Survival Horizon: How Long the Institution Lasts Under Stress

The survival horizon counts days. The horizon is how long an institution can meet the cash leaving under a chosen stress before its buffer reaches zero. Inside Vindhya Commercial Bank Limited, an invented bank, Rs 14,400 crore of buffer reaches zero on day 34 under that bank's own severe outflow path. Day 34 is an event on a calendar, not a percentage, and a day count is not the coverage ratio in days.

Three ratios have already appeared in this subject, and each one answered its question with a percentage. The survival horizon answers with a date. Asked what the liquidity position of Vindhya Commercial Bank Limited, invented, is, the treasurer's honest reply is not a number between zero and two hundred: it is thirty four mornings, after which there is nothing left in the buffer to pay with. A percentage invites comfort or discomfort. A day count invites a look at a calendar and a question about what could be finished by then.

A single number written on a board pack looks solid in a way the arithmetic behind it is not, and that is at once the appeal of the day count and its danger. Thirty four is the output of two inputs and about six choices. Every one of those choices can be recomputed, and four of the thirty four days can be lost to a change smaller than the number suggests.

What is the survival horizon actually counting?

The measure counts mornings. The survival horizonThe number of days an institution can meet its modelled net outflows out of its buffer alone, before that buffer reaches zero. is the number of days an institution can keep paying what a chosen stress says will leave, using only the stock of liquid assets it already holds, before that stock reaches zero. Two words in that sentence do the work. Only means nothing else is counted: no new borrowing, no asset sale beyond the buffer, no help from anybody. And chosen matters because the outflows are not a measurement of anything that has happened. Somebody decided them.

Here is the version anyone can feel. A household loses its single salary on the first of the month and has money in hand. Somebody asks how long that money lasts. A percentage cannot answer that. The money comes out, the calendar comes out, and the days get crossed off one at a time, and the crossing off is not even: the rent goes in the first week, the school fee goes in the first week, and the weeks that follow are only groceries and travel. The money runs out on a particular Tuesday. Nobody in that household would accept the answer expressed as a coverage percentage. The household needs to know which Tuesday. An institution is that household with more zeroes and a committee.

The count is useful and fragile for exactly the same reason. A percentage hides its assumptions inside a single division, so it is hard to argue with. A day count puts every one of its days on view, so anyone in the room can ask why day 11 costs less than day 4. Being arguable is a feature and not a defect. The measure is built to be argued with, and an institution that reports the day count without printing the path underneath has removed the only thing that made it worth reporting.

What two inputs make the number, and what is deliberately left out?

Two, and only two. The first is a stock: the liquidity buffer of Vindhya Commercial Bank Limited, invented, being Rs 14,400 crore made of components H1 to H4. The contents of those four components, the prices the bank assumed it could sell them for, and the haircut it applied to component H4 are covered separately, and the total is taken as given here. The stock stands still while it is consumed: it earns nothing, grows by nothing and is topped up by nothing.

The second is a net outflow pathThe amount of cash the model says leaves each day under a scenario, stated day by day rather than collapsed into one total.: how much cash leaves each day under the bank's own severe scenarioThe institution's own chosen set of stressed assumptions, harsher here than the standardised computation the same institution also runs.. The design of that scenario, being what the bank assumed about its depositors, its wholesale providers and its undrawn lines, is covered separately in this sequence and is used here as it stands. Five rates, all of them the invented bank's own working numbers and not a requirement issued by anybody: Rs 720 crore a day on days 1 to 5, Rs 600 crore on days 6 to 10, Rs 420 crore on days 11 to 20, Rs 240 crore on days 21 to 30, and Rs 300 crore a day from day 31 onward.

Now the list of what is not in the number. The exclusions run longer than the inputs, and every one of them is a place where a reader quietly adds something back. The bank has a written contingency funding plan holding six actions numbered F1 to F6, and not one rupee of that plan is counted in the 34 days. Whether those actions arrive, and how much of them arrives inside the window, is a separate question with its own arithmetic and is covered under the contingency funding plan. No central bank response is assumed, in any form and on any terms. No loan is assumed to be repaid earlier than the model already says. No deposit that leaves is assumed to come back. Nothing is sold that is not already inside the buffer, and a repo, a certificate of deposit and a government security are named here as things this invented bank holds and deals in rather than explained.

How does the buffer actually get consumed, day by day?

By subtraction, repeated until something reaches zero. Repeated subtraction is the entire method. Saying so plainly matters because the measure has a serious reputation and a five line arithmetic. Take the stock. Take off what the model says leaves on day 1. Take off what it says leaves on day 2. Keep going. Write down the day the remainder crosses zero. The survival horizon is the answer to a subtraction that anybody can check on a sheet of paper, and that checkability is why the measure is worth reporting.

