Investor and Market Behaviour: From One Decision to the Aggregate

Individual behaviour becomes market behaviour only when it lines up. Errors that point in random directions cancel in the aggregate and leave no trace in a price. Errors that share a direction survive averaging and become the whole story. The direction of the errors decides which documented effects in behavioural finance ever reach a market at all.

A single arithmetic fact underlies the whole subject, familiar from other settings and rarely applied to people: averaging destroys what is random and preserves what is shared. A hundred kitchen scales, each one wrong by up to fifty grams in a direction nobody controls, average to a reading that is very nearly right. Bias every one of them the same fifty grams heavy, and the average is wrong by exactly fifty grams, however many scales are added. Once averaging is seen to keep what is shared and throw away what is not, most arguments about whether a bias matters to a market collapse into one question: whether that bias points the same way in enough people.

What is investor behaviour, and what is Market Behaviour?

Investor behaviour and market behaviour are two different objects, and a great deal of loose writing treats them as one. Investor behaviour is what a person did: bought, sold, waited, added, ignored a statement, moved a date. Investor behaviour lives in a record. The record carries a name, a time, and usually a reason that either was written down or was not. Market behaviour is what a level did: it rose, it fell, it went nowhere for a quarter. Market behaviour lives in a series of numbers and has no names in it at all.

The distinction is clearest away from the trading floor. In a vegetable market at closing time, one vendor dropping her price by Rs 10/- is one vendor's behaviour, and she can be asked why. The whole market's prices falling at six o'clock is something else: no single person decided it, nobody can be asked about it, and it is perfectly possible that most of the vendors would say they held their price. The second thing is not simply the first thing repeated forty times. The whole market falling is a different object with different evidence behind it.

Set the invented Palash decision log beside that. On 12 October, Meera Sundaram sold Suvarna Chemicals Limited whole at Rs 4,60,000/- against a cost of Rs 4,00,000/-, booking Rs 60,000/-, and kept Kesari Logistics Limited, then standing Rs 1,05,000/- below what she paid for it. The entry is investor behaviour in its complete form: dated, attributable, and readable line by line. The two objects are established by different evidence and answer different questions, so nothing in that entry is market behaviour and no amount of staring at it will turn it into market behaviour.

How does one become the other, and why is that step not automatic?

The step from many decisions to one level is an aggregateThe sum or average across everybody, as against any one person's position., and aggregating is not a neutral act of collection. Aggregating is an operation that throws some information away on purpose. The discarding is not a defect. Throwing information away is the entire reason a single number can stand for sixty people at once, and it is the reason the number cannot be run backwards to recover any of them.

Ten households live on one street. A guest comes, a bill falls due, or nobody feels like cooking, so in a given week each one spends Rs 500/- more or less than usual. The overspending of one house sits on top of the underspending of another, so the street's total spending for that week is almost unchanged. Now let the same ten households all receive the same electricity bill on the same Tuesday. Every one of them spends more, in the same direction, in the same week, and the street's total moves by the full amount. The households were no more emotional in the second week than in the first. The only thing that changed was whether their departures pointed the same way.

The step from individual behaviour to market behaviour is an averaging, and averaging is a filter: what survives it is whatever the individuals had in common, and what does not survive it is everything they did not. The filter is why an account can be completely right about a person and completely wrong about a price, and why the two mistakes look identical until the correlation question is asked.

Why do errors in random directions leave no trace in a price?

Work the arithmetic. The arithmetic is the argument. There are 60 investors in the Palash decision log. Suppose every one of them misjudges the value of the same thing by a full 1.0 point, a large error, and suppose the direction each one gets wrong is unrelated to the direction anybody else gets wrong. In the clean case, 30 of them are 1.0 point too high and 30 are 1.0 point too low. The sum of the sixty errors is 30 minus 30, or zero. Divide by 60 and the aggregate deviation is zero as well.

Sixty errors meeting and offsetting is cancellingErrors in opposite directions offsetting so the average is close to zero., and cancelling is the ordinary case rather than the exception. A bias can be universal, large and thoroughly documented at the level of the individual, and still be entirely absent from every level a market publishes, for no deeper reason than that the plus signs and the minus signs met each other on the way in. Daniel Kahneman, Olivier Sibony and Cass Sunstein, in their 2021 book Noise, make exactly this separation the centre of their argument: scatter around a target and a shared pull away from it are two different failures, they have different remedies, and confusing them is common. Scatter is what averaging removes. A shared pull is what it leaves standing.

