Open Position: Unhedged Exposure to a Market Variable

An open position is the unhedged exposure itself to a market variable, and it exists whether or not anybody measures it. Vindhya Commercial Bank Limited, invented, carries five currency positions which its own method aggregates to Rs 192 crore against a Rs 240 crore cap. Adding the same five rows differently gives Rs 72 crore or Rs 312 crore, and all three of those totals come off one invented bank's own book.

Almost everything else in this subject is a measure. A measure is a sentence somebody wrote about a position, computed on a Tuesday morning by a person with a method and a data set. An open position is the other thing, the one the sentences are written about, and it is much less discussed precisely because it is much less interesting to compute. The position is what is actually held; every measure elsewhere in this sequence is a claim about it. Get that separation clear and a surprising amount of confusion falls away, including the confusion that makes a bank with five open currency positions look nearly flat on a spreadsheet.

What is an open position, and when does one exist?

An open positionAn exposure to a market variable that has not been closed or covered, existing whether or not anybody measures it. is an exposure to a market variable that has not been closed and has not been covered. The definition stops there, and the two words doing the work are open and exposure. Open means something could still be done about it and has not been. Exposure means a move in a price or a rate lands on it.

Take an ordinary household before touching a balance sheet. Suppose a household in Nagpur has agreed to pay for a daughter's first year of study abroad, and the fee is fixed at an amount in a foreign currency, payable in six months. On the afternoon the offer was accepted, that household acquired an open position. Nobody in the house calls it that. Nobody has opened a spreadsheet, looked up a rate or written a figure anywhere. The exposure is nonetheless complete and dated: if the rupee weakens over the next six months, the household pays more rupees for exactly the same fee, and no amount of not thinking about it changes that.

The moment that matters is the moment the exposure is taken, not the moment somebody computes it and not the moment somebody reports it. A great deal of institutional behaviour quietly assumes the opposite, so the timing is worth being stubborn about. A position taken at four in the afternoon and captured by a system at nine the next morning was open all night. A position that a report does not pick up is not a smaller position; it is the same position with a reporting gap sitting on top of it.

Vindhya Commercial Bank Limited carries five such currency positions at month 12, and the whole of the arithmetic below runs on those five rows.

Why is a position not the same thing as a measure of it?

Because one of them is a thing and the other is a sentence about the thing. A household does not become lighter by staying off the weighing scale, and it does not become heavier by weighing itself twice. The scale produces information. The mass was already there.

The distinction matters because the rest of this sequence is almost entirely about scales. A sensitivity figure, a one-day value at risk figure, an expected shortfall figure and a change in the value of equity are all statements about positions, produced by a method, with assumptions inside them, and every one of them could be computed differently and give a different answer tomorrow morning without a single rupee of exposure having moved. A measure can be recomputed, revised, disputed or abandoned, and the position sits there unchanged through all four.

Look at what this invented bank holds and what it says about what it holds. The bank holds five currency positions, a Rs 3,600 crore held for trading book, a repricing mismatch spread across eight buckets numbered RB1 to RB8, and a net investment of Rs 480 crore in one overseas branch. All four are things. Against them it computes a one-day value at risk of Rs 15.6 crore on the trading book, a change in the value of equity of minus Rs 840 crore under its own 200 basis point scenario, and a limit L7 utilisation of 80.0 per cent on the currency book. All three are sentences.

The practical consequence is not academic. If the model that produces the Rs 15.6 crore figure were switched off tomorrow, the Rs 3,600 crore of securities would still be sitting there taking price moves. If the behavioural assumption underneath the minus Rs 840 crore figure were changed, that number would move a very long way without one rupee of the balance sheet being bought or sold. A measure can be lost while the exposure stays exactly where it was, and that asymmetry is why the object comes before the arithmetic.

Which five currency positions does this bank actually carry?

