Stress Testing: Severe But Plausible, and Working Backwards

A stress test runs a deliberately severe set of conditions through an institution and reports the result as a distance from a threshold it must not cross. A reverse stress test turns the question round: it fixes the failure first and solves for whatever would have to happen to produce it. One hunts for an outcome, the other hunts for a cause.

The two directions find different things, and that is the whole argument for running both. A forward test can only ever explore the scenarios somebody thought of, so it inherits that person's imagination and reports comfort whenever the imagination was narrow. A backward test does not begin from a scenario at all, so it cannot inherit anybody's imagination. The test begins from the one result nobody is allowed to reach and works outward until it collides with something real. On the case below it collides with an exposure that was already sitting on the balance sheet and had already been written up and sent to a committee.

The whole of the arithmetic below is worked on Vindhya Commercial Bank Limited, an invented mid-sized Indian commercial bank with a balance sheet of Rs 96,000 crore. Every scenario, every ratio, every threshold and every assumption below is the bank's own. None of them is a requirement, a minimum or a market normal.

What is a stress test, and what question does it answer?

The shape is identical at household scale, and the arithmetic there is small enough to hold in the head. A household runs on one salary of Rs 80,000/- a month, spends Rs 62,000/-, and keeps Rs 3,60,000/- in the bank. Somebody asks what happens if that salary stops. The answer is not a feeling, it is worked: at Rs 62,000/- a month, savings of Rs 3,60,000/- last 5.8 months. The 5.8 months then gets set against the month the household must not reach, the month the rent cannot be paid. The answer is not that the household would cope. The answer is a distance: a little under six months of room, on the stated assumption that spending does not fall. In a real household spending would fall.

A stress testA deliberately severe set of conditions run through an institution to see what it does to a measure that matters. at a bank is that same shape at scale, with the measure changed. The measure is a capital ratio, the threshold is a floor, and the reported result is the gap between them stated in two units. The analyst chooses a set of conditions, pushes them through the same balance sheet without letting anything else move, reads the ratio that comes out at the far end, and subtracts the floor. The sentence that arrives on a committee paper is not the word passed. The reported result is a distance.

The three inputs matter in that order. Somebody chooses the conditions. A person is therefore responsible for them and can be asked why. The balance sheet is held still. Holding it still is a simplification everybody knows about and nobody can avoid: a bank allowed to react to its own stress will always survive it on paper. And the threshold has to exist before the test runs. A stress test with no threshold behind it produces a number with nothing to be measured against, and a number with nothing to be measured against gets described rather than acted on.

What does severe but plausible mean, and who decides where plausible ends?

Severe but plausibleA supervisory phrase for a scenario chosen to be hard without being fanciful, and the judgement sits entirely in the second word. is a supervisory phrase, and it is worth slowing down on because it contains two words doing two completely different jobs. Severe is a dial. Anybody can turn it. The baseline credit cost of Rs 648 crore, multiplied by three, gives the credit cost of ST3 at Rs 1,944 crore. Multiplied by ten instead, it gives a scenario nobody will argue with because nobody will act on it either. Severity is arithmetic and costs nothing to increase; plausible is a judgement a named person has to make, defend and write down.

Look at where this bank put the dial. Its baseline ST1 carries gross non-performing assets of 3.0 per cent, the level the book actually shows at month 12. ST2, a moderate downturn, takes that to 4.4 per cent. ST3, the one the bank calls severe but plausible, takes it to 6.4 per cent, or 2.13 times the level the bank is living with today. Somebody in that institution decided that a little more than doubling the bad-loan rate in a year is hard but conceivable, and that something worse than that belongs in a different conversation. No formula sits behind that decision. The choice is a judgement about the Indian credit cycle, this bank's own book, and how far a committee is willing to be argued with.

Which is why the phrase is more useful than it first looks. The phrase refuses two failures at once. Set the dial too low and nothing tested was actually hard, so the test reports comfort that has not been earned. Set it too high and the test reports a catastrophe nobody will plan against. The honest response to an implausible scenario is to ignore it. The phrase forces the person choosing to sit between those two, and to say out loud which side of the line they think they are on.

