Recovery Rate: What Is Left After a Borrower Stops Paying

A recovery rate is how much of the amount owed comes back after a borrower stops paying, written as a percentage of that amount. Fix a recovery rate and a spread, and the arithmetic gives the yearly default rate that spread is paying for; fix the default rate instead, and it gives back the spread. The recovery figure is chosen, not measured, and this guide shows what that choice does.

The panel opens on a worked case, and the figures are worth having in ordinary text too. Palash Cements Limited, an invented manufacturer, owes Rs 1,000.00/-. The pledged assets are valued to realise Rs 775.00/-, of which 80 per cent, or Rs 620.00/-, reaches this claim. Rs 87.60/- goes on the costs of getting it back, leaving Rs 532.40/-. The Rs 532.40/- arrives three years later and is divided by 1.331000 at a 10.00 per cent a year discount, so it is worth Rs 400.00/- today. Rs 400.00/- against Rs 1,000.00/- owed is a recovery rate of 40.00 per cent, a loss given default of 60.00 per cent, and the 3.6667 per cent a year implied default rate the rest of this guide works with. The figure that should never be quoted as the recovery rate is the Rs 620.00/- one, 62.00 per cent, taken before the costs and before the wait.

Underneath sits one idea. A spread is not a charge for the trouble of lending. A spread is a price put on an expected loss, and an expected loss has exactly two parts: how often the borrower stops paying, and how much fails to come back each time. The recovery rate settles the second part outright, and once it and the spread are both fixed, the yearly default rate stops being a matter of judgement and becomes a division.

What actually survives when a borrower stops paying?

A neighbour borrows Rs 40,000/- from a lender and then loses the work that was going to repay it. All of it is unlikely to come back, and so is none of it: there is a scooter, there is a deposit with a landlord, and there is a brother who settles part of it. Some fraction of Rs 40,000/- comes back, and that fraction is what a recovery rate measures.

A borrower that stops paying almost never leaves nothing behind, and the share that does come back is what a recovery rate measures. A business that cannot meet its promises still has machines, land, stock and money owed to it by its own customers. A formal process turns those things back into cash, an order decides who is met out of that cash, and a share of what was promised reaches the lender at the end of it.

Two of those three are named here and then left to the authorities that own them. The formal process and its length are covered separately, and so is the seniorityThe order in which competing claims on a failed borrower are met. Who stands where decides what actually comes back, and it is settled well away from this arithmetic. that decides who is met before whom. Both belong to the insolvencyThe condition of a borrower that cannot meet what it has promised to pay. The formal process that follows is covered separately. authority at ibbi.gov.in, and either of them written out from memory would be wrong the first time the process was revised. One number is all that is taken from them here, and it is the one the panel above asks for: the share that reaches the claim.

Why does a lender who might not be paid charge more?

A lender who may not be repaid in full will not lend at the same rate as a lender who will be. The extra rate is called a spread, and it sits on top of the rate the government pays for money borrowed over the same length of time.

The spread is not a fee for the paperwork and it is not a reward for bravery: it is the price of an expected loss, and it can be checked against that loss. A fee could be any number at all and there would be nothing to compute. An expected loss has parts, so a price can be taken apart: the parts are put back together and set against the price.

The arithmetic runs on two definitions, so both have to be said cold. A five year government SPOT rate is the single rate applying to money handed over today and returned at one date five years out, with no credit element in it. A SPOT rate is not a FORWARD rate. A forward rate applies to a lending that begins on some later date, and no forward rate is used below or given a value. The same figures on a half yearly convention would not price the same, so every rate here is quoted on annual compounding, one payment a year.

What goes into the calculation, and in what form?

Three quantities, and all three are never needed at once. Supply any two and the third follows. The arithmetic is closed rather than estimated.

The spread has to be measured against the government rate at the same maturity, or the number is measuring a difference in waiting time as well as a difference in credit. Set a five year issue against a two year government SPOT rate and part of the result is the shape of the curve rather than the borrower. On the invented curve used here the five year government SPOT rate is 6.90 per cent a year, and the five year issue is what gets set against it. Same length, same units, nothing else in the subtraction.