Most individual error never reaches any price at all, and the reason is arithmetic rather than luck. The arithmetic brings a relief in one direction and a warning in the other. The relief is that a market is not simply the sum of everybody's worst afternoon. The warning is that a bias being everywhere is no evidence at all that it matters to anybody's price.

Why do shared errors survive the very same averaging?

Run the identical arithmetic the other way and nothing about the method changes. Sixty investors, each still wrong by 1.0 point, but now every single one of them is wrong in the same direction. The sum is 60 points. Divide by 60 and the aggregate deviation is 1.0 point: the entire individual error has come through the averaging completely undamaged. Adding more people does not help, and this is the part that surprises. Six hundred investors sharing the same 1.0 point error still produce a 1.0 point deviation. Size of the group is not the defence people assume it is.

Between those two extremes sits everything real. Suppose 12 of the 60 share a direction while the remaining 48 still scatter and cancel. The 12 contribute 12 times 1.0, or 12 points. The 48 contribute nothing. The aggregate deviation is 12 divided by 60, or 0.2 points. Against an index levelA single number standing for the value of a group of holdings at a point in time. of 131.0, that 0.2 is 0.15 per cent. A deviation of 0.15 per cent is a small number. One fifth of the people produced all of it while four fifths produced nothing at all, and that is the point worth carrying.

The same operation that erases a universal error can transmit a minority one at full strength, and which of the two happens is decided by direction rather than by numbers. The sections that follow lean on the middle row, so the middle row repays recomputing before going on.

What actually makes errors line up?

A correlated errorA mistake several people make in the same direction at the same time. is not a mysterious thing, and it does not require anybody to be imitating anybody. Three ordinary routes produce it, and they are worth separating because only one of them involves people watching each other at all, and it is not the one on this list.

The first is common information. Sixty people reading the same quarterly statements in the same week, from the same eligible list, are not sixty independent judgements. Because the input was shared before the thinking started, the sixty are one judgement made sixty times with small variations. The second is a common triggerOne event that reaches many people at once and prompts the same response.: one event that arrives at many people simultaneously. In the cohort, 71 of the 240 logged decisions, or 29.6 per cent, fell within 48 hours of a news item. Of the 96 buys, 41 followed a media mention within three days, a share of 42.7 per cent against the 11.0 per cent of the eligible list mentioned at all in a given week. On 19 February a television segment named Suvarna Chemicals Limited and Meera added Rs 1,00,000/- to it the same evening. She was not copying anyone. She was reached.

The third is common rules. People who have never met use the same round numbers, the same month ends, the same standing instruction dates and the same habit of waiting for a purchase cost to come back. Meera's sentence about selling Kesari Logistics Limited when it gets back to Rs 3,00,000/- is a rule of that kind, and it is a rule thousands of people apply to their own different numbers on the same day. Shared inputs, shared timing and shared rules will manufacture correlated error in a population where nobody is watching anybody. Explaining correlation by imitation alone is therefore usually too quick.

How much lining up does it take before an aggregate moves?

How much lining up it takes is what the control below answers, and the guess most people make before moving it is wrong in an instructive way. The control below moves one thing only: how many of the 60 investors make the same error in the same direction. Everything else is held still. Each investor is wrong by exactly 1.0 index point, those who share a direction add together, and those who do not are assumed to offset in pairs and contribute nothing at all.

What does the Palash 100 index show when the log is set beside it?

The illustrative Palash 100 index stands at 100.0 at the open and then at 118.0, 131.0, 112.0, 104.0, 116.0, 124.0, 121.0 and 127.0 at the eight quarter ends. The recomputing is the exercise, so the path repays recomputing rather than skimming. From the opening 100.0 to the peak reading of 131.0 is a gain of 31.0 per cent. Dividing 112.0 by 131.0 gives 0.855, so from that peak to the next reading of 112.0 is a fall of 14.5 per cent. The reading after that, 104.0, is a further fall of 7.1 per cent from 112.0. Peak to low, 131.0 down to 104.0, is 20.6 per cent, and that is the whole of the fall rather than any part of it.

Now set the log beside the path. Cohort turnoverHow much of a holding is bought and sold over a period, as a share of its size. ran at 3.1 times its eight-quarter median in the quarter that ended at the peak reading of 131.0, and at 0.4 times its median in the quarter that ended at the low reading of 104.0. Individual activity and the aggregate moved together: most of the buying and selling happened when the level was highest, and almost none of it happened