Exposure and Leverage: Gross and Net in the Same Book

Gross exposure and net exposure are two different numbers describing two different risks in the same book. Nilgiri Absolute Return Fund, invented, holds Rs 6,50,00,00,000 long and Rs 2,50,00,00,000 short on Rs 5,00,00,00,000 of net assets, so gross is Rs 9,00,00,00,000 at 180.0 per cent and net is Rs 4,00,00,00,000 at 80.0 per cent.

One of those two figures arrives on its own. One number, in one line of reporting, with the other one nowhere in sight, is how exposure normally arrives. That single number, whichever of the two it happens to be, cannot answer the question a reader is almost certainly about to ask it. The number is not a bad one, and nobody computed it wrongly. It was built to answer a different question, and it answers that one perfectly while staying completely silent on the reader's.

The subject is narrow and it is arithmetic. Three input figures go in. Two measures come out. One measure adds two of the inputs and the other subtracts them, and everything that follows comes from that one difference of sign. Both measures are computed below on one invented fund's own book, the question each one answers is named, so is the far more useful matter of what each one is blank about, and the whole range they can take between them is laid out as a ladder a book can be read off. No level of either measure says anything about the fund holding it. The arithmetic supports no such judgement.

What are the three inputs, and why do only two measures come out of them?

Start away from funds altogether. Think about a vegetable seller who sets up outside a station every morning. She buys Rs 8,000 of stock at the wholesale market before dawn. The stock is her whole position: eight thousand rupees of tomatoes and onions that can go up or down in value between the market and the evening. Now add one thing. A neighbouring stall has run short and asks her to deliver Rs 3,000 of onions tomorrow, at today's price. She agrees before she has bought them. She has now promised to hand over goods she does not have. If onion prices fall overnight, she buys them cheaper than the price she has locked and gains on that promise. If they rise, she loses on it.

How much of her morning is exposed to the price of vegetables has two entirely different, entirely correct answers. Every rupee of both the stock and the promise moves with a price, so adding the two gives Rs 11,000. On a day when the whole vegetable market moves in one direction, part of what she loses on the stock she makes back on the promise, so subtracting the two gives Rs 5,000. The two answers are not rivals. The two questions are different, and the seller needs both answers to know what her day looks like.

A fund running a bought side and a borrowed-and-sold side is that stall at a very large scale, with three figures instead of two. The first is the long bookThe total value of everything the fund has bought.. The long book is the total value of everything the fund has bought and holds. The second is the short bookThe total value of everything the fund has borrowed and sold.. The short book is the total value of everything the fund has borrowed and sold, and therefore has to hand back at some point. The third is net assetsWhat the fund holds less what it owes, which is the denominator of both measures.. Net assets are what the fund holds after everything it owes has been taken off, and net assets are the money that actually belongs to the people who subscribed.

Only two useful measures come out of three inputs because there are only two things that can be done with the first two figures before dividing by the third. The long book and the short book can be added, or one can be taken away from the other. Every exposure measure a reader will meet on a long and short book is one of those two arithmetic moves, followed by a division by net assets, and there is no third move that means anything. The pair of moves is worth holding on to. It turns what looks like a jargon problem into something that can be done on the back of a receipt.

Two words get used as if they were interchangeable and they are not. One point of vocabulary comes before the arithmetic. Exposure is how much position is on, measured against net assets. LeverageHolding more than net assets would buy, which shows up as gross exposure above 100 per cent. is the separate matter of holding more than the fund's own money would buy. Leverage is what allows exposure to run past one hundred per cent in the first place. The two are related and they are not the same word. Where a long book is larger than net assets, somebody has lent the difference, and in this invented fund's case that somebody is its prime broker, Marudhar Securities Private Limited, invented. One counterparty holds the positions, lends the stock that is sold short, lends the cash that funds the long side and sets the margin. The concentration of four roles in one relationship is covered separately.

What is gross exposure, and what does adding the two sides answer?

