How to Map a Derivative Exposure: Two Columns, Never One

An exposure map records what a single party is exposed to under one derivative agreement. Six steps fill four columns that are never totalled together: the multiplier every rate is applied to, the amount that actually settled for the period, what moves that amount and in which direction, and the cells nobody can fill from the agreement alone, each written up with the reason instead of left blank.

Underneath that sits a distinction the agreement does not draw. The figure the rates are applied to and the money that changes hands are two different quantities, and the document prints the first of them in the largest type on its opening sheet. Once somebody has added those two together, no later step can pull them apart again. Everything the routine does afterwards depends on their never sharing a column.

What is a derivative exposure map actually a map of?

A delivery van shows it plainly. A courier picks up a sealed box, and the paperwork taped to the lid declares the contents at Rs~2,00,000/-. The fee for carrying it across town is Rs~250/-. The courier's exposure has two very different answers, depending on which of those two figures is reached for. The declared value is real, it is printed in bold, and it decides how carefully the box gets handled. The declared value is not what the courier earns, loses or settles. Confuse the two and the courier looks like a business turning over lakhs a day.

A derivative agreement puts those same two figures side by side and gives the larger one the better position. An exposure map exists to keep them in separate columns for long enough that neither one can be mistaken for the other. An exposure map is not a valuation, not an opinion, and not a summary of the agreement. The map is a short worksheet with four columns and one row for each thing the party is exposed to, built so that a reader who has never seen the agreement can still say what moves, how much of it moves, and what would change it.

There is a second thing to get straight before any step is taken, and it is the one most often got wrong. The routine maps one party, and not the agreement. Two people can sit at opposite ends of the same document and produce two entirely different maps, matching in every size and reversed in every direction. An agreement is a sheet of paper and a sheet of paper is exposed to nothing. A party is exposed to something. The routine therefore opens by choosing a side rather than by opening the file.

Why does this routine exist at all?

Routines earn their place by preventing something specific, and the exposure map prevents a single error. The headline on the agreement reads Rs~1,000 crore. The map, once it is finished, reads Rs~12.00 crore of net difference for the opening period. The headline copied straight into the exposure column overstates what this party settles by 83.33 times, before one rate has been read off the document. Nobody had to be careless. The figure was correct, it was copied faithfully, and it was put in the wrong column.

A vegetable stall on a Tuesday morning is the same shape. Rs~1,00,000/- of stock passes across the counter over the month, and Rs~1,200/- of it stays with the person behind the counter. Both numbers describe the stall. Only one of them is the stall's money, and it happens to be the same 1.2 per cent share this arrangement produces. Everyone on that street understands the difference between what a trader handles and what a trader keeps, so quoting the first figure as the value of the business would be absurd. The reason the same distinction gets lost on a derivative agreement is not that it is harder, it is that the document prints only one of the two figures and leaves the other to be computed.

So the map has a fixed shape, and it is worth knowing what is being built before the first step. Four columns. One row for each thing the party is exposed to under the agreement. And a rule, written at the top of the sheet, that the leading two columns are never totalled together. The rule against totalling is not fussiness. Keeping those two columns apart is the only thing standing between a correct worksheet and a figure that travels into a summary and cannot be caught.

What are the six steps, in order?

The whole routine is six steps and it has an end. Having an end matters. Mapping an exposure is often treated as an act of judgement, something a more experienced person does better. It is not. The routine is a procedure, it produces a described output, and two people running it on the same agreement for the same party should produce the same sheet.

