Earnings at Risk: What a Rate Move Does to Interest Income

Earnings at risk answers one question: how much would net interest income change over the next twelve months if rates moved by a stated amount. The measure is the repricing gap multiplied by the rate move multiplied by the average time each rupee stays repriced inside those twelve months. At Vindhya Commercial Bank Limited, invented, a 200 basis point rise adds Rs 156 crore and a fall takes Rs 336 crore.

The whole measure is that short, and the shortness is the point. Three numbers produce the line, and a handful of words has to be printed beside it before anybody else can read it. Where the three numbers come from is a separate question. Here they are taken as inputs, the way a carpenter takes a measurement without re-surveying the building.

What question does earnings at risk actually answer?

Earnings at riskThe change in net interest income over a stated horizon under a stated rate move, computed from the repricing gap. asks a narrow, dated, answerable question: over the next twelve months, if rates move by a stated amount, how much more or less interest income does this institution collect. Not whether the move will happen. Not whether it is likely. Not the institution's worth afterwards. Only what lands in the income statement over one specific stretch of time. Every complaint anybody ever makes about this measure comes from expecting it to answer a question it never claimed to.

The mechanism is identical at every scale, so start with the household version. A household has money coming in and money going out, and both are priced. The salary is revised once a year, in a month somebody at an employer decides. The rent is revised once a year too, on the anniversary of a lease signed at a different time. If rents across the city rise ten per cent, this household does not feel it evenly across the year: it feels it from the month the lease renews, and not one day earlier. Somebody asking how much worse off that household is over the next twelve months has to know two things, not one. How big the rent is, and when in the year it changes.

Swap salary for interest earned on loans and rent for interest paid on deposits and the result is a bank. Vindhya Commercial Bank Limited, invented, holds Rs 96,000 crore of assets and earned net interest income of Rs 2,880 crore over the twelve numbered months of this case. The Rs 2,880 crore is not a single price; it is the sum of thousands of separate prices, each of which resets on its own date. Earnings at risk is the arithmetic that turns a pile of reset dates into one number a committee can hold.

What are the three inputs, and why is that the whole of it?

The measure takes exactly three numbers and multiplies them together. The first is the repricing gapAssets repricing in a period less liabilities repricing in the same period, being a stock rather than a flow. over the horizon in question. For an income question over twelve months that is the cumulative gapThe repricing gap added up across every bucket out to a stated horizon, which is what a twelve month income question needs. out to one year. The second is the size of the rate move being asked about, stated in basis pointsOne hundredth of a percentage point, so 200 basis points is 2.0 percentage points.. The third is the average share of the year each repriced rupee spends earning the new rate. There is no fourth input, no calibration and no distribution. An argument about the answer is therefore always an argument about one of the three numbers and never about the arithmetic.

The absence of a fourth input is unusual and worth dwelling on. Most risk measures in an institution are estimates dressed as computations: a percentile of a simulated distribution, a probability of default fitted to a history, a haircut somebody chose. Earnings at risk on the rise is not one of those. The measure is a multiplication. Three people given the same three numbers will produce the same answer to the last decimal. The property is worth having, and almost nothing else on a risk report can claim it.

Each of the three numbers has a fixed home. Finding it is a question about location rather than about meaning, and the table below answers only that.

Why is the gap multiplied by a half?

The multiplication by a half is the step everybody gets arithmetically right and conceptually wrong. A gap is a stock: the gap says how much more repriced in a period than out of it, measured in rupees, as at a date. Income is a flow, and income accrues day by day across a year. A stock cannot be multiplied by a rate to give a flow without saying how long the stock was earning the rate for, and that is the only job the half does.

Take one rupee inside the Rs 15,600 crore. The rupee reprices on some date inside the next twelve months, and from that date it earns the new rate for whatever is left of the year. A rupee that reprices in month three earns the new rate for nine months. A rupee that reprices in month eleven earns it for one. A large book of separate contracts spreads the repricing dates evenly across the year, and the average remaining timeThe share of the year a repriced rupee earns the new rate, averaged across the year, which is where the half comes from. is exactly half a year. The half is a fact about dates, and it is not a probability, not a haircut and not a conservatism margin.

