How to measure Foreign Exchange Exposure

Foreign exchange exposure is measured in seven steps: list the exposures by type, decide which entity and which book each sits in, convert at a stated rate, aggregate under a stated rule, read the result against the limit, test what the measure cannot see, and state the horizon. At Vindhya Commercial Bank Limited, invented, the same five positions report Rs 192 crore or Rs 72 crore.

Neither of those two answers is wrong. Both are produced by correct arithmetic on the same five rows on the same day, and a third correct arithmetic on the same five rows gives Rs 312 crore. So the interesting part of measuring a currency exposure is never the adding up. The interesting part is the sequence of decisions taken before anybody adds anything, and the one decision taken after. The sequence runs in order and is seven steps long.

Why does foreign exchange exposure need a method rather than a formula?

A household with one earner posted abroad shows the same shape. Money arrives every month in another currency and the rent is due here in rupees. Asked how exposed it is to the currency, that household will produce a number, and the number will depend entirely on what the person counted. Did they count only next month's transfer, or the whole year's? Did they count the small savings account still open in the other country? Did they count the flat there that nobody is selling? Each of those is a real answer to a real question, and none of them is the same question. The number is never in dispute; what is in dispute is what the number was counting.

A bank has the same problem with three more zeroes on it and a limit sitting over it. Vindhya Commercial Bank Limited, invented, carries a balance sheet of Rs 96,000 crore and, at month 12, holds five currency positions and one investment in an overseas branch. Its board has set a cap on its currency exposure. Somebody has to produce one figure and put it in front of a committee every month. A formula takes a list and returns a number. Nobody has yet decided what goes on the list, so no formula can produce that one figure.

So the method has seven steps, and the reason it is worth learning as a sequence rather than as a habit is that six of the seven steps have nothing to do with arithmetic at all. Six of the steps are decisions: what counts, whose it is, at what rate, under what rule, against what cap, with what left out, over what horizon. Only one step adds anything up, and that step is trivial. The method exists because the trivial step is the only one anybody remembers to do.

What has to be listed before a single position is converted?

Step 1 asks for a list, and it asks for the list to be sorted by exposure typeWhich of the three kinds a currency exposure is, and the first thing the method sorts by before it sorts by anything else. before it is sorted by anything else. There are three types, and this bank carries an instance of two of them.

The first is transaction exposureAn obligation or a receipt in another currency whose amount in the reporting currency is not yet fixed, so the cash that moves may differ from the cash expected.: an obligation or a receipt in another currency where the rupee amount is not yet settled. Cash will actually move, and how much rupee it turns out to be is the open question. The second is translation exposureA balance already held in another currency being restated into the reporting one, where nothing moves except the number.: a balance already held in another currency being restated into rupees for reporting. Nothing moves except the number in the accounts. The third type is the effect of a currency on what a business can sell in future and at what price, and this case carries no instance of it at all, so it is named without a figure attached. A method that quietly invents an example for the type it has no instance of has stopped measuring and started decorating.

Why the order matters

The everyday version runs like this. A person has a savings account abroad and a bill to pay abroad next month. Both are in the same currency, and it is tempting to write one line that says how much of that currency the household is dealing with. But one of the two is going to become a real payment out of a real bank account and the other is a balance that just sits there. Putting them on one line headed by the currency throws away the only distinction that changes what anybody would do about them.

At the bank the same thing happens on a larger scale, and it is irreversible. A dollar payable that will reach the profit and loss account when it settles and a dollar net investment that moves a reserve inside equity and never touches profit are two different animals. Merged under a row headed US dollar, the two cannot be pulled apart again by any arithmetic further down the method. The arithmetic downstream sees only a currency and a number. The sorting done first is the only sorting that can still be undone, so type comes first and currency second.

Which entity and which book does each exposure belong to?

Step 2 is the step that gets skipped by anyone building a spreadsheet quickly, and it is the step that stops a report being nonsense. Two questions: which institution holds this exposure, and which measure is it part of.

The institution question sounds trivial until there are two institutions in the room. Beside the bank stands Nirjhar Industries Limited, an invented steel and alloys maker whose treasury runs its own currency exposures on the other side of the table. Nirjhar holds a payable in dollars and a net investment in Nirjhar Trading FZE, an invented free zone establishment (FZE) trading overseas. The group's exposures are real, and they are real to a different balance sheet. No total may cross between two institutions, and a report that adds one to the other is not conservative, it is meaningless.

