IRRBB vs Market Risk: The Banking Book and the Trading Book

The two measures are not two versions of one thing. Traded market risk measures a Rs 3,600 crore book over one day at Vindhya Commercial Bank Limited, invented, and reports Rs 15.6 crore. Interest rate risk in the banking book (IRRBB) measures Rs 84,000 crore over twelve months and a lifetime of value, and reports plus Rs 156 crore and minus Rs 840 crore. Different books, horizons and measures.

One fact sits under the whole comparison, easy to say and surprisingly hard to accept. Whether a position sits in the trading book or the banking book is a decision recorded about that position, tested against written criteria, rather than a property of the thing itself. The same government security can sit in either book, at the same bank, on the same morning, depending only on why it was bought. Every difference drawn below runs downstream of that single decision.

Think about a shop that has a delivery van. If the shop bought the van to run its deliveries, the van is equipment: nobody reprices it every evening, and what it would fetch on the second hand market is somebody else's problem until the day it is actually sold. If the same shop bought three identical vans to resell at a margin, those three are stock: their market price this week is the whole business, and a fall in it is a loss now. Same vehicle, same street, same registration papers. The intention recorded when each van was bought is what differs, and that intention decides which questions the shop has to answer about it every week. A bank splits its balance sheet on exactly that logic, and the two questions on either side of the split get two different answers from two different measures.

Both sides need defining in full first, each with its own book, its own arithmetic and its own machinery, before any contrast between them means anything.

What does traded market risk measure at this bank?

Traded market risk measures one book and one book only. At Vindhya Commercial Bank Limited, invented, the investment portfolio comes to Rs 26,400 crore and splits three ways: held for tradingThe classification that puts a position into the trading book at this invented bank, covering Rs 3,600 crore of its investments and nothing else. Rs 3,600 crore, available for sale Rs 8,400 crore, and held to maturity Rs 14,400 crore. The trading bookThe positions an institution holds to trade, classified as such against written criteria at the moment the position is taken. is the held for trading slice and nothing else. The other Rs 22,800 crore of investments, being 86.4 per cent of that portfolio, sit in the banking bookEverything an institution holds to run its business rather than to trade, including its loans, its deposits and the investments it does not intend to sell., and no traded measure at this bank goes anywhere near them.

On that Rs 3,600 crore the bank runs a distributional measure every morning: value at risk at one day and a 99 per cent confidence levelThe share of days on which a stated loss figure is not expected to be exceeded. Choosing it is one of the decisions that makes a distributional measure mean anything at all., by historical simulation over five hundred days. The month 12 reading is Rs 15.6 crore, and that Rs 15.6 crore is a one day trading loss measure rather than any of the other figures at this invented bank that happen to share those digits. The Rs 15.6 crore runs against the bank's own limit L5 of Rs 18.0 crore, so limit L5 utilisation stands at 86.7 per cent. A second cap sits beside it: limit L6 holds month to date trading losses to Rs 30.0 crore and stands at Rs 8.4 crore, being 28.0 per cent of its own cap. Everything on the traded side is built for a book that could be sold this afternoon, so its unit of time is a single day and its unit of control is a cap that gets tested again tomorrow morning.

Two more things belong to the traded side and both matter later. The traded measure was formally backtestedA comparison of a measure against what actually happened, over a stated number of days. One of the two measures can have one and the other structurally cannot. over 250 observation days, producing seven exceptions numbered X1 to X7 against an expectation of about 2.5, so exceptions ran at 2.8 per cent of days against an expected 1.0 per cent. And the whole package goes to the market risk committee G7, six members, every month, together with that backtest and the currency position.

What does banking book interest rate risk measure at this bank?