Basis points are hundredths of a percentage point, so 220 of them and 2.20 percentage points are one size written on two scales. A division that feeds one into a formula expecting the other is out by a factor of a hundred. Nobody catches an error that large as an arithmetic slip; they read it as a surprising finding instead.

Where does each of these three numbers actually come from?

The spread comes out of two prices, the recovery rate comes out of somebody's head, and only one of those two facts is usually written down. The spread is a subtraction: the yield on the issue, less the government rate at the matching maturity. Both sides come from what buyers and sellers are doing, so anybody with the same prices can check it. Nobody has to agree with a spread; anybody can compute it.

No instrument carries a line that reads recovery rate, so the recovery rate cannot be computed that way. No recovery study stands behind the figure used below either, and inventing one to fill the gap would be worse than leaving the gap visible. The panel above instead builds the figure out of rupees that can be pointed at, and even then the discount rate inside it stays an assumptionA value put in by whoever is running the calculation, rather than read off a document or a screen. Two people running the same arithmetic can honestly use different ones. chosen by whoever runs the calculation.

The default rate is the output here, so in the direction worked first it is not an input at all. Where it is supplied, it has to be a rate per year, matched to the year the spread is quoted for.

Three more things are set by their keepers rather than derived here. The meaning of each step on a grading ladder is set by the rating agencyA firm in the business of publishing an opinion on whether a borrower will pay. The agency and the regulator set what its labels mean, and no label appears here. that publishes it and by the Securities and Exchange Board of India (SEBI) at sebi.gov.in, and no such label appears here for any borrower. The same authorities set what a trusteeA party appointed to hold and act on the lenders rights under a borrowing, so that hundreds of separate lenders do not each have to act alone. must put on record. And what recovery figure a supervised holderA lender or fund whose balance sheet is watched by a supervisor, so several of its choices are made by rule rather than by preference. is obliged to use, if it is obliged to use one at all, is set by the Reserve Bank of India at rbi.org.in.

How does a recovery rate become a loss given default?

One subtraction, and it earns a block of its own for a reason that has nothing to do with difficulty. The subtraction is the place where two numbers get quoted as though they were two findings.

Set the recovery rate at 40 per cent of the amount owed, and 60 per cent of the amount owed does not come back when the borrower stops paying. The 60 per cent that does not come back is the loss given default. Both figures are percentages of the amount owed, not of the price paid and not of the size of the holding, and naming that base in the same breath as the number is not optional. The panel above makes the difference visible: switch its base to the price paid and the very same rupees read 51.28 per cent of the Rs 780.00/- paid rather than 40.00 per cent of the Rs 1,000.00/- owed.

The amount owed throughout is a stated Rs 1,000.00/-. At a 40 per cent recovery, Rs 400.00/- comes back and Rs 600.00/- does not. Both numbers are the two sides of one cut. Move the boundary anywhere along that Rs 1,000.00/- and both of them move together.

Because they add to a hundred by construction, quoting one has already quoted the other. A note reporting a 40 per cent recovery rate and a 60 per cent loss given default as two conclusions has reported one conclusion twice.

How do a spread, a recovery rate and a default rate fit together?

The whole engine fits in three sentences. The spread is compensation for the expected loss. The expected loss over a year is the yearly default rate multiplied by the loss given default. So the yearly default rate the spread is paying for is the spread divided by the loss given default.

The units are where this goes wrong, so both quantities have to be written on the same scale before the division runs. A spread of 2.20 percentage points divided by a loss given default of 0.60 gives 3.6667 per cent a year. Feed 220 in as basis points against the same 0.60 and the answer reads 366.67. Nobody would print that, but it is exactly the sort of figure that survives a spreadsheet. All three quantities carry a period as well: they are all per year, and on the same year.

Notice what has happened to the word implied. The output is not a count of anything. The output is the default rate at which this spread would exactly cover the losses, and that rate is a fact about the price and the assumption together.