The book question is the second half. At the bank, the five currency positions FX1 to FX5 are the population that limit L7 is measured on. The net investment in the overseas branch is not part of that population. The exclusion is a decision recorded in the bank's own policy, and step 6 is where the arithmetic proves the decision was taken rather than merely asserted. For now, hold the shape: two institutions, and inside one of them, two books.

What does step 3 add, if converting is simple arithmetic?

Converting a position into the reporting currencyThe currency the entity reports in, being rupees for both invented entities in this guide, and the thing step 3 converts everything into. looks like the least interesting thing on the list, a matter of multiplying and moving on. Step 3 exists because of the second half of its own instruction: state whose rate was used.

Every rupee figure in this guide is a conversion, and every conversion rateThe rate used to restate an amount into the reporting currency, which is always somebody's chosen and recorded figure rather than a fact about the world. behind one is somebody's chosen and recorded figure. Take the group's payable. Nirjhar owes 24 million United States dollars (USD) and converts at its own contracted Rs 84.00 to the dollar, so 24 million times 84 gives Rs 201.6 crore. The Rs 84.00 is the group's own contracted figure and not a market rate for anything. A rupee figure in a currency report is always an answer to the question "at whose rate", and a report that does not say whose rate has left out half of every number on it.

The reason this matters more than it sounds is that two people can run the same method on the same book and produce different rupee columns without either of them being careless. One used the closing rate, one used a contracted rate, one used an average. The figures then get compared across months, or across two institutions, and the comparison silently mixes three conventions. Step 3 does not stop that. Step 3 only makes the mixing visible, and making it visible is all a method can ever do.

What rule turns a list of positions into one number?

Now the arithmetic step, and it is one line long. Here is the bank's book at month 12, five positions, all stated in Rs crore equivalent after step 3 has done its work.

The aggregation ruleThe rule that turns a list of positions into one number, written down before the number is produced rather than after it. this bank follows is recorded in its own policy and it reads: take the greater of the summed long side and the summed short side. Long side Rs 192 crore, short side Rs 120 crore in absolute terms, greater of the two Rs 192 crore. Rs 192 crore is the net open positionThe single figure the aggregation step produces, being Rs 192 crore at this invented bank under its own greater-of rule. the bank reports.

The order in that sentence is the whole of step 4: the rule is written down before the number, not after it. A rule chosen after the number is visible is not a rule at all, it is a preference with arithmetic attached. The distinction is not pedantic. The same five rows read three different ways under three defensible rules, as the figure below shows.

What do the same five rows report under three different rules?

Against the bank's own cap of Rs 240 crore under limit L7, the three arithmetics read 30.0 per cent, 80.0 per cent and 130.0 per cent. One book, one day, five positions, no rupee of position changing between the three readings.

The bottom reading, Rs 72 crore added with signs, lets the longs and the shorts cancel each other on paper in a way they would not cancel in the world. A bank holding five open currency positions then reports at under a third of its cap. The top reading, Rs 312 crore, assumes every currency moves against the bank at once and reports a live breach. The gap between the lowest and the highest reading is the gap between comfortable and breached, and it is produced entirely by the rule rather than by anything the bank did.

How does the result read against the limit?

Step 5 is the shortest step to describe and the easiest to describe carelessly. The reported figure is Rs 192 crore, the cap under limit L7 is Rs 240 crore, and utilisation is 192 over 240, being 80.0 per cent. Headroom is Rs 48 crore.

Now say the second half of that sentence. Most reports do not. The headroom is Rs 48 crore on the long side. The long side is what is binding, so the Rs 48 crore of room the bank has is room to take on more long position, not room in general. If the bank instead added Rs 48 crore to its short book, the short side would go from Rs 120 crore to Rs 168 crore, still below the long side of Rs 192 crore, and the reported figure would not move at all. Headroom under a greater-of rule is directional, and a headroom figure quoted without its side has been quoted without half its meaning.

What does the measure not see inside its own scope?

Step 6 is the step nobody runs, and it has two halves. The first half asks where the measure is blind inside its own scope. The shape of the rule settles that half. The second half asks what sits outside the scope entirely. The population step 2 defined settles that one.

Start inside. Under a greater-of rule the measure only ever reports the binding side, so every position on the other side is invisible to it. Close the entire Rs 96 crore euro short and the long side is still Rs 192 crore, the short side falls to Rs 24 crore, and the reported figure is still Rs 192 crore at 80.0 per cent. The bank's second largest currency position could be closed in full and the headline number would not move by one rupee. Run it the other way and there is a floor. With the short side unchanged at Rs 120 crore, no amount of closing the long book takes the measure below Rs 120 crore, or 50.0 per cent of the cap. Inside its own scope the measure is blind on one side and cannot fall past a floor, and both of those are properties of the rule rather than of the book.