Five rows, and they are worth reading slowly because the entire rest of this guide is arithmetic on them. At month 12, Vindhya Commercial Bank Limited holds a US dollar long positionA position that gains when the price or rate of the thing held rises. of Rs 144 crore, a euro short positionA position that gains when the price or rate of the thing owed falls. of Rs 96 crore, a pound sterling long of Rs 36 crore, a Japanese yen short of Rs 24 crore and a United Arab Emirates (UAE) dirham long of Rs 12 crore. Dollars cannot be added to yen, so every one is stated in rupee crore equivalent.

Long and short are the only two directions there are, so each is worth one sentence. Long means the bank holds more of that currency than it owes, so it ends up better off if the currency strengthens against the rupee. Short means the opposite: the bank owes more of that currency than it holds, so it does better if the currency weakens. The household version is a person who has already bought foreign currency for a trip, who is long, sitting next to a person who has promised to pay a foreign fee later and has bought nothing, who is short.

The five rows are five separate exposures to five separate market variables, not one exposure with five parts. The dollar can strengthen on a morning when the euro weakens. The dirham can sit still for a month. Nothing in the list requires any two of them to do anything in particular, and holding on to that fact is what makes the next section land.

How do five rows become one reported figure?

By a rule, and the rule is somebody's choice. Vindhya Commercial Bank Limited sums its long positions, sums its short positions in absolute terms, and reports whichever of the two totals is larger. The mechanism stops there, and it follows the shorthand methodThe aggregation that takes the greater of the summed long side and the summed short side, published by the Bank for International Settlements and followed by this invented bank. published by the Bank for International Settlements at bis.org.

Work it. The long side is the dollar at Rs 144 crore plus sterling at Rs 36 crore plus the dirham at Rs 12 crore, and that comes to Rs 192 crore. The short side is the euro at Rs 96 crore plus the yen at Rs 24 crore, and that comes to Rs 120 crore. The greater of the two is Rs 192 crore, and that is the net open positionThe aggregated figure a bank reports across several positions, which depends entirely on the aggregation method chosen. this bank reports. Against limit L7, its own cap of Rs 240 crore, that is 80.0 per cent utilisation.

Why the greater rather than the smaller, or the sum, or the average? Because the two sides answer a plain question about one bad state of the world. Suppose every currency in the book moved against this bank at once, in the sense of every foreign currency strengthening against the rupee together. The long positions gain and the short positions lose. Suppose they all weakened together instead: the longs lose and the shorts gain. In the first state the loss is the whole short side. In the second it is the whole long side. The greater of the two sides is the larger of those two losses, so it answers how much a single common move could cost, and that reasoning is what the method rests on.

One small calculation is worth keeping, and it makes the three totals below fall out of each other rather than arriving as three unrelated facts. The two sides added together come to Rs 312 crore. One subtracted from the other leaves Rs 72 crore. Half of their sum plus half of their difference is Rs 192 crore, the greater of the two, and half of their sum minus half of their difference is Rs 120 crore, the lesser. The three headline totals are not three separate calculations; they are the sum, the difference and the larger half of one pair of numbers.

Why do the same five rows produce three different totals?

Because there are three defensible ways to add up a list of signed numbers, and each one is answering a different question. Take them in the order a person actually meets them.

The algebraic sumAdding the positions with their signs, which treats a short in one currency as offsetting a long in another. is what a spreadsheet gives when the column is selected and the total key pressed. Rs 144 crore less Rs 96 crore plus Rs 36 crore less Rs 24 crore plus Rs 12 crore is Rs 72 crore, or 30.0 per cent of the Rs 240 crore cap. The arithmetic is flawless and the answer is nonsense. The algebraic sum assumes a euro short cancels a dollar long. Two currencies only cancel if they always move together, and if they always moved together they would be one currency.

The absolute sumAdding the positions ignoring their signs, which assumes every currency moves against the holder at once and is a scenario rather than a position. ignores the signs entirely. Rs 144 crore plus Rs 96 crore plus Rs 36 crore plus Rs 24 crore plus Rs 12 crore is Rs 312 crore, or 130.0 per cent of the same cap, and that would put the bank in breach on a book it reports as comfortably within. The absolute sum assumes every currency moves against this bank at once, longs falling and shorts rising in the same afternoon. The assumption is a scenario. A scenario is a perfectly reasonable thing to run, and a scenario is not a description of a position.

