Interest Rate Risk in the Banking Book: The Measures and the Mandate

Interest rate risk in the banking book is what a rate move does to the income and to the value of everything a bank holds outside its trading book. Vindhya Commercial Bank Limited, invented, slots Rs 84,000 crore of assets and Rs 84,000 crore of liabilities into eight repricing buckets, and its own 200 basis point scenario adds Rs 156 crore to income while taking Rs 840 crore off value.

Start with a household. The shape of the problem is identical and much easier to feel. A salary lands on the same date every month and does not change until the next appraisal. The floating rate home loan sitting against that salary changes the moment its reference rate moves. Nobody in that household bought anything, sold anything or made a decision, and yet a rate move has changed what is left at the end of the month. The exposure came from a mismatch that was already sitting there, not from an action anybody took. A bank is the same arrangement written very large, pointing the other way, and repeated across every deposit and every loan it carries.

A mismatch that was already in place, moving on its own the moment a rate moves, is the whole of the subject, and everything below is bookkeeping about where each balance sits and how long it is before its rate moves. Two things have to be held together before any of the numbers mean anything. The first is that interest rate risk in the banking bookThe exposure of a bank's income and of the value of its balance sheet to a change in interest rates, on everything it holds outside the trading book. bites without a single trade being executed. The second is that it produces two answers rather than one, and those two answers are routinely read as rivals when they are nothing of the kind.

What is interest rate risk in the banking book, and why does it get a subject of its own?

A bank keeps its positions in two places. The trading book holds what it took on in order to trade, marked to market daily and measured with the distributional measures. Everything else is the banking book: the loans it made and intends to hold, the securities it bought and intends to keep, and the deposits and borrowings funding both. At Vindhya Commercial Bank Limited, an invented bank whose every figure in this guide is its own, the investment book of Rs 26,400 crore splits into a held for trading portfolio of Rs 3,600 crore, an available for sale portfolio of Rs 8,400 crore and a held to maturity portfolio of Rs 14,400 crore.

The available for sale and held to maturity portfolios are banking book positions, so Rs 22,800 crore of the investment book, being 86.4 per cent of it, belongs to this guide and the remaining Rs 3,600 crore does not. The Rs 3,600 crore held for trading portfolio is where value at risk lives, and value at risk is covered separately. Splitting them is not administrative tidiness. The two books are held over different horizons, treated differently in the accounts, reported to different committees and built to answer different questions, so a measure designed for one of them says very little that is useful about the other.

Why does the same Rs 36,000 crore turn up in four tables with four different answers?

Vindhya Commercial Bank Limited carries Rs 76,800 crore of deposits, of which current accounts are Rs 9,600 crore and savings accounts Rs 26,400 crore. Together that is Rs 36,000 crore of non-maturity depositsA balance repayable on demand with no contractual maturity date, so it has to be slotted by judgement rather than by reading a contract., being 46.9 per cent of the deposit book, and it is the most load-bearing single figure at this bank. Every one of those depositors could ask for the whole of it tomorrow morning. None of them will.

Because the contract answers nothing at all about timing, four different tables at the same bank put that one balance in four different places, and each of them is answering a different question. None of the four tables competes with the others. Each is the right answer to its own question. The repricing ladder asks when the rate on the balance next changes and slots all of it at one to three years. The economic value computation asks what that balance is worth today at a new rate and gives it an average behavioural life of 0.5 years. The liquidity maturity ladder asks when the cash actually leaves and places 5.0 per cent of it, being Rs 1,800 crore, in its first bucket LB1 with the remainder spread across LB5 to LB8. The thirty day coverage computation asks what walks out in a stressed month and blends Rs 26,400 crore of savings balances at 7.5 per cent with Rs 9,600 crore of current balances at 40.0 per cent, giving Rs 5,820 crore.

Set the last two of those side by side. Both land on one scale, and the size of the disagreement states itself. Rs 5,820 crore against Rs 1,800 crore is a blended 16.2 per cent against the maturity ladder's 5.0 per cent, being 3.23 times as much and a difference of Rs 4,020 crore on one balance. Neither table is in error. The maturity ladder describes an ordinary month and the coverage computation describes a stressed one, and a balance can be perfectly sticky in fair weather and quick to leave in a storm. The maturity ladder LB1 to LB8, the coverage computation and everything built on them belong to the liquidity subject and are named here for this one purpose and no other.

What is a repricing ladder, and which date does it slot a balance by?

A repricing ladderA table slotting every rate sensitive asset and liability into time buckets by next repricing date, so that the mismatch can be read off rather than guessed at. is a table with four columns and, at this bank, eight rows. Each row is a time bucket. Into it goes every asset and every liability whose rate will change inside that bucket, and the fourth column is assets less liabilities. The fourth column is the entire subject, and the first three exist to produce it.