Why does the distinction matter if the arithmetic is the same either way? Because of what happens in the meeting. If somebody at the table believes the half is conservatism, they will argue for removing it in a good year and doubling it in a bad one, and the number will stop being reproducible. If somebody believes it is a probability, they will ask what confidence level it corresponds to. There is no answer. The half corresponds to no confidence level at all. A number nobody can locate the meaning of is a number nobody can challenge, and a risk report full of unchallengeable numbers is decoration.

What does a positive gap mean when rates rise?

A positive gapMore repricing in than out, so a rise in rates adds income over the horizon and a fall removes it. means more rupees reprice into the institution over the horizon than reprice out of it. In plain terms: more of what it earns resets inside the year than of what it pays. So when rates rise, the earning side catches the new higher rate faster than the paying side does, and income goes up. When rates fall, the same asymmetry runs the other way and income goes down.

The street version is a food stall that buys vegetables at this morning's price and sells thalis at a price written on a board that gets repainted once a month. Costs reprice daily, revenue reprices monthly. The stall has a negative gap on its costs: when vegetable prices rise, the pain lands immediately and the relief takes up to a month. A stall that instead had a monthly supply contract and a daily price board would be the other way round. Neither arrangement is smarter than the other. Which arrangement is better depends entirely on which way prices move, and the measure exists for exactly that reason: the sign of the gap decides the sign of the answer, and nothing else in the computation can flip it.

What does the number come out at for this bank?

Now run it on Vindhya Commercial Bank Limited at month 12. Month 12 is the reporting date throughout. Every figure is that bank's own working number rather than a requirement placed on it by anybody.

Start with the gap. The repricing ladder is read down to the end of the one year bucket and the bucket gaps are added: plus 18,000, plus 6,000, minus 3,600 and minus 4,800, adding to plus Rs 15,600 crore. The gap is an input here and is built elsewhere, taken as read the way a payroll clerk takes a headcount as read. The gap is positive, and the sign already fixes the direction of the answer before any multiplication happens.

So the line that appears on the monthly report reads plus Rs 156 crore on the rise and minus Rs 336 crore on the fall. The two figures are not produced the same way, and the difference between them matters more than either number on its own. Getting the sign right from the gap alone, before any control is touched, is the skill this tool teaches.

Why is the fall not the mirror image of the rise?

Look again at the two figures on the report line. A 200 basis point rise gives plus Rs 156 crore. A 200 basis point fall gives minus Rs 336 crore. The fall is more than twice as large in the opposite direction, on the same book, on the same day, from the same size of move. Where does the extra Rs 180 crore come from?

Not from the arithmetic. The arithmetic is symmetric: a multiplication run with a negative rate move gives exactly the negative of the same multiplication run with a positive one. The asymmetryA fall producing a different figure from the mirror of the rise, because the institution assumes its own rates move differently in each direction. comes from somewhere else entirely. The asymmetry is a view the institution holds about its own behaviour. When rates fall, its loan rates follow them down fairly closely and its deposit rates do not follow them down nearly as far. A savings rate that is already low has very little room left underneath it, and customers notice a cut in a way they do not notice an increase they never received.

The view may well be correct. An institution learns that sort of thing from its own history, and supervisors expect institutions to think about it. But it is a behavioural assumptionA choice about how customers and the institution will act, which is not derivable from a contract and always has an owner. and not an arithmetic consequence of anything on the balance sheet. The rise is computed and the fall is asserted, and knowing which is which is more useful to a reader than either number on its own.

How does the answer sit against the board's own appetite clause?

A measured figure with nothing to compare it against is trivia. The comparison here is an appetite clauseA board statement of how much of something the institution is willing to accept, against which a measured figure is reported.: this board has eight of them, and the second one, A2, says that net interest income over the next twelve months does not fall by more than Rs 360 crore under a 200 basis point move in either direction. The clause is the board's own choice and not a requirement placed on it by anybody.

Set the measured fall against it. Rs 336 crore against a cap of Rs 360 crore is 93.3 per cent of the clause used and Rs 24 crore of room left. Rs 24 crore is less than one per cent of a year's net interest income. The position is much narrower than the comfortable-sounding 93.3 per cent makes it look. A reader who takes 93.3 per cent as a reassuring number has read the percentage instead of the position.