Who chooses the severity, and why is the chooser the weakest point in the exercise?

Follow the responsibility. The model is not the weak point; a model does what it is told. The data is not the weak point either. The book is the book. The weak point is the moment a person decides that gross non-performing assets of 6.4 per cent is the outer edge of the credible and that 8.0 per cent is not. Every reassuring stress result in history was produced by a scenario somebody chose, and the choosing happened before any arithmetic ran.

The everyday version is a shopkeeper deciding how much stock to carry against a bad month. If she defines a bad month as takings falling by a fifth, she will carry a certain buffer and sleep well. If the office block across the road empties out and a bad month is actually takings falling by half, her buffer was correctly computed against a wrongly chosen scenario. She was not bad at arithmetic. She was optimistic about what a bad month looks like, and the arithmetic obediently carried that optimism through to a number she then trusted.

Two habits make this less dangerous, and neither is a technique. The first is naming the person: at this bank the chief risk officer, Sunanda Ravikumar, puts her name against the scenario set, so the scenario is arguable at a meeting rather than inherited from a spreadsheet. The second is publishing the severity alongside the result, so a reader can judge the choice and the conclusion separately. A capital ratio of 11.8 per cent means nothing on its own. A capital ratio of 11.8 per cent under a scenario that a little more than doubles the bad-loan rate is a statement somebody can disagree with, and being disagreed with is exactly the point.

How does a ladder of scenarios read once it is turned into capital consumed?

Four scenarios reported as four capital ratios is four numbers a reader has to hold apart. Convert every one of them into the same unit and it stops being four numbers. Capital consumed is the fall in the total capital ratio multiplied by risk weighted assets of Rs 60,000 crore, and once every rung is expressed that way the ladder becomes one object with a floor at the bottom of it.

Work the conversion. The bank starts at a total capital ratio of 15.0 per cent, or Rs 9,000 crore of total capital against Rs 60,000 crore of risk weighted assets. ST2 takes it to 13.4 per cent, a fall of 1.6 percentage points, and 1.6 per cent of Rs 60,000 crore is Rs 960 crore. ST3 takes it to 11.8 per cent, a fall of 3.2 points, being Rs 1,920 crore. The bank's own 11.0 per cent floor sits 4.0 points below where it stands, being Rs 2,400 crore. A conversion that cannot be reversed is not a conversion, so the check then runs backwards: Rs 9,000 crore less Rs 960 crore over Rs 60,000 crore is 13.4 per cent, less Rs 1,920 crore is 11.8 per cent, and less Rs 2,400 crore is 11.0 per cent. Every locked ratio reproduces exactly.

Two things fall out that the ratio table hides completely. The first is that the rungs are not evenly spaced: the step from ST2 to ST3 is 1.6 points and the step from ST3 to the floor is 0.8 points, half the size. The last step to failure is the shortest one on the ladder. The second is what those consumptions are as shares of the Rs 2,400 crore the bank can absorb before its own floor: ST2 uses 40.0 per cent of it, ST3 uses 80.0 per cent, and the floor is 100.0 per cent by construction. The scenario this bank calls severe but plausible already stands four fifths of the way to the point it has told itself it will not reach.

What actually moved between the baseline and the severe scenario?

A reader who has just watched Rs 1,920 crore of capital disappear will reasonably ask where it went, and the honest answer is a little uncomfortable. The scenario table states two effects. Credit cost rises from Rs 648 crore in ST1 to Rs 1,944 crore in ST3, exactly three times the baseline and an extra Rs 1,296 crore. Net interest income falls with the margin: 3.00 per cent of Rs 96,000 crore of assets is Rs 2,880 crore, and 2.64 per cent of the same assets is Rs 2,534.4 crore, so the margin costs another Rs 345.6 crore. Together they come to Rs 1,641.6 crore.

Against Rs 1,920 crore of capital consumed by ST3, that is 85.5 per cent. The two effects the headline table names explain most of the fall and not all of it, and the remaining Rs 278.4 crore comes from lines the table never shows. There is a strong temptation at this point to nudge a number until the reconciliation ties. Resist it. A stress result is a model output, not a subtraction anybody can reproduce from four headline figures, and saying so is the more useful sentence. Saying so tells a reader that the number carries assumptions they have not seen, and it stops them treating a summary table as a working.

