How to measure Interest Rate Risk in a Banking Book

Interest rate risk in a banking book is measured in seven steps: scope the book, choose which question is being asked, slot every balance by next repricing date, state every behavioural assumption as a number, choose the shock and say whose it is, compute both answers, then test the limit and report the assumption beside the result. Skip step four and nothing after it can be defended.

Every one of those seven steps is obvious on its own. The order is not. Three of the seven exist only because of what goes wrong when they are taken out of turn, and that is the whole reason this is a method rather than a list. A slotting rule decided after the balances are already in buckets produces a table nobody can rebuild. A behavioural judgement stated after the answer has been circulated produces an argument nobody can settle. A result reported without the judgement inside it produces a number that will be quoted for a year by people who never saw what it turns on.

The worked run below is Vindhya Commercial Bank Limited, invented, a mid-sized Indian commercial bank with a balance sheet of Rs 96,000 crore. Every figure in the run belongs to that invented bank. Every shock size, cap and run-off percentage in it is one the bank chose for itself and recorded in its own policy. A figure chosen that way can be compared with another bank's only when both banks state theirs.

Why does one balance sheet produce different answers before a single balance is placed?

The everyday version is the same mechanism at a scale small enough to hold in the head. A household has a home loan whose rate resets every three months and a fixed deposit whose rate is locked for two years. A rate rise moves that household one way or the other depending entirely on which question was asked. Over the next twelve months the loan reprices four times and the deposit not at all, so the monthly outgo rises and the income does not: the household is worse off on cash flow. Asked instead what the whole arrangement is worth today, the two-year deposit has become a below-market asset while the loan has not become a worse liability, so the answer moves the other way. Nothing about the household changed between the two answers; only the question did.

A bank is that household at Rs 96,000 crore, with hundreds of thousands of balances instead of two, and with one extra difficulty the household does not have: a large part of its funding has no contractual date at all. A savings account can be emptied this afternoon and has sat untouched for nine years. Whatever number the bank publishes about rate risk contains a judgement about that balance, and the judgement is not visible in the number. The method exists to make it visible.

Step 1: what goes into the table, and what does not?

Scoping sounds like paperwork and is the step that quietly decides the size of every number after it. Four decisions are taken here and all four are written down: the legal entity; the currency; the book; and the balances that count as rate sensitiveA balance whose rate changes inside the horizon of the table, and therefore one that belongs in it at all. at all. At this invented bank the answers are one entity, rupees, the banking book, and a total of Rs 84,000 crore on each side.

Where does Rs 84,000 crore come from when the balance sheet is Rs 96,000 crore? Rs 96,000 crore less Rs 84,000 crore is Rs 12,000 crore, and that residual is the set of balances whose rate never changes because they carry no rate: cash and balances with the central bank, fixed assets and other assets on one side, and other liabilities and equity on the other. A balance that carries no rate cannot reprice, so putting it in a repricing table would add rupees and no information.

Now the trap, and it is a naming trap rather than an arithmetic one. Three different objects in this bank are each Rs 12,000 crore, and step 1 has to say which one it means. There is the non rate sensitive residual just described. There is Rs 12,000 crore of undrawn committed lines sitting off the balance sheet. And there is Rs 12,000 crore of rate sensitive assets inside bucket RB5. Three unrelated things, one number, and a scoping note that says only Rs 12,000 crore has told the reader nothing.

The two common conventions give different totals, so a second scoping decision here deserves to be visible rather than assumed. The bank's trading book, the held for trading portfolio of Rs 3,600 crore, is measured every day by a different method and against a different limit. One convention lifts it out of the repricing table as well and leaves the asset column at Rs 80,400 crore. Vindhya Commercial Bank does not lift it out: its ladder is drawn on the full Rs 84,000 crore of rate sensitive balances, and the trading book's Rs 3,600 crore sits inside that total. Neither convention is wrong and the difference between them is Rs 3,600 crore of assets. The Rs 3,600 crore is exactly why the choice is a step 1 decision that gets written down rather than a preference somebody carries in their head.