The greater of the two sides sits between them at Rs 192 crore and 80.0 per cent, and it has the reasoning set out in the previous section behind it. One book, one day, five rows, and the utilisation of a cap reads 30.0, 80.0 or 130.0 per cent depending on nothing but how the rows were added.

The household version is a person totalling their month. The household owes Rs 30,000/- of rent on the fifth and a friend owes them Rs 30,000/- some time soon. Netting the two to zero is the algebraic sum, and it is fine right up until the friend is slow, at which point the rent is a real obligation and the receivable is a hope. Treating both as full-size problems at once is the absolute sum, and it overstates a month that will probably be fine. Working out which of the two is the larger and planning for that is closer to this bank's own rule.

What shape does this bank's own measure actually have?

Not a straight line. The first surprise is the bend in it, and the bend is where the interesting behaviour lives. Hold the euro short, the sterling long, the yen short and the dirham long exactly where they are and move only the dollar. Neither of the two short rows is being touched, so the short side stays at Rs 120 crore throughout. The long side is the dollar plus the Rs 48 crore of sterling and dirham sitting behind it.

Start with a dollar position of nothing at all. The long side is Rs 48 crore, the short side is Rs 120 crore, and the greater of the two is Rs 120 crore. Now buy dollars. At Rs 48 crore of dollars the long side is Rs 96 crore, still under the short side, and the reported figure is still Rs 120 crore. At Rs 72 crore of dollars the long side reaches Rs 120 crore exactly, and the two sides are equal. The point where the two sides cross is the kink. Past it, every further rupee of dollar long adds a rupee to the reported figure. The long side has become the binding sideWhichever of the long or short total is larger, and therefore the only side the greater-of measure can see today..

Below the kink the reported figure does not move at all when the dollar book changes, and above it the reported figure moves rupee for rupee. The bank sits at Rs 144 crore of dollars, comfortably above the kink, so today it is in the second regime. The second regime is why the whole of its measured headroom, Rs 48 crore of it, sits on the long side and nowhere else. Taking the dollar long from Rs 144 crore to Rs 192 crore puts the long side at Rs 240 crore, exactly the cap.

Two things in that table repay a second look. The first three rows are identical in the last two columns while the first column changes by Rs 72 crore, and that is the flat stretch drawn above. And the sixth row is not a hypothetical: Rs 276 crore is exactly the figure this bank's overnight position reached in month 9, breach B2, and the overnight cap below comes back to it.

What happens if the bank closes its second largest position?

How far down can the reported figure go if the bank tries?

Not to zero, and this is the mirror image of the blind side. Suppose the treasury desk sets out to bring the number down and works only on the long book, the side the headline is reading today. The desk sells dollars, then sterling, then the dirham, until the long side is nothing at all. The short side is still Rs 96 crore of euro plus Rs 24 crore of yen, a total of Rs 120 crore. The greater of the two is Rs 120 crore, and utilisation is 50.0 per cent of the Rs 240 crore cap.

With the short side untouched, no amount of work on the long side takes the reported figure below Rs 120 crore, so the utilisation of this cap has a hard floor of 50.0 per cent. A hard floor is a striking thing for a control to have. Half the range of the number is unreachable by managing the side the number is currently reading, and getting into that half requires working on the side the number is currently blind to.

The two findings are the same fact seen from opposite ends. Above the kink, adding to the long side moves the headline one for one and the short side is invisible. Below the kink, the short side sets the number and the long side is invisible. The greater-of measure always has exactly one side it can see, and the other one is doing nothing to the headline at all until it becomes the larger.

Which other open positions does this bank carry?

Currency is the easiest open position to see, because a currency row is obviously a balance in something other than rupees. Currency is not the only open position, and three more sit on this invented bank's own sheet.