The spread comes from two rates, both read at five years, and the distance between them is the only thing the calculation uses.

How does the same relationship run the other way?

Running it backwards is not a second lesson. The backward run is the check, and the check is the difference between having used a formula and having understood one.

Take the 3.6667 per cent a year back and multiply it by the same 0.60 loss given default. The result is 2.2000 percentage points, the 220 basis points the argument started from. Nothing was proved by that: the round trip closes by construction. A division that used the wrong scale will not come home, so the return journey catches a mixed unit. Landing on 220.00 basis points means the units were consistent. Landing anywhere else means something on one side of the division was written on the wrong scale. The fault is arithmetic rather than a discovery about the borrower.

One honest wrinkle is worth printing rather than hiding. The PRINTED 3.67 multiplied back by 0.60 gives 2.2020 percentage points, or 220.20 basis points, so the trip misses by 0.20 of a basis point. Nothing is wrong with the borrower or the method: 3.67 is a display of 3.666667, and a display is not an input.

Now hold the implied default rate at 3.6667 per cent a year instead and ask what spread each recovery assumption would justify. At a 50 per cent recovery the loss is 0.50, and the unrounded 3.666667 times 0.50 gives a wanted spread of 183.33 basis points. At 40 per cent it is 220.00, and at 30 per cent it is 256.67.

Run forwards, equal steps in the assumption produce unequal steps in the answer; run backwards, the very same steps produce equal ones. That is not a curiosity but the shape of division against multiplication.

What does changing the recovery assumption do to the answer?

Freeze the spread at 220 basis points. Touch nothing any buyer or seller did. Change only the figure somebody chose.

The last row is the one to sit with. The issue pays 9.10 per cent on the Rs 1,000.00/- owed, or Rs 91.00/-, against the 6.90 per cent that is Rs 69.00/-, so the extra is Rs 22.00/- a year. The Rs 22.00/- never moves. Divide it by the rupees lost per default and the three rates come straight back out: Rs 22.00/- over Rs 700.00/- is 3.1429 per cent, over Rs 600.00/- is 3.6667 per cent, and over Rs 500.00/- is 4.4000 per cent. The rupee route carries no rounding anywhere, so it reproduces all three rates exactly and shows that the assumption alone did the moving.

The swing is 1.2571 percentage points a year, taken as 4.4000 less 3.142857. Subtracting the two printed figures would have given 1.26 instead. Nothing about any borrower changed to produce it. Nobody traded. Somebody picked a different number.

The two lifts in that drawing are not the same size, and the reason is the base. Both steps take ten points of recovery away from what is lost, but the second takes them off a smaller base: 0.10 against 0.60 is a bigger proportional bite than 0.10 against 0.70. The ratio of the two steps is exactly 1.4000, or 0.70 divided by 0.50, and it would be that ratio whatever the spread happened to be. The spread cancels.

The implied default rate is therefore a statement about the spread and the assumption together, and it is never a statement about the spread alone. A quotation of 3.67 per cent a year that does not say 40 per cent in the same sentence is half a number.

What does the whole thing look like worked end to end?

Palash Cements Limited carries no grade, and no grade can be made up to fill the space. Here is the full run, four steps and a check, with the assumption named as an assumption where it enters.

Four numbers went in: 9.10, 6.90, the Rs 1,000.00/- owed and the 40 per cent recovery. Only the first two were observed by anybody. The empty slots are as much a part of the finding as the filled ones, so they are worth drawing.

What are the three limits on this number?

This arithmetic returns a figure that looks far more solid than it is, so three limits apply and none of them is droppable. Take them in order of how easily they slip past a reader.

One: the recovery rate was chosen

No study fixes the recovery at 40 per cent rather than 30 or 50. The panel at the top builds the figure instead of picking it. The build still rests on a valuation, a share, a cost estimate and a discount rate that were all supplied rather than observed. Move any of them and the answer moves: across 30 to 50 per cent of recovery the swing is more than a percentage point a year.