Banking book interest rate risk measures almost everything else. The rate sensitive bookThe Rs 84,000 crore of assets and Rs 84,000 crore of liabilities at this invented bank whose interest rates reset at some future date. Cash, premises and equity carry no resetting rate. at Vindhya Commercial Bank Limited, invented, is Rs 84,000 crore of assets against Rs 84,000 crore of liabilities. On the asset side that is the whole Rs 26,400 crore investment portfolio plus the Rs 57,600 crore of net advances, tying exactly to Rs 84,000 crore. The Rs 12,000 crore left out is cash and balances with the central bank, balances with other banks and money at call, premises and other assets. None of those carries a rate that resets.

The rate sensitive book produces not one answer but two, and the two answers come off two different sets of machinery. The first is a repricing table of eight buckets, RB1 to RB8, slotting every balance by the date its rate next changes. The running total through the one year point is a gap of plus Rs 15,600 crore, and the bank's own 200 basis point rise applied to that gap for an average half year remaining gives plus Rs 156 crore of net interest income over twelve months. The second is a duration computation: Rs 84,000 crore of assets at a modified duration of 3.00 years against Rs 84,000 crore of liabilities at 2.50 years, a gap of 0.50 years, and the same 200 basis point rise takes minus Rs 840 crore off economic value. The same shock adds Rs 156 crore to income and removes Rs 840 crore of value, both answers are right, and neither of them is a traded number.

The minus Rs 840 crore runs against the bank's own limit L8 of Rs 990 crore, so limit L8 utilisation stands at 84.8 per cent. Naming the object matters. The figure 84.8 per cent also turns up elsewhere at this invented bank, attached to a completely unrelated count of models. The behavioural assumptions the whole computation depends on, including how long balances with no maturity date are assumed to stay, are set by the asset liability management committee G4, nine members, meeting monthly.

Two full definitions are now in place, and they have almost nothing in common except the word risk. One is a book that could be sold today, measured by what a bad day looks like. The other is a balance sheet that cannot be sold at all, measured by what a rate move does to a year of income and to a lifetime of value. Six differences follow, and every one of them is a consequence of the classification decision rather than a separate design choice somebody made.

So what actually separates the two?

Six things, and it is worth having them all on one screen before any of them is unpacked. The six are the book each one measures, the horizon each one uses, the measure each one runs, how each one shows up in the accounts, the committee that receives each one, and whether either can be checked against what actually happened. Because all six fall out of the single decision about which book a position was put in, read the table below as one column of consequences rather than as six independent design choices.

Which book does each one measure, and how big is each?

Size is the axis people underestimate. The trading book is Rs 3,600 crore, being 3.75 per cent of total assets of Rs 96,000 crore. The rate sensitive book the banking book measure runs on is Rs 84,000 crore. The trading book is not a separate pile sitting beside the rate sensitive one. The trading book is inside it, so the arithmetic has to be done carefully. Rs 26,400 crore of investments plus Rs 57,600 crore of advances is Rs 84,000 crore exactly, and the held for trading Rs 3,600 crore is part of that Rs 26,400 crore.

So the honest way to size the two is as shares of one book. The trading book is 3,600 over 84,000, being 4.3 per cent of the rate sensitive asset side. Everything else on that side, Rs 80,400 crore, is 95.7 per cent. The 4.3 per cent carries a measure every morning, two daily caps, a formal backtest and a monthly committee, and the 95.7 per cent carries one measure against one internal scenario. That is not a criticism of anybody. A book that can be sold in an afternoon needs a measure that can keep up with an afternoon, and a book that reprices over years does not. But a reader who has only ever seen a bank's market risk pack has seen the machinery attached to a twenty third of the balance sheet.

What horizon does each measure use, and why does that change everything?

The traded measure looks one day ahead. The book can be sold tomorrow, and whatever it is worth tomorrow evening is a fact rather than a projection. So the horizon is one day precisely, not one day as an approximation of a short period. The banking book measure looks two distances at once. A planning year runs twelve months, so twelve months is the horizon for the income answer. A present value contains every remaining cash flow on both sides, so the whole remaining life of the book is the horizon for the value answer.

