How to assess Counterparty Exposure: A Seven Step Method

Seven steps in a fixed order. Each step produces what the next one needs. Settle which legal entities count as one counterparty, convert every arrangement into a figure, net only where an agreement is enforceable, add the potential future exposure, apply collateral to severity, measure against the limit, then record what could not be measured. On C1 that runs Rs 1,680 crore to Rs 2,160 crore to Rs 2.20 crore of expected loss.

Every part this method assembles is already familiar: what a charge over stock does to severity, what a netting agreement does to two contracts pointing opposite ways, what a probability of default is, and how current exposure, potential future exposure and exposure at default differ from one another. The one thing not yet given is the order in which those parts are picked up, and the order is not a filing convenience. The order is the method.

Everything that follows runs on one name at one bank. Vindhya Commercial Bank Limited, an invented lender, has assessed its counterparty C1, the invented Nirjhar Industries Limited, and every rupee figure, assumption and factor below belongs to those two. Each of those factors, haircuts and caps is that bank's own choice rather than a threshold anybody imposed on it, and another bank would set them differently.

What is the order, and why does the order decide the answer?

The shape of the problem, before any arithmetic. A counterparty is not one thing that can be looked up. A counterparty is instead a set of legal entities that somebody has to decide belong together, holding a set of arrangements that arrive in different states of certainty, some of which can be set against each other and some of which cannot, secured by property whose value is a judgement, measured against a cap that was set on one definition of exposure and is often reported on another. Every one of those is a decision, and every decision changes the number that comes out.

The everyday version comes first because the shape is exactly the same. Suppose a lender has lent money to a cousin who runs a small trading business. How much is owed? The first question is whether the loan given to the cousin's brother-in-law for the same shop counts as the same debt, and that decision is the perimeterThe decision about which legal entities count as one counterparty, taken before any figure is added. question. Then what has actually gone out of the lender's hand is counted against what has been promised if the cousin asks. Then the lender remembers that the cousin is owed something in return, and has to ask whether anyone would honour that set-off if things went badly. Only then does the gold the cousin left behind come into it, and only after that does the running total get held up against whatever line the lender privately set. Changing the order of those questions produces a different answer to the same question. The order is the method rather than a matter of taste.

The middle column of that drawing matters more than the right one. Every step needs something that only the step above it can hand over, and none of those handovers is optional. Netting before the entities are settled nets a contract belonging to a company that turns out not to be inside this assessment at all. Dividing collateral into the exposure before the exposure is finished divides it into the wrong denominator. Writing a utilisation before stating what it was measured on produces a percentage that nobody can line up against any other paper about the same name on the same day. None of those three mistakes produces an error message, a mismatch or a failed check: each one produces a number that looks finished.

Which legal entities are one counterparty, and who decides that?

Step EA1 is the only step in the method that adds nothing and changes everything. Step EA1 answers one question: which legal entities are being assessed together as one counterparty. On this name the answer is not obvious. C1 is Nirjhar Industries Limited, a steel and alloys maker. Nirjhar Alloys Private Limited is a wholly owned subsidiary of it and borrows from the same bank, and it is a separate legal person with its own board, its own accounts and its own agreements. The bank reports it inside the group line rather than as a single name, so on the single name list of ten largest exposures it does not appear at all.

Assessed as a single name, C1 carries funded exposure of Rs 1,680 crore, an undrawn committed line of Rs 720 crore and derivative current exposure of Rs 96 crore. The reported total is Rs 2,496 crore, and 1,680 plus 720 plus 96 is 2,496. Assessed as a borrower group, add Nirjhar Alloys Private Limited at funded 660, undrawn 12 and derivative nothing, being Rs 672 crore, and the total is Rs 3,168 crore. The two totals run against different caps: limit L1 on single name exposure is 40.0 per cent of tier 1 capital of Rs 6,600 crore, being Rs 2,640 crore, and limit L2 on borrower group exposure is 60.0 per cent of the same, being Rs 3,960 crore. Both limits are the invented bank's own.

Read the two bars as two different claims about the world rather than as two views of one claim. The upper bar says the bank has one borrower carrying Rs 2,496 crore. The lower one says it has one economic obligor carrying Rs 3,168 crore across two legal persons that share a controlling shareholder, a management and, in all likelihood, a cash position. No arithmetic step later in this method moves the answer by anything close to the Rs 672 crore that this single decision moves it by, and this step involves no arithmetic at all. The size of that move is why the entity decision goes first, and why an assessment that starts by pulling the list of arrangements has already answered the hardest question by accident.

