Counterparty Exposure: Measuring What Is Actually at Risk

A counterparty exposure calculator takes one counterparty and turns four facilities into one number. The calculator asks for the funded balance, the undrawn committed line with a drawdown assumption, the current exposure of any contracts and the add-on that goes with them, then reports both bases: the reported total a limit is usually measured on, and the exposure at default a loss computation needs. On C1 those are Rs 2,496 crore and Rs 2,160 crore.

A counterparty is never one facility. The habit of thinking in single facilities is the whole reason the measurement needs a method, and people find that hardest to believe until they have watched a single name produce two correct answers on the same afternoon. Money lent, money promised and not yet taken, contracts worth something today and contracts that could be worth more tomorrow all sit under one name, and every one of them is a different kind of claim. Adding them takes a decision at each step. A tool that hides those decisions inside one printed figure is not saving anybody time; it is producing a number nobody can take apart when it matters.

What does this working tool compute?

Start with the shape of the thing rather than the arithmetic. Four items go in and four items come out, and the four inputs are not equally solid. Exactly one of them is a fact that can be read off a system, and the other three are judgements the bank made, wrote down and now applies every month without reopening. The reason this tool shows its inputs rather than only its answer is that three quarters of the answer is assumption.

The mechanism is identical at every scale. Here is the household version before the bank version. Suppose a lender has lent a cousin Rs 40,000/- and it is fully drawn. The same lender has told a neighbour who runs a tiffin service that Rs 20,000/- is there whenever she needs it, and she has not touched it. And there is an arrangement with a scrap dealer under which he owes for one delivery and is owed for another. How much is at risk with those three people cannot be answered without first deciding three things: how much of the tiffin line she is likely to take, whether the two scrap deliveries can be set against each other, and how much bigger the scrap position could get before it settles. The drawdown share, the set-off and the future movement are exactly the three decisions the tool asks a bank to make.

What has to be entered before a counterparty exposure figure means anything?

Input one, the funded balance, which is the only input that is a fact

Rs 1,680 crore is drawn and outstanding to Nirjhar Industries Limited, the invented steel and alloys maker that is counterparty C1 and the largest single name in this bank's book. Nobody has to estimate that. The drawn balance sits on a loan account, and it will be the same figure whoever pulls it, on whatever day, into whatever report. Two people working independently are certain to agree on the funded balance, and on no other input in this tool. Everything downstream of it involves a view. A reader handed only a final exposure figure should always ask what share of it came from a system and what share came from a policy.

Input two, the undrawn line and the assumption applied to it

C1 has a committed line of Rs 720 crore that it has not drawn. A committed line is a promise the bank cannot walk away from because the customer is having a bad year, and a customer having a bad year is precisely when a line gets drawn. So the tool cannot treat the undrawn line as nothing, and it cannot sensibly treat it as certain either. The tool applies a drawdown assumptionThe share of an undrawn line assumed to be taken before a default, here this bank's own 50.0 per cent., and at this bank that assumption is 50.0 per cent, set internally rather than imposed from outside. Half of Rs 720 crore is Rs 360 crore.

The drawdown assumption carries a full Rs 720 crore of range behind it. No other input in this tool comes close, so no other input matters as much. Set at zero, it says a distressed borrower draws nothing. Set at a hundred, it says every promise gets called. A bank only sees the drawdown behaviour of the borrowers who actually defaulted, and that is a small and unrepresentative set. The truth is somewhere in between, and no system observes it. The simulation further down shows exactly how far the answer moves across that range, and the size of the movement is the argument for showing the assumption on the face of the report rather than burying it.

Input three, what the contracts are worth today

C1 has two contracts with the bank. One is worth plus Rs 132 crore to the bank and one is worth minus Rs 36 crore. The tool needs a single netted current exposureThe positive and negative values of contracts under one enforceable agreement collapsed into a single figure., and whether it is allowed to produce one is a legal question rather than an arithmetic one. Without an enforceable agreement covering both contracts, the losing one gives the bank no credit at all in a default: the bank still owes its Rs 36 crore and simply joins the queue for its Rs 132 crore. With such an agreement, the two collapse. Rs 132 crore less Rs 36 crore is Rs 96 crore.

The two contracts on C1 are covered by one netting agreement, so the tool reports Rs 96 crore, a fall of Rs 36 crore against the gross figure and a reduction of 27.3 per cent. A signed document produces the difference between Rs 132 crore and Rs 96 crore, and nothing else does. So the tool asks whether the agreement exists before it asks what the contracts are worth. Note also what Rs 96 crore is not: it is the netted current exposure and it is not the exposure at default, and those two figures appear separately in the counterparty table for exactly that reason.

Input four, how big the contracts are

The fourth input has nothing to do with what the contracts are worth today. The fourth input asks how big they are. A contract worth almost nothing this morning can be worth a great deal by the time a default is actually worked through. C1's contracts carry a notional of Rs 1,600 crore, and the bank applies its own add-on factor of 1.5 per cent to that notional to get Rs 24 crore. The Rs 24 crore is the allowance for movement between today and the day the position is closed out.

