Short Selling: The Mechanics and the Asymmetry

Short selling is approach 7 of the eight, and it is also the machinery several of the others run on. The fund borrows stock it does not own, sells it, and must return the same stock later. A price can only fall to nil, so the gain is bounded. A price can rise without limit, so the loss is not.

The asymmetry is the whole of the subject. Most readers meet the payoff first, as a line on a chart, and never meet the four steps underneath it. The four steps underneath the payoff are where the asymmetry comes from. Why the loss has no ceiling only becomes visible once it is clear that the fund owes a quantity of a specific stock rather than an amount of money. So the mechanics come first, the shape comes second, and the arithmetic that produces the shape comes third.

What does a short position actually rest on?

Start away from any market. A neighbour has a sewing machine of a particular model. She agrees to lend it out on two conditions: that the same model comes back, and that a small fee is paid for every month it is out of her house. The borrower takes it, and because the borrower happens to think the model will be cheaper in six months, sells it in the second-hand bazaar for Rs 8,000 that afternoon.

The debt at that point is worth stating exactly. The debt is not Rs 8,000 but one sewing machine of that model, and the Rs 8,000 is simply cash held until the day one is bought. If the model becomes cheaper, say Rs 5,000, the borrower buys it, returns it, and keeps Rs 3,000 less the fee. If it becomes dearer, the machine is still owed. At Rs 12,000 the borrower is Rs 4,000 down. At Rs 40,000 the borrower is Rs 32,000 down. Nothing in the arrangement caps what the machine can cost on the day one has to be bought.

Every feature of a short position in this guide comes from that single difference between holding a thing and owing one. An obligation denominated in something whose price can rise has no natural ceiling. The party who lent the thing can ask for it back. And the party financing the arrangement watches its size grow as the price of the thing goes up. Owing rather than holding does all three, in a bazaar or in a market, and all three would be just as true of rice, brass or a sewing machine.

What is selling short, step by step?

Short sellingSelling stock the seller has borrowed and must return later. is the sewing machine arrangement, run on stock, inside a contract. The arrangement has four steps and they always happen in the same order. Nilgiri Absolute Return Fund, an invented open-ended fund, is registered as a Category III Alternative Investment Fund and holds net assets of Rs 5,00,00,00,000 at its record date.

Step one, the fund borrows the stock from somebody who has it, under an agreement that says the same stock comes back. Step two, the fund sells that borrowed stock in the market and receives cash. Step three, the fund sits with an obligation open, paying a fee for the loan of the stock for as long as it stays open. Step four, the fund buys the same stock back and returns it. Buying it back and returning it is coveringBuying the stock back and returning it, which ends the position., and the position is then over.

The fund picks the moment for step one and step two, and it usually picks the moment for step four, but only usually, and that word is doing an enormous amount of work. Step three is not a decision at all: it is a state the position sits in, and the fee runs while it does. Step four is the fund's decision right up until the day the lender asks for its stock back, at which point it stops being the fund's decision entirely. Two of the four steps are the fund's own and the last one is not.

Where does the stock come from, and what does borrowing it cost?

Somebody has to be willing to lend it. Lending stock out for a fee is a stock borrowThe arrangement under which the stock is lent to the fund, for a fee., and for this fund the borrow runs through one counterparty. Marudhar Securities Private Limited, invented, is the prime broker of Nilgiri Absolute Return Fund: it holds the positions, lends the stock that is sold short, lends the cash that funds the long book, and sets the margin. One counterparty holding all four of those roles at the same time is covered separately. Only the stock lending and the margin setting matter below, and both are taken as settled.

The borrow costs a rate on the value of stock borrowed, running by time, and the fee is charged whatever the position does. Nilgiri's own contracted borrow feeWhat the fund pays each year for the loan of the stock, whatever the position does. is 0.75 per cent a year. Its short book is Rs 2,50,00,00,000 of stock it does not own, so the borrow fee on the whole short book is Rs 1,87,50,000 a year. Taking a quarter at 91 days, that is Rs 46,74,658 in a quarter, rounded to the nearest rupee. The borrow fee is payable whether the position is working or not, so the fee is the only certain number in the whole arrangement.

The reach of that figure is narrow. The 0.75 per cent is this fund's own contracted rate with its prime broker. The rate is not a market figure, and it is not what borrowing stock costs anybody in India. Real borrow rates move with how easy the stock is to find.

What happens when the lender asks for its stock back?

