The Risk Limit Framework: Cascading Appetite Into Operations

A risk limit framework is the machinery that turns a sentence the board wrote into a number somebody is measured against on a working Tuesday. The framework runs in two directions and has to be read in both. Downward, every appetite clause should reach a limit. Upward, every limit should sit under a clause. At Vindhya Commercial Bank Limited, invented, it is 4 of 8 one way and 4 of 12 the other.

A cascade is not a diagram. A cascade is a claim, and the claim is testable in two directions at once. The claim says that everything the board cares about reaches somebody who is measured on it, and that everything somebody is measured on came from something the board cares about. Read it downward and it usually looks respectable. Read it upward and it usually does not. Reading it both ways, on one bank's own eight clauses and twelve limits, is the whole of this guide.

What is a risk limit framework actually for?

A board writes a risk appetite statement once a year. The statement is a short document, one or two printed sides, and it is written in sentences: the bank will not lose more than this, will not concentrate more than that, will survive this long under its own severe scenario. Nobody in a branch or on a desk can act on a sentence, so the statement is honest and useless at the same time on a Tuesday morning. A branch or a desk can act on a number attached to a measure, with a name beside it. A limit frameworkThe machinery that connects an appetite statement to the numbers people are actually measured against. is the machinery in between, and it exists for one reason: a sentence cannot be breached, but a number can.

Take the household version first. The shape is identical and only the scale is not. A household decides, in as many words, that the school fee will never go unpaid. The fee decision is the household version of a board sentence. The decision is genuinely meant and it changes nothing by itself. The cascadeThe connection running downward from a board sentence to a measured limit, and upward from a limit to the sentence it serves. is what happens next: the sentence becomes a rule that Rs 60,000/- sits in the fee account by the twenty fifth of every month, the person who does the banking checks it, and if it is short they say so at dinner rather than in April. Now there is a number, a measure, a checker and a moment. The sentence has reached the working month. Most households never do this. For them the fee is a crisis and not a line item.

Vindhya Commercial Bank Limited is that household at Rs 96,000 crore. Its board has approved eight appetite clauses, numbered A1 to A8, and its risk function runs twelve limits, numbered L1 to L12, each with a cap, a current reading and a utilisationWhat is running against a limit, expressed as a percentage of it, with anything above 100 being a live crossing. figure at month 12. Which body approves the clauses and which body sets the limits is a separate subject, covered separately. The narrower and harder question is whether the eight and the twelve actually connect, and how anybody would know.

The answer is to count, twice, in opposite directions, stating the denominator each time. Counting twice sounds trivial. The count is not trivial. The two counts on this bank's own sets come out at 50.0 per cent and 33.3 per cent from exactly the same four connections, and an institution quoting one number without the other is quoting the flattering half of its own framework.

What does a cascade sentence look like when it is written down properly?

The unit of a limit framework is not the limit. The unit is the cascade sentenceThe one line that names the clause, the measure, the number and the body that will read it., and the cascade sentence has exactly four parts. The clause it comes from. The measure it is stated in. The number. The body that reads it. A cascade with any one of those four missing cannot be tested by anybody. Most limit frameworks are untestable rather than wrong.

Here is one written out in full from this invented bank. Appetite clause A4 says no single sector exceeds 12.0 per cent of gross advances. Gross advances at month 12 are Rs 58,800 crore, so 12.0 per cent of that is Rs 7,056 crore, and that number is limit L3, read by committee G2 at each of its six sittings a year. Clause, measure, number, reading body. Every part of it is now checkable. The largest sector, infrastructure and power, stands at Rs 7,644 crore, being 13.0 per cent of gross advances and 108.3 per cent of the cap. The sector has been over since month 5. Every one of those statements is checkable by a reader with nothing but this paragraph, and that is the test a cascade sentence has to pass.

Taking a part away shows what each one carries. Without the clause, nobody can say why Rs 7,056 crore exists or whether it is the right size. Without the measure, two teams will compute sector exposure two ways, both convinced they are right, and the argument will happen in the month the limit is crossed rather than in the month it was written. Without the number there is an aspiration, and an aspiration cannot be breached. Without the reading body there is a number nobody looks at until it appears in a post mortem. Each of the four parts makes one of the other three usable.

Reading downward, which of the eight clauses reach a limit?

Downward coverageThe share of appetite clauses that reach at least one limit. follows the way the document was written, and it is the reading everybody does: start at the board sentence, ask what number carries it. Do it on all eight clauses of this invented bank and the count is four.

Four of eight is 50.0 per cent, and that is the number this bank would quote if anybody asked how connected its framework is. The count is not dishonest. A2 really does cascade into L8, the economic value of equity sensitivity limit of Rs 990 crore, and L8 stood at Rs 840 crore at month 12. L8 utilisation is therefore 84.8 per cent. This bank’s model inventory completeness of 28 registered models against 33 found in use is the same fraction to one decimal and a completely different subject, so it is worth saying which 84.8 per cent is meant. A3 cascades into L2 at Rs 3,960 crore, A4 into L3 at Rs 7,056 crore, A7 into L11 at Rs 60.0 crore. Four sentences reached the working month.