Two: the whole spread has been treated as payment for credit

Every basis point of the 220 went into the numerator as though credit were the only thing being paid for, and in a real market it is not. Part of what a lender is compensated for is liquidityHow easily something can be turned into cash quickly without having to accept a worse price for the haste., meaning how hard the holding may be to pass on at short notice, and that part has nothing to do with whether the borrower pays.

Suppose, as a declared illustration with nothing in this record behind it, that 40 of the 220 basis points paid for that difficulty. The credit part is then 180 basis points. The implied default rate is 1.80 divided by 0.60, or 3.0000 per cent a year, and the original figure was 0.6667 percentage points a year too high. Treating the whole spread as credit puts more compensation into the numerator than credit accounts for, so the implied default rate comes out above what the credit part alone would justify.

The 40 basis points taken out is 18.1818 per cent of the spread, and the drop from 3.6667 to 3.0000 is 18.1818 per cent of the answer. Identical, and forced: whatever share of the spread is misattributed, exactly that share of the answer is misattributed with it.

Three: an implied default rate is what the price says

The number wears the costume of a probability, so this third limit is the one a reader most needs and the hardest to hold. The rate is a percentage. The rate is per year. The rate sits between nought and a hundred.

The rate is not a forecast, it is not a measured frequency and it is not the chance that this borrower stops paying: it is the default rate at which this spread would exactly pay for the losses, given an assumption somebody made. Nothing in the calculation looked at Palash Cements. The calculation looked at two rates and one chosen fraction.

How does somebody actually use this at a desk?

Three uses, and none of them is forecasting.

A lender pricing a new facility runs it backwards. The lender starts from what it believes it would lose in a bad outcome, puts a default rate against that from its own experience of similar lending, and multiplies the two to get the compensation it needs. The multiplication is the 3.6667 times 0.60 direction, and the answer is a spread the lender can quote. The recovery figure is not idle there: it is the difference between wanting 183.33 basis points and wanting 256.67 for the same view of how often borrowers stop paying.

An analyst comparing two spreads runs it forwards, as a translator rather than a measurement. Two issues at different spreads become two implied default rates on one recovery assumption, and the comparison is then between like and like. The assumption has to be held identical across both, and stated, or the comparison has smuggled in a second variable.

A capital treatmentHow much of its own money a supervised lender has to keep against a risk it has taken on. The sizing is written by the supervisor rather than chosen by the lender. is where this stops being anybody's choice. On a supervised balance sheet several of these inputs are not the holder's to select, and how much must be held against a credit exposure is set by the Reserve Bank of India at rbi.org.in. The requirement is revised from time to time and is read at that address on the day it matters.

The household version of all three is the one to keep: a shopkeeper who lends stock on credit to two customers charges the one with a scooter to repossess less than the one with nothing to repossess, at the same view of who is likely to disappear. The recovery assumption is what turns a view about people into a price, and if it is never said out loud, the price cannot be argued with.

Why does the panel take documents rather than a dial on the assumption?

A dial over the recovery assumption would be a dial over the one input nobody measured, and a dial invites a hunt for the right setting. There is no right setting. Every field asks instead for something that can be looked up, and the recovery rate falls out of those fields rather than being chosen. The one slider it does carry is the wait, which is a pair of dates on a record rather than a preference.

Asking for documents also makes the failure producible rather than merely described. At the opening setting two figures sit 22.00 points apart. Rs 620.00/- reaches the claim, or 62.00 per cent of what is owed, and after Rs 87.60/- of costs and three years of waiting the lender is holding 40.00 per cent. Push the costs up or drag the wait out and the figure reaching the claim does not move while the recovery underneath it falls further. Take the recovery the other way, all the way to a hundred. Nothing is lost, the spread has nothing to be divided by, and the panel stops printing an implied default rate. A recovery rate quoted before the costs and before the wait is a bigger number about a different thing, and the panel strikes that sentence through.

Palash Cements Limited is invented.
Educational material. Not advice on any investment, tax, budget or market position.