Because the rate changes only five times, the whole path collapses into five rows. Here it is for Vindhya Commercial Bank Limited, invented, worked band by band, with the running total and what is left after each one.

Two figures in that table are worth stopping on before anything else. Cumulative consumption at day 30 is Rs 13,200 crore, or 91.7 per cent of the buffer, leaving Rs 1,200 crore of unspent buffer on the thirtieth morning, being 8.3 per cent of it. And the burn rateThe amount of buffer consumed per day at a given point in the path, which changes as the scenario moves through its phases. from day 31 onward is Rs 300 crore a day. The remainder therefore lasts four more days. Thirty plus four is the whole derivation of the 34, and both halves of it are visible only because the path was printed rather than totalled.

Notice something the table shows and a single number never could. The burn rate falls through the month, from Rs 720 crore a day in the first week to Rs 240 crore a day in the fourth, and then it rises again to Rs 300 crore a day from day 31. The burn rate does not decay smoothly and it is not a curve. The path is five flat rates, chosen by the bank, and the small rise at the end is the bank saying that in its own scenario the pressure does not simply fade away once the month is over.

The second thing the path hides inside a single number is where the money goes. Split the buffer by which band consumed it and the shares are nothing like the shares of the calendar. The first five days take a quarter of the buffer and one seventh of the time. The fourth week takes a sixth of the buffer and nearly a third of the time. The buffer is half gone during day 12, and the second half then lasts twenty two days. A reader who hears thirty four days and pictures a steady drain has pictured the wrong shape entirely, and would set the wrong day in the diary to start worrying.

Why does the shape of the path matter and not just its total?

Ask it the other way round. If two scenarios both take Rs 13,200 crore out over thirty days, does it matter in which order the money leaves? The instinct says no on the ground that the arithmetic is the same. The instinct is right about day 30 and wrong about almost everything before it.

Take the invented bank's own front loaded path and set two illustrations beside it, both built for comparison rather than run by the bank. The first is a level path: the same Rs 13,200 crore spread evenly at Rs 440 crore a day. The second reverses the bank's own five rates so the pressure builds instead of fading. All three arrive at exactly Rs 13,200 crore on day 30, so all three leave exactly Rs 1,200 crore of the buffer unspent on the thirtieth morning, and against the real buffer of Rs 14,400 crore all three finish within a day and a half of each other.

Now shrink the buffer to Rs 10,800 crore and ask the same question again. The bank's front loaded path is exhausted on day 20. The level path lasts until day 24.5. The reversed path lasts until day 26.7. Same thirty day total, same starting stock, and a spread of nearly seven days purely from the order in which the money leaves. Printing the path is the whole argument. The total gives what happens at the end of the month. The shape gives what happens on every morning before it, and the mornings before it are where anyone actually has to act.

There is a working lesson buried in that. When an institution is comfortably above its thirty day total, arguments about the shape of the scenario are worth very little and arguments about the size of the buffer are worth everything. When it is below, the reverse holds, and the fight over which week the deposits leave in stops being academic. Knowing which of those two situations an institution is in is most of the skill in reading this measure.

Why is this not the liquidity coverage ratio expressed in days?

Because the two measures put different outflows under the same buffer, and the difference between those outflows is exactly measurable. The measurement comes first, before either headline is read. Meeting the two figures in the wrong order is how a reader decides one of them must be wrong.

Vindhya Commercial Bank Limited, invented, runs two outflow computations. The standardised computationA ratio computed on a published set of factor categories, which produces a comparable number rather than the institution's own view of a stress. puts thirty day net cash outflows at Rs 11,520 crore, using categories and factors that are covered separately in this sequence. The bank's own severe path, the one consumed throughout this guide, takes Rs 13,200 crore out over the same thirty days. Dividing the second by the first: 13,200 over 11,520 is 1.1458. Averaged out, Rs 440 crore a day against Rs 384 crore a day. The bank's own scenario is 14.6 per cent harsher over thirty days than its standardised computation, and that single figure reconciles everything that follows.

Now the headlines, in the order they make sense. Against the standardised outflow of Rs 11,520 crore, the buffer of Rs 14,400 crore reads 125.0 per cent. A reading of 125.0 per cent sounds like a quarter more than is needed, and it is the number that goes on the cover. Against the bank's own harsher outflow of Rs 13,200 crore, the same buffer reads 109.1 per cent. And the same arithmetic said a third way is the one this guide started with: the severe path consumes 91.7 per cent of the buffer inside thirty days, leaving 8.3 per cent of it. One buffer, two outflow assumptions, three headlines, and not a single contradiction between them.

