Market Risk: The Exposures a Balance Sheet Carries to Prices

Market risk is what a balance sheet loses when a price moves against it. Vindhya Commercial Bank Limited, invented, carries a Rs 3,600 crore trading book measured at Rs 15.6 crore of value at risk a day, and Rs 84,000 crore of rate sensitive positions whose value falls Rs 840 crore under its own 200 basis point scenario. Two books, two measures, and both figures are the bank's own.

Hold on to the shape of that answer. A great deal of what goes wrong in this subject goes wrong in the gap between its two halves. One measure is small, precise, produced every morning and looked at by six people once a month. The other is large, coarse, produced against a single made-up rate move, and settled once a period by a different committee. The two are measuring one institution against one interest rate, and they disagree by a factor of more than fifty. Neither is a mistake. The two measures are answers to questions that were never the same question.

What is market risk actually asking, and what is it not asking?

Market riskThe loss a position takes when a market price or rate moves against it, whether or not any counterparty fails. asks one question and refuses another. The question it asks is: what is this position worth now that the price has moved? The question it refuses is: will the other side pay? Whether the other side will pay is a real question, it is measured with great care, and it belongs under credit risk. Market risk asks what a position is worth when a price moves, and it asks that even when every counterparty is perfectly good for the money.

The separation is easier to feel in a household than on a balance sheet, so start there. Suppose a lender has advanced Rs 2,00,000/- to a cousin who has never missed a repayment in his life. Repayment is settled, and settled well. Now suppose the loan runs at a fixed rate for five years and rates in the market rise sharply next month. Nothing about the cousin has changed. The holder is now locked into receiving less than the going rate for another four and a half years, so the loan the lender holds is worth less than it was. Not a rupee of repayment has been lost. Value has been lost, and it was lost to a price rather than to a person.

The household case is the whole of it in miniature. A bank is doing the same thing in Rs 96,000 crore rather than Rs 2,00,000/-, and across thousands of positions at once rather than one. The counterparties are fine. The prices moved. Something is worth less. The moment a loss no longer requires somebody to fail, the subject is market risk.

Which market variables actually reach a balance sheet?

Four of them, and only one of the four goes anywhere near a dealing room, so it is worth being precise about which part of the bank each one touches. The first is the interest rate, and it is by a wide margin the largest of the four in this invented bank. The loan book, the deposit book and the investment book are each a promise to pay or receive an amount of money at a date, and the worth of such a promise moves when rates move, so the interest rate reaches all three at once.

The second is the exchange rate. At Vindhya Commercial Bank Limited, invented, it reaches five currency positions numbered FX1 to FX5, and one net investment of Rs 480 crore in a single overseas branch. The third is the price of a traded instrument itself, and this is the one that reaches the Rs 3,600 crore of securities the bank holds in order to trade them. The fourth is the least obvious, and it is the one that produced this bank's only value at risk limit breach of the year: the spread between two things that were expected to move together, and then did not. Three of the four variables reach parts of the balance sheet nobody would describe as trading, and market risk is mostly what happens in those three.

The fourth deserves a sentence of its own. An experienced reader is caught there more often than anywhere else. In month 3 of this invented bank's year, two government bond maturities that the bank's model had been treating as offsetting each other widened apart. Nothing defaulted. No single price collapsed. The two prices simply stopped moving in step, and a position that had been reported as nearly flat turned out not to be. The widening apart is breach B5, and the point to carry away is that a hedge is a claim about a relationship, and relationships are themselves a market variable.

Why does one bank carry this exposure in two places at once?

Because a bank does two different things with securities and rates, and it does them for different reasons. The bank holds a small book in order to trade it, buying and selling to make a margin on the movement. And it runs a very large book in order to be a bank at all: taking deposits, making loans, and holding investments it intends to keep. Both books move when rates move. Only one of them is anybody's idea of trading.

The trading bookThe positions an institution holds in order to trade them, marked to market and measured daily. At this invented bank it is the held for trading book of Rs 3,600 crore and nothing else. at Vindhya Commercial Bank Limited, invented, is Rs 3,600 crore, being 3.75 per cent of total assets of Rs 96,000 crore. The trading book carries a measured figure every morning, a cap in the form of limit L5 at Rs 18.0 crore, a formal test of the measure against what actually happened, and a monthly seat at committee G7. The banking bookEverything else the institution holds to run its business, including the loan book and the investments it does not intend to trade. carries Rs 84,000 crore of rate sensitive positions. The banking book gets one measure against one internal scenario, and it depends on a behavioural assumption set by a different committee. The present value it predicts is not observable day by day, so the banking book measure cannot be tested against realised outcomes at all. The book that gets a number every morning is one twenty-third the size of the book that does not.