1. Choose the side and write it at the topName the party. Beside the name, write which leg it pays and which leg it receives, in those words.
   Checking: read that line aloud against the document. A swapped pair produces a map that is internally consistent and points the wrong way throughout.
2. Record the multiplier in column one, with its markThe notional, the word the agreement uses for it, and a note that it does not appear in the schedule of movements.
   Checking: is the mark actually written? An unmarked figure is a figure waiting to be added to something.
3. Work what actually settled into column twoBoth legs in full for the period being mapped, then the difference between them.
   Checking: can somebody who did not do the arithmetic reproduce the difference from what is on the sheet?
4. Record what moves the settlement into column threeOne entry on an arrangement of this kind, and the direction it runs in for this side.
   Checking: is there a size, a range or a likelihood anywhere in this column? There should not be.
5. Mark the cells that cannot be filled into column fourFour of them here. Each one carries the reason it is empty rather than a blank, a dash or a zero.
   Checking: could a reader tell, from the cell alone, who would fill it or what reading is missing?
6. Read the map across, and stopOne sentence spanning the four columns. The routine produces a description, and it does not produce a view.
   Checking: does the sentence contain the word should? If it does, the routine has been run past its end.

Step one: whose exposure is this?

Exposure is a statement about a party. Not about a contract, not about a market, and not about a rate. So the first thing that goes on the sheet is a name, and the second thing is the pair of legs that name is attached to. Chitrakoot Cements Limited, an invented manufacturer, pays the fixed leg and receives the floating leg. Saranga Capital Limited, an invented lender at the far end of the same document, pays the floating leg and receives the fixed leg.

Every direction on the rest of the map is read off that one line. So the line is written before anything is computed. Written backwards, nothing will look wrong. The sizes will all be right, the arithmetic will reconcile, the cells will be filled in the same order, and the finished sheet will describe a party that is exposed to the exact opposite of what it is actually exposed to. The check attached to step one is therefore to read the direction line out loud against the document, rather than to look at it again on screen. Silent re-reading confirms what the reader already believes.

Step two: why does the headline figure get a column of its own?

Column one holds the notional. On this agreement the notional is Rs~1,000 crore, written out in full as Rs~10,00,00,00,000/-. Beside it goes the word the agreement itself uses for that figure, and then the mark that makes the column work: this figure does not appear in the schedule of movementsThe part of an agreement that lists what is paid, by whom and on which dates. If an amount is not named in there, it never leaves anybody's account. Finding it is the job of the routine for reading an agreement. anywhere. Nobody pays it, nobody receives it, and nobody lodges it. The notional sits in the document to be multiplied by.

A reader may fairly ask why it is on the map at all, if nothing about it moves. Two answers. The first is that it sets the scale of everything in column two: take the notional away and there is no way to show why the settlement came out at the size it did rather than at ten times or a hundredth of it. The second answer is the practical one. The notional is the largest number on the opening sheet, so it is going to be on somebody's desk regardless, and a map that does not account for it leaves that figure loose. Better to give it a column, put a mark beside it, and know exactly where it is.

The mark is what makes the column work rather than an ornament on it. A figure written down with no mark against it is a figure waiting to be totalled with whatever sits underneath it, and the totalling is the one thing this whole routine exists to prevent. In practice the mark is a few words. Multiplier only. Never settles. Not in the payment schedule. Any of those will do, as long as the sheet cannot be read without meeting it.

Step three: what goes in the column that records what actually moves?

Column two is worked rather than copied. For the period being mapped, compute each leg in full, write both of them down, and then record the difference between them. The fixed leg on this agreement runs at 7.20 per cent a year, applied to the notional over a day count fractionTwo agreements can carry the identical rate and settle different amounts, and this is the number that does it. The fraction arrives from whichever counting rule the parties wrote down, and that counting rule is worked through separately. of 1.0000, and gives Rs~72.00 crore gross. The floating leg runs at the reading of 6.00 per cent a year that this arrangement holds for its opening period, and gives Rs~60.00 crore gross. Take one from the other and Rs~12.00 crore of net difference leaves Chitrakoot Cements Limited.

Both legs get written down even though only the difference moves, and that is deliberate. A map showing the net alone asks a reader to take it on trust. Trust is the one thing a worksheet is built to remove. Rs~72.00 crore against Rs~60.00 crore is where Rs~12.00 crore comes from, and anybody holding the sheet can check it in their head. Show the result on its own and the checking has to start from the agreement again.

