How Long-Short Strategies Work: Two Books and One Net

A long-short book is two books and one net. Nilgiri Absolute Return Fund, invented, holds Rs 6,50,00,00,000 long and Rs 2,50,00,00,000 short against Rs 5,00,00,00,000 of net assets at the record date. Its result splits exactly into two parts: what the net between the books earned or lost from the market move, and what the choice of positions added on each side.

A long-short result rests on a single arithmetic fact, and it is worth holding still for a moment before any rupee figure arrives. When a fund has bought some things and has sold other things it does not have, a general move in prices does not act on everything it holds. The move acts on the difference. The two books push in opposite directions, and only what is left over after they have cancelled is exposed to the market at all. That leftover is one subtraction, it is a number in rupees, and once it is in hand the whole of a long-short result can be pulled apart into a part that came from the market and a part that came from choosing.

The second fact is that pulling the result apart is not an interpretation. The split is an identity. The result on the long book plus the result on the short book is exactly equal to the net between the books multiplied by the market move, plus each side's own difference from the market. Because the second count is the first one rearranged, the year can be counted up book by book or source by source, and the two counts give the same rupee figure every time. The split can therefore be shown rather than argued about, and what a long-short manager is actually being paid for becomes answerable in numbers instead of adjectives.

What is a long-short book actually made of?

The whole structure fits in a kitchen, so start there. Suppose a household keeps two cooking gas cylinders at home, both bought and paid for. Then a neighbour lends the household a third cylinder, and it is sold to somebody down the lane for whatever it fetches today. There is now money in hand from that sale, and there is a promise: at some point a cylinder must be handed back to the neighbour. The cylinder handed back does not have to be the same one. Any cylinder will do.

Count the household's exposure. There are three cylinders' worth of position, but they do not all point the same way. Two of them are things that have been bought, and if the price of a cylinder in the town rises, those two are worth more. One of them is a thing that is owed, and if the price rises, buying a replacement to return costs more. Two up and one down leaves the household, on the whole, standing behind one cylinder. The household is net long one cylinder even though it is handling three, and that gap between three and one is the entire idea a long-short book is built on.

Now put a fund where the kitchen was. The long bookEverything the fund has bought. is everything the fund has bought and holds. If those shares rise, the fund gains; if they fall, the fund loses. Nothing about it is unusual, and it is exactly what any ordinary buyer of shares carries. The short bookEverything the fund has borrowed and sold. is the borrowed cylinder at scale. The fund borrows shares it does not have, sells them into the market at today's price, and carries an obligation to return those shares later. If those shares fall, it buys them back cheaper and keeps the difference. If they rise, it must pay more to return them than it received for selling them.

Both books exist at the same time, in the same fund, on the same day. Two books at once are what make the arrangement long-short rather than simply long or simply short. A fund with only a long book is a buyer. A fund with only a short book is running a different approach again, and that approach is covered separately. The fund that runs both at once behaves like neither, and the difference shows as soon as prices move.

The figures below stay fixed throughout. Nilgiri Absolute Return Fund, invented, is an open-ended fund managed by Nilgiri Alternatives Advisors Private Limited, invented. At the record date it holds long positions of Rs 6,50,00,00,000 and short positions of Rs 2,50,00,00,000, against net assets of Rs 5,00,00,00,000. Those three numbers are all that is needed. Every other figure is derived from them and from clearly labelled assumptions.

There is something odd about that list. The long book alone, at Rs 6,50,00,00,000, is larger than the fund's whole net assets of Rs 5,00,00,00,000. The fund has bought more than it has. Buying more than it has is possible because somebody lent the fund the difference, and because somebody lent it the shares it sold short. In this arrangement one counterparty, Marudhar Securities Private Limited, invented, holds the positions, lends the stock that is sold short, lends the cash that funds the long book, and sets the margin. One counterparty carrying all four of those roles at once is a subject in its own right and is covered separately. Take the financing as settled and work on the books themselves.

What does one subtraction show that the two books cannot?