The date the table slots by is the repricing dateThe next date on which the rate applied to a balance changes, which is a different question from when the balance matures or when the cash moves., meaning the next date on which the rate applied to the balance changes. The repricing date is a different question from when the balance matures and a different question again from when the cash moves, and confusing the three is the single commonest error in reading one of these tables. A ten year loan whose rate resets every three months is a three month position in this table and a ten year position in a maturity table. A two year term deposit at a fixed rate is a two year position in both. A savings balance repayable on demand is whatever somebody decides it is, and that decision is the subject of everything below.

Only rate sensitiveA position whose rate changes within the horizon of the table, and therefore one that belongs in the ladder at all. positions go in. A branch building does not carry a rate, so it never appears. Nor does share capital. The ladder at Vindhya Commercial Bank Limited holds Rs 84,000 crore on each side, so the bucket gaps have to sum to zero.

What does this bank's ladder say, and what is the Rs 12,000 crore that is not in it?

Read the rows. A large share of this bank's lending is on floating rates that reset almost immediately and very little of its funding does, so RB1 carries Rs 24,000 crore of assets against Rs 6,000 crore of liabilities for a gap of plus Rs 18,000 crore. RB2 adds another plus Rs 6,000 crore. RB3 and RB4 turn slightly negative at minus Rs 3,600 crore and minus Rs 4,800 crore. Then RB5 arrives with Rs 12,000 crore of assets against Rs 42,000 crore of liabilities, a repricing gapAssets less liabilities repricing inside one bucket, and the thing that makes income move when rates do. of minus Rs 30,000 crore, more than five times the size of any other row in the table. RB6, RB7 and RB8 run positive again at plus Rs 3,600 crore, plus Rs 7,200 crore and plus Rs 3,600 crore.

The ladder holds Rs 84,000 crore, and total assets are Rs 96,000 crore, so Rs 12,000 crore of the balance sheet is not in the table at all. The rate sensitive asset side is exactly the investment book of Rs 26,400 crore plus net advances of Rs 57,600 crore, and everything else on the asset side carries no rate that moves. Care is needed with that figure. Rs 12,000 crore names four different objects at this bank: the assets outside the ladder, the liabilities and equity outside it, the Rs 12,000 crore of assets sitting in bucket RB5, and the Rs 12,000 crore of undrawn committed lines that appear nowhere in this table at all. The object needs naming every time the number is printed.

The last block of that table is the one place where this bank's own description of its ladder does not quite tie. Other liabilities and provisions of Rs 3,120 crore plus share capital and reserves of Rs 7,680 crore come to Rs 10,800 crore, not Rs 12,000 crore. The ladder total and the balance sheet total are both locked, so a further Rs 1,200 crore of deposit and borrowing balances is being treated as not repricing, and the honest thing is to print that line rather than let two totals disagree quietly. The residual changes no result at this bank, and it is exactly the sort of line a reader should look for in any ladder handed to them.

What shape does the cumulative gap make, and which part of it carries information?

The bucket gaps on their own are not what anybody measures income on. The figure that matters is the cumulative gapThe running total of the bucket gaps up to a point in time, which is the figure the income measure is built on., the running total up to a chosen point. Everything that reprices before that point has already repriced. Run the eight rows through and the curve goes plus Rs 18,000 crore, plus Rs 24,000 crore, plus Rs 20,400 crore, plus Rs 15,600 crore, minus Rs 14,400 crore, minus Rs 10,800 crore, minus Rs 3,600 crore, zero.

Three of those five movements say something. The curve rises to a peak of plus Rs 24,000 crore at three months. At that peak the bank is at its most exposed to a rate fall and its most rewarded by a rate rise. The curve drifts down to plus Rs 15,600 crore at one year, and that fourth figure is the one the income measure uses. The curve then falls straight through zero inside RB5 and stays negative for the rest of the table. Two columns of Rs 84,000 crore each have no choice but to end level, so the final zero at RB8 is the one figure in the row that tells a reader nothing at all. A ladder that ties to zero at the end is arithmetic doing what arithmetic does, and a committee that reads comfort into it has misread a subtraction.

What makes bucket RB5 five times the size of every other row?

Go back to the Rs 36,000 crore. The Rs 36,000 crore is contractually repayable on demand, so on a literal reading it belongs in RB1 with everything else that could reprice tomorrow. The bank does not put it there. The bank slots the whole of it at one to three years on a judgement about how the balance actually behaves: current and savings balances at a branch network sit for years, they do not chase every quarter point, and the rate on them moves rarely and by less than the market does. The judgement is a behavioural assumptionA stated judgement about how a balance actually behaves, used where the contract does not answer the question the table is asking., and it is a decision somebody made rather than a fact somebody read off a contract.