What happens to an appetite clause that reaches nothing?

Something specific, and it is worth stating precisely rather than dramatically. An orphan clauseAn appetite clause with no limit beneath it, so nothing reports on it between board sittings. does not stop being true. The board still means it. A bank computes its capital ratio and its non-performing share whether or not a limit exists, so the underlying quantity is still measured somewhere by somebody. The missing element is the carrying number, a number that turns up in an operational report with a cap beside it and a name attached. A movement toward the edge is then noticed by somebody whose job it is to notice.

The consequence is a gap in time. Committee G1, the board, sits 6 times a year in this bank, an interval of 60.8 days and an average wait of 30.4 days from any given moment to the next sitting. No operational number sits underneath clauses A1, A5, A6 and A8 for anybody to read in between, so for those four the wait is the reporting cycle. Nothing is being hidden and nobody is being careless. The board sentence and the working month are simply connected by a document that arrives six times a year rather than by a limit that is read continuously.

Three of those four could carry a limit tomorrow. A1 measures a capital ratio, A5 measures a share of a book, A6 measures a survival horizon, and all three are continuous quantities that a cap can sit on. A8 is different, and the difference is honest rather than sloppy. A8 says there is no tolerance for a breach of a statutory obligation, and that any such breach reaches committee G2 within 5 working days. A8 states a process and not a cap. A number written under it would be a level of statutory breach the board finds acceptable, and setting such a level is precisely what the clause was refusing to do. Some appetite clauses genuinely cannot become a number, and forcing one is worse than leaving it uncascaded.

Reading upward, how many of the twelve limits have a clause above them?

The upward reading is the awkward direction, and almost nobody runs it. Start at the limit instead of the clause. Take L1, the single name exposure limit of Rs 2,640 crore, being 40.0 per cent of tier 1 capital, running at 94.5 per cent against counterparty C1. Ask one question: which sentence in the appetite statement does this number serve? Then do the same for L2, and for the other ten.

The answer is four. L8 serves A2, L2 serves A3, L3 serves A4, L11 serves A7, and the other eight serve no clause in the statement at all. The four connections are the ones counted a moment ago, read backwards, and they produce 4 of 12 rather than 4 of 8, being 33.3 per cent rather than 50.0 per cent. Nothing changed except the denominator, and stating the denominator is the whole discipline here. Upward coverageThe share of limits that sit under an appetite clause. is the number an institution almost never quotes about itself, for the obvious reason that it is the smaller one.

Are the eight orphan limits wrong limits?

No, and this is where the subject is most often taught badly. An orphan limitA limit with no appetite clause above it, which is not necessarily a wrong limit. is usually a perfectly sensible control that arrived from somewhere else: a supervisory conversation, an old incident, a treasurer who wanted a cap on something before it became a problem, a policy written by a team that never read the appetite statement because it was not their document. L5, the trading book value at risk limit of Rs 18.0 crore running at 86.7 per cent, is a good limit. Nobody looking at it would say it should not exist.

Being an orphan does not cost correctness. The cost is the ability to answer one question. If somebody asks why the cap is Rs 18.0 crore rather than Rs 9.0 crore or Rs 36.0 crore, a connected limit answers by pointing upward: it is 12.0 per cent of gross advances because the board said 12.0 per cent of gross advances. An orphan limit has no upward answer, so nobody in the institution can say whether the number is the right size or twice what it should be. The orphan also raises an authority question that a clause with no limit does not raise: somebody is being measured, every month, against a number the board never asked for. The arrangement is not scandalous. The number is just unexamined, and unexamined numbers acquire authority by surviving.

How far does tidying the framework actually get?

Repairing it is the interesting part. A surprising distance can be covered with no new decision from anybody. The move is simple: each orphan limit goes under the orphan clause that already measures the same thing. The mapping below is an analyst’s exercise on an invented bank’s own two sets, and not something the bank did. The case record holds only the four connections already counted. The exercise establishes the place where it stops.

A1, capital, already measures the total capital ratio. L1, single name exposure, is written as 40.0 per cent of tier 1 capital, being Rs 2,640 crore, so it is a capital measure wearing a credit label. L1 goes under A1. A5, asset quality, already measures the non-performing share at 3.0 per cent against a 3.5 per cent clause. L4, the sub-investment grade share limit of Rs 8,820 crore running at 93.3 per cent, is the same book one grade earlier, and that earlier book becomes A5 next year. L4 goes under A5. A6, liquidity, already measures survival under the bank’s own severe scenario at 34 days against a thirty day clause, and three orphan limits feed exactly that: L9, the 1 to 14 day structural gap at 89.3 per cent of its cap; L10, wholesale funding share at 112.8 per cent; and L12, depositor concentration at 120.8 per cent on a Rs 76,800 crore deposit base. All three go under A6.

Five of the eight orphans are now placed, and both readings move a long way. Downward coverage rises from 4 of 8 to 7 of 8, or 50.0 per cent to 87.5 per cent. Upward coverage rises from 4 of 12 to 9 of 12, or 33.3 per cent to 75.0 per cent. Nobody changed a limit, nobody wrote a new clause, nobody asked the board for anything. All that happened is that somebody sat down with two lists and asked, for each row, what it was already measuring. And then it stops dead.

Why can three of the limits not be placed at all?

What does each direction of the check catch that the other cannot?

Both readings use the same four connections, so it is tempting to think one of them is redundant. Neither is redundant, and the reason is that the two readings fail differently. Reading downward catches board sentences that never reached the working month; reading upward catches numbers people are measured against every month that no board sentence ever asked for. Each reading starts at the end where its own kind of gap is invisible, so neither can see the other kind of gap.

Run it as a routine and it takes a morning. Put the appetite statement in one column and the limit set in the other. Go down the first column and write, against each clause, the identifier of every limit that carries it; count the clauses with at least one entry and divide by the number of clauses. Then go down the second column and write, against each limit, the identifier of the clause it serves; count the limits with an entry and divide by the number of limits. Two fractions, two denominators, both stated. In this invented bank the answer is 4 of 8 and 4 of 12. Anybody with the two documents can reproduce that in an hour, and reproducibility is exactly what makes it a useful check rather than an opinion about culture.

The household version of the second reading is the one that stings. Most households can say what they are worried about. Very few can go the other way and name the worry that each standing instruction and each rule they follow was set up to answer. The test bites on a monthly recurring deposit that somebody started nine years ago. The rule is still running, the money still moves, and the reason it was set up may have stopped existing years ago. A rule that has outlived its reason does not announce itself; it just keeps executing. An orphan limit is a rule of exactly that kind, and the upward reading is worth its awkwardness for catching one.

Who actually reads a limit framework, and what do they do with it?

Three different people pick a limit framework up for three different purposes, and watching each of them use it is the fastest way to see what a limit framework is for.

The independent director on committee G2 reads it for authority. She sits six times a year, sets every limit L1 to L12, and accepts or refuses every breach. The two readings give her a question she can ask without any technical preparation at all: of the twelve numbers in front of me, how many did this board actually ask for? Four is an uncomfortable answer, and the discomfort is useful. The count tells her precisely which conversations are about performance against the board’s own statement and which are about somebody else’s judgement that she has been endorsing by signing it off. She does not need to re-derive a single limit to ask that.

Devendra Achar, the head of treasury, reads it for exposure of a different kind. He is the risk owner of breaches B3 on L10 and B4 on L12, both open at month 12, and both of those limits are orphans. When he takes a crossing to G2 he is defending a number against a cap that no board sentence stands behind. The conversation is then harder than it should be in both directions: harder for him to justify the exposure, and harder for the committee to say what refusing would be in service of. Connect L10 and L12 to A6 and the same conversation acquires a spine. The question is then whether the bank still survives thirty days of its own severe scenario, a sentence the board wrote and meant.

The credit analyst at another institution, looking at this bank from outside as a counterparty, reads it for shape. She cannot see the limits at all, but she can see the appetite statement if it is published, and she can ask on a call which of its clauses carry an operational limit. An institution that can answer that question quickly, in both directions, is telling her something about how it is run that no ratio on its balance sheet tells her. An institution that has never computed the upward reading will not be able to answer at all, and the pause is the information.

What can a limit framework not do?

Three things, and every one of them is oversold somewhere. First, a cascade decides nothing. A cascade records which board sentence a number serves. The cascade does not choose the number, does not approve a breach, does not set a remediation date and does not decide who is answerable. All of that sits with people and committees, and a perfectly drawn framework changes none of it.

Second, connection says nothing about size. L3 is connected to A4 in the most direct way possible: the clause says 12.0 per cent of gross advances and the limit is 12.0 per cent of gross advances, being Rs 7,056 crore. The match establishes that the cap is faithful to the sentence. The match establishes nothing about whether 12.0 per cent was the right sentence to write about a bank with Rs 58,800 crore of gross advances and Rs 7,644 crore in one sector. Faithfulness and wisdom are different properties, and a cascade can only ever check the first.

Third, and this is the one worth ending on, a complete cascade is not a safe bank. Three limits are in breach at month 12: L3 the sector concentration limit at 108.3 per cent, L10 wholesale funding share at 112.8 per cent, and L12 depositor concentration at 120.8 per cent. L3 is one of the four limits that does sit under a clause. L3 has been over its cap since month 5, committee G2 accepted it as a temporary excess in month 6 with a remediation plan running to month 18, and the sector stood at 13.0 per cent of gross advances at month 12 against 12.2 per cent when it first crossed. Being connected to the appetite statement did not shrink the exposure by one rupee; it only made it possible to say exactly which board sentence was being missed. Naming the missed sentence is worth having. Naming it is not the same as control.