Subtract. Rs 6,50,00,00,000 less Rs 2,50,00,00,000 is Rs 4,00,00,00,000, and that figure has a name. The figure is the fund's net exposureThe long book less the short book, which is what the market move acts on., and it is the amount a general market move actually multiplies. Against net assets of Rs 5,00,00,00,000 it is 80.0 per cent, and the two books added together, being Rs 9,00,00,00,000, are 180.0 per cent of net assets. Both figures belong to Nilgiri Absolute Return Fund, invented, as at the record date, and neither is anything beyond what this one book happens to hold.

The gross figure and the net figure answer different questions, and a reader who has only one of them has an incomplete picture. The Rs 9,00,00,00,000 shows how much position is being handled: how many things can go wrong individually, how much borrow has to be arranged, how much margin has to be posted. The Rs 4,00,00,00,000 shows how much is riding on the direction of the market as a whole. Because the net figure is the one that turns into rupees when the market moves, the arithmetic below works with it. The full picture of how those two figures behave across every setting a book could take is covered separately.

Go back to the kitchen for one sentence. Three cylinders were being handled and one cylinder was the exposure. Rs 9,00,00,00,000 is the three, and Rs 4,00,00,00,000 is the one. Nothing more complicated than that has happened.

The single most useful habit with a long-short fund is doing that subtraction first, before reading anything else about it. A factsheet that quotes a long book and a short book has handed over the ingredients. Until they are subtracted, what the fund's result will do when the whole market moves remains unknown, and no amount of description about the positions will settle it.

Where does a result come from, and why can it be split at all?

A share does not move for one reason. On any given stretch of time some of what a share did was what everything did, and some of it was what that share did differently from everything. Splitting a share's move into those two parts discovers nothing. The split simply writes the same move as a sum. A sum can always be rearranged, and rearranging it is the whole trick.

Running the split needs a way of talking about the second part. If the market as a whole rose 10.0 per cent and a particular share rose 12.0 per cent, the share did 2.0 percentage pointsThe unit of difference between two percentages, used here to keep the two apart. better than the market. A move of 2.0 per cent better would mean something else entirely. The gap is 2.0 points, added on top. Keeping the two units apart is fussy, and it matters. Every figure in the worked cases below is one or the other.

The assumptions for the whole of what follows are set here, and they are assumptions rather than anything that happened. The long book of Nilgiri Absolute Return Fund, invented, is held 2.0 percentage points ahead of the market, and the stocks it has sold short run 3.0 percentage points behind the market, at every setting used below. Those two numbers are the fund's choices, expressed as numbers. Those two point-differences are the only thing standing in for skill, and both are assumptions of the illustration, exactly as the market moves used below are.

With that in place the decompositionSplitting one total into parts that add back to it exactly. falls out. The long book's move is the market move plus 2.0 points. Because the fund owes those shares rather than holding them, the short book's stocks move by the market move less 3.0 points and the fund's result on that book carries the opposite sign. Multiply each book by its own move, add the two, and gather the terms. Everything that multiplies the market move collects into the net exposure times the market move. Everything else collects into the two point-differences, one on each book. Two parts, and they add back to the total exactly.

Which kind of market move the split assumes, and which it does not

There are two entirely different things a reader might mean by a move of x per cent, and they give different numbers and answer different questions. Every worked case below takes the first of the two.

The first reading, and the one used on every worked case below, is a market move: one number that acts on both books at the same time and in the same direction. The market rises 10.0 per cent and the long book's shares rise, and the shares the fund has sold short also rise. A general market move does exactly that. Both books move together, and the fund's result depends on how far apart they end up.

The second reading is a dispersion move: the longs fall x per cent while the shares sold short rise x per cent at the same time, so the two books move apart in the worst possible direction at once. A dispersion move is not a market move at all. Nothing in the market went up or down as a whole; the fund's chosen longs simply did badly and its chosen shorts did well, both against it. Because both books lose together instead of offsetting, dispersion is a real risk and it produces quite different arithmetic. Dispersion answers a different question, and every figure below is the market reading and only the market reading. Under that second reading it is the Rs 9,00,00,00,000 of the two books added together that the move bites on rather than the Rs 4,00,00,00,000 of net, and that alone is enough to show why the two readings can never be swapped for one another.

What is the market component, and how much choosing went into it?