Horizon is not a detail. The horizon decides what counts as a bad outcome, what counts as evidence, and how long the wait runs before it is clear whether the measure was right. A one day measure is wrong or right within twenty four hours and can be scored two hundred and fifty times a year. A measure whose subject is the present value of a book stretching out over a decade cannot be scored at all in any comparable way, and that single fact produces the sixth axis below. Changing the horizon changes not just the size of the number but whether the number is the kind of thing that can ever be checked.

Which measures belong to which, and can they be swapped?

Not at this bank, and the reason is that each measure needs an input the other book cannot supply. Value at risk of the kind used here is built by taking five hundred days of realised price moves on the same positions and reading a percentile off the resulting distribution. Historical simulation needs daily prices for the positions in question. The banking book's largest single item is a deposit balance that has no market price at all, so there is no series to build a distribution from and no value at risk figure for the banking book exists in this case.

Run it the other way and it fails just as cleanly. The economic value computation needs a modified duration for the positions it is applied to, and the case carries a blended duration of 3.00 years across the whole Rs 84,000 crore asset side but no separate duration for the Rs 3,600 crore trading book. So no economic value figure exists for the trading book either. Two books make four possible measure and book pairings, and this case supplies numbers for exactly two of them. Nothing shows more cleanly that the two measures are not interchangeable. That gap is what makes the failure set out below bite.

Why can a value change of Rs 840 crore be real and invisible at the same time?

Because the two books are measured differently in the accounts, and that is the fourth axis. The trading book is marked to marketValued at what the position would fetch now. A price move then shows up straight away rather than being spread over the years the position is held.: what it would fetch today is what it is carried at, so a bad morning arrives as a loss in the accounts on the morning it happens. Nobody has to be persuaded that it was real. The loss is in the numbers.

The banking book is not carried that way. A loan made at a fixed rate three years ago is still carried on the terms it was made on, and a rise in rates does not produce an entry anywhere saying that loan is now worth less than it was. The minus Rs 840 crore of economic value change at Vindhya Commercial Bank Limited, invented, is a change in the present value of future cash flows, and it appears in no profit and loss account and on no balance sheet. The minus Rs 840 crore surfaces in exactly one place, a risk pack. The banking book measure exists precisely because the accounts will not report this number, so if nobody computes it and nobody caps it, nobody in the institution ever sees it.

Being invisible in the accounts is not the same as being unreal. Rs 840 crore is 12.7 per cent of this invented bank's tier 1 capital of Rs 6,600 crore, and that is the size of the thing nobody books. The accounting treatment of positions in each book, meaning how each is measured and where any movement is presented, belongs to financial reporting and is covered separately.

Who receives each number, and how often?

Two books, two rooms. The market risk committee G7, six members, meets monthly and receives the traded position, the backtest and the currency position. The asset liability management committee G4, nine members, meets monthly and does something rather different: it sets the behavioural assumptions that the banking book measure depends on, including how long balances repayable on demand are assumed to stay.

Notice the asymmetry. Skimming past it is easy. One committee is a recipient and the other is an author. G7 is shown a number that has already been computed and decides what to do about it. G4 decides an input, and the input it decides is the one the banking book answer is most sensitive to. Meanwhile the cap that answer runs against, limit L8 at Rs 990 crore, is set by a third body altogether, the board risk management committee G2. The room that sets the assumption and the room that sets the limit the assumption decides the answer to are not the same room. The split is a structural feature of how mandates are drawn rather than anybody's mistake. How that gap is governed belongs to the risk governance material and is named here rather than worked.

Which of the two can be checked against what actually happened?

Only one, and this is the axis that most cleanly proves the two are different kinds of object. The traded measure predicts a loss on a day. Days arrive one after another, and each morning's measure can be laid beside that evening's realised loss. Done 250 times, that comparison becomes a formal test. At Vindhya Commercial Bank Limited, invented, that test produced seven exceptions numbered X1 to X7 against an expectation of about 2.5, so exceptions ran at 2.8 per cent of days against an expected 1.0 per cent. Whatever conclusion follows from seven exceptions against an expected 2.5, a conclusion was available at all.