The everyday version is a household with a small share portfolio and a large home loan. The number is there and it moves, so the portfolio is checked on a phone most evenings. The home loan is a far larger exposure to the same interest rate, it is checked roughly never, and when it does move it moves by a multiple of anything the portfolio does. Attention follows the number that is easy to see, and the number that is easy to see is rarely the one carrying the exposure.

What is in the trading book, and what is deliberately kept out of it?

This is where most readers acquire their first wrong idea, and it is worth being blunt about it. The investment book at Vindhya Commercial Bank Limited, invented, is Rs 26,400 crore. The investment book splits three ways: held for trading Rs 3,600 crore, available for sale Rs 8,400 crore, and held to maturity Rs 14,400 crore, and those three add to Rs 26,400 crore exactly. The trading book for market risk measurement in this invented case is the held for trading book of Rs 3,600 crore and nothing else. The remaining Rs 22,800 crore, being 86.4 per cent of the investment book, sits in the banking book alongside the loans and is measured by the rate measures instead.

Notice what that sentence is and is not. The classification is not a fact about a bond. The same security, bought on the same day at the same price, sits in one book or the other depending on what the bank intends to do with it and how it has classified it. The classification is a decision, recorded, with consequences that run all the way through to which limit the position consumes and which committee argues about it. A reader who assumes that classification follows automatically from the instrument has missed the one place where a bank's own judgement enters the arithmetic before any arithmetic happens.

What does each market risk measure claim, and what can it not see?

There are four kinds of measure in ordinary use, and the fastest way to stop confusing them is to write down what each one claims in a single line. Not how it is built, but what it claims. Each measure has a treatment of its own under its own name, so the table below is a map rather than a lesson in any one of them.

The first is the open positionThe exposure itself, unhedged, to a market variable. It exists whether or not anybody measures it. itself, and it is not a model at all. The open position is a statement of how much exposure is there. The five currency positions of this invented bank aggregate to Rs 192 crore against limit L7. The second is the sensitivity measureA number produced by moving one market variable and reporting what the position is then worth., and it moves one variable to report the new worth of the position. A sensitivity measure is the workhorse, and it says nothing about how likely the move is. The third is the distributional pair, being value at riskA loss figure a book is not expected to exceed on a stated share of days over a stated horizon, and it says nothing about the days it is exceeded. and expected shortfallThe average of the losses beyond a stated cut-off, which is a different question from where the cut-off sits., and both put a rupee figure on a bad day. The fourth is the pair used on the banking book, one asking what a rate move does to twelve months of income and one asking what it does to the value of everything held.

Read down the third column and the shape of the subject appears: every measure on the list is defined as much by its blind spot as by its claim. A bank therefore runs several measures rather than picking a favourite, and a committee shown one number has been shown one answer to one question.

Where did the habit of one number for traded risk come from?

The habit of one number for traded risk is so settled that it now looks inevitable, and it is not. Before a single figure was workable, each desk described its own exposure in its own units: so many bonds of such a maturity, so much of one currency, so many contracts. Every description was accurate and none of them added up. A senior person asking how much traded risk the institution as a whole was carrying got a stack of papers rather than a number.

The RiskMetrics technical document of 1994 changed that by publishing two things together: a method for turning positions into one loss figure, and a data set to run the method on. The idea of a percentile was old. The difference came from publishing a workable method alongside the data needed to use it. Within a few years the single firm-wide figure was the ordinary way traded risk was reported. Peter Bernstein tells the longer story of how measuring risk became possible at all in Against the Gods, 1996, and it is worth reading for how recent all of this is.

What does this bank's market risk limit set actually look like?

Four limits out of the twelve this invented bank runs, and each of the four is measured on a different kind of object. The difference between the four objects is easy to skate past, and it matters more than the numbers. Limit L5 caps a distributional measure. Limit L6 caps a realised loss accumulated through a month. Limit L7 caps an aggregated position. Limit L8 caps a change in value under a scenario. Four caps, four different objects, and the only thing they have in common is that the board risk management committee G2 set every one of them.

Every one of those caps is this invented bank's own decision, recorded in its own policy and set by its own board committee. None of them is a requirement from anywhere. The cap and the utilisation are printed together throughout: a percentage on its own invites a reader to treat the denominator as a standard, and it is not one.

Who sees these numbers, and how often do they see them?

Two committees carry the market risk load at this invented bank, and they carry different halves of it. The market risk committee G7 has six members, meets monthly, and receives the value at risk position, the test of that measure against realised outcomes, and the open currency position. The asset liability management committee G4 has nine members, meets monthly, is chaired by the chief executive, and sets the behavioural assumptions on which the banking book measure depends. The board risk management committee G2 sets every one of the twelve limits and decides what happens when one is passed.

Notice that the assumption and the limit it decides the answer to are set by two different bodies, so no single paper in this invented bank carries both. Who should see what, and what a governance structure does about a gap like it, is covered under risk governance.