The market componentThe part of a result produced by net exposure multiplied by the market move. is net exposure multiplied by the market move, and nothing else goes into it. On this book, with the market up 10.0 per cent, the market component is Rs 4,00,00,00,000 times 10.0 per cent, being Rs 40,00,00,000. Two numbers went into that: how big the gap between the books was, and what the market did. Not one decision about any individual position enters the market component at all.

Sit with how strange that is for a moment. A fund can employ analysts, meet managements, build models, argue about a company for three months, and none of that work appears anywhere in the Rs 40,00,00,000. The market component would have been Rs 40,00,00,000 if the fund had bought a slice of everything in sight and shorted a smaller slice of everything in sight, so long as the gap between the two came to Rs 4,00,00,00,000. The market component is what the shape of the book earned, not what the contents of it earned.

A shopkeeper knows this feeling without any of the vocabulary. A shop on a street that suddenly gets a metro station does better, and so does the shop next door, and so does the shop across the road. Some of the extra takings belong to the shopkeeper's own work and some belong to the street. Nobody hands a shopkeeper a statement separating the two. The split hands exactly that statement to somebody reading a long-short fund.

What is the selection component, and where does it come from?

The selection componentThe part produced by each side differing from the market. is what is left after the market component has been taken out, and it has two halves, one from each book.

The long half is the long book multiplied by how far it ran ahead of the market. Rs 6,50,00,00,000 times 2.0 per cent is Rs 13,00,00,000. Read that carefully. The point-difference applies to everything the fund actually holds, so the multiplier is the whole long book, not the net.

The short half is the short book multiplied by how far the shorted stocks fell behind the market. Rs 2,50,00,00,000 times 3.0 per cent is Rs 7,50,00,000, and it is a gain to the fund. A gain on a short book in a rising market catches people out, so it is worth stating slowly. The fund owes those shares. Anything that makes them cheaper than they would otherwise have been reduces what the fund must pay to return them. The shorted stocks rising by less than the market is exactly that. The fund still loses money on the short book in a rising market, but it loses less than the market alone would have cost it, and the size of that saving is Rs 7,50,00,000.

Add the two halves. Rs 13,00,00,000 plus Rs 7,50,00,000 is Rs 20,50,00,000. The selection component depends only on the two point-differences and on the size of the two books, and none of those three things moves when the market does, so the figure is fixed for the whole of what follows. Hold on to it. The same Rs 20,50,00,000 reappears, unchanged to the rupee, in every case below.

What happens when both books rise together?

Three cases follow, and they are the spine of the whole split. In every one of them the book is the same, both choices are the same, and only the market changes. Adjectives hide exactly what needs to be seen, so every figure is in rupees.

Case one. The market rises 10.0 per cent. The long book, running 2.0 points ahead, is up 12.0 per cent, so Rs 6,50,00,00,000 becomes worth Rs 78,00,00,000 more. The shares the fund has sold short, running 3.0 points behind, are up 7.0 per cent, so returning them costs Rs 2,50,00,00,000 times 7.0 per cent, being Rs 17,50,00,000 more than the fund received for selling them. Rs 78,00,00,000 less Rs 17,50,00,000 is Rs 60,50,00,000 for the constructed year on Nilgiri Absolute Return Fund, invented.

The same year counts the other way too. Market component: Rs 4,00,00,00,000 times 10.0 per cent, being Rs 40,00,00,000. Long selection: Rs 13,00,00,000. Short selection: Rs 7,50,00,000. Added together they come to Rs 60,50,00,000, to the rupee. The two counts had to agree, and the fact that they do is not a coincidence to be admired but a check to be run every time.

Read what that split says. Of the Rs 60,50,00,000, Rs 40,00,00,000 came from carrying 80.0 per cent of net assets as net exposure into a market that rose. The market component is 66.1 per cent of the result, and it required no view about any company. The Rs 20,50,00,000 that came from the two choices is the remaining third. The whole figure is 12.1 per cent of the fund's Rs 5,00,00,00,000 of net assets over the constructed year.

What happens when both books fall together?

Nothing about the fund changes here. The same Rs 6,50,00,00,000 long, the same Rs 2,50,00,00,000 short, the same 2.0 points ahead and 3.0 points behind. Only the market is different.