How does each arrangement become an exposure figure?

Step EA2 lists every facilityOne arrangement between the bank and the counterparty, of which a counterparty usually has several. the admitted entities hold and turns each one into a rupee figure. The reason this is a step rather than a lookup is that the arrangements are in three completely different states, and each state needs a different kind of work. ConversionTurning a facility into an exposure figure, which is a reading for what is drawn and a judgement for everything else. is a reading for one of them and a judgement for the other two.

The first state is drawn. C1 has Rs 1,680 crore of funded exposure, meaning money that has already left the bank and is sitting on the borrower's side of the table. The funded balance is read out of the record and nothing is decided about it. The second state is promised. C1 holds an undrawn committed line of Rs 720 crore. The bank has bound itself to provide that money on request, and nobody has asked for it yet. Nobody knows how much of it would be drawn if the borrower were sliding towards default, so the bank applies its own drawdown assumption of 50.0 per cent, giving Rs 360 crore, and 720 times 0.50 is 360. The 50.0 per cent drawdown assumption is the invented bank's own number and it is a choice, not a reading. The third state is contracted: two derivative trades with the same counterparty, one worth plus Rs 132 crore to the bank and one worth minus Rs 36 crore. The two trades need a valuation before they need anything else.

Two of the three states produce a figure that somebody chose, and only the drawn balance produces one that somebody read. Add the two settled parts and the running figure after EA2 is 1,680 plus 360, being Rs 2,040 crore, with the contracts still open. The drawdown assumption is worth pausing on. A committed line that is never drawn costs nothing; a committed line drawn to the last rupee in the month before a default costs everything, and the honest answer sits somewhere between. Halving it is not a discovery about C1. The halving is a policy the bank applies to every name and then reports as though it were a measurement of this one.

When may two contracts be set against each other?

Step EA3 is where the method stops being arithmetic for a moment. Two trades sit against one counterparty. One is worth plus Rs 132 crore to the bank and one is worth minus Rs 36 crore. If the counterparty fails tomorrow, does the bank stand in the queue for Rs 132 crore or for Rs 96 crore? The arithmetic is trivial in both directions. 132 minus 36 is 96, and 132 on its own is 132. The question is which of those two the law would honour, and the answer sits in a document rather than in the numbers.

The bank has an enforceable netting agreementAn agreement that would actually be honoured on default, which is a legal opinion and not a calculation. covering both trades with C1, so the current exposure is Rs 96 crore, a reduction of 27.3 per cent on the gross figure, and 36 over 132 is 0.2727. Without such an agreement it would be Rs 132 crore. A trade that is out of the money gives the bank nothing at all in a default: the administrator collects on it, and the bank still queues for the other one. Nothing in the two values shows which of those two worlds applies, and an assessment that nets because netting is arithmetically available has answered a legal question with a subtraction.

The running figure after EA3 is 2,040 plus 96, being Rs 2,136 crore. Notice how little of that Rs 96 crore is a measurement. The plus 132 and the minus 36 are valuations: model output on a market that moved this morning. The decision to subtract one from the other is an opinion about how a court would read a contract on a day nobody has lived through yet. The netting decision is the second of the three moves in the build that the bank made up rather than looked up.

Why is the add-on computed on the notional and not on the value?

Step EA4 adds the part of the exposure that has not happened yet. The Rs 96 crore is today's value of the position, and a position is not going to sit still until the contract matures. The bank adds an allowance for how far the value could travel between now and then, computed as an add-on factor of 1.5 per cent applied to a notional of Rs 1,600 crore, being Rs 24 crore. The 1.5 per cent is the invented bank's own factor and is used here purely to work the method.

The choice of base is the whole teaching point. Applying the factor to the Rs 96 crore the position is worth today gives Rs 1.44 crore. Worse, a position sitting exactly at zero today would carry an allowance of nothing, and that is a claim that a contract which has not moved yet can never move. The claim is plainly false, and it is false in the direction that hurts. The notional is the only number inside a contract that measures how much is at stake, so it is the only sensible base for an estimate of how far the value can travel. The running figure is now 2,136 plus 24, being Rs 2,160 crore, and that figure is the exposure at default. Check it the other way: funded 1,680, plus half of the undrawn line at 360, plus a derivative exposure at default of 96 plus 24 being 120, and 1,680 plus 360 plus 120 is 2,160.

