Short-Sale Constraints: Why Bad News Travels Slower

A short-sale constraint is anything that stops a pessimist acting on a negative view: a prohibition, a cost, no stock available to borrow, or an unwillingness to carry a loss with no ceiling. Miller argued in 1977 that when only optimists can act, the price reflects the optimistic end of opinion rather than its middle. A price set that way is biased upward, and bad news reaches it slowly.

Start with something that has nothing to do with money. A residents' meeting is called to decide whether the street vendor outside the gate should stay. Fifty households live on the street and opinion is genuinely split. But the rule of the meeting is that only households who want the vendor to stay are allowed to speak, and everyone else may attend in silence. The minutes will record something perfectly true and completely misleading: every view expressed was in favour. Nothing about the street changed; only the rule about who could speak changed, and that alone moved the recorded verdict. Put numbers on it. 26 of the 50 households want the vendor to stay, so true support is 26 of 50, being 52.0 per cent. The minutes record 26 of 26, being 100.0 per cent. The gap of 48.0 points was made entirely by the rule. A constrained price is that meeting over again, with a price in place of the minutes.

The reason a rule about who may sell belongs in a study of behaviour rather than a study of market plumbing takes some earning, and it turns on a paper most short accounts of the subject leave out. The conclusion, when it arrives, is far more careful, and far less usable, than the first half of the argument makes it look.

What is a short-sale constraint, and what forms does it take?

Selling something a person does not hold is how a negative view gets acted on. Buying is how a person acts on a positive one, and everybody understands that half instinctively. The mirror half is stranger: for somebody who thinks a thing is dear and holds none of it, doing nothing is not the same as expressing that view. Doing nothing leaves no trace anywhere. To make the view count, that person would have to sell the thing without holding it first. Selling first means borrowing the thing from somebody who does hold it, selling it, and buying it back later to return.

A constraint is anything that stops that happening. A constraint takes four separate forms, and the four are not variations on one another. The first is prohibition: a rule, a mandate or the terms of an arrangement simply forbid it. Prohibition is the position of a very large share of the people who hold anything at all. The second is cost: the arrangement is permitted but the fee for borrowing eats the expected gain, so only a very strong negative view is worth acting on. The third is availability: nobody holding the thing is willing to lend it, so a willing pessimist is turned away at the door. The fourth is self-imposed, and it is the most interesting. A purchase can lose at most what was paid. A sale of something not held loses without a ceiling if the price keeps rising, and a great many people who face none of the first three constraints decline anyway because a loss with no ceiling is not a shape they will carry. Any one of the four is sufficient on its own, and each arrives by a different route at the same result: a negative view that never reaches the price.

Put an illustrative count on it. Of thirty participants who cannot act, suppose 14 are stopped by prohibition, 7 by cost, 4 by nothing available to borrow and 5 by an unwillingness to carry a loss with no ceiling. The four counts sum to 30. Lift prohibition entirely and 16 of the 30 are still silenced, being 53.3 per cent. The split between the four routes is stipulated, so only the total and the arithmetic carry the point.

The fourth form is worth a number of its own. On Rs 3,00,000/- put in, the very most a purchase can lose is Rs 3,00,000/-, being 100.0 per cent of it. The same amount committed the other way is down Rs 6,00,000/- if the price trebles, and the list does not end anywhere.

Whose opinion actually reaches a price?

The sentence the whole argument rests on is arithmetic rather than psychology. A price is made by the people who act, not by the people who hold views. Most of the time those two groups are close enough that nobody notices the difference, and the moment a rule silences one side of the opinion spread, they come apart completely.

Picture sixty participants looking at the same thing and disagreeing about what it is worth. The spread of sixty is stipulated rather than observed, and the numbers are chosen to make the mechanism visible. Their valuations run evenly from 80 at the gloomiest to 140 at the keenest, in points on an invented scale. The middle of that spread sits at 110. If every one of the sixty could act in either direction, buying when they think it cheap and selling when they think it dear, pressure from below and pressure from above would meet, and the price would settle somewhere near that middle.

Now apply the constraint. Acting on a view below 110 would mean selling something they do not hold, so the thirty who value it there can no longer act on that view at all. The thirty do not leave the room. Their opinion is unchanged and they would say so if asked. The opinion simply has nowhere to go. The acting group is now the thirty who value it between 110 and 140, and the middle of that group sits at 125. SelectionWhich part of a distribution reaches an outcome. Here, which opinions get into a price and which never arrive at all. is at work: nobody changed their mind, nobody was fooled, and the price moved by fifteen points.

Ranked as a ladder, the same point becomes exact. Sixty points of spread across sixty participants is one point each, so the unconstrained price sits at the boundary between the thirtieth and thirty first ranked view and the constrained price sits between the forty fifth and forty sixth. Fifteen rungs of one point each is fifteen points.