Now read the two columns across rather than down, and the whole routine pays off. Rs~12.00 crore of net difference set against a notional of Rs~1,000 crore is 1.2 per cent of it. The gap between the two rates is 1.20 percentage pointsThe unit produced by subtracting one rate from another. 6.00 per cent taken away from 7.20 per cent leaves 1.20 of these, not 1.20 per cent of anything, and the difference matters the moment somebody multiplies by it., and that gap is the whole of what settles. Which leaves 98.8 per cent of the headline figure as scale rather than money. Reading the columns down and totalling them would have produced Rs~1,012.00 crore, a figure describing nothing at all.

Step four: what makes the settlement change, and in which direction?

Column three is unlike the two before it, in that it records no size at all. The column records what moves the settlement, and which way. On an arrangement of this kind there is exactly one entry to make: the benchmark reading taken at the next resetA date written into the agreement on which somebody looks up the benchmark and records what it says. Before that moment the floating leg carries no figure; afterwards it carries one that will not move again for that period..

The direction gets written out in words rather than left to be inferred. Chitrakoot Cements Limited pays the fixed leg, so it receives more as the reading rises and receives less as it falls, point for point. Saranga Capital Limited reads the same line the other way round: it receives more as the reading falls. Two sentences, one for each side, and the map only carries the one belonging to the party at the top.

Now the harder half of this step: what column three does not contain. No probability. No range of likely readings. No view about which way anything is going to go. A reader arriving at a column headed what moves this will expect a forecast to be sitting in it. There is none. A direction is not a prediction, and no distribution of benchmark readings stands behind these figures to build one out of. One reading exists here and it belongs to the opening period. Where the benchmark reading goes after that is not written into the agreement, not recoverable from anything standing behind it, and not something careful phrasing can supply.

Step five: which cells on this map cannot be filled at all?

The finished map has a hole in it, and the hole is labelled. Labelling the hole is the whole of step five. Four cells stay empty here, and they stay empty for two quite different reasons. Separating those two reasons before any cell is written is worth the minute it takes.

One of them is empty because the reading that would fill it has never been taken. What would this arrangement cost to close outEnding an arrangement before the date it was written to run to, by agreement with the other side. Somebody has to be paid to take on whatever is left of it, and working out how much that is takes a valuation. today? The answer is priced off a schedule of expected benchmark readings stretching out over the remaining periods. No such schedule sits behind this material, none was constructed for it, and none was borrowed from anywhere else. So the map prints the question, names the reading that would answer it, and refuses to print a number in the box. Refusing to print a number is not a gap in the work. It is the work.

The other three are empty because an authority sets them. Reporting on a privately agreed arrangement, what has to be reported and to whom and by when, is settled by the Reserve Bank of India at rbi.org.in. Whether the arrangement qualifies for hedging treatmentA status a party may claim in its accounts for an arrangement entered into to offset something it already carries. Whether a given arrangement qualifies, and what has to be kept on file to demonstrate it, is set by an authority rather than by the two parties., and on what evidence, goes to the same address. The collateralMoney or securities lodged with somebody else to put something solid behind a promise. How much, in what form and how often it is topped up are all set by an authority. a party dealing in exchange traded contracts places is settled by the Securities and Exchange Board of India (SEBI) at sebi.gov.in. Each of these moves, and a figure written out here would be wrong on the day it changed.

And then the rule that governs the whole column, the rule that separates a map from a guess. An empty cell carries its reason. A cell left blank looks like work that has not been done yet, and the next person to pick up the sheet will either fill it with something plausible or quietly ignore it. A cell carrying what would fill it, and who would fill it, is finished work that happens to have no number in it. Write the reason, not a dash and not a zero.

Step six: what can the finished map be used to say?

Read the four columns across in one line and the map has done its job. Chitrakoot Cements Limited settles a difference computed on a multiplier it never pays; that difference moves with one reading taken on one day; and what the arrangement would cost to leave early is not in front of anybody here. Three clauses, and every one of them is checkable against the sheet.