Gross exposureThe long book plus the short book, against net assets. is the long book plus the short book, divided by net assets. On Nilgiri Absolute Return Fund, invented, at the record date, that is Rs 6,50,00,00,000 plus Rs 2,50,00,00,000, giving Rs 9,00,00,00,000. Dividing Rs 9,00,00,00,000 by net assets of Rs 5,00,00,00,000 gives 1.80, or 180.0 per cent.

The addition is the part that surprises people, so it is worth being slow about it. A short position feels like a negative, and in one specific sense it is: it moves the other way from a long one when the market as a whole moves. But it is not a negative amount of risk. Every rupee on the short side is a rupee of position that exists, that has to be closed out one day, and that can move. Adding the two sides says how much position is actually on, and it is the right answer whenever the two sides can move against the fund at the same time. Two sides moving against the fund at once is not exotic. A long holding falling while a short holding rises is one bad afternoon in two different sectors, and both halves of the book are perfectly capable of doing it on the same day.

Gross exposure of 180.0 per cent says something very concrete and nothing more. The figure says that for every one hundred rupees of money belonging to the people who subscribed, there are one hundred and eighty rupees of position out there able to move. The figure does not say the fund borrowed eighty rupees, though on this book the long side does exceed net assets and so a part of it is indeed financed. It does not say the fund will lose one hundred and eighty rupees for every hundred the market falls. And nothing in it says whether that book is a sensible one. Gross exposure is a size, and a size on its own is not a verdict.

What is net exposure, and what does subtracting them answer instead?

Net exposureThe long book less the short book, against net assets. is the long book less the short book, divided by the same net assets. Rs 6,50,00,00,000 less Rs 2,50,00,00,000 is Rs 4,00,00,00,000. Over Rs 5,00,00,00,000 that is 0.80, or 80.0 per cent. Same three inputs, same denominator, one sign changed, and the answer is now less than half the size.

The subtraction answers a completely different question: how much of the book a general market move actually reaches. Go back to the vegetable stall. On a morning when every vegetable in the market is dearer by a tenth, the seller gains a tenth on her Rs 8,000 of stock and loses a tenth on her Rs 3,000 promise, and what is left over is a tenth of Rs 5,000. The two sides offset, and they offset for that one kind of move and no other. A move that lifts or drops everything at once is exactly the move the short side is positioned against, so net exposure is the figure a general market move acts on. On this fund's book, a general market move of ten per cent acts on Rs 4,00,00,00,000, which is Rs 40,00,00,000, or 8.0 per cent of net assets.

Put the other way round, that becomes useful. Net exposure of 80.0 per cent means the book leans towards things going up, but leans by less than the fund's own money. Net exposure of 100.0 per cent would mean the book moves with the market as if every rupee of subscribed money were in it and nothing more. Net exposure of nil would mean the book does not move with the general market at all. Nil is a real and reachable setting, and it appears on the ladder further down. And net exposure below nil is a book leaning the other way. Such a book has its own name and its own arithmetic.

Notice the one thing the two measures genuinely share: the denominator. Both are divided by net assets. The shared denominator carries a consequence worth storing away now. It becomes important the moment a book has a bad week. If net assets fall and not one position is bought or sold, both measures rise. The numerators sat still while the thing underneath them shrank. Where that chain leads is covered separately, but the mechanism belongs here: both measures can move sharply without anybody at the fund placing a single trade.

What is each of the two numbers silent about?

The silences are what make the pair worth learning, and they are the part most treatments skip. Each measure answers its own question well. Each is completely blank on the other one. The two measures are not two views of the same thing, the way a photograph from the front and a photograph from the side are still both pictures of one chair. The two are separate readings, and where one speaks the other has nothing at all to say.

Gross exposure is silent about direction. The addition throws the direction away on purpose, so gross exposure cannot say which way the book leans. A book of Rs 6,50,00,00,000 long and Rs 2,50,00,00,000 short and a book of Rs 2,50,00,00,000 long and Rs 6,50,00,00,000 short have exactly the same gross exposure of 180.0 per cent, and the second one gains when the market falls while the first one loses. From the gross figure alone those two books are indistinguishable. Gross exposure says how much is on and refuses to say which way it points.

Net exposure is silent about size. The subtraction throws the size away instead, so net exposure cannot say how much position is on. The point stops being abstract once the fund's net exposure is held at 80.0 per cent and the question becomes what books could produce it.