How does the argument work on an actual spread of opinion?

Miller set this out in Risk, Uncertainty and Divergence of Opinion in the Journal of Finance in 1977, and the argument is short enough to work through completely. The ingredients are two: a divergence of opinionHow widely the participants' valuations of the same thing differ from one another. about what a thing is worth, and a rule that lets only one side act.

Work it in numbers. Sixty participants, valuations spread evenly from 80 to 140. The spread is stipulated rather than measured. Line them up in order and the middle of the whole spread is 110. 110 is the unconstrained price: the level at which the keenest half would be buying from the gloomiest half if both could act. Apply the constraint and the acting group becomes those valuing it at 110 or above, running from 110 to 140. The middle of that group is 125. Fifteen points divided by 110 is 0.13636, or 13.6 per cent when rounded to one decimal place. The constraint has produced an upward biasA price sitting above where unrestricted opinion would have put it. of 13.6 per cent without a single participant being wrong about anything.

Notice what the price now represents. The price is not the average view. The price is the view of the marginal participantThe one whose view sits at the edge of the acting group. The price then rests on that view rather than on the average of everybody's. in a group that has already had its gloomier half removed. Reading such a price as a consensus is reading the minutes of the residents' meeting as the opinion of the street.

Read the same number one more way. At 125, everybody valuing it from 80 up to 125 thinks it worth less than it costs, and that is 45 of the 60, being 75.0 per cent. At 110 the same count was 30 of 60, being 50.0 per cent. A constrained price is a price that most participants privately think dear.

What sets the size of the bias, the constraint or the disagreement?

The result that surprises people is the actual content of Miller's argument rather than the headline everyone remembers. Keep the constraint exactly as it is. Do not loosen it, do not tighten it, do not change who may act. Change only how much the sixty participants disagree with each other, keeping the middle of their opinion at 110 throughout.

Widen the disagreement first. Let the valuations run from 50 to 170 instead. The middle is still 110, so the unconstrained price has not moved at all. But the acting group now runs from 110 to 170, whose middle is 140, and the bias is 30 points. Thirty divided by 110 is 0.27272, or 27.3 per cent. Now narrow the disagreement instead: valuations from 100 to 120, middle still 110, acting group 110 to 120, middle 115, bias 5 points. Five divided by 110 is 0.04545, or 4.5 per cent. Between the narrow case and the wide case the bias runs from 4.5 per cent to 27.3 per cent, and the constraint never changes by so much as a comma. The bias is a function of disagreement rather than of the tightness of the rule.

The finding has a consequence worth sitting with. Two things can face identical constraints, identical rules, identical borrowing conditions, and carry biases six times apart, purely because people agree about one and argue about the other. The same finding means that when everybody agrees about something, the constraint barely matters. The constraint only bites where there is disagreement for it to select from.

The relationship underneath is simpler than it looks. The acting group is always the upper half, so its middle always sits one quarter of the band width above the unconstrained price, and the bias is that quarter divided by 110. The bias therefore rises in a straight line from nothing at complete agreement, and the constraint contributes no size of its own at all.

The three settings worth stopping at are the three worked above. Narrow, at 100 to 120, gives a middle of 110, an acting group of 110 to 120, a middle of 115, and a bias of 5 divided by 110, or 4.5 per cent. Middling, at 80 to 140, gives an acting middle of 125 and a bias of 15 divided by 110, or 13.6 per cent. Wide, at 50 to 170, gives an acting middle of 140 and a bias of 30 divided by 110, or 27.3 per cent. The unconstrained price is 110 at all three.

Does the bias survive if everybody can see the constraint?

Most short accounts of this subject stop here, and stopping here leaves a reader holding a result the literature does not actually support. Diamond and Verrecchia, writing in the Journal of Financial Economics in 1987, asked a question that sounds almost too simple to be devastating. If the constraint is public, why would anybody be fooled by it?

Follow the logic. The rule silencing the pessimists is not a secret. Everybody in the room knows that the gloomy half cannot act. So a thoughtful buyer looking at a price of 125 does not read it as the market's view of the thing's worth. She reads it as the view of a group she knows has been pre-filtered, and she makes an adjustmentCorrecting a reading downward or upward for a known distortion in the way it was produced. for that. She knows roughly how the filter works, so she knows roughly how much to take off. If she and everybody like her take off the right amount, their bids sit lower, and the price comes back toward 110. The bias should largely close, not because the constraint went away, but because a distortion everybody can see is a distortion everybody can correct for.