Is the largest single currency exposure inside the reported figure?

Now the second half of step 6, and it is the part of this method that changes how every later currency report is read. The bank holds a net investment of Rs 480 crore in one overseas branch. The branch investment is a translation exposure. The Rs 480 crore is two and a half times the reported net open position and twice the cap. The question step 6 forces is a completeness question rather than an arithmetic one: is that Rs 480 crore inside the Rs 192 crore the bank reports?

The completeness question can be settled from the figures alone, without asking anybody, and that is what makes it worth asking. The quiz below settles it, and the controls beneath then size what has been proved.

The proof is short, and it is the one thing this guide adds that no earlier reading of the case supplies. If the Rs 480 crore net investment were inside the long side, then the long side would be at least Rs 480 crore. The reported figure is the greater of the two sides, so it would be at least Rs 480 crore too. Against the Rs 240 crore cap that is at least 200.0 per cent utilisation. The case locks utilisation at 80.0 per cent. Therefore the largest single currency exposure this bank holds is not inside the measure that runs against its currency limit, and the arithmetic settles it rather than the wording of any policy.

Read the proof carefully. The proof is not an accusation, easy though it is to hear as one. Nothing is wrong. A net open position measure is scoped to the positions it is scoped to, and somebody took that decision deliberately. The exposure is recorded, it is reported, and it moves a reserve rather than profit. Step 6 does not require that the exposure be added to the number. Step 6 requires that a sentence saying what the number covers sits beside the number. Without that sentence a reader takes Rs 192 crore for the bank's whole currency exposure, and the conclusion is false while every figure on the report is true.

What horizon does the measure cover?

Step 7 asks a question that sounds procedural and is not. Limit L7 caps the overnight positionThe exposure carried through to the next working day, which is the instant the cap in this case measures., meaning the exposure carried through to the next working day. The overnight position is one instant out of every twenty four hours. Everything the position did during the working day is a different quantity, and this case records no intraday positionThe exposure carried during a working day, which an overnight cap does not measure and which this case records nowhere. at all.

The worked instance is breach B2. In month 9 a customer deal was booked after the cut-off, and the overnight figure reached Rs 276 crore against the Rs 240 crore cap. The excess was Rs 36 crore, being 15.0 per cent over the cap, and the position was squared on the morning of the following working day. The breach was picked up by the end of day position report, escalated to Devendra Achar the same evening and taken to the market risk committee at its month 9 meeting. Duration: one business day. The deal was inside the day the cap does not measure and outside the cut-off the cap does, so the breach happened in the gap between two scoping decisions.

What does this method not produce?

A method is worth as much for the questions it refuses as for the ones it answers, and this one refuses four that readers reliably ask.

Naming the four silences is part of the method rather than an apology for it. A reader who knows what a number is not can use it, and a reader who assumes it covers everything cannot. The temptation in each of the four is the same: a plausible figure could be produced, it would look like the rest of the report, and nobody would query it. Nobody querying it is exactly why the method produces none of the four.

Who actually runs these seven steps, and what do they do with the answer?

Three people read this figure, and they read it for three different things. The sentence step 6 asks for therefore matters more than any of the three realise.

Devendra Achar, head of treasury at the invented bank, reads it as a control on his own dealing. He needs the headroom, and he needs it by side. Rs 48 crore of room on the long side is an instruction about what he may still do today, and a Rs 48 crore addition to the short book is not the same instruction. Breach B2 was escalated to him the evening it happened, so the horizon question is not academic for him either.

Sunanda Ravikumar, who runs the risk function, reads it as an independent check that the rule was followed. She asks not for the number but for the rule that produced it, and whether that rule was the one written down beforehand. Step 4 is a control for exactly that reason: a rule set in advance and applied without discretion is checkable by a second person, and a rule chosen in the moment is not.

And a credit analyst at another institution, looking at this bank as a counterparty rather than from inside it, reads it for the thing nobody inside the building thinks to say. The analyst has a published figure of Rs 192 crore, no access to the position book, and one question: what was scoped in. The analyst who asks what a currency figure was scoped to include is doing step 6 from the outside, and it is the only step an outsider can run at all.

The household version is the same shape once more. A person moving abroad states how much of the other currency they are dealing with. Asked whether the figure includes the property they still have there, the pause tells more than either number.

What goes wrong when the method is run correctly?

Which questions belong to other subjects?