Every row on that picture has net exposure of exactly Rs 4,00,00,00,000, being 80.0 per cent of the same Rs 5,00,00,00,000 of net assets. A book of Rs 4,50,00,00,000 long against Rs 50,00,00,000 short gives it. So does Rs 5,50,00,00,000 against Rs 1,50,00,00,000. So does this fund's own Rs 6,50,00,00,000 against Rs 2,50,00,00,000. So does Rs 8,50,00,00,000 against Rs 4,50,00,00,000, and so does Rs 10,50,00,00,000 against Rs 6,50,00,00,000. The gross figures for those five are 100.0, 140.0, 180.0, 260.0 and 340.0 per cent. Five books, one net figure, and gross figures that are nothing like each other. No cleaner demonstration exists that the net number on its own has not described a book.

Take it to the extreme and the point gets sharper still. A book with Rs 6,50,00,00,000 long and Rs 6,50,00,00,000 short has net exposure of nil. So does a book with Rs 20,00,00,000 long and Rs 20,00,00,000 short. Both are equally untouched by a general market move. One of them has Rs 13,00,00,00,000 of position on, being 260.0 per cent of net assets, and the other has Rs 40,00,00,000, being 8.0 per cent. A book can have no net exposure to the market at all and still have a great deal of position at work, and the net figure will report nil for both of them without blinking.

What happens to both measures as the short book grows?

Now to the ladder. On the ladder the two measures stop being definitions and start being a shape that can be held in the head. Two of the three inputs stay completely still. The long book stays at Rs 6,50,00,00,000 and net assets stay at Rs 5,00,00,00,000. Only the short book moves, from nothing at all up to Rs 7,50,00,00,000, with both measures read off at each setting.

The highlighted row is the fund's own book. Everything above and below it is the same fund with a different short side and nothing else changed, and none of the other rows is a thing this fund has ever done. The other rows are there to show the shape.

The invariant, and why it makes the ladder readable at a glance

Look down the last column. The column reads 260.0 nine times. The repetition is not a coincidence and it is not rounding being kind. While the long book and net assets are both held still, gross exposure plus net exposure is a constant, and that constant is twice the long book divided by net assets. Twice Rs 6,50,00,00,000 is Rs 13,00,00,00,000, and over Rs 5,00,00,00,000 that is 260.0 per cent.

The reason is one line of algebra that can be done in the head. Gross is the long side plus the short side. Net is the long side less the short side. Add those two expressions together and the short side cancels itself out, leaving twice the long side. The short book has vanished from the sum entirely, and a sum without the short book in it cannot move when the short book does.

The practical version is a see-saw. Every Rs 25,00,00,000 of short added is 5.0 per cent of net assets, so it lifts gross exposure by 5.0 points and lowers net exposure by the same 5.0 points, at every setting, all the way down. The see-saw means any row can be read off any other row without dividing anything. The two have to add to 260.0, so gross exposure of 230.0 per cent on this held long book puts net exposure at 30.0 per cent. Given net exposure fallen to nil, gross is at 260.0, and that follows without the short book being stated at all.

One caution on the invariant. The invariant is a tool and not a law of nature, and it holds only while the long book and net assets are both held still. Move the long book and the constant moves with it: a long book of Rs 5,00,00,00,000 on the same net assets gives a constant of 200.0 rather than 260.0. Move net assets and it moves again. The see-saw is a property of one held long side, not a fact about exposure in general, and a reader who forgets that will apply 260.0 to a book it was never derived from.

Where are the three boundaries of the whole range?

Any book sits in one of the regions the ladder divides into, so the ladder has three places on it worth naming. Knowing the region indicates what to expect from the two figures before either has been read.

Boundary one is a book with no short side at all, and there the two measures are the same number. Long plus nothing and long less nothing are the same arithmetic. On this held long book both read 130.0 per cent. The identity is the whole reason a fund with no short side is quoted with one exposure figure rather than two: the second one would be a copy of the first, and nobody prints a number twice. Where a single exposure figure arrives with nothing else attached, the first question is not what it means but whether there is a short side at all. If there is a short side, one of two numbers has gone missing.