People already do this without thinking, everywhere else in life. A wedding caterer offers a book of testimonials, and the reader of it knows perfectly well that the unhappy customers are not in the book, so glowing testimonials read as ordinary and ordinary ones as poor. No new information has been supplied. A reading known to be selected has been adjusted, and that adjustment is what stops the selection working.

Correction is not a switch, either. If buyers take 5 points off the 125, the price is 120 and 10 points of bias remain, being 9.1 per cent. Take 10 off and 5 remain, being 4.5 per cent. Take the full 15 off and nothing remains. The surviving bias is precisely whatever they fail to take off.

Why is this a claim about behaviour rather than a claim about arithmetic?

Put the two arguments side by side and something important falls out. Miller's arithmetic is not in dispute: if the acting group is the upper half, its middle is higher, and that is not a matter of opinion. The dispute is over whether anybody buys at that middle without thinking about where it came from. Miller's upward bias survives only if participants fail to correct for a constraint they can plainly see. The bias is therefore a claim about how people read a price rather than a claim about how a price is calculated. A claim about how people read a price is precisely why the subject belongs in a study of behaviour. Presenting the bias as automatic teaches something the literature stopped agreeing with within ten years of the original paper.

The test for whether a failure of that kind survives at all is set out under investor and market behaviour, and the test is the aggregationWhether individual errors cancel one another out or survive into a market outcome. Scattered errors cancel; shared ones do not. step. Errors that scatter cancel. Errors that share a direction survive. Take twelve participants, each one's adjustment a little wrong, in a further invented illustration. Suppose their errors run minus 9, minus 7, minus 5, minus 3, minus 1, 0, 0, plus 1, plus 3, plus 5, plus 7, plus 9. The twelve errors sum to zero, so the average correction is exactly right, the price returns to 110.0, and the surviving bias is nothing at all. Now suppose instead that every one of the twelve under-corrects, by amounts of 4, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7 and 7 points. The twelve under-corrections sum to 72 and average 6.0. The price lands at 116.0, and 6 divided by 110 is 0.05454, or 5.5 per cent of bias surviving out of an original 13.6.

So the honest statement of the result is conditional, and the condition is the interesting part. If people under-adjust for known selection in a shared and directional way, some of Miller's bias survives, and how much depends on how badly they under-adjust. If their adjustments scatter, Diamond and Verrecchia win and there is nothing left to explain. Which of those the world does remains open, and the answer is empirical rather than logical.

Split the fifteen points by what actually carries them. The arithmetic step, that the middle of 110 to 140 is 125, carries none of the dispute. The behaviour step, that a buyer pays 125 without discounting for a filter she can plainly see, carries all fifteen of them.

Why does bad news travel slower than good news?

Now the title pays off. Good news and bad news do not face the same crowd. When good news arrives, acting means buying, and everybody can buy. Anybody who believes the news can act on it, whether or not they hold anything. When bad news arrives, acting means selling, and for everybody but the holders that would mean selling something they do not have. Only the people who already hold the thing can act on it.

Stipulate, still within the same invented illustration, that twelve of the sixty participants hold the thing. Good news reaches a price through sixty possible actors. Bad news reaches it through twelve. The other forty eight can register a belief in the bad news only by declining to buy, and a price barely notices that. The asymmetry is not that people dislike bad news; it is that the arrangement gives bad news five times fewer routes into a price than good news has. The adjustment to bad news therefore arrives in instalments, as holders sell one after another, rather than all at once.

The sentence needs care. The careless version of it is wrong. The claim is not that bad news is ignored. The claim is not that a price is always too high. The claim is that the number of people who can express a negative view at any moment is smaller than the number who can express a positive one, and that a smaller acting group takes longer to move a price a given distance. How much longer is an empirical question.

Read the same asymmetry one participant at a time. The twelve who hold the thing face a menu with both moves on it, being 12 of 60, or 20.0 per cent. The other 48, being 80.0 per cent, face a menu with one move simply missing.

What does the decision log say about any of this?

Almost nothing, and saying so plainly is more useful than dressing up a number. The Palash decision log is an invented record of 240 decisions taken by 60 investors over eight quarters at Palash Advisory Services Private Limited. The 240 break into 96 buys, 84 sells, 36 switches and 24 pauses of a standing instruction, and those four counts sum back to 240. Read down the list of what those decisions could be and notice the category that is missing: not one of them is a position taken against something. Every single decision in the record is either putting money into something, taking money out of something already held, or moving money between two things.

The missing category is not an accident of the record, but what the constraint looks like from inside an ordinary account. Meera Sundaram, one of the 60, held Kesari Logistics Limited at Rs 1,95,000/- on 30 September against a cost of Rs 3,00,000/-. Her only route for a negative view about it was to sell what she held, and on 12 October she sold Suvarna Chemicals Limited at Rs 4,60,000/- instead and kept Kesari Logistics. The decision itself is taken apart properly under the disposition effect. Whatever is made of it, the shape of the menu she was choosing from is the thing to notice. A record containing no positions taken against anything holds no observations of the effect, so the log cannot measure it at all. Any rate squeezed out of the log would be invented evidence.