Case two. The market falls 10.0 per cent. The long book, still 2.0 points ahead, is down 8.0 per cent, so it loses Rs 6,50,00,00,000 times 8.0 per cent, being Rs 52,00,00,000. The shorted stocks, still 3.0 points behind, are down 13.0 per cent, so the fund buys them back Rs 2,50,00,00,000 times 13.0 per cent cheaper than it sold them, gaining Rs 32,50,00,000. Minus Rs 52,00,00,000 plus Rs 32,50,00,000 is minus Rs 19,50,00,000 for the constructed year on Nilgiri Absolute Return Fund, invented, being minus 3.9 per cent of its net assets.

Count it by source and watch what moved. Market component: Rs 4,00,00,00,000 times minus 10.0 per cent, being minus Rs 40,00,00,000. Long selection: plus Rs 13,00,00,000. Short selection: plus Rs 7,50,00,000. Total minus Rs 19,50,00,000, again to the rupee.

The selection component was Rs 20,50,00,000 in case one and it is Rs 20,50,00,000 in case two, exactly. The market component went from plus Rs 40,00,00,000 to minus Rs 40,00,00,000. Identical choices, opposite results, and the whole of the difference between the two years is the market component and nothing else. No other sentence in this arithmetic is worth carrying away as firmly.

What happens when the two books simply move apart?

Case three strips the market out altogether, and it is the case that shows what a long-short book is for.

The market does nothing at all, ending the year exactly where it started. The long book is still held 2.0 points ahead of it, so the long book is up 2.0 per cent, gaining Rs 13,00,00,000. The shorted stocks are still 3.0 points behind it, so they are down 3.0 per cent, and buying them back cheaper gains the fund Rs 7,50,00,000. Total: Rs 20,50,00,000, being 4.1 per cent of net assets for the constructed year on Nilgiri Absolute Return Fund, invented.

Count it by source and there is nothing to count on one side. Market component: Rs 4,00,00,00,000 times nothing, being nothing. Selection component: Rs 20,50,00,000. The whole of the result is the two books moving apart from each other, and the market contributed not one rupee of it.

Case three is worth understanding before any of the others. A fund that has bought one set of things and sold another set short is not, in the first instance, taking a view about whether prices go up. The view being taken is that the things bought will do better than the things sold, and case three is what that view is worth on its own when nothing else happens. The result comes from the two books moving apart, and the market move is a separate matter that gets added on top or taken off.

Three cases are three points. The control below is the same arithmetic run at every point in between, and it is worth predicting before it is moved.

At what market move do the two parts cancel each other out?

The total has now gone up and gone down, and somewhere in between there is a setting where it is exactly nil. Finding it is one division, and the division is worth doing by hand because it makes the structure obvious.

The total is nil when the market component is exactly the negative of the selection component. The selection component is Rs 20,50,00,000. So the market component has to be minus Rs 20,50,00,000. The market component is Rs 4,00,00,00,000 times the market move. So the market move has to be minus Rs 20,50,00,000 divided by Rs 4,00,00,00,000, being minus 5.125 per cent.

The fund's constructed book breaks even on a market fall of 5.125 per cent, and that number is not a judgement about anything: it is one figure divided by another. Below that fall the book loses money; above it the book makes money. Slide the control to minus 5.125 per cent and the pale selection block and the bright market block are exactly the same size, one above the zero line and one below, and the dark total rule sits flat on the line between them.

Two things follow from that single number and both are worth noticing. The first is that the break-even point moves whenever either input moves. Make the choices better and the selection component grows, so the market can fall further before the book is under water. Make the net exposure bigger and the market component grows faster, so a smaller fall wipes the same selection component out. The second is that the break-even point is not a floor. A market that falls 20.0 per cent takes this book to minus Rs 59,50,00,000 even though the selection component is still the same positive Rs 20,50,00,000, and there is nothing in the arithmetic that stops at any particular number.

What is a long-short manager actually being paid for?

The split makes that question answerable, and the answer is uncomfortable in both directions.

Take the rising year. The fund made Rs 60,50,00,000 and Rs 40,00,00,000 of it came from the size of the gap between the books meeting a market that went up. Suppose the whole of that year's work on individual companies had been abandoned and the fund had simply held the same net exposure in whatever was cheapest to hold. On these assumptions it would have made Rs 40,00,00,000 anyway. The work produced the Rs 20,50,00,000, on the numbers of this constructed case.