Return to the sewing machine for a moment. Suppose the neighbour's own tailor breaks down and she needs her machine back next week. The agreement said that model would be returned, and it did not say the borrower chooses the week. So next week the borrower goes to the bazaar and buys one at whatever it costs that day. Whether the borrower still believes the model will be cheaper six months from now is not a fact about next week.

The lender of the stock asking for it back is a recallThe lender demanding its stock back, forcing the fund to buy the same stock in the market.. The fund then has to buy inPurchasing the stock in order to return it, at whatever price stands that day., meaning purchase the same stock in the market so that it can be handed over. A recall moves the timing decision from the fund to somebody else. A position can end on a day chosen by a party with no interest at all in what the fund thinks. The fund's own view of the price does not enter it, because the obligation is to deliver stock and not to be right.

A recall is the single largest difference between a short and a long, and it is the one that almost never appears in an explanation built around a payoff diagram. Somebody holding stock can wait for as many years as they like. The position asks nothing of anybody. A borrowed position is held on somebody else's stock, so it carries somebody else's decision inside it from the first day.

Why does the margin requirement rise as the position moves against the fund?

Think about a shop taken on rent where the deposit is written as a share of the current rent rather than as a fixed rupee sum. Rent goes up, and the landlord asks for a bigger deposit. Nothing unfair has happened and nobody has changed the terms. The deposit was always defined as a percentage of a number that moved.

A short position works that way. While the position is open the broker holds collateral against it, and this fund's contracted maintenance marginCollateral the broker requires against the position while it is open, which it can reset. is 15.0 per cent of the gross value of the position. Gross value is today's value of the position, not the value it carried on the day it was opened. So take one short of Rs 25,00,00,000 in Nilgiri Absolute Return Fund. At the start, 15.0 per cent of Rs 25,00,00,000 is Rs 3,75,00,000, and that is what is posted.

Now the price rises 20.0 per cent. A short's value is the cost of buying back what is owed, and that cost has just gone up, so the position is worth Rs 30,00,00,000. Two things happen in the same moment, and it is worth writing them as two separate lines because they are two separate demands.

The collateral demand and the loss arrive together rather than one after the other, so a reader who sized this position off the payoff alone would have budgeted Rs 5,00,00,000 and would be short by Rs 75,00,000 on the day. And the direction is the part to hold on to. On a long position that falls 20.0 per cent, the position is now worth less, so a requirement set as a percentage of current value goes down. On a short that rises, it goes up. The requirement moves with the position, and the position moves the wrong way exactly when the fund would rather it did not.

What shape does the payoff actually have?

Here is the arithmetic, and it is the whole of the asymmetry. A position is sold short at Rs 100 a unit. The result on each unit is Rs 100 less whatever price is paid to buy it back. The single subtraction produces everything below.

If the price falls to nil, the fund gains Rs 100 a unit and no more. There is nowhere below nil for a price to go. The gain is boundedHaving a ceiling that arithmetic imposes, as a fall to nil imposes on a short's gain. at exactly the price the position was sold at. If the price rises to Rs 200, the fund loses Rs 100. The loss already equals the largest gain the position could ever have made. At Rs 400 the fund loses Rs 300, three times that largest possible gain. At Rs 900 the fund loses Rs 800. There is no price on the upper side at which the subtraction stops producing a bigger number, so the loss side has no stated limit at all.

Now look at what that does to a picture. Any honest drawing of this has one side that halts against a hard line and one side that simply keeps going. Six prices are drawn below on one rupee scale, at 0.70 pixels a rupee for every bar without exception. The bars can therefore be compared against each other by length alone. Five of them fit. The sixth does not, and that is not a drafting problem.

Why is the asymmetry arithmetic rather than opinion?

Because it can be produced without knowing anything at all about the stock, the market, the year or the fund. The subtraction stands on its own. The result a unit is 100 less P, where P is any price that can exist. A price is not a negative number, so the set of possible values of P has a floor at nil, and no ceiling is written anywhere. Putting the floor into the subtraction gives a maximum result of plus 100. There is no other end of the set, so there is nothing to put into the other side.

The subtraction is the whole proof. Notice the missing pieces: no probability, no expectation, no view about whether any price will move at all. A statement that the loss has no upper bound is a statement about the range of a subtraction. The statement is the same kind as saying a rectangle's diagonal is longer than either side. Whether any particular price ever goes anywhere near the far end of that range is a completely separate question.

An explanation usually slides into something else at this point, so the claim is worth stating exactly. The claim is: the maximum gain equals the sale price and the maximum loss is not a number. The claim is not that a rise is likely, or unlikely, or that anybody should feel any particular way about the shape. Claims about likelihood would need different evidence entirely.