One choice about human behaviour is what makes RB5 minus Rs 30,000 crore, and take the Rs 36,000 crore out of the bucket and the same row turns to plus Rs 6,000 crore. Nothing about the bank would have changed. No deposit would have moved, no loan would have been written and no rate would have shifted. The largest single number in the table is produced by a view about human behaviour, and if that balance were slotted anywhere else the largest gap in the ladder would be somewhere else too. A reader looking at a repricing ladder is looking at a table of contracts with one judgement dropped into the middle of it, and the judgement is usually the biggest thing in the table.

What do the two measures say about the same 200 basis point rise?

The bank runs one scenario across the banking book: a parallel shockA rate change applied equally across every maturity, which is the shape of this bank's own internal scenario and a simplification worth naming. of 200 basis points. The 200 basis points is this bank's own choice, written into its own policy, and not a requirement taken from anywhere. The bank then computes two answers, and they point in opposite directions.

The first measure asks what happens to earnings. Take the one year cumulative gap of plus Rs 15,600 crore. Every balance in that gap reprices inside the next twelve months, on average with half the year still to run, so the effect on a full year of income is Rs 15,600 crore times 2.0 per cent times 0.5, giving plus Rs 156 crore of net interest income over twelve months, being 5.4 per cent of the bank's net interest income of Rs 2,880 crore. A rise helps this bank's income because more of its assets reprice quickly than its liabilities do. A 200 basis point fall is not the mirror image. Deposit rates do not fall as far as loan rates do, so the fall costs Rs 336 crore, and that Rs 336 crore runs at 93.3 per cent of the Rs 360 crore of earnings tolerance in appetite clause A2. Note the figure carefully. Rs 360 crore also names two other objects in this case and is not one number used three times.

The second measure asks what happens to value. The bank holds Rs 84,000 crore of rate sensitive assets at a modified duration of 3.00 years and Rs 84,000 crore of rate sensitive liabilities at a modified duration of 2.50 years. Both durations are used here as locked inputs and are derived in the fixed income subject. Assets run 0.50 years longer than liabilities, and that 0.50 years is the duration gap. The same 200 basis point rise changes economic value of equity by 0.50 times 2.0 per cent times Rs 84,000 crore, giving minus Rs 840 crore, being 12.7 per cent of tier 1 capital of Rs 6,600 crore and 84.8 per cent of the Rs 990 crore cap set by limit L8, leaving headroom of Rs 150 crore. Longer assets than liabilities cost value when rates rise, and the minus sign is saying exactly that.

Both are right. One asks what the book earns over the next twelve months given which balances reprice inside them, and the other asks what every cash flow on both sides is worth today at a new rate. A rise that lets a bank reprice its lending quickly is good news for a year of income and bad news for the present value of a long book, and there is no contradiction in that at all. A committee shown only one of the two has been shown half the position. Which of the two should carry more weight, and what each is fit for, is argued out where earnings at risk and economic value at risk are compared directly, and that comparison is covered separately.

One more caution belongs with that figure. The 84.8 per cent is the utilisation of limit L8. The same figure is also, by coincidence of arithmetic, the completeness of this bank's model inventory. The inventory holds 28 registered models against 33 found in use. Rs 840 crore over Rs 990 crore reduces to twenty eight over thirty three exactly. Two entirely different objects, one number, and a reader skimming a committee pack could easily carry the wrong one away.

How far can the assumed deposit life move before limit L8 is breached?

The economic value computation gives the Rs 36,000 crore an average behavioural life of 0.5 years. The repricing ladder gives the same Rs 36,000 crore a life of one to three years. The two tables give two different answers to one question at one bank, and nobody has reconciled them.

The consequence is arithmetic. Extending the assumed life by one year moves the value result by Rs 36,000 crore times 2.0 per cent, or Rs 720 crore, and that figure is locked in this case. So at 0.5 years the answer is minus Rs 840 crore. At 1.5 years it is minus Rs 120 crore. At about 1.67 years it is zero. At 2.0 years, the midpoint of the bank's own RB5 bucket, it is plus Rs 240 crore, so on the deposit life the bank's own ladder implies, its headline interest rate risk number changes sign. At 2.5 years it is plus Rs 600 crore. The bank is not reporting a wrong number. The bank is reporting one of two numbers that its own two tables both support.