What did the twelve months actually look like at this bank?

Compressed into one paragraph, the year reads like this. On the trading book the measure was passed by a realised loss on seven days, numbered X1 to X7, against roughly two and a half such days expected across two hundred and fifty. The measured figure itself went over the Rs 18.0 crore cap of limit L5 on two days in month 3, breach B5, and positions were reduced. The currency position went over the Rs 240 crore cap of limit L7 for one day in month 9 after a customer deal was booked after the cut-off, breach B2, and it was squared the next morning. Both of those breaches are closed. On the banking book the headline reading finished the year at Rs 840 crore, being 84.8 per cent of the Rs 990 crore cap of limit L8, and it was never passed.

A limit breach and a backtesting exception look similar in a summary and they are not the same thing at all. A limit breach is a measured number going over a cap the bank set. A backtesting exception is a realised loss going over the number the measure produced that morning. One is the control failing, the other is the measure failing, and this invented bank had both in month 3 on different days. Breach B5 was days 21 and 22. Exceptions X2 and X3 were days 14 and 15. A week apart, same month, and merging them would hide two separate faults behind one story.

What happens to income and to value when the same rate moves?

Here is the part of this subject that surprises careful readers, and it is worth slowing down for. The banking book at this invented bank produces two answers to one rate move, and the two answers have opposite signs. Both are correct. The two answers are not two attempts at the same calculation.

The income answer comes from the repricing gapThe difference between assets and liabilities repricing inside one time bucket, which is what makes income move when rates do.. More of this bank's assets reprice inside a year than its liabilities do, so the one year cumulative gap is plus Rs 15,600 crore. When rates rise, those assets start earning more before the funding starts costing more, and twelve months of net interest income go up. On the bank's own 200 basis pointOne hundredth of one percentage point, and the unit every interest rate move in this case is stated in. scenario, applied to that gap for an average of half a year remaining, income rises by Rs 156 crore.

The value answer comes from duration. The assets have a longer modified durationA locked input in this case, used as a number and never derived here, that turns a rate move into a value change. than the liabilities funding them, 3.00 years against 2.50 years, so the gap is 0.50 years on Rs 84,000 crore. When rates rise, the present value of the assets falls further than the present value of the liabilities, and the difference lands on the economic value of equityWhat a rate move does to the present value of everything on both sides of the balance sheet, expressed as a change in the value of equity.. The same 200 basis point rise takes Rs 840 crore off it, which is 84.8 per cent of the Rs 990 crore cap of limit L8.

The same shock adds Rs 156 crore of income and removes Rs 840 crore of value, and a committee shown only one of the two has been shown half the position. The everyday version is a household that switches from a fixed rate deposit to a floating one just before rates rise. Next year's interest income goes up, and the gain is real. The value of what the household holds, if it had to sell today, went the other way, and that loss is equally real. Two true statements about one decision.

Two notes on that table. The Rs 990 crore cap is reached exactly at 235.7 basis points, and because the control moves in whole basis points, 236 is the first step past it, and the row therefore reads Rs 991 crore rather than Rs 990 crore. And the ratio between the two answers never changes: 4.2 divided by 0.78 is 5.38, at fifty basis points, at two hundred and at four hundred. Both are straight lines through the same origin, so the value answer is 5.38 times the income answer everywhere on this table.

Where do these standards come from, and what actually binds an Indian bank?

Think about how a building gets put up in an Indian city. There is a model code, written carefully by people who study structures for a living, and there is the municipal rule that decides whether a plan is sanctioned. The model code is where the thinking came from. The municipal rule is what stops the concrete. Somebody who quotes the model code at the sanctioning desk has named the right ideas and answered the wrong question, and will be sent away to read the rule that actually applies.

Market risk works exactly that way, and this is the one habit worth building at the start of a sequence of eighteen. Naming where a standard came from and naming what actually binds are two separate acts, and performing only the first is the confident and common error. The Bank for International Settlements, at bis.org, publishes the Basel market risk framework, the interest rate risk in the banking book standard, the standardised interest rate shocks, the outlier test, the shorthand method for aggregating an open currency position, and the traffic light approach for counting realised losses against a measure. The Basel documents are the origin, the place where the reasoning was worked out and where to look to understand why any of it is shaped the way it is.

The Reserve Bank of India, at rbi.org.in, sets what an Indian bank must actually do. Which book a position is allowed to sit in. Which measurement approach may be used. Which figures must be computed, and how often. Which of them must be reported, and to whom. How much capital must be held against the result. And from what date each of those applies. Vindhya Commercial Bank Limited is an Indian bank, invented, so the second list is the one that governs it and the first is the one that explains it. A reader who can only recite the first has learned the subject and not the job.

