths of 5.0, 15.0 and 80.0 percentage pointsThe plain arithmetic difference between two percentages. Twenty per cent less five per cent is fifteen percentage points, which is a different statement from a fifteen per cent change in something. against shares of 5.0, 15.0 and 80.0 per cent. Same three figures, doing a job that has nothing to do with proportional ownership.

Amounts are what a document contains, so the two boundaries are worth writing down as amounts as well as percentages. Rs 60 crore of pool loss is where the mezzanine piece starts taking damage. Rs 240 crore of pool loss is where the senior piece starts. Rs 60 crore and Rs 240 crore are the entire content of the phrase risk profile, at least as far as four amounts and a sequence can support it.

What does one percentage point of pool loss cost each piece?

The order can be turned into a rate of exchange. The pool never changes, so one percentage point of it is Rs 12 crore and stays Rs 12 crore. The amount those Rs 12 crore are measured against is what changes.

Set them against the equity piece of Rs 60 crore, and they are 20.00 per cent of it. Set the same Rs 12 crore against the mezzanine piece and they are 6.6667 per cent. Against the senior piece they are 1.25 per cent. Read as multiples of the one per cent they represent at pool level: 20.00 times, 6.6667 times and 1.25 times, each holding only while that piece is the one doing the absorbing. The smaller the tranche, the harder each point of pool loss lands on it while its own band is being crossed.

None of that is extra risk created out of nothing; it is one unchanged rupee amount of loss divided by a smaller number. Which brings up the discipline that matters most here: the base is named every single time. On a loss of Rs 60 crore the pool has given up 5.0 per cent of itself, while the equity piece has given up 100.0 per cent of itself. Both statements are true, they describe one event, and they differ by a factor of twenty. A note that says the loss was five per cent, without saying five per cent of what, has handed the reader two possible worlds and no way to tell which one they are in.

What happens when the bottom piece is made bigger?

Here is where a tranche stops being an abstraction. Hold the pool at Rs 1,200 crore and hold the senior piece at Rs 960 crore, then change nothing except the size of the bottom piece. The mezzanine piece is whatever is left over, so it moves in the opposite direction, rupee for rupee.

The four positions work out as follows. An equity piece of Rs 30 crore leaves a mezzanine piece of Rs 210 crore. Rs 60 crore leaves Rs 180 crore, the structure used throughout. Rs 90 crore leaves Rs 150 crore, and Rs 120 crore leaves Rs 120 crore, at which point the two lower pieces are the same size and there is nothing further to see.

Now read what sits beneath the senior piece at each of those four positions. The same figure four times over, Rs 240 crore at every one of them. Resizing the bottom piece moves the boundary underneath the mezzanine piece and leaves the boundary underneath the senior piece exactly where it was. Nothing demonstrates more clearly that a tranche is a boundary and not a size. A fifth of the pool has to go before the senior piece is touched, and it stays a fifth however the bottom two are arranged, because the pool did not grow and the senior piece did not shrink.

Why can one borrower's price imply a rate when a stack's cannot?

A single borrower's price was taken apart earlier in this subject area, and the contrast with a stack shows exactly what a tranche is missing. Palash Cements Limited, invented, issues five year debt at 9.10 per cent a year. The government rate recorded at the five year node is 6.90 per cent a year, annual compounding. Set one rate against the other and the gap, its spreadHow much more a borrower is charged each year than the government pays over an identical period. Settled earlier in this subject area, and not re-opened here., comes to 2.20 percentage points. Stated in basis pointsOne part in ten thousand of a rate, so a hundred of them make up a percentage point. The unit exists so that a move in a rate is never confused with a percentage change in the rate itself., that is 220 of them.

Put an assumed recovery of 40 per cent on the table. The share a lender then fails to collect, its loss given defaultWhat a lender fails to get back when a borrower defaults, written as a share of the amount owed. One hundred per cent less whatever is assumed recovered., is the remaining 60 per cent. Dividing 2.20 by 0.60 gives 3.6667 per cent a year. Printed to two places that is 3.67 per cent, and the figure is what the price impliesWorked backwards out of a price while an assumption is held fixed. What comes out reports the price. It says nothing about what will happen, and it has not been counted off any history.. Multiply 3.6667 by 0.60 and the 2.20 points come straight back. One price. One assumption. One answer.