The band inside which limit L8 is satisfied is solved in full where economic value of equity is the subject, and the result is reproduced here rather than worked again. Limit L8 caps the measure at Rs 990 crore in either direction, so the assumption may run from 0.2917 years to 3.0417 years, being from 3.5 months to 36.5 months, a window 2.75 years wide. The bank sits at 0.5 years, a full 0.2083 years inside the near edge, being two and a half months. Two and a half months of assumption is all that stands between a limit reported as comfortably within and a limit reported as breached, and no control test anywhere in the bank measures that distance.

One more collision to name before moving on. At 2.0 years the value effect of plus Rs 240 crore would be reported as 24.2 per cent of limit L8, and Rs 240 crore over Rs 990 crore reduces to eight over thirty three exactly, just as Rs 840 crore over Rs 990 crore reduces to twenty eight over thirty three. The same thirty three that appears in the model inventory as the count of models found in use is a different object entirely. Read the label, not the digits.

Who sets the assumption, and who sets the limit that depends on it?

Follow the decisions rather than the numbers. The asset liability management committee G4, nine members meeting monthly and chaired by the chief executive, sets the behavioural assumptions at this bank, including how long the Rs 36,000 crore of demand repayable balances is assumed to stay. The board risk management committee G2, five members of whom three are independent directors, meeting six times a year, sets every limit L1 to L12 and accepts or refuses every breach, including limit L8. Both bodies are doing exactly the job written into their mandateThe written scope of what a committee decides, which in this bank is the reason the assumption and the limit sit in two different rooms., and neither has done anything wrong.

The problem is that no single paper carries both decisions, so the body that sets the cap has no line of sight to the one input that decides whether the number under the cap is minus Rs 840 crore or plus Rs 240 crore. G2 receives a measure at 84.8 per cent of its own limit and a comfortable reading, and the input that would move it is discussed monthly in a different room by different people looking at a different paper. The number does not travel everywhere either: the market risk committee G7 receives the value at risk position, the backtest and the foreign exchange open position, all of which sit in the trading book, and the banking book measure is not on that list.

What would actually escalate here, and where would it go?

Take the ordinary path first. The value measure runs against limit L8 at 84.8 per cent with Rs 150 crore of headroom. Utilisation above 100 per cent is a live breach, and every breach at this bank goes to G2 to be accepted or refused. There is a worked precedent sitting in the same set: breach B1 on limit L3, sector concentration, first crossed in month 5 at 12.2 per cent against a 12.0 per cent cap and standing at 13.0 per cent at month 12, was accepted by G2 in month 6 as a temporary excess with a remediation plan running to month 18. Accepting a breach with a dated plan is a decision, not a failure to act, and it is what an escalation route is for. At month 12 the three live breaches are B1 on limit L3, B3 on limit L10 and B4 on limit L12, all three of them concentrations, and limit L8 is not among them.

Now take the path that matters at this bank, and notice that no such path was ever built. Nothing in the framework escalates a change in an assumption. A limit escalates an outcome: a measured number crossing a cap. Move the deposit life from 0.5 years to 0.29 years and the outcome crosses the cap and the machinery fires correctly. Move it from 0.5 years to 2.0 years and the number improves to plus Rs 240 crore, at 24.2 per cent of the same cap, and nothing fires at all, even though the bank has just learned that its headline number was on the wrong side of zero. On the income side the same shape holds: appetite clause A2 caps the fall in twelve month net interest income at Rs 360 crore and the bank's worst case of minus Rs 336 crore sits at 93.3 per cent of it. Escalation frameworks watch results. Nobody at this bank is watching the inputs that produce them.

How does anybody outside the bank actually use any of this?

Three readers use these numbers, and they use them differently. An analyst reading a published banking book disclosure has three questions and should ask them in order: which of the two measures is this, what shock is it computed on, and what behavioural life has been given to the demand repayable deposits. Two banks reporting the same headline figure on different deposit assumptions are not reporting the same thing, and the third question is the one that is almost never asked. If the disclosure does not answer it, the honest conclusion is that the figure cannot be compared with anybody else's.

A treasurer inside the bank uses the ladder as a working table rather than a report. The eight rows say where repricing can be added or shed, and the Rs 15,600 crore one year cumulative gap is the handle on the income measure. Someone judging whether to lengthen funding is asking what that would do to RB1 and RB2 and to the duration gap of 0.50 years, in that order.

And a household holds the same exposure in miniature. One salary that resets once a year against a floating home loan that resets whenever its reference does is a positive repricing gap on the liability side of a personal balance sheet. A fixed deposit maturing in eleven months is an RB4 asset. How long a household will really leave a balance in a savings account before moving it is the household version of the assumption that decides the sign of this bank's headline number, and it is just as much a judgement when it is made about oneself.