Step 2: which of the two questions is being asked?

Two questions can be asked of one balance sheet and they are not two views of one thing. The first asks what a rate move does to net interest income over the next twelve months. The second asks what it does to the present value of everything the bank holds and owes, over the whole remaining life of those balances. The two questions need different tables, they run over different horizons, and at this bank the same shock moves them in opposite directions.

Return to the household for a moment. The cash flow question is what the monthly payment becomes. The value question is what the whole position is worth if somebody had to buy it today. A person on a tight monthly budget cares almost entirely about the first. A person selling up next year cares almost entirely about the second. Both are rational, and neither answer is a check on the other. A bank asks both because it has to survive twelve months and stay solvent over the life of its book, and step 2 exists so that whoever reads the output knows which question produced it.

Vindhya Commercial Bank asks both, and asks them separately. Asking both is the honest choice and it costs something: two computations, two sets of assumptions and two numbers that will be quoted against each other by people who never learned they answer different questions.

Step 3: which date does every balance get slotted by?

Step 3 places every rupee of the Rs 84,000 crore into a bucket, and it does so by next 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.. Not by maturity. Not by when the cash leaves. By the next date on which the rate applied to that balance changes.

Repricing date, maturity date and cash date come apart constantly. A ten-year floating rate loan matures in ten years and reprices in three months. A twelve-month fixed deposit matures in a year and reprices on the same day, so for that balance the two coincide. A savings account has no maturity date at all and reprices whenever the bank changes its card rate. A table that mixes the three questions is not a table with an error in it, it is a table that cannot be interpreted at all.

The second half of step 3 is the half people skip. The slotting basisThe rule the whole table is built on, written at the top before any balance is placed, because a table whose basis is decided afterwards cannot be rebuilt by anybody. is written at the top of the table before any balance is placed. Not in a covering note, not in a modelling document, not in the head of the person who built it. At the top, on the same sheet the buckets are on. A table whose basis was settled after the balances were slotted cannot be rebuilt by anybody who was not in the room, and in eighteen months nobody will be.

What step 3 produces: the ladder RB1 to RB8

Step 3 run across the whole book gives eight buckets with two columns and a gap. The asset column totals Rs 84,000 crore, the liability column totals Rs 84,000 crore, and because both totals are identical the eight gaps must sum to zero. The zero is a construction fact rather than a finding, and it is worth saying out loud before anybody reads meaning into it.

Step 4: what has to be written down about every behavioural assumption?

Look at the drawing again and one bar dwarfs the rest. RB5 is minus Rs 30,000 crore, and it is that shape because Rs 36,000 crore of current and savings balances went into it. The current and savings balances are repayable on demand. Their contract says today. The bank has slotted them at one to three years, and it has done so because the contract answers a question the table is not asking: contractually they could all leave this afternoon, and observably almost none of them ever does.

Slotting a demand balance at one to three years 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 the required output of step 4., and there is nothing improper about making one. Every bank in the world makes it. The alternative is a table that says all deposits leave today, and no day that has ever happened looks like that. Step 4 does not object to the assumption. Step 4 requires that the assumption stop being a modelling detail and become a record with five columns.

The five columns are: the balance; the treatment; the model that produced it; the committee that approved it; and whether that model has ever been validated. The first four get filled in almost everywhere. The fifth is the one that goes blank, and it is the one that changes how everything downstream should be read.

Two things follow from that last column and both belong in the report itself rather than in a footnote. The validation statusWhether an independent review of a model's fitness for use has ever been performed, which step 4 requires beside the assumption. of model V1 is never. Model V1 also cannot be backtested in the ordinary sense. The quantity it predicts, how long a deposit stays, is observable only over years rather than arriving as a new outcome every morning. Who should validate it, what an unvalidated model should trigger, and how a model inventory is run are questions this method names and hands on to the subject area that holds model governance. The method insists only that the status field is filled in and travels with the number.

Why does one Rs 36,000 crore balance sit in four tables at once?