What is Reverse Stress Testing, and why is it a different question?

Everything so far has run in one direction. Choose conditions, push them through, read a result. Reverse stress testingThe same machinery run backwards: the outcome is fixed at failure and the scenario that would produce it is solved for. runs the same machinery the other way round. The analyst fixes the outcome at failure first, and then solves for whatever would have to happen to produce it. The input is not a scenario. The input is a result nobody in the institution is allowed to reach, and the output is the scenario itself.

The household version again makes the difference obvious. Forward: what happens to the household if the salary stops for four months? Backward: how long would the salary have to stop before the school fee could not be paid? The first question can be answered comfortably and filed away. The second question produces a number of months, and then a much more uncomfortable second step: going and looking at whether anything in the household's actual circumstances could plausibly stop a salary for that long. The second question is harder to run and harder to ignore.

Why bother, when the forward test already said the bank survives? Because of what a forward test structurally cannot do. A forward test can only test the conditions somebody wrote down. If the person writing them did not think of a scenario, the test does not cover it, and the report still comes back clean. A backward test needs nobody to have imagined the scenario in advance, so it has no such hole. The backward test starts at the failure and works outward until it hits an exposure that is actually on the balance sheet. A forward test can report comfort. A reverse stress test begins at the one result that is not comfortable, so structurally it cannot.

There is one more property worth naming before the arithmetic. A reverse stress test frequently finds nothing new. The test finds something already known, already measured and already written down somewhere else, and nobody had put it on the same table as the capital floor. Exactly that happens at this bank, and the timeline below is the whole of it: the exposure the test lands on had crossed its cap in month 5, been discussed and formally accepted in month 6, and carried a remediation plan running out to month 18. The reverse stress test did not discover it in month 12. The test connected it.

How to run Reverse Stress Testing: what are the six steps?

The procedure is shorter than people expect, and five of its six steps are arithmetic. Only the last one requires anybody to imagine anything. A forward test is precisely the opposite: the imagining happens first and the arithmetic follows.

Step one, fix the failure point. For this bank the failure point is its own internal capital floorThe lowest capital ratio an institution will allow itself to reach. Here it is internal and chosen by the bank, and it is not a stated requirement of anybody. of 11.0 per cent, applied to risk weighted assets of Rs 60,000 crore. Fixing this is a decision and it should be made explicitly. A different failure point produces a different answer, and an institution that runs the exercise against a threshold it has not thought about has skipped the only part of the test that reflects its own judgement.

Step two, compute the loss that reaches it. Total capital is Rs 9,000 crore. A floor of 11.0 per cent on Rs 60,000 crore of risk weighted assets requires Rs 6,600 crore. The difference is Rs 2,400 crore, and that is the loss capacity of this bank: the most it could lose in a year before its own floor is touched. If that figure looks familiar it should. Rs 2,400 crore is the same figure that appears when loss capacity is computed forwards from capital and a floor. The reverse stress test simply arrives at it from the other end. The bank's own definition makes the number ignore one thing: it holds risk weighted assets still at Rs 60,000 crore and therefore takes no account of the fall in risk weighted assets as losses are written off. The direction of that simplification is known. The simplification makes Rs 2,400 crore conservative.

Step three, turn the loss into exposure. A loss is not an exposure. Getting from one to the other needs an assumption about how much of a failed exposure is actually lost, and this bank assumes a loss given defaultThe share of an exposure an institution assumes it would not recover if the borrower failed. Forty paise in the rupee here, and it is this bank's own assumption. of 40.0 per cent. Forty paise lost in every rupee that fails means Rs 2,400 crore of loss needs Rs 6,000 crore of exposure to go bad. The loss given default assumption is doing an enormous amount of work, and that is why it gets its own control below.

Step four, express the exposure as a share of the book. Rs 6,000 crore against gross advances of Rs 58,800 crore is 10.2 per cent. The step exists for one reason: 10.2 per cent of a loan book is a quantity a person can react to, and Rs 6,000 crore on its own is not. The share sounds enormous. Hold on to that feeling for one more step.