Now take the falling year. The fund lost Rs 19,50,00,000, and a reader looking at that line alone would say the year went badly. Yet the work produced exactly the same Rs 20,50,00,000 it produced in the good year. Without it the loss would have been Rs 40,00,00,000 rather than Rs 19,50,00,000. The selection component never changed, so it was the same in the year that looked good and the year that looked bad.

So there are two separate jobs inside one fund, and they reach a reader added together as one number. The first job is choosing what to hold and what to owe, and its whole output is the selection component. The second job is deciding how big the gap between the two books should be. The decision is about the shape of the book rather than about any company in it, and its whole output is the market component. A reader who wants to know what a manager did has to know which of those two produced the result, and a single total will never say.

Whether Rs 20,50,00,000 a year of selection component is good, adequate, poor, or worth what the fund charges for producing it is a separate question. Answering it needs a comparison and figures the split does not supply. The split only stops the question from being answered by accident.

What risk does this arrangement carry, in its own terms?

Four things, and each one is arithmetic rather than opinion.

The first is what all of the arithmetic above establishes. The market component exists whether anybody intended it or not. Nobody at the fund has to decide to take a view on the direction of the market. If the two books are different sizes, a view on direction has been taken, and its size in rupees is the difference between them. A book that is Rs 4,00,00,00,000 net long is carrying Rs 4,00,00,00,000 of market direction, and calling the arrangement long-short does not remove one rupee of it. The only way to have no market component at all is to have no net exposure at all, and a book deliberately built so that its net exposure is nil is a different construction with different behaviour, covered separately.

The second is that the selection component can be negative. Every figure in this guide assumed the long book ran ahead of the market and the shorted stocks ran behind it. Reverse those two assumptions and the same arithmetic runs the other way. A long book behind the market and shorted stocks ahead of it produce a selection component that subtracts from the result rather than adding to it. The selection component never depended on the market, so the subtraction happens in a rising market and a falling one alike. Nothing in the structure makes the selection component positive. The structure only makes it separable.

The third is the short book's own asymmetry, a subject in its own right and covered separately. A position sold short can lose more than it can gain. A price can fall to nothing and no further, so the gain is capped at the whole value of the position. The loss has no such stopping point.

The fourth is that everything above is gross of what it costs to run. Borrowing shares to sell them short is paid for. Borrowing cash to hold a long book bigger than the fund is paid for. Every execution is paid for. Excluding all of it keeps the decomposition clean. No figure above is a return to any investor in anything.

What can be done with one factsheet and ten minutes?

One factsheet and ten minutes are the practical end of the subject. Far more people read about a long-short fund than run one, and the reading is where this arithmetic earns its keep. An analyst covering a manager, somebody sitting on an investment committee, a student writing up a case, and a person whose savings sit inside something that in turn sits inside one of these are all doing the same job: turning a reported number into an understood number.

First comes finding the two books and subtracting them. A document that reports a long book and a short book has supplied everything the market component needs. If it reports only a net figure, how much position is being handled to produce it cannot be seen, and if it reports only a gross figure, how much direction is being carried cannot be seen. Whichever one is missing is worth asking for, and its absence is information in itself.

Second, multiply. Take the net figure and multiply it by whatever the broad market did over the same period. The product is the market component, and it is the part of the result nobody had to choose. Subtract it from the reported total and what remains is everything the choices contributed. A real book's positions do not all move with the market to the same degree, so the calculation on real data is rough. It is close enough to change most conclusions and it takes under a minute.

Third, run it again on a period when the market fell. Running the split on a falling period is what separates a reading from an impression. A manager whose selection component holds steady across a rising period and a falling one has produced something the market did not hand over. A manager whose good period is entirely market component and whose bad period is entirely market component has been carrying direction. Carrying direction is a perfectly ordinary thing to do and a completely different thing from what the words long-short suggest.

Fourth comes holding on to what cannot be got. Two of the four inputs to this split are things a reader has to assume rather than read: the market move chosen to measure against, and how far each book ran from it. The split is only ever as firm as those two assumptions, and saying so out loud is the difference between an analysis and a number with a decimal point in it. A household deciding anything at all, or an institution running a formal process, both need that sentence attached to the arithmetic rather than left off it.