Two consequences fall straight out of that reconciliation, and both are easy to miss. The first is that an early warning indicator can change colour without a single rupee moving. Indicator W7 watches the horizon and indicator W6 watches the buffer against thirty day outflows, turning amber below 115 per cent and red below 105, and every one of those triggers is the invented bank's own. On the standardised outflow W6 reads 125.0 per cent and is comfortably green. On the bank's own severe outflow the same indicator would read 109.1 per cent and sit in its own amber band. Which denominator the definition names decides the colour, so the definition is part of the indicator and not a footnote to it.

The second is a warning about figures that look alike. At this bank, Rs 11,520 crore is the thirty day net cash outflow, and Rs 11,520 crore is also the sum of buffer components H2 and H3, and it is also the wholesale term deposit balance on the balance sheet. Three different objects wearing one number, and the first two sit inside the same ratio, one in the denominator and one inside the numerator. Naming every figure rather than leaving it bare is the only defence against that collision, and the habit is worth carrying into any real institution where round numbers repeat.

What does the horizon have to be measured against to mean anything?

On its own, 34 days is decoration. Thirty four days is a number with no direction attached: nobody in the room can tell from it whether to relax, act or escalate. A measure becomes a control only when something has been written down in advance about what its readings mean, and at Vindhya Commercial Bank Limited, invented, two such things exist and they disagree in a productive way.

The first is an appetite clauseA sentence in the board's risk appetite statement setting what the institution is willing to accept, which here asks for thirty days.. Clause A6 says the bank survives thirty days of its own severe scenario with no recourse to the central bank. Clause A6 is the board of an invented bank choosing a number for itself rather than a requirement issued by anybody. At 34 days the clause is met, with four days and Rs 1,200 crore of unspent buffer to spare.

The second is an early warning indicatorA measure with a defined trigger and a defined action attached, so that crossing it starts something rather than merely reporting something.. Indicator W7 watches the horizon and turns amber below forty days and red below thirty, again on the bank's own invented triggers. At 34 days W7 is already amber. So on the same morning, with the same number, the board's own liquidity clause is satisfied and the indicator that watches that clause is flashing.

Both readings are correct, and a reader who thinks one of them must be a mistake has misunderstood what an early warning indicator is for. The warning is set inside the clause on purpose, exactly as a smoke alarm is set to go off while there is still a kitchen. If W7 only turned amber at twenty nine days it would be telling the treasury team something it already knew from the clause having failed. The value of the indicator is entirely in the distance between forty and thirty days. Ten days of room is what the institution has to act in while acting is still cheap.

There is a governance point sitting underneath this, covered properly in the limit framework and only named here. Of the eight appetite clauses A1 to A8 at this bank, four cascade into a limit and four do not, and A6 is one of the four with no limit beneath it. Nothing reports on the board's central liquidity statement between board meetings, so indicator W7 is doing the work a limit would otherwise do, without a limit's escalation route attached to it. The same gap is worth noticing on any real institution: the measure that watches the most important sentence in the framework is often not the measure with the most authority behind it.

Why does the horizon fall faster than the scenario worsens?

Here is the arithmetic behind that prediction. Failing clause A6 means the buffer is gone on or before day 30. Consumption to day 30 therefore has to rise from Rs 13,200 crore to the full Rs 14,400 crore. Divide: 14,400 over 13,200 is twelve over eleven, being 1.0909 to four places. A uniform worsening of 9.1 per cent, applied to every day of the path, is the entire distance between meeting the board's liquidity clause and failing it. Four days of headroom sounded like a lot. Less than a tenth of one assumption set does not.

Call that uniform multiple m and turn it. The multiple is a device for asking how wrong the scenario is allowed to be, not a second scenario the bank runs: a real stress does not politely multiply every day by the same factor. Multiply the whole path and hold the buffer still, and the horizon does this.

Look at the row for double severity. The horizon does not go from 34 days to 17. The horizon goes to 11.4, a fall of 66 per cent for a rise of 100 per cent. Severity and days stand in a non-linearA relationship in which the output does not move in proportion to the input, so an intuition built on halving and doubling gives the wrong answer. relationship in the direction that hurts, and there are two reasons stacked on top of each other. The first is that a fixed stock divided by a rising flow was never going to fall in a straight line. The second is the shape of this particular path: at double severity the whole of the first thirty days is compressed into ten, so the days that survive are the expensive early ones, and the cheap Rs 240 crore days at the end of the month never arrive at all.

What does an extra rupee of buffer actually buy?