Step five, go and find that much exposure in one place. Here the exercise stops being an exercise. Sector concentrationHow much of a loan book sits in one industry, measured against a cap the institution has set for itself. at this bank puts infrastructure and power at Rs 7,644 crore, or 13.0 per cent of gross advances against limit L3 of 12.0 per cent, and it has been in breach since month 5. Rs 6,000 crore is 78.5 per cent of that one sector, so a bank that has just been told it survives a severe downturn is also being told that just over three quarters of one already-breaching sector would take it to its own floor.

Step six, and only now, ask what would make it default. Everything to this point was division. Step six is the one that needs a story: a power sector receivables cycle, a set of stalled projects, a policy change on tariffs, a group of connected borrowers. The question lands differently once the exposure is known to exist and the required size is known. A forward test asks somebody to imagine a scenario in the abstract. A reverse stress test hands them a named sector, a required size, and a question that is now specific enough to argue about at a meeting.

Before the control below is touched, it is worth seeing how much of that chain rested on one number. Steps one and two used the balance sheet. The balance sheet is measured. Steps four and five used the loan book. The loan book is measured. Step three used an assumption, and an assumption is not a measurement. How much the answer moves when that assumption does is worth finding out.

A reader arriving later needs the numbers without the control, so four settings are worth writing down as text.

Read the two crossings carefully. Both are stated to one decimal place and the arithmetic behind them is exact. At 31.4 per cent the exposure required is Rs 7,643.3 crore, a whisker under the sector's Rs 7,644 crore. At that setting one sector stops being large enough on its own. At 34.0 per cent the requirement is Rs 7,058.8 crore, just over the Rs 7,056 crore cap of limit L3. There a sector obeying its cap stops being large enough. Below roughly a third of loss given default, no single sector on this book can reach the capital floor alone, and above it one sector can. The whole finding turns on a number nobody measured.

And the direction of the danger is the opposite of what most readers guess. Less exposure is needed to produce the same loss, so a higher loss given default makes the reverse stress test worse, not better. Vindhya Commercial Bank holds provision coverage of 68.0 per cent against the loans that have already failed. Run its own reverse stress test at its own realised experience rather than its assumption and the exposure required falls to Rs 3,529.4 crore, or 6.0 per cent of the book and 46.2 per cent of one sector. Under half of one sector. The institution's own experience after default makes its own reverse stress test worse, and the case records that the two figures have never been reconciled inside the bank.

What does Stress Testing vs Reverse Stress Testing come down to?

Everything that separates the two follows from one thing: which end the analysis starts at. A stress test takes a scenario in and produces an outcome; a reverse stress test takes an outcome in and produces a scenario. Get that straight and the rest of the differences stop needing to be memorised. Each of them is just a consequence.

Take the input first. A stress test needs somebody to have written a scenario down, and the quality of the whole exercise is capped by the quality of that writing. A reverse stress test needs somebody to have named a failure point, a much smaller and much more stable act. Failure points change rarely. Scenarios change every cycle, and every change is an argument.

Take the output. A stress test produces a number and that number gets read against a threshold, so the reporting sentence is a distance: 11.8 per cent against a floor of 11.0 per cent, with 0.8 percentage points or Rs 480 crore of headroomThe distance between a stressed result and the threshold it must not cross, best stated in both ratio points and rupees.. A reverse stress test produces a scenario and a size: Rs 6,000 crore of exposure, being 10.2 per cent of the book, findable in a single named sector. The two outputs go to different places in an institution. The first goes to whoever holds capital. The second goes to whoever holds concentration.

And take what each can report. A stress test can come back comfortable, and frequently does, for the plain reason that the scenario was allowed to be mild. A reverse stress test begins at the failure, so it cannot come back comfortable. The most reassuring thing it can ever say is that the scenario it solved for is one that is hard to believe, and even then it has named exactly which exposure to watch. One of these two tests can accidentally reassure and the other one structurally cannot, and that is the strongest argument for never running only the first.

What does a stress test not tell the reader?

Three things, and every one of them gets forgotten by somebody every year.