The add-on is taken on notional and never on value. People building this calculation for themselves get that convention wrong more often than any other. Take a percentage of a contract's current value instead, and a contract sitting exactly at zero today would carry no allowance for future movement at all. A contract at zero can move as far as any other, so an allowance of nothing is plainly wrong. Size is what drives movement, so size is what the add-on is taken on.

How is the funded, undrawn and derivative exposure of one name brought into a single figure?

With the four inputs together, an attempt to add them runs into trouble immediately. The four cannot be added, at least not once. There are two defensible ways to combine them and they answer two different questions, so the tool produces both rather than choosing between them. The first is the reported totalFunded exposure plus the undrawn line in full plus current exposure, which is the basis a single name limit is usually measured on here., built from the funded balance, the whole undrawn line and the current exposure of the contracts. The second is the exposure at defaultFunded exposure plus the drawn share of the line plus current exposure plus the add-on, which is the basis a loss computation needs., built from the funded balance, the drawn share of the line, the current exposure and the add-on on top.

Counterparty C1 worked end to end

Every figure below belongs to Vindhya Commercial Bank Limited, an invented lender, and to Nirjhar Industries Limited, and every factor in it is this bank's own. Read the two right-hand columns as two different questions being asked of one set of facilities on one day.

A tool nobody checks is a tool nobody trusts. Check the two totals yourself. On the first basis, 1,680 plus 720 plus 96 is 2,496. On the second, 1,680 plus 360 plus 96 plus 24 is 2,160. One counterparty, one day, one set of facilities, and two figures Rs 336 crore apart, both of them correct. The two bases differ on exactly two rows, and they differ in opposite directions. The net gap is therefore smaller than either move that produced it.

Which basis is the figure on, and why does one counterparty produce two different utilisations?

A figure on its own is not yet a measurement. A figure becomes one when it is laid against something, and here that something is limit L1A cap on exposure to one counterparty. Here it is 40.0 per cent of tier 1 capital, this bank's own figure rather than a regulatory cap., the bank's own single name cap, set at 40.0 per cent of tier 1 capitalThe capital measure this bank sets its single name and group caps as a percentage of, being Rs 6,600 crore here. of Rs 6,600 crore. Forty per cent of Rs 6,600 crore is Rs 2,640 crore. Divide each of the two figures by that cap, and one counterparty on one day yields two utilisationWhat is running against a cap, expressed as a percentage of it, which means nothing until the basis is named. readings. 2,496 over 2,640 is 94.5 per cent, and 2,160 over 2,640 is 81.8 per cent.

Twelve point seven percentage points separate two correct answers about the same counterparty, and the only thing that decides which one appears is a convention nobody wrote at the top of the report. The bank publishes the reported total, so 94.5 per cent is the figure that binds internally and the figure Manjari Sondhi, who runs wholesale banking and carries C1 as a risk owner, is held to. A loss computation cannot use it. The reported total counts a whole undrawn line that will not be wholly drawn, and it leaves out an add-on that will actually be there. Each basis is right for its own job and wrong for the other one.

The Rs 336 crore between the two is not a mystery and it should never be presented as one. The gap is two moves in opposite directions. The exposure at default takes half the undrawn line rather than all of it, and half of Rs 720 crore removes Rs 360 crore. Then it adds the potential future exposure the reported total leaves out entirely. The derivative measure rises from Rs 96 crore to Rs 120 crore, putting Rs 24 crore back. Rs 360 crore off and Rs 24 crore on is Rs 336 crore net, and 2,496 less 336 is 2,160. A gap that decomposes exactly into two named moves is an explanation; a gap presented as a single net figure is an invitation to guess.

What does the tool do with collateral, and what does it deliberately not do?

C1 has given a charge over inventory and receivables valued at Rs 1,440 crore. The bank cuts that valuation by its own haircut of 35.0 per cent, leaving eligible collateralCollateral value after the haircut, being what the lender is willing to count on. of Rs 936 crore. Against the exposure at default of Rs 2,160 crore that covers 43.3 per cent. The instinct almost everybody has here is wrong. Now watch where the Rs 936 crore actually goes.

The collateral does not come off the exposure. Neither reported total nor exposure at default moves by a single rupee. The collateral cuts the severity instead. Loss given default falls from this bank's assumed 40.0 per cent to 40.0 times one less 0.4333, or 22.67 per cent. The expected loss on C1 falls from Rs 2,160 crore times 0.45 per cent times 40.0 per cent, being Rs 3.89 crore, to Rs 2,160 crore times 0.45 per cent times 22.67 per cent, being Rs 2.20 crore. The fall is 43.3 per cent, exactly the share of exposure the collateral covers.

Collateral belongs in severity because a limit is measured on exposure, and collateral does not reduce what the counterparty owes. If the tool deducted it, C1 would report an exposure of Rs 1,224 crore against a cap that was set on gross terms, and a name at 46.4 per cent of its limit invites no question at all. Deducting collateral is the arithmetic by which an institution talks itself under a cap it is actually running close to. The rule to hold is simple: the exposure line answers how much is at stake, and the collateral line answers how much of it comes back.