The same exercise attempted on the banking book measure fails. The banking book measure predicts that if rates rise 200 basis points, the present value of everything the bank will ever receive and ever pay falls by Rs 840 crore. There is no outcome to set against that, and no date on which to set it. No day settles it. No year settles it. The value it describes is only observable as the book actually runs off over its remaining life, by which time the balance sheet has been replaced many times over and the shock never occurred in that exact shape anyway. The banking book measure cannot be backtested, and that is a property of what it measures rather than a shortage of effort or data. What it gets instead is validation, meaning a review of whether the method and the assumptions are sound, and validation is covered separately in the model risk material.

Are the two reported numbers comparable as shares of their own books?

The comparison as shares of their own books is often attempted, so it is worth killing carefully. Rs 15.6 crore is 0.43 per cent of the Rs 3,600 crore trading book. Rs 840 crore is exactly 1.0 per cent of the Rs 84,000 crore rate sensitive book. Both are now percentages, both are small, and one is a bit over twice the other. The temptation is to say the banking book is running about twice the risk density of the trading book.

The density comparison is not a statement about anything. Turning two numbers into percentages of their own denominators makes them look like the same kind of quantity, and they are not. The first is a one day loss at a 99 per cent confidence level on positions carried at what they would fetch today. The second is a change in the present value of an entire balance sheet under one chosen rate scenario, over the remaining life of every cash flow, resting on a behavioural assumption about how long deposits stay. The two percentages share a symbol and nothing else, and a ratio between them is arithmetic performed on objects that were never in the same units. No bank computes or reports a risk density. The word names the ratio rather than any measure this invented bank runs.

What decides which book a position sits in?

Intent, recorded at the moment the position is taken and then tested against written criteria. Recorded intent is the whole answer. Most readers arrive expecting the answer to be a property of the asset instead. A dealer at Vindhya Commercial Bank Limited, invented, buys a government security at ten in the morning meaning to sell it inside the week. The dealer's intention is recorded, the position is managed by a trading desk against trading caps, and it enters the held for trading book. The treasury desk buys the identical security the same morning, same coupon, same maturity, meaning to hold it until it repays. The treasury desk's intention is recorded too, and the position enters the held to maturity book. One bank, one morning, one instrument, two books. A recorded decision about purpose, tested against written criteria, separates the two, and nothing whatever about the security itself does.

Here is the household version. Two people walk into the same shop on the same afternoon and buy the same gold chain at the same price. The first buys it to wear at a wedding in four months. The second buys it because she thinks the price is low and means to sell it when it moves. The chain is identical. The receipt is identical. But the second person checks the price every morning and feels every rupee of movement, and the first does not look at the price again until the wedding, if then. Nobody would say the two chains are different objects. Everybody would agree the two people have to answer different questions about them. Classification is a statement about why something is held, and why is what decides which questions have to be answered afterwards.

Which is exactly why intent is not left as a private matter. If a recorded intention alone decided the answer, an institution could quietly move a position into whichever book produced the more comfortable number on any given morning. So the tests are written down: whether there is a genuine intention to trade, whether the position can be valued reliably and often enough to be marked, whether it is run by a trading desk under trading caps, how the intent is evidenced, and how rarely a recorded classification may be revisited afterwards. The classification criteriaThe written tests that decide which book a position belongs in. For an Indian bank they are set by the Reserve Bank of India. that actually bind an Indian bank are set by the Reserve Bank of India at rbi.org.in.

What happens to the reported numbers if a position is reclassified?

Now push the idea until it breaks. Suppose Vindhya Commercial Bank Limited, invented, takes its entire Rs 3,600 crore held for trading book and puts it through a reclassificationMoving a position from one book to the other. Reclassification changes what is measured and what is reported without changing anything the institution actually holds. into the banking book overnight. Nothing is sold. No counterparty is called. The same securities are in the same accounts on the same custody statement the next morning. Then what happens to the reported traded number?