Where the routine stops is as much a part of it as where it starts. The map produces a description and it does not produce a view. Nothing on the finished sheet says whether this party ought to be in this arrangement, whether the rate written into it was a good one, or what anybody should do next. If the sentence written off the map contains the word should, the routine has been run past its end and something has been added that the four columns do not support.

What does the routine look like run end to end?

Here is the whole thing on one side of the invented agreement. A map belongs to a party, so Chitrakoot Cements Limited goes at the top. Everything below is either taken from the document or computed from what was taken.

Now the fastest available proof that a map belongs to a side rather than to a document. Run the same two lines for Saranga Capital Limited. Saranga Capital pays the floating leg and receives the fixed leg. Its column one reads Rs~1,000 crore, its fixed leg reads Rs~72.00 crore gross, its floating leg reads Rs~60.00 crore gross, and its net difference reads Rs~12.00 crore arriving rather than leaving. Every size is identical and every direction is turned around. Two maps of the same agreement drawn from opposite ends of it produce exactly that.

What happens when the two columns are merged?

The failure this routine prevents is not produced by careless people. Careful people working quickly produce it, and that is why it survives.

Who actually sits down and does this?

Three people, roughly, and each of them wants a different column first.

A credit officer at a lender opens the borrower's file and finds a line reading Rs~1,000 crore of derivative notional. The officer is not asking after the value of the arrangement. The question is how much cash this borrower has to find on a settlement date, and cash on a settlement date competes directly with the loan repayment. Column two answers that and column one does not, and the mark beside the notional is therefore the single most useful thing on the sheet from a lender's chair. A borrower whose settlement obligation is Rs~12.00 crore and a borrower whose settlement obligation is Rs~1,000 crore are not remotely the same borrower, and the opening sheet of the agreement reads identically for both.

An analyst reading a disclosure wants column three before anything else. Sizes are already published; what is usually missing is which way the party's position runs. Knowing that a party pays the fixed leg tells the analyst that its settlement improves as the benchmark rises, and that single sentence is worth more than a table of notionals. A direction can be set against everything else the party does. A notional cannot. A business whose own receipts fall when rates rise is in a different situation from one whose receipts rise, and neither situation is readable off the notional.

A treasurer inside the party runs the map for the opposite reason: to check that the sheet in front of the board says the same thing as the agreement in the drawer. The step that earns its place here is step five. A board paper with an empty cell in it, labelled with what would fill it and who sets it, ends an argument that a board paper with a confident number in it starts. And the counterpartyThe other side. Whoever has signed the same agreement and taken on the opposite obligations under it. is running its own version of the same sheet, matching this one in every size and disagreeing with it in every direction.

The household version of this is smaller and identical in shape. Somebody asks what a home loan costs. There is a figure that is the loan and there is a figure that leaves the account each month, and only the second one competes with the electricity bill. Everyone gets this right at home. The map exists because the same instinct stops working the moment the two figures appear on a printed sheet with one of them in bold.

What does a finished map still not say?

A reader holding a completed map still cannot say whether this party ought to be in this arrangement, and the routine does not pretend to answer that. Being specific about what would have to be known first is worth the trouble. Vagueness is what lets people fill the gap themselves.

Answering it would take knowing what the party already owes and on what basis. An arrangement that offsets an existing obligation and one that adds a fresh one look identical on this map. A direction only means something set against the direction of everything else the party holds, so answering would also take knowing what the party's own receipts and payments do when a benchmark reading moves, and over what stretch of time. And it would take knowing what the party would do on a period where the difference runs the other way, a question about the party rather than about the agreement.

None of that is in the agreement, and none of it sits behind this material. The map is a description of one side of one document for one period. The map is a genuinely useful thing to have on a desk, and it is not the same thing as a decision. Anyone reading a settlement that ran against them should also hear this plainly: a period that goes one way is not a mistake and not a failure, it is what a two sided arrangement does.