Every figure used here belongs to one invented bank and was recorded in that bank's own policy by its own committees. The 200 basis point move used throughout is this invented bank's own internal scenario and is not a requirement from anywhere. So is the Rs 18.0 crore cap of limit L5, so is the Rs 990 crore cap of limit L8, and so is the choice to measure value at risk over one day at 99 per cent. The binding numbers move, so they are read at the two sites named above.

Who actually reads these numbers, and what does each reader want from them?

One pack leaves the risk function every month at this invented bank. The pack carries a small number of figures, and four quite different people open it looking for four quite different things. A measure only means something once it is clear who is going to act on it.

Start with the person closest to the position. Devendra Achar, an invented head of treasury at this bank, reads the pack the way a driver reads the fuel gauge before a long drive: not to admire the number but to work out what he can still do. The trading book measure sits at Rs 15.6 crore against the Rs 18.0 crore cap of limit L5, so there is Rs 2.4 crore of measured headroom before a cap the bank set itself is reached. The aggregated currency position sits at Rs 192 crore against limit L7's Rs 240 crore, leaving Rs 48 crore. A limit reader is not asking how large the risk is, but how much more of it a decision this morning is allowed to add. Headroom is a different reading of the same numbers, and it is the reading that governs behaviour.

Second, somebody lending money to this bank, or placing a large wholesale deposit with it. A wholesale lender does not care about the headroom at all. Such a lender wants to know how much of the result comes from one desk and one currency, and whether the figure on the paper is measured on the part of the balance sheet that could actually hurt them. Reading Rs 15.6 crore and stopping there tells them about Rs 3,600 crore of a Rs 96,000 crore institution. A lender who takes the trading measure as the market risk of the bank has been shown 3.75 per cent of the balance sheet and told it was the whole of it. The figure they actually need is the one on the other Rs 84,000 crore, and that figure is minus Rs 840 crore of value under this bank's own 200 basis point rise, being 84.8 per cent of the Rs 990 crore cap of limit L8.

Third, a board member. The job from that seat is not arithmetic, it is noticing what is missing. The same 200 basis point rise produces two answers here, plus Rs 156 crore of income over twelve months and minus Rs 840 crore of value, and they point in opposite directions. A board member who is handed only one of them has been shown half the position, and the half they were shown was chosen by somebody. The right question from a board seat is not what is this number, it is what is the other number and who decided I would not see it.

Fourth, and this is the reader nobody puts on the distribution list, the depositor. A schoolteacher with Rs 4 lakh in a term deposit at this invented bank reads none of these figures, receives none of these packs, and is exposed to every one of them through the institution holding her money. Nirjhar Industries Limited, invented, the bank's largest single-name borrower at counterparty C1, is a rupee borrower, so market risk reaches this bank through the rate on that loan and the rate on the deposits funding it rather than through anything that name does. The exposure does not require anybody to be watching it. The control apparatus exists precisely for that reason, and a limit nobody reads is not a control.

What is the commonest way this subject goes wrong on a first reading?

What has been established, and what comes next?

The subject began as a word and ends as a map. Market risk is the loss a position takes when a price moves against it. Market risk asks that question even when every counterparty is perfectly good for the money, and one sentence is all that separates it from the credit question. Four market variables reach a balance sheet: interest rates, exchange rates, the price of a traded instrument, and the spread between two things that were expected to move together. Only one of those four stops at a dealing room, and even that one does not stay there.

The classification decision matters more than it looks. The investment book of this invented bank, Rs 26,400 crore, splits into held for trading Rs 3,600 crore, available for sale Rs 8,400 crore and held to maturity Rs 14,400 crore, and only the first row is the trading book for measurement. The other Rs 22,800 crore sits in the banking book alongside the loans, and the interest rate block therefore reaches much further than the daily measure does. Which book a position sits in is a decision made about the position and not a fact about the asset, and that decision is what determines which measure ever sees it.

The four caps this bank set itself have also appeared. Limit L5 caps a distributional measure at Rs 18.0 crore and runs at 86.7 per cent. Limit L6 caps a month to date stop loss at Rs 30.0 crore and runs at 28.0 per cent. Limit L7 caps an aggregated currency position at Rs 240 crore and runs at 80.0 per cent. Limit L8 caps a change in value at Rs 990 crore and runs at 84.8 per cent, that utilisation being the Rs 840 crore value effect measured against that cap. Four caps, four different objects measured, and every one of the four is the invented bank's own number rather than anybody's requirement.

And there is the year. Seven exceptions X1 to X7 against about 2.5 expected in 250 days, and that count triggered this bank's own escalation at five and its own model review at seven. One closed limit breach on the traded measure, B5, in month 3. One closed currency limit breach, B2, in month 9. A headline banking book number sitting at 84.8 per cent of its cap and never breached all year. Nothing on that list is a scandal, and all of it together is a picture of an institution whose largest market exposure is the one with the fewest controls on it.