The first is the held for trading book of Rs 3,600 crore. Whatever is inside it, the bank is exposed to the prices of those instruments, and that exposure is open unless something has been put against it. The second is the repricing mismatch across the eight buckets RB1 to RB8. More of this bank's assets reprice inside a year than its liabilities do, and that difference is an open position in interest rates: nobody bought it deliberately, it emerged from taking deposits one way and making loans another, and it is exposed all the same. The third is the Rs 480 crore net investment in one overseas branch. The investment is an open currency position sitting outside the five rows, and it is treated separately because a rate move on it lands somewhere other than the profit and loss account. The separate treatment is a comparison of its own, covered under transaction exposure against translation exposure.

Now the observation that ties this section to everything before it. Vindhya Commercial Bank Limited set four caps that touch market risk. Limit L5 caps a one-day value at risk figure at Rs 18.0 crore. Limit L6 caps a month to date stop loss at Rs 30.0 crore. Limit L8 caps a change in the value of equity at Rs 990 crore. Limit L7 caps the aggregate net open currency position at Rs 240 crore. Of the four, exactly one is a cap on a position and the other three are caps on a number computed about one. The count is not a criticism of any of the four. A limit on an exposure and a limit on an estimate of an exposure fail in completely different ways, so the word limit is worth reading carefully: the first is breached by a decision somebody took, and the second can be breached or unbreached by a change of method.

What does an overnight cap not see?

The working day, and that omission follows from how the limit is defined rather than from any oversight. Limit L7 caps the net overnight open foreign exchange position, meaning the exposure this bank carries through to the next working day. An overnight positionThe exposure carried through to the next working day, which is what limit L7 caps in this invented bank. is what is left after the desk has finished squaring up, and it is a single measurement taken at a single moment.

An intraday positionThe exposure carried during a working day, which an overnight cap does not measure and which can be much larger. is a completely different quantity. Deals arrive, get warehoused for an hour and get offset later in the afternoon, so between the opening and the cut-off a dealing desk can be very much larger than it ends up. Every one of those hours is real exposure. A cap measured at the cut-off records none of it.

The everyday version is almost exact. A speed limit checked only at the moment the car is parked says nothing about the drive. If the only measurement is taken in the parking bay, every reading is zero, and the reading is honest about what it measured and silent about everything else.

Month 9 day 2 at this invented bank is what happens when the overnight figure itself goes over. A customer deal was booked after the cut-off, the position reached Rs 276 crore against the Rs 240 crore cap of limit L7, an excess of Rs 36 crore being 15.0 per cent over, and it was squared on the morning of day 3. The excess is breach B2, it lasted one business day, it was picked up by the end of day position report and it was escalated the same evening. The breach was found because a measurement happened to be taken at the one moment the cap is defined on, a good outcome and a narrow one. How the deal came to be booked after the cut-off is a question about process and controls, answered in the operational risk sequence.

Two failures share a date and must not be run together. Month 9 day 2 also carries this bank's worst backtesting exception of the year on the trading book. The excess and the exception are two different failures on one bad day, neither caused the other, and they are measured on different books by different means.

What does closing a position do that hedging does not?

Closing removes the exposure. Removing the exposure is the entire difference, and it sounds too simple to need saying until three quite different acts are described with the same casual verb in the same meeting.

Closing a positionRemoving the exposure, which is a different act from hedging it and a very different act from measuring it. means the balance in that currency is gone. Nothing is left to move when the rate moves. There is no residual, no counterparty and no document. Hedging means the exposure stays exactly where it is and something is put against it, and a move on the exposure is then met by an opposite move on the cover. Hedging is a different act with its own decision, its own counterparty and its own documentation requirement, and the hedging policy that governs it is covered separately. Measuring, the third verb, does neither: it produces a sentence and leaves both the exposure and the cover untouched.

The household version is a coat that is no longer wanted. Returning it to the shop is closing. Keeping it and taking out insurance against it being ruined is hedging. Writing down what it cost is measuring. Only the first means the coat is gone, and only the second means there is now a relationship with an insurer as well as a coat.