The reason has to be stated before the four treatments are shown. A reader who meets the second treatment without the reason spends the next hour hunting a reconciliation nobody can produce. Four tables in this one bank treat the same Rs 36,000 crore four different ways because they ask four different questions. One asks when the cash leaves in ordinary conditions. One asks how much of it leaves in a thirty day stress. One asks when the rate on it changes. One asks how long it stays, measured in value terms. Four questions, four answers, and none of the four is a check on any other.

Two of the four cover the same thirty days and are the pair most likely to end up in one committee pack, so they are worth putting side by side in rupees. Treatment A places 5.0 per cent of the balance, being Rs 1,800 crore, in the nearest bucket. Treatment B blends savings of Rs 26,400 crore at an assumed 7.5 per cent, giving Rs 1,980 crore, with current accounts of Rs 9,600 crore at an assumed 40.0 per cent, giving Rs 3,840 crore, for Rs 5,820 crore in total and a blended 16.2 per cent. Rs 5,820 crore against Rs 1,800 crore is 3.23 times as much and a difference of Rs 4,020 crore over the same thirty days, and both are this invented bank's own working numbers. Every run-off percentage in both is the bank's own and none of them is a requirement from anywhere.

Step 5: whose shock is it, and what shape does it have?

A shock has three attributes and all three get written down: a size, a shape and an owner. Vindhya Commercial Bank uses 200 basis points, applied as a parallel shockA rate change applied equally across every maturity, which is a simplification the method names out loud rather than hiding. across every maturity, and it is the bank's own internal scenario. Not a requirement. Not a threshold anybody imposed. A number this bank chose and recorded in its own policy.

Saying whose it is matters more than it sounds. Two banks publishing a rate sensitivity figure on two different shocks are publishing two numbers that cannot be compared, and a reader who assumes a common shock will compare them anyway. Step 5 exists so that whoever reads the output knows whose shock produced it, and it is the cheapest step in the method to do and the easiest to leave out.

Step 6: what gets computed, and in what order?

Four computations, and the order is fixed because each one feeds the next. First the bucket gaps: assets less liabilities in each of the eight buckets. Second the cumulative gapThe running total of the bucket gaps up to a point in time, which is what the income answer is built on.: the running total. Third the income answer, taken from the cumulative gap at one year. Fourth the value answer, taken from the duration gap on the whole book.

The cumulative run through the eight buckets is 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 and zero. The column of bucket gaps is a list. The cumulative curve is a shape, and the shape is where the reading is.

The income answer takes the cumulative gap at one year, being plus Rs 15,600 crore, and applies the shock to it for an average of half a year of remaining time inside that year: Rs 15,600 crore times 2.0 per cent times 0.5 gives plus Rs 156 crore of net interest income over twelve months. Against net interest income of Rs 2,880 crore that is 5.4 per cent. More of this bank's assets reprice inside a year than its liabilities do, so a rate rise helps its income.

The value answer uses the duration gapThe modified duration of the assets less that of the liabilities, used here as a locked number of 0.50 years and never derived.. Rate sensitive assets of Rs 84,000 crore carry a modified duration of 3.00 years and rate sensitive liabilities the same Rs 84,000 crore at 2.50 years, so the gap is 0.50 years. Minus 0.50 times 2.0 per cent times Rs 84,000 crore gives minus Rs 840 crore, being 12.7 per cent of tier 1 capital of Rs 6,600 crore. The same 200 basis point rise adds Rs 156 crore to income and takes Rs 840 crore off value, and a committee shown only one of the two has been shown half the position.

Step 7: how is the limit tested, and what goes beside the answer?

Limit L8 caps the value answer at 15.0 per cent of tier 1 capital, being Rs 990 crore, measured against a 200 basis point parallel move. The answer is Rs 840 crore, so utilisation is 840 over 990, being 84.8 per cent, and the headroomThe distance between the answer and the cap it is measured against, which can be read as a rupee amount or as a percentage of several different inputs. is Rs 150 crore. The 84.8 per cent is the utilisation line, it is correct, and on its own it is not step 7.