The reported traded number goes to zero. Value at risk at this bank is measured on the held for trading book and on nothing else, so a book that is no longer classified as held for trading produces no figure at all. Nothing is left inside the measure's own perimeter, so the Rs 15.6 crore that ran at 86.7 per cent of limit L5's Rs 18.0 crore cap becomes nothing, and limit L5 utilisation becomes nothing. Not one rupee of exposure has left the building, and the headline risk number has vanished.

Taken in slices, the arithmetic is straightforward under one stated assumption. Measured risk falls in proportion to the size of the position. Proportional scaling shows the shape and is not this bank's method. A smaller book is not a scaled copy of a larger one, and this case gives no method for recomputing the measure on a subset. Holding the density at 15.6 over 3,600, being 0.4333 per cent, the reported figure at a reclassified share of t is 15.6 times one less t.

Where do the two standards come from, and what binds an Indian bank?

Two different documents, and this is the last place a reader goes wrong. The Bank for International Settlements at bis.org publishes a market risk framework, and it separately publishes an interest rate risk in the banking book standard. The two documents are not one publication with two chapters, they were not written at the same time, and they do not share a measurement approach. One is built around a traded portfolio that can be revalued daily; the other is built around a balance sheet whose largest liability has no maturity date at all. Treating them as one standard is the single most common way of collapsing the two subjects back into one.

Then comes the second layer, the one that binds. The Reserve Bank of India at rbi.org.in sets what an Indian bank must actually compute, report and hold capital against, separately on each side. An Indian bank therefore has two sets of expectations to follow rather than one, and reading the global document alone gives the shape of a measure but not what any institution in India is required to do with it. The 200 basis point move used throughout is this invented bank's own internal scenario, chosen by that bank.

How does anybody outside a bank actually use this distinction?

The analyst's use is the immediate one. Any bank's disclosures carry a market risk section with a value at risk figure and, somewhere else entirely, an interest rate sensitivity section with an income figure and a value figure. An analyst who reads the first and stops has read the exposure on a small corner of the balance sheet. At Vindhya Commercial Bank Limited, invented, that corner is Rs 3,600 crore of a Rs 96,000 crore balance sheet, being 3.75 per cent of it, and 4.3 per cent of the rate sensitive asset side. The first question a practitioner asks of any risk number in a bank's disclosures is which book it was measured on, and that question is asked before the number is read rather than after.

Now the lender, or anybody extending money to a bank, including a large depositor. The lender cares about whether a rate move hurts. The traded number is one day on a small book, so it will not tell them. The banking book pair will, and the two halves of it point in opposite directions at this invented bank: the same 200 basis point rise adds Rs 156 crore to twelve months of income and takes Rs 840 crore off value. A lender who has seen only the income half has been shown a bank that gains from rising rates. One who has seen only the value half has been shown a bank that loses Rs 840 crore, being 12.7 per cent of its tier 1 capital of Rs 6,600 crore. Both readings come from the same shock on the same balance sheet.

Then the person reading a risk pack from inside. Check what the machinery is attached to before being reassured by how much machinery there is. A daily measure, two caps, a formal backtest and a monthly committee is a great deal of apparatus, and at this bank all of it sits on 4.3 per cent of the rate sensitive asset side. The other 95.7 per cent has one measure against one internal scenario, and the assumption that measure is most sensitive to is set in a different room from the one that sets its cap.

And the household version, where this began. A household running on one salary can watch its monthly grocery bill obsessively. The bill is visible and it arrives every month. The same household may never once ask what happens to its home loan payment if rates rise by two percentage points. The grocery bill is the traded book: small, visible and measured constantly. The loan repricing is the banking book: large, invisible, and only measured if somebody decides to measure it. The most frequently measured book very rarely carries the most exposure. The accounts will never raise the other one, and that silence is why the second measure exists.