Boundary two is the point where the short book equals the long book, so net exposure reaches nil while gross exposure stands at 260.0 per cent. This is the single most instructive reading on the whole range. A book at that setting does not move with the general market. Lift every price by a tenth and the gain on the long side is matched rupee for rupee by the loss on the short side. And yet Rs 13,00,00,00,000 of position is on, being two and a half times the fund's own net assets, and every rupee of it can still move if the two sides move differently from each other. A book with no market exposure is not a book with no exposure. The two are different sentences, and only one of them is true there.

Boundary three is past that point. The short book is larger than the long book there, and net exposure falls below nil. A book in that region is net shortA book whose short side is larger than its long side, so net exposure is below nil., which means it now leans towards prices falling rather than rising. At a short book of Rs 7,50,00,00,000 against the held long book, net exposure is minus Rs 1,00,00,00,000, being minus 20.0 per cent, and gross exposure is 280.0 per cent. Read together, the two figures say what that book is: it leans modestly one way, and it does so with a great deal of position on. Either figure alone says no such thing.

The short side is doing a great deal of work here, so it earns one sentence of its own. The price cannot fall below nothing, so a short position sold at a hundred rupees can gain at most a hundred rupees, while its loss has no arithmetic ceiling at all. The asymmetry is covered under short selling.

What goes wrong for a reader handed only one of the two numbers?

What does an adverse move do to both measures at once?

Here is a trap that has caught careful people, and it is a trap about words rather than arithmetic. A move of ten per cent against the fund can mean one of two completely different things, and the two give different answers. Which one is meant has to be stated every time.

An adverse move of ten per cent, as the phrase is used here, means the long side falls ten per cent and the short side rises ten per cent at the same time. Both halves of the book go the wrong way together. An adverse move is the move gross exposure was built to answer, and on this book it costs Rs 65,00,00,000 on the long side plus Rs 25,00,00,000 on the short side, being Rs 90,00,00,000, or exactly ten per cent of the gross book.

A general market move of ten per cent means something else entirely: every price rises ten per cent, or every price falls ten per cent, and the two sides move the same way. A general market move is the move net exposure was built to answer, and a ten per cent rise on this book leaves net assets Rs 40,00,00,000 better off, being ten per cent of the net book. Read the phrase the second way when the first was meant and the answer comes out at 183.3 per cent where it should have been 209.8 per cent, with nothing at all to signal the error.

The reason both measures move at all after such a move is the shared denominator. Net assets fall by the loss, so both ratios are divided by something smaller than before. Here are the three adverse settings worked through on this book, with every figure computed on the whole rupee amounts rather than on the percentages.

Take the middle row slowly. Another treatment builds a whole scenario on that row. A ten per cent adverse move leaves the long side at Rs 5,85,00,00,000 and the short side at Rs 2,75,00,00,000. The long side shrank by more than the short side grew, so gross exposure in rupees has actually fallen, to Rs 8,60,00,00,000. Net assets have fallen further in proportion, to Rs 4,10,00,00,000. Rs 8,60,00,00,000 over Rs 4,10,00,00,000 is 209.8 per cent, up from 180.0. Both measures moved, the fund sold nothing and bought nothing, and gross exposure rose by nearly thirty points purely because the denominator shrank faster than the numerator did.

The chain a large loss starts, including what a prime broker asks for when it happens, is covered separately, and the 209.8 per cent reading is the scenario that treatment is built on.

How does somebody reading a fund actually use the two figures together?

Take an analyst at an institution that has money with several outside managers and has to write a short internal note on each of them every quarter. Her routine is mechanical, and it is worth watching: it is exactly the arithmetic above put to work.

She reads three figures off the reporting rather than one: the long book, the short book and net assets. Everything else she computes herself in about a minute, and she is never at the mercy of which of the two measures a particular manager chose to print. She writes both down side by side, and she writes down the quarter they belong to. An exposure figure without a date attached is a figure about nothing.