There is a second trap in that percentage, and this bank contains both halves of it. Limit L4 caps the share of gross advances sitting in the weakest three internal grades, and it runs at Rs 8,232 crore against a cap of Rs 8,820 crore. Both fractions reduce to fourteen over fifteen, so limit L4 also runs at 93.3 per cent. One is an earnings sensitivity against a board appetite clause and the other is a credit concentration limit utilisation. The two are the same number and nothing else about them is the same. Any report line carrying 93.3 per cent has to say which one it means.

What does earnings at risk not answer?

Everything above is about twelve months of income. Twelve months of income leaves out most of a balance sheet. Most of a balance sheet stretches far past twelve months, and the value of a long asset changes when rates move even if not one rupee of this year's income does.

So the same institution measures a second thing on the same shock: what a 200 basis point rise does to the economic value of everything on its book. At this bank that answer is minus Rs 840 crore, being 12.7 per cent of tier 1 capital of Rs 6,600 crore. The same rise that adds Rs 156 crore to a year of income takes Rs 840 crore off value. Both numbers are right, they answer different questions, and a committee shown only one of them has been shown half of its own position.

How can that be? Because they are asking about different stretches of time. The income measure looks at one year and asks what gets collected. The value measure looks at every future cash flow on the book, discounts them all, and asks what the whole thing is worth today. A book that reprices quickly in the first year and slowly after that will look good on the first question and bad on the second. Neither answer is a correction of the other. The value measure and how it is built belong to the market risk material and are covered there.

What must sit beside the number on the report line?

Suppose a monthly report arrives carrying one line: earnings at risk, minus Rs 336 crore. The trouble with that line is not the figure. The figure arrives with none of the terms it was computed under, and a conclusion published without its working is all the reader gets.

Four items fix it, and all four fit on the same line. First the horizon: a twelve month figure and a three month figure are different objects. Then the size of the move: a figure at 200 basis points and one at 100 are different objects too. Then the gap it was computed on, the only input the reader could argue with. And last, who chose the behavioural assumptions: the asymmetry that makes the fall bigger than the rise is a judgement made by a person in a role, not a property of arithmetic. Without those four, minus Rs 336 crore cannot be challenged, cannot be compared with last month and cannot be reproduced by the person reading it. Challenge, comparison and reproduction are the only three things a report line is for.

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

Three people pick up the same Rs 336 crore and do three unrelated things with it, and only one of them can change it. Knowing which reader that is matters before deciding how to present the figure.

The independent director on the board risk management committee reads it against clause A2 and wants one thing from it: how much room is left. The answer is Rs 24 crore, and everything else on the report is context for that number. She cannot move a repricing date and would not want to; her question is whether the position her board signed up to still holds, and if it does not, which plan replaces it and by when.

The treasury desk reads it as a consequence of a gap it can actually change. Lend at a different repricing date, fund at a different one, and the cumulative gap moves, and with it the answer. The desk is the only reader who can move the number, so the figure has to reach it in a form it can act on rather than as a headline. Telling a desk that earnings at risk is minus Rs 336 crore tells it nothing; telling it the gap is plus Rs 15,600 crore tells it exactly which lever exists.

The analyst at another institution, looking at this bank as a counterparty rather than as an employer, reads the line as a claim and immediately checks the four items beside it. A published sensitivity with no horizon, no shock size and no stated gap is not evidence about the bank; it is evidence about the reporting. And the household version of this reader is the person comparing two fixed deposit offers who asks not about the rate but about when it resets. The instinct is the same at a different scale.

Where do the shocks and the measures come from?

The 200 basis points used throughout is the invented bank's own internal scenario. The scenario is not a standard, not a requirement and not a number anybody imposed on it. A different institution running a different scenario would produce a different answer from the same gap, and neither answer would be more official than the other.

Behind the practice sits a published framework. The Basel Committee, at the Bank for International Settlements, is where the standardised interest rate shocks and the structure that sets an earnings measure beside a value measure come from, and it is the reason almost every institution computes both rather than one. The Reserve Bank of India, rather than any framework, sets what an Indian bank must actually compute, report and hold capital against, and that is a separate question with a separate answer. Both have to be checked at source.