The three verbs act on different things: closing acts on the exposure, hedging adds a second exposure that is meant to move the other way, and measuring acts on nobody's balance sheet at all. A great deal of confusion in a treasury conversation comes from the middle one being described in the language of the first, as though a hedged position were a closed one. It is not. A hedged position is two open positions that are expected to offset, and expectation is a thing that can be wrong.

Who actually manages to this number, and what for?

Four people read the same Rs 192 crore and do four different things with it, and none of them is reading it the way a textbook would.

Devendra Achar, head of treasury at this invented bank, reads it as headroom. Not as a statement of risk but as a permission: there is Rs 48 crore between today and the cap, and every dollar deal that lands this afternoon consumes some of it. He knows something the number does not say: all of the headroom is on one side. Buying dollars uses it up rupee for rupee. The headline is not reading the euro row today, so selling euro creates none. A limit reader is not asking how much risk there is; they are asking how much more of it this afternoon is allowed to add, and on which side of the book.

Sunanda Ravikumar, the chief risk officer, reads the same figure and asks a different question: which side is binding, and therefore which half of the book has been invisible to the control this month. The question has a real answer that changes over time, and the answer is not on the report. A risk function that cannot say which side is binding today is managing to a number without knowing what the number can see.

An analyst or a lender outside the bank reads Rs 192 crore and should immediately ask how it was aggregated. Two banks holding identical books can report Rs 72 crore, Rs 192 crore or Rs 312 crore, and comparing the reported figures without knowing the method compares three different questions. The right first question of any aggregate is not how big is it but what was added to what.

And then there is the reader nobody thinks about, the household on the other side of a transaction with an institution like this one. A person buying foreign currency for a child's fees deals with a bank whose own currency book is open somewhere in the background. The household will never see Rs 192 crore, will never hear the word aggregation, and is nonetheless in a system where somebody's method choice determines whether an exposure looks like 30.0 or 130.0 per cent of a cap. The exposure exists for everybody in the chain and the reporting choice exists only for the institution.

Where does the method come from, and what binds an Indian bank?

The greater-of arithmetic did not start at Vindhya Commercial Bank Limited. The Bank for International Settlements at bis.org publishes the shorthand method for aggregating a foreign exchange position, and that is the origin of the two sided construction: sum the longs, sum the shorts, take the greater. Naming that origin is the easy half.

The half that decides what actually happens in India is separate. The Reserve Bank of India at rbi.org.in sets what an Indian bank must compute for its open currency position, on what basis it must aggregate, how large a position it may carry, what must be reported, to whom and from what date. Every cap and every figure worked above belongs to Vindhya Commercial Bank Limited, and limit L7's Rs 240 crore is that invented bank's own internal number rather than anybody's requirement.

What is worth carrying away?

Six things, and they are all checkable against the five rows already set out.

An open position is an exposure that has not been closed and has not been covered, and it exists from the moment the exposure is taken. An open position is not a measure, and every figure elsewhere in this sequence is a sentence about a position rather than a position. Vindhya Commercial Bank Limited holds five currency rows: a dollar long of Rs 144 crore, a euro short of Rs 96 crore, a sterling long of Rs 36 crore, a yen short of Rs 24 crore and a dirham long of Rs 12 crore.

The five rows aggregate to Rs 192 crore on this bank's own greater-of method, and Rs 192 crore is 80.0 per cent of its own Rs 240 crore cap. The same five rows give Rs 72 crore added algebraically at 30.0 per cent, and Rs 312 crore added in absolute terms at 130.0 per cent, a breach. The greater-of figure has a kink at a dollar long of Rs 72 crore, a floor of Rs 120 crore and 50.0 per cent, and a blind side: closing the entire euro short moves it by nothing at all.

Limit L7 caps the overnight figure, so it never sees the working day, and in month 9 that overnight figure reached Rs 276 crore against the cap, an excess of Rs 36 crore, being breach B2. And of the four market risk caps this bank set itself, only limit L7 is written on a position at all. One sentence carries the rest: the exposure is the thing, the total is a choice, and the choice decides what anybody thinks they are looking at.