Two unrelated things in this bank both read 84.8 per cent, and the difference between them has to be named before going on. The first is limit L8 utilisation. The other is model inventory completeness, at 28 models registered against 33 found in use. The two figures coincide because 840 over 990 reduces exactly to 28 over 33. The coincidence is one of arithmetic and not a relationship between the two facts. A report that says 84.8 per cent without saying which has said nothing.

Headroom can be read three ways and they all agree. The duration gap could widen from 0.50 years to 0.5893 years before the answer reaches the cap. The shock could rise from 200 basis points to about 235.71 basis points. Or the liability duration could fall from 2.50 years to 2.4107 years and widen the same gap. Each of those is 17.9 per cent more than the bank currently has. Three readings, one distance, and none of them is the reading that matters most.

How far can the assumption move before the limit stops holding?

Movement in the assumption is the reading that matters most, and it is why step 7 is compulsory rather than a courtesy. The value answer is built on an assumed deposit life of 0.5 years for the Rs 36,000 crore. Move that assumption by one year and the answer moves by Rs 36,000 crore times 2.0 per cent, being Rs 720 crore. Rs 720 crore is an enormous sensitivity against a headroom of Rs 150 crore.

Walk it out. 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. At 2.5 years it is plus Rs 600 crore. On the deposit life the bank's own repricing ladder implies, its headline interest rate risk number changes sign, and nothing on the balance sheet has moved.

The bandThe range of assumed deposit lives inside which the limit is satisfied, being 0.2917 to 3.0417 years for this bank. inside which limit L8 holds runs from an assumed life of 0.2917 years to one of 3.0417 years, a width of 2.75 years. The bank's 0.5 years sits 0.2083 years, being 2.5 months, from the near edge. And the top of its own repricing bucket, 3.0 years, sits about two weeks of assumed deposit life from the far edge, where the limit would break with the opposite sign. A utilisation figure of 84.8 per cent carries none of that.

What does this method not measure?

A number that arrives without its edges will be asked to answer questions it was never built for, so an honest step 7 ends by saying what it has not touched. The method produces two answers and cannot produce a third.

It stresses nothing: a scenario and a stress are different objects, and the stress method belongs to a different subject. It handles no rate move that is not parallel, and step 5 already said so. It produces one locked income point for a rate fall and no value figure at all in that direction, so there is no downward line to draw. And it cannot be backtested, the sharpest of the four. A measure that cannot be scored against outcomes has to be governed by argument and independent review rather than by counting how often it was right.

Who actually runs this, and what do they do with the output?

Four different people pick this output up and none of them reads it for the same thing. Knowing what each one wants comes before writing the report they will read.

The head of treasury, Devendra Achar at this invented bank, reads it as a position to manage. He is the person who can change the answer, by lengthening or shortening what the bank holds, and the number he acts on is the value answer against its cap, the only one with a limit under it. The asset liability management committee, G4, reads it as the owner of the assumption: it approved the behavioural deposit life, and the sensitivity line is the only part of the pack that tells it what its own approval was worth in rupees.

An analyst at another institution, looking at this bank as a counterparty rather than as an employer, reads it for something different again: not the number but the disclosure around it. A bank that publishes a rate sensitivity figure with its shock, its shape and its deposit life assumption stated is a bank whose figure can be compared with somebody else's. A bank that publishes the figure alone has published something uncomparable, and an analyst who compares it anyway is doing arithmetic on two different things.

The household version holds all the way down and is worth carrying for exactly that reason. A person deciding whether to prepay a home loan is running the same seven steps in miniature: scope, meaning the balances in the decision; question, monthly outgo or lifetime cost; slot, meaning the commitments that actually reprice; assumption, how long they think they will stay in that house, the behavioural judgement everything turns on; shock, how much they think rates might move; compute; and then the honest step, saying out loud that the whole answer rests on the number of years they assumed. The person who writes down the assumed years beside their answer can revisit the decision when life changes, and the person who does not has a conclusion with no way back into it.