Then she does two multiplications. Ten per cent of the net figure gives her the size of a general market move on this book. Ten per cent of the gross figure gives her the size of a move where both sides go the wrong way at once. On this invented fund at the record date those are Rs 40,00,00,000 and Rs 90,00,00,000, and her note carries both. A note carrying one of them has answered half a question. She does not write that either figure is large or small. She writes what they are and what each one would cost.

Last, she compares this quarter's pair against last quarter's pair, and she asks the question the shared denominator makes necessary: did these ratios move because somebody traded, or because net assets moved underneath them? If the long book and short book in rupees are unchanged and both percentages have risen, nobody traded and the fund lost money. If the rupee figures have changed, somebody made a decision. Two ratios and their three inputs, read together across two dates, separate a decision from a consequence, and neither ratio alone can do it.

A lender looking at the same fund is doing something adjacent. The financing behind a long book larger than net assets has to come from somewhere, and the counterparty providing it holds the positions and sets the margin against them. The counterparty's demands are set by its own contract with the fund, and they are covered separately. The connection worth carrying away is only this: exposure above one hundred per cent and borrowing are two descriptions of related facts, but they are not the same measurement, and an account that treats them as one word will confuse both.

Where does each of the three inputs actually come from?

Field notes, and they are notes about where a figure is found rather than about what any level of it means. Three inputs, three places to look, and one of them is not in the same document as the other two.

The long book is read off the schedule of positions, added up on the bought side. The long book is a total of values and not a count of positions, so a book of four holdings and a book of four hundred can produce the same figure. It is stated at what the positions are carried at on the date of the schedule. For anything quoted that is a price, and for anything not quoted it is a mark somebody struck.

The short book is read off the same schedule, added up on the borrowed-and-sold side. The one thing to be careful about here is which value is being shown: a short position is carried at what it is worth now, not at the price it was sold at, and those two are the same figure only on the day the position is opened. In this invented fund's case, Palani Valuation Advisors LLP, an invented limited liability partnership, is the independent valuation agent behind marks that are not simply read off a screen.

Net assets come from somewhere else entirely: the statement the administrator strikes. The administrator for this invented fund is Kolar Fund Services Private Limited. The statement gives what the fund holds less what it owes, and that figure is what investors are dealt in and out at. Net assets are the denominator of both measures, so both ratios move whenever net assets move, whether or not a single position has changed. The shared denominator is the point worth carrying out of the field notes, and it is why the date on a net asset figure matters as much as the figure.

Two smaller notes. First, the three inputs are struck as at a date, and a schedule of positions and a statement of net assets are not always struck as at the same date. Where they are not, an exposure ratio is mixing two moments, and the honest thing is to say which date each input came from. Second, none of the three inputs is a cash figure. Both measures are position measures, so what the fund pays to borrow stock, what it pays on cash lent to it and what it pays in fees enter neither. The costs are real and are covered separately. Adding them to an exposure number would produce something that is neither one thing nor the other.

What does the Securities and Exchange Board of India set about leverage, and why is no figure here?

One question follows every account of exposure: how much is a fund allowed to have?

Nilgiri Absolute Return Fund, invented, is registered as a Category III Alternative Investment Fund. Alternative Investment Fund categories, registration, reporting and conduct in India are set by the Securities and Exchange Board of India, at sebi.gov.in. Conditions attaching to that registration, including anything at all about leverage, borrowing or the use of positions of the kind computed above, are set there and there only. Requirements of that kind change. A number printed in a reference text is frozen on the day it was written, and a reader who takes it as current has been handed a stale figure dressed up as a fact.

Every setting on the control above is arithmetic on an invented book rather than a statement about what any fund may do. Limits, caps, conditions, minimums, permitted levels and effective dates belong to the authority named, and the current text at sebi.gov.in is the only source that can be right on the day it is read.

The same discipline runs one step further. No level of exposure is large or small here in any sense that carries a judgement. Gross exposure above one hundred per cent means a loss can exceed what the same move would do to a fund holding only its own money. Mechanism of that kind is the subject. Calling that arrangement dangerous, or calling a lower one safe, is a verdict, and the arithmetic gives no basis for one. Different books look different from each other and each carries its own arithmetic. A tool stops there.