The four positions on 30 September show the same shape. The Vindhya index scheme stood at Rs 3,36,000/- on a cost of Rs 3,00,000/-, the Nilgiri mid-cap scheme at Rs 2,55,000/-, Suvarna Chemicals Limited at Rs 4,60,000/- on a cost of Rs 4,00,000/-, and Kesari Logistics Limited at Rs 1,95,000/- on a cost of Rs 3,00,000/-, being Rs 12,46,000/- against Rs 13,00,000/-, down 4.2 per cent. Every one of the four is a thing bought.

How does anybody use this without acting on it?

The useful residue of the argument is a question, not a number, and it is a question about how to read agreement. When Devika Rao, the adviser at Palash Advisory Services Private Limited, hears a client say that everybody thinks a thing is worth having, the observation that follows is not that the thing is dear. The observation that follows is that the sentence may be describing who was allowed to speak rather than what people think. The two follow-up questions are how widely people actually disagree, and whether the people who disagree have any route to act. Neither question has an answer that tells anybody what to do; both change how much weight a statement of consensus deserves.

For a person deciding alone, with no adviser and no committee, the same reading applies to every source of apparent agreement they meet. A discussion board where the sceptics stopped posting, a scheme document that carries the risk statement on printed side 31 in eight point type, a list of testimonials that no unhappy customer appears in: each is a distribution with one end removed, and each will feel like a consensus. Spotting biased prices needs a spread of opinion nobody can observe, and it is not the transferable skill here. The transferable skill is noticing when a reading has been produced by a process that could only ever have produced one answer. The habit costs nothing and needs no market at all.

Cross the two questions and four combinations fall out. Only one of them, wide disagreement with the route blocked, carries a large bias, and picking that one out of the four would need the spread of opinion.

The invented record measures one version of the same reading directly. The scheme document runs to 46 printed sides with the risk statement on side 31 in eight point type, and 7 of 30 readers could state the main risk afterwards, being 23.3 per cent. Given a 90 word version at the top instead, 24 of 30 could, being 80.0 per cent, a gap of 56.7 points made by placement rather than by content.

Why is an upward bias not an opportunity?

Everything above explains a price level. None of it is an instruction to buy anything, sell anything, avoid anything or wait for anything, and none of it is evidence that acting on it would pay. The reasoning genuinely does point at the opposite conclusion, and it points hard, so the boundary has to be said in plain words here more than in most places. Three independent reasons hold the line, and any one of them is sufficient on its own.

The first is the identity at the centre of the whole subject. The constraint that produces the bias is the same constraint that stops anybody capturing it. For a person who concludes that a constrained thing sits above where unrestricted opinion would put it, the action that follows is to sell something not held. Selling something not held is exactly the action the constraint forbids. The explanation and the obstacle are not two facts that happen to sit together; they are one fact seen from two sides. Shleifer and Vishny set that argument out in The Limits of Arbitrage in the Journal of Finance in 1997.

The second is cost. A documented effect is almost always measured before what it costs to act on it, and acting is not cheap. The invented Palash log measures this directly for its own 60 investors: sorted into five groups of twelve by how much they traded, annual turnover ran 9, 34, 71, 128 and 210 per cent, gross returns ran 11.2, 11.0, 11.1, 10.9 and 11.0 per cent, and costs ran 0.3, 0.6, 1.5, 2.5 and 4.1 points. Gross returns sit within 0.3 points of each other across all five groups. Net returns, at 10.9, 10.4, 9.6, 8.4 and 6.9 per cent, run 4.0 points apart. The gap was made by the trading and not by the picking, and 4.1 points a year is larger than most documented effects are before costs, never mind after them.

The third is publication. An effect described in a paper is known to everybody who read the paper, so what it did before it was published is not evidence of what it does afterwards. The standing tension in the study of market efficiency is the one Fama set out in Efficient Capital Markets in the Journal of Finance in 1970: any pattern that can be acted on cheaply attracts the acting that removes it. A behavioural account of why a price sits where it does is a description, and it stays a description no matter how confident the description becomes.

Set the cost against the picking one last way. The busiest group gave up 4.1 points a year, and the whole spread in gross returns across the five groups is 0.3 points, so what acting cost is 13.7 times the entire difference in what was picked.

Meera Sundaram, Devika Rao, Palash Advisory Services Private Limited, the Palash decision log, the Vindhya index scheme, the Nilgiri mid-cap scheme, Suvarna Chemicals Limited and Kesari Logistics Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.