Turn the other control now. Hold the path exactly where the bank set it and move the stock instead. Moving the stock is the question a treasury team is actually asked in a planning meeting. The path is a modelling argument, and the buffer is a cheque somebody has to write.

The mapping from buffer to days is piecewise, and the pieces are the bands. Below Rs 3,600 crore of buffer every Rs 720 crore buys one day. Between Rs 6,600 crore and Rs 10,800 crore every Rs 420 crore buys one day. Between Rs 10,800 crore and Rs 13,200 crore every Rs 240 crore buys one day, the cheapest stretch on the whole map. And above Rs 13,200 crore, where this bank actually sits, every Rs 300 crore buys exactly one more day, however far the map is extended.

Two crossings matter at Vindhya Commercial Bank Limited, invented, and both are exact. Take Rs 1,200 crore off the buffer, being 8.3 per cent of it, and the horizon falls to exactly 30 days. Day 30 is the edge of the red band on indicator W7 and the exact point where clause A6 fails. Add Rs 1,800 crore to it, being 12.5 per cent more buffer, and the horizon reaches exactly 40 days and W7 turns green. Twelve and a half per cent more buffer buys six more days and moves the indicator a whole colour. A treasury team can carry a sentence like that into a planning meeting.

The position of this bank on that map is easy to miss and worth stating on its own. Vindhya Commercial Bank Limited is not sitting in the cheap stretch. The bank is past that stretch, in the Rs 300 crore a day tail it wrote into its own scenario for day 31 onward. Buying days beyond day 30 costs this bank a quarter more per day than buying days in the fourth week, so the marginal cost of a longer horizon has already started rising by the time anyone reads the number.

What does the number assume about the day after it ends?

Nothing. Not a pessimistic assumption, not an optimistic one, none at all. The computation stops when the remainder crosses zero because there is nothing left to subtract from, and it carries no statement whatsoever about day 35. The survival horizon measures how long there is to act, and it is not in any sense a measure of what happens if nobody acts.

The quietest of the ways the number misleads is that nothing about it looks wrong. A board pack reading 34 days invites a reader to picture something happening on day 34, and the honest position is that the model has simply run out of arithmetic. Whether the outflows continue at Rs 300 crore a day beyond day 34, stop, or accelerate is not stated anywhere in the scenario. The actions the institution would have taken by then are a different subject with their own arithmetic, and at this bank they are the contingency funding plan, covered separately and counted here at zero.

Said out loud in a meeting, the number changes character usefully. The horizon stops being a forecast of when the bank fails and becomes what it always was: a countdown clock on the time available to do the things somebody has already written down. A countdown clock is a more useful object and a more honest one. Described that way, the number makes the next question in the room the right one. Which of those things can actually be finished inside 34 days?

How does a reported horizon mislead the people reading it?

Who actually reads this number, and what do they do with it?

Three readers, three different uses, and the differences are worth knowing because they explain why the same number is reported in three places with three different things printed beside it.

The head of treasury reads it as a schedule. At Vindhya Commercial Bank Limited, invented, that is Devendra Achar, and the question in front of him is not whether 34 is a good number. His question is how the things already written down sort into three groups: finished inside 34 days, started but not finished, and simply too slow to matter. A horizon turns every contingency action into a deadline, and an action with a longer delivery time than the horizon is not a contingency action for this scenario at all. The comparison of delivery times against the horizon belongs to the contingency funding plan and is not made here.

The board reads it as a test of a sentence it wrote itself. Clause A6 asks for thirty days without recourse to the central bank, the reading is 34, and the only decisions available are to accept the position, to raise the buffer, or to change the clause. The chief risk officer, Sunanda Ravikumar at this invented bank, brings the same number with indicator W7 attached to it. Attaching the indicator is what turns a comfortable reading into a conversation.

Someone outside reads it as a claim to be interrogated. If a horizon appears in a disclosure, the three questions that matter are whose scenario produced it, what the buffer was valued at, and what was counted inside it. Two institutions reporting 34 days can be in completely different positions, and nothing on the face of the number says which is which. The same interrogation works one layer down: a lender looking at a corporate borrower such as Nirjhar Industries Limited, invented, is asking the identical question about cash in hand against committed outflows, and a household counting months of expenses in a savings account is asking it about itself. The shape of the question does not change with the size of the balance sheet, only the number of zeroes and the number of people who argue about the assumptions.

Knight, in Risk, Uncertainty and Profit in 1921, separated the measurable from the merely uncertain, and this measure sits exactly on that line. The 34 days are measured, in the sense that they follow with certainty from two stated inputs. Everything on the far side of day 34 is not measured at all, and no amount of care with the first part turns the second part into arithmetic.