Why does a losing short get bigger while a losing long gets smaller?

The second asymmetry is almost never taught, and it has nothing to do with the payoff. The weight of the position after it has moved is what does the damage.

Take two positions in Nilgiri Absolute Return Fund, each Rs 25,00,00,000 at the start, against net assets of Rs 5,00,00,00,000. Each is 5.00 per cent of the fund. Now let each of them lose exactly Rs 5,00,00,000. The long falls 20.0 per cent and is now worth Rs 20,00,00,000. The short rises 20.0 per cent and is now worth Rs 30,00,00,000. Same loss, in the same rupees, on the same day.

Net assets after that loss are Rs 4,95,00,00,000 in each case. So the long that lost money is now 4.04 per cent of the fund and the short that lost money is now 6.06 per cent of it. The losing short is exactly one and a half times the weight of the losing long, purely because losing made one of them larger and the other smaller. Nothing was bought and nothing was sold to produce that. Arithmetic did it.

The change in weight matters more than it first sounds. Every position that goes wrong on a long book gets quieter as it goes wrong: it takes up less of the book, so its next move matters less. A short that goes wrong gets louder. Its next move matters more than its last one did, and it keeps mattering more for as long as it keeps going the same way. A household analogy: a loan whose instalment grows with every month of arrears behaves like the short, and a shop whose stock loses value behaves like the long. One recedes, the other advances.

What does it cost to hold the position open?

Three things, and only one of them depends on which way the price goes. The first is the borrow fee already worked above: 0.75 per cent a year on the value of stock borrowed, so Rs 18,75,000 a year on one position of Rs 25,00,00,000, and Rs 4,67,466 in a quarter of 91 days, rounded to the nearest rupee. The second is the cost of executing, at this fund's contracted 0.05 per cent of value on each execution. A short involves two executions, the sale and the buy-back, so on Rs 25,00,00,000 that is Rs 1,25,000 each and Rs 2,50,000 for the pair if the position is bought back at the same value. Buy it back at Rs 30,00,00,000 and the second execution is Rs 1,50,000 instead.

A year of holding one Rs 25,00,00,000 short therefore carries Rs 21,25,000 of borrow fee and execution cost, being 0.85 per cent of the position, and not a paisa of that depends on the price going anywhere. The third item is the margin, and it is a different kind of thing entirely: Rs 3,75,00,000 posted at 15.0 per cent of the opening value is collateral, not expenditure. The margin sits with the broker and comes back when the position closes. The cost of the margin is not the margin itself, but everything the fund cannot do with that money while it sits there.

How does somebody reading a factsheet actually use any of this?

Very few readers will ever place a short. A great many will be handed a factsheet or an offering document and asked to say what is in it, and that is what the mechanics above are actually for. The work they do follows.

First, the two books add on the gross line and subtract on the net line, so a short book is what makes a fund's gross figure exceed its net figure. Nilgiri Absolute Return Fund stood at 180.0 per cent gross exposure and 80.0 per cent net exposure at its record date, on net assets of Rs 5,00,00,00,000. The two figures are different statements about the same book, and how a whole ladder of such figures is read is covered separately. The mechanics above supply the reason the two numbers separate at all: something in there is owed rather than held.

Second, a fund known to carry a short book is known to have a stock lender, a borrow fee running by time, and a collateral requirement that moves with the position. So the questions that follow are mechanical rather than clever. What is the borrow costing a year? Who is the counterparty on the borrow, and is it the same counterparty as everything else? What happens on a recall? How is margin reset, and by whom? None of those questions asks whether the approach works, and every one of them can be answered out of an offering document by somebody who has followed the mechanics above.

Third, a rising short is a growing short. So when a report shows a short book that has grown between two dates, growth is not by itself evidence that anybody added to it. The positions may simply have moved. The distinction between a book that grew because somebody sold more and a book that grew because prices rose is the most common misreading in this area, and it costs nothing to check: compare the number of units against the value.

Where does the mirror between a long and a short break?

What does the Securities and Exchange Board of India set here?

A great deal, and all of it sits at the source rather than in the mechanics. Selling short is rule-bound in practice: what may be sold short, by whom, on what terms, with what said to whom and by when, are all matters of conduct set by an authority and revised by it over time.

Any of those conditions can be replaced tomorrow, and a condition that has been replaced binds nobody. The current text held by that authority is the only place the conditions in force actually exist, in both directions: what is required and what is forbidden.