What the tool will not do, and why each refusal matters

A calculator that always produces a figure is more comfortable to use and much worse to rely on. The tool refuses three things, and each refusal marks a place where a real exposure report quietly invents something. With no notional entered, it computes no add-on. With no enforceable agreement recorded, it does not net two contracts. And an empty security field is never read as an absence of security. Every one of those three shortcuts produces a figure that looks right, reconciles to nothing and cannot be traced back to anybody's decision.

How does the answer move when the drawdown assumption moves?

Everything above is arithmetic on figures somebody chose. Here is the one that matters most. Hold every other input still and move only the drawdown assumption from zero to a hundred per cent, and the exposure at default runs from Rs 1,800 crore to Rs 2,520 crore. The whole undrawn line of Rs 720 crore is the range, and that is six times the entire derivative position of Rs 120 crore. The single input nobody observes moves the answer further than every input anybody measures put together.

The assumption enters the arithmetic once and multiplies one fixed quantity. The shape is therefore a straight line. Five points on it are worth memorising: at zero the exposure at default is Rs 1,800 crore, being 68.2 per cent of limit L1. At 25 per cent it is Rs 1,980 crore, being 75.0 per cent. At 50 per cent, this bank's own assumption, it is Rs 2,160 crore, being 81.8 per cent. At 75 per cent it is Rs 2,340 crore, being 88.6 per cent. At 100 per cent it is Rs 2,520 crore, being 95.5 per cent.

Two crossings are worth naming before the control is touched. The exposure at default equals the reported total of Rs 2,496 crore at a drawdown assumption of 96.7 per cent, very nearly the whole line. Past that point the exposure at default becomes the larger of the two figures. The limit itself is never reached. Rs 2,640 crore would need a drawdown assumption of 116.7 per cent, and that is more of the line than exists. On the exposure at default basis this counterparty cannot breach its single name cap at any assumption a bank could set, and saying that plainly is better than leaving a reader hunting for a crossing that is not there.

What can this tool not tell an analyst about a counterparty?

The tool cannot say which of its two answers belongs in a paper, and that is where the damage actually happens. Both figures reproduce perfectly from the same inputs. Nothing about either is arithmetically wrong. So a limits pack quoting 94.5 per cent and a counterparty review quoting 81.8 per cent both survive every check anybody runs on them, and a committee holding one of each has two numbers about one name with no line anywhere telling it why they differ.

There are other things this tool cannot do. The tool measures size rather than quality, and whether C1 is a good counterparty is a question about quality. A haircut is an estimate, and inventory sold under pressure is a different asset from inventory sitting in a shed. Whether the Rs 936 crore of collateral would actually realise that much in a distressed sale is beyond the arithmetic. And it says nothing at all about the other nine names in the book: it takes one counterparty at a time, and what happens when several names move together is a separate question with a separate treatment.

Who actually picks up a two basis exposure figure, and what do they do with it?

Four people read this output, and they read it for four different things. Printing both bases therefore costs nothing and saves a great deal.

The relationship person who covers Nirjhar Industries Limited reads the reported total. Only the reported total tells her whether she can write more business. At Rs 2,496 crore against a Rs 2,640 crore cap she has Rs 144 crore of headroom on paper, and a single new facility of any size would take her past it. The cap is measured on the reported total. The reported total is therefore the figure that governs behaviour. The exposure at default of Rs 2,160 crore is genuinely irrelevant to that question, and quoting it to her would be worse than useless.

A loss computation needs a figure that reflects what will actually be owed rather than what could theoretically be owed. The credit risk analyst preparing the loss provision therefore reads the exposure at default. Rs 2,160 crore multiplied by the grade 4 probability of default of 0.45 per cent and by a severity of 22.67 per cent gives Rs 2.20 crore of expected loss on this name for the year. The reported total fed into the same computation overstates that number by Rs 336 crore of exposure. Overstating it is not conservative but simply wrong.

The independent director on the board risk management committee reads neither figure on its own; she reads the gap. A committee that is shown 94.5 per cent one month and 81.8 per cent the next, without being told the basis changed, has been given a false sense of movement in a position that did not move. A convention that stays put is what makes two months comparable. A governance reader needs the stated convention from an exposure tool, not the tightest number. Whether that convention is right is a separate argument and one worth having; whether it is stated is not negotiable.

And a credit analyst at another institution, looking at Vindhya Commercial Bank Limited itself as a counterparty rather than as a lender, reads it for something different again. The single largest name is 94.5 per cent of a self-set cap on the bank's own published basis. The 94.5 per cent says a great deal about how much room this bank has left before its own arrangements start binding, and nothing at all about whether the name is sound. The household version is the same shape: knowing that Rs 60,000/- rides on one cousin is a different question from knowing whether the cousin will pay, and the honest answer is that both are needed and they come from different places.

Where do the measurement conventions actually come from?

The measurement itself is jurisdiction free: four facilities, two bases, one cap. But the conventions the tool applies did not appear from nowhere, and a reader who needs the binding version should know where to go and read it. The methods are international and what actually binds an Indian bank is not, and mixing the two up is the most common error in this whole subject.