Now ask the same of a piece of Sarvani Receivables Trust and count what has gone missing. No price is quoted on any of its three pieces, so there is nothing to work backwards from before the question even begins. And a price would not be enough on its own. A single borrower's fate turns on one event, whether that borrower fails, and one recovery assumption covers it. A piece of a structure turns on how much of a whole pool is lost, so working anything backwards out of its price would need every possible size of pool loss weighed against its own chance of arriving, rather than a single assumption. One borrower needs an assumption. A stack needs a loss distributionA schedule pairing each possible size of loss with the chance of that size arriving. Without such a schedule no tranche can be given odds at all., and it would need a view on correlationHow far two things tend to go wrong together rather than separately. Whether the receivables in a pool fail independently or in company changes the shape of the answer completely. among the receivables besides.

No assessment is attached to Palash Cements Limited, and none to any piece of this structure. A scale on which a note may be assessed, and the meaning attached to each step of it, sit with the agencies that publish those scales, and with the Securities and Exchange Board of India (SEBI), whose address is sebi.gov.in. Both of those get rewritten.

What does this look like away from a balance sheet?

Three people buy a delivery van between them. The one who put in the most is written into the agreement as the last to be asked for a repair bill. The one who put in the least is asked first, and keeps paying until the money they put in has gone. A cracked windscreen comes out of the third person's stake alone and costs the other two nothing at all. A van written off costs all three of them everything they put in.

Nothing in that agreement touched the van; it decided the sequence in which the three of them would find out about the van. A mechanic inspecting it would find exactly the same vehicle before the agreement was signed and after. The same is true of the receivables in a pool. Borrowers repay or they do not, and no clause about who absorbs first reaches back into a single one of them.

The van is also useful for the move readers most want to make next: calling the first person's position safe. Safe against what? A windscreen, certainly. A written-off van, not at all. Whether the position is safe depends entirely on how likely each size of repair bill is, and three people splitting the cost of a van have not measured that.

Who reads a boundary, and what do they read it for?

An originator that has kept the bottom piece watches one figure, and it is not a share of anything. The figure is how far the pool's losses have run into the 5.0 points sitting underneath everything else. Rs 12 crore of pool loss has used a fifth of that room. Rs 60 crore has used all of it, and the next rupee lost is somebody else's problem for the first time since the structure was written.

An analyst opening a structure for the first time does the job the axis above does: put pool loss on one line, mark where the boundaries fall, and read off which piece a given loss lands in. Both boundaries come out of documents rather than out of judgement. Two analysts working from the same documents therefore produce the same two numbers. Reproducibility of that kind is rarer than it sounds, and it is most of what makes the boundaries worth writing down.

Somebody already holding the senior piece is checking a different thing between reports: whether the two pieces beneath it are still standing at their full amounts. A boundary is worth exactly what is behind it, and what is behind it can be spent. Rs 240 crore of protection that has already absorbed Rs 100 crore of losses is Rs 140 crore of protection, and the senior piece has moved without anybody amending a single document.

A treasury team reconciling to a trustee's report treats Rs 240 crore as a documented amount to be agreed against a statement. Agreement against a statement is the whole use of it, and it is a real use. None of those four readings settles whether a piece should be held by anybody, and no amount of arithmetic here would turn one of them into that.

What can nobody write about a tranche from this material?

By this point in an account of tranches a reader is waiting for one more sentence, and it is always the same sentence: how secure the top piece really is. The sentence cannot be written from four amounts and a sequence, and saying so plainly is more useful than any amount of hedging.

Look at what the material actually contains. Four amounts and a sequence. Four amounts and a sequence settle which piece is reached first and at what level of pool loss each piece begins and ends. Settling how often anything is reached at all is a different question, and answering it means knowing the chance attached to each size of pool loss. The structure's documents supply no such chances, no view on whether the receivables fail together or separately, and no schedule of periods over which any of it happens.

Three sentences are therefore unavailable, and each is worth naming out loud: no tranche may be given a chance of being touched, no tranche may be assessed on any scale, and no tranche may be called safe. The restriction is a real one. The material that is available is complete in itself and worth having: the two boundaries, the three widths, and the order. A reader who leaves with those three things and without the fourth has the part that can be checked against a document, and has left behind the part that nobody measured.