A stress test does not say what will happen. A scenario is a chosen set of conditions, not a forecast, and a result under it is conditional on it. The sentence a stress test supports is that if these conditions occurred, this is roughly what the model says would follow. Nothing in the exercise estimated a probability, so the result supports no sentence at all about how likely those conditions are. A reverse stress test is even further from a prediction: the scenario it produces is one that would cause failure, not one anybody expects. Reading Rs 6,000 crore of required default as a claim that Rs 6,000 crore will default gets the exercise exactly backwards.

A stress test does not establish that the institution is safe. The result says that under one chosen set of conditions, one measure landed at a stated distance from one threshold. A different threshold changes the answer. A different severity changes the answer. A different loss assumption, of the kind the control above allows, changes the answer by a factor of nearly two between this bank's own two figures. Everything the test says is conditional on choices somebody made, and a result reported without those choices attached is not a result, it is a mood.

And it does not establish that the model is right. The Rs 1,920 crore of capital consumed by ST3 could only be explained to 85.5 per cent by the two effects the scenario table states. Whatever produced the remaining Rs 278.4 crore is inside the model and is not on the paper the committee received. A modelled residual of that kind is normal, and it is not a scandal. The residual becomes a problem the moment somebody treats the output as an arithmetic fact rather than as a modelled estimate carrying assumptions they have not seen.

Where do the expectations on an Indian bank actually come from?

The mechanism itself is jurisdiction-free. A scenario, a threshold, a distance, and the same machinery run backwards would work identically at an institution anywhere. The expectation is not jurisdiction-free: what an institution must run, how severe it must be, how often, and what it must report.

Two bodies matter here and they do different jobs. The Basel Committee on Banking Supervision, whose work is published by the Bank for International Settlements at bis.org, is where the stress testing principles come from and where the phrase severe but plausible is published. Basel is where the vocabulary of stress testing comes from. The requirement an Indian bank must actually run, at what severity, on what frequency and with what result reported to whom, comes from the Reserve Bank of India at rbi.org.in. Naming only the global standard is the confident and common error on this subject. The standard is where the ideas came from, and the Indian requirement is what an Indian bank is actually held to. Name both, in that order, and go to the source for either.

Who actually reads a stress test result, and what do they do with it?

Inside the bank, the person who has to act on the number is whoever grants capacity to lend. When the forward result comes back at 11.8 per cent against an 11.0 per cent floor, the sentence that matters to committee G2 is not the ratio, it is Rs 480 crore. Rs 480 crore is the capital left over under the severe scenario, and it is the pool from which every request for a larger limit is implicitly funded. Sunanda Ravikumar, the chief risk officer at this invented bank, can set the two numbers side by side: Rs 480 crore of headroom under ST3, and a request to raise one sector cap. Committee members who cannot argue about a ratio can argue about that.

Outside the bank, the reader is somebody trying to judge a balance sheet from the published material. A stress test result is one of the very few forward-looking statements about an institution that is ever put in writing, and the useful part of it is not the pass but the severity that was chosen. A mild scenario always passes, so an analyst who reads only the conclusion learns nothing. An analyst who reads that the scenario a little more than doubles the bad-loan rate and still leaves 0.8 percentage points of room has learned something they can compare across institutions and across years, provided each one publishes what it chose.

And the same six steps work on any balance sheet that has a threshold in it. Nirjhar Industries Limited, invented, the steel and alloys maker that sits opposite this bank as a borrower, has thresholds of its own written into its lending arrangements, and its group treasurer Girish Talwalkar can run exactly this procedure: fix the point at which a threshold is crossed, compute the loss that reaches it, convert the loss into whatever quantity actually causes it, express it as a share of the business, and then go and see whether one customer or one contract is big enough on its own. The answer is uncomfortable at a company for the same reason it is uncomfortable at a bank: concentration is usually already visible and usually already accepted.

The household version is the one to keep. Fix the month the fee could not be paid. Work out how many months of salary that takes. Then ask what in the household's actual circumstances could stop a salary for that long, and how often the honest answer is one thing already known about, one employer, one client, one contract, sitting in plain sight and never written down next to the number it could break. The entire value of running the question backwards, at every size, sits in that answer.