The build in four moves, and where each one came from

Before going on to collateral, stop and look at what has just been assembled, because the four moves are not four of the same kind of thing. Rs 1,680 crore was read from a record that a third party could in principle inspect. Rs 360 crore came out of an assumption the bank wrote for itself. Rs 96 crore came out of a valuation and a legal opinion. Rs 24 crore came out of a factor the bank set. Three of the four are internal choices, and once they are added together into a single figure the difference between them disappears completely.

Where does collateral enter, and where must it never enter?

Step EA5 is where most readers want the problem to be solved, and it is the step the method is most careful about. C1 has given the bank a charge over inventory and receivables valued at Rs 1,440 crore. Stock and book debts of a steel maker sold quickly by an administrator do not fetch what they are carried at, so the bank applies its own haircut of 35.0 per cent to that valuation, giving eligible collateralCollateral value after the haircut, being what the lender is willing to count. of Rs 936 crore, and 1,440 times 0.65 is 936.

Now the part that matters. CoverageEligible collateral divided by exposure at default, which must be computed on the completed exposure and not on a running figure. is 936 over 2,160, being 43.3 per cent, and it is divided into the completed exposure at default produced by EA4 and into nothing else. Loss given default then falls from the bank's own 40.0 per cent assumption to 40.0 times 1 minus 0.4333, being 22.67 per cent. At internal grade 4 the bank's own one year probability of default is 0.45 per cent, so expected loss is 2,160 times 0.0045 times 0.2267, being Rs 2.20 crore, against 2,160 times 0.0045 times 0.40, being Rs 3.89 crore, with no collateral counted at all. The Rs 936 crore changes what a default costs and does not change what is at risk in one, so the exposure figure stays exactly at Rs 2,160 crore all the way through this step.

The same thing runs the other way, as a reduction of exposure from Rs 2,160 crore to Rs 1,224 crore at an unchanged 40.0 per cent loss given default, and 1,224 times 0.0045 times 0.40 is also Rs 2.20 crore. Both routes are correct arithmetic and both land on the same rupee. The two routes are one answer expressed twice, not two answers, and a paper that shows both without saying which it used has manufactured a disagreement out of nothing. The first route is the one taken here. The exposure figure therefore never moves.

Expected loss also fell by 43.3 per cent, from Rs 3.89 crore to Rs 2.20 crore, and 43.3 per cent is exactly the share of the exposure the collateral covers. The equality is not a coincidence and it is not a check on anything: collateral acts through loss given default, and the arithmetic makes the fall in expected loss equal to the coverage by construction. The equality is worth knowing so that it is never mistaken for a validation.

What no haircut can fix

There is a temptation, once collateral is on the table, to treat the haircut as the dial that decides whether this exposure is secured. The haircut is not that dial, and the fastest way to see why is to imagine the bank being maximally generous with itself. Suppose the haircut were zero, so the full Rs 1,440 crore valuation were counted. Coverage of the Rs 2,160 crore exposure at default reaches 1,440 over 2,160, being 66.7 per cent, and stops. Rs 1,440 crore of property cannot cover Rs 2,160 crore of exposure however generously it is counted, so no haircut anywhere between 0 and 100 per cent makes this collateral fully cover this exposure. Rs 720 crore of the exposure is unreachable by definition.

How is the result measured against a limit without misleading anybody?

Step EA6 puts the answer beside the cap, and it is the shortest step with the largest scope for confusion. Limit L1 on single name exposure is Rs 2,640 crore. There are two entirely defensible figures to put against it. The reported total from the counterparty table is Rs 2,496 crore, or 94.5 per cent of the limit, and 2,496 over 2,640 is 0.94545. The exposure at default this method just built is Rs 2,160 crore, or 81.8 per cent, and 2,160 over 2,640 is 0.81818. The two are 12.7 percentage points apart on one name on one day.

Both are right. The two figures differ because one counts the undrawn line in full and the other counts half of it, and because one carries derivative current exposure while the other carries a derivative exposure at default including the add-on. So step EA6 writes both, and writes each one with its basisWhich definition of exposure a utilisation was measured on, without which the percentage cannot be reconciled to any other paper. in the same line as the percentage rather than in a note at the foot of the paper. A percentage with no statement of what it was measured on is not a conservative figure or an aggressive one, it is an unreconcilable one, and the reader who holds a different paper about the same name on the same day cannot tell whether the two documents disagree or agree.

What should the assessment say about what it could not measure?

Step EA7 produces no number at all, and it is the step most often left out. The assessment has now produced Rs 2,160 crore of exposure at default and Rs 2.20 crore of expected loss, both to the second decimal place, both looking like measurements. Three of the inputs behind them are nothing of the kind, and step EA7 writes each one down as a named gapSomething the assessment could not measure, recorded explicitly, because an assessment silent about its gaps is read as complete. rather than dissolving them into a paragraph of caveats that nobody reads twice.

Frank Knight drew the line this step depends on in Risk, Uncertainty and Profit, published in 1921: a measurable risk, where the distribution is known well enough to be worked with, is a different object from an uncertainty, where it is not. Every one of the three gaps below is on the second side of that line, and the reason for writing them separately is that arithmetic has no way of expressing the difference. Rs 2.20 crore looks exactly as solid whether the inputs behind it were measured or guessed.

Silence is indistinguishable from confidence on a sheet of numbers, so an assessment that stays quiet about what it could not measure is read as complete, whatever it says elsewhere. Notice what step EA7 is not. Step EA7 is not a disclaimer but a list. A disclaimer protects the writer and a list informs the reader. A disclaimer says the figures may be wrong. A list says exactly where, exactly why, and exactly what kind of thing would have to change for the number to move.

What is the small error that runs the same way every time?

What can this method not do at all?

Two things, and both are worth stating plainly because a method that is not honest about its edges gets used past them. The first appears on the coverage line: this method cannot make Rs 1,440 crore of collateral cover Rs 2,160 crore of exposure at any haircut, and no amount of care in EA5 changes that. The remedy for a shortfall of Rs 720 crore is more collateral, less exposure or a different price for the risk, and none of those is an assessment step. The remedy is a lending decision, and it belongs to somebody else.

The second is narrower and catches people out more often. Step EA4 has nothing to multiply the add-on factor by when a contract has no notional, so this method cannot compute an exposure at default for that contract. A guarantee with no stated cap, a commitment expressed as a facility to be agreed, an obligation whose size depends on a future event: each of those breaks the fourth step, and the honest response is to record it in step EA7 as something that could not be measured rather than to substitute the current value and call it finished. A method that fails loudly on the arrangements it cannot handle is safer than one that produces a plausible figure for every input it is given.

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

Inside the invented bank, an assessment of this shape is the working paper behind a lending decision. Manjari Sondhi, who runs wholesale banking, needs it because she is asking to lend more to a borrower already at 94.5 per cent of limit L1, and the paper tells her that the request has Rs 144 crore of room on the reported footing and rather more on the exposure at default footing, and that which of those the credit risk management committee treats as binding decides whether the request is even in scope. Sunanda Ravikumar, the chief risk officer, reads the same paper for step EA7. The three gaps are the only part of it that tells her how much weight the Rs 2.20 crore can carry.

An analyst at another lender looking at Vindhya Commercial Bank Limited as a counterparty rather than as an institution reads it differently again. The interesting number is not the exposure, it is the perimeter decision: whether Rs 3,168 crore of exposure to one economic obligor is being reported as one number or as two. A bank that reports it as two has a concentration it can describe in a way that sounds smaller than it is. And a lender in a completely different business runs the same seven steps without knowing it. A jeweller who lends against gold asks whose debt this is, what has gone out against what was promised, whether the customer is owed anything back, what the ornament fetches in a distress sale, and whether the total has crossed the line he privately set. The steps do not change with the size of the balance sheet.

The household version is the sharpest test of understanding for step EA5. Suppose a person has lent Rs 3,00,000/- to a relative and holds Rs 1,30,000/- of that relative's gold as security. How much is at risk? Rs 3,00,000/- is at risk, and what the gold changes is how much of the Rs 3,00,000/- comes back if the worst happens. Nobody who has actually been in that position confuses the two, and the reason a professional assessment gets it wrong is precisely that the numbers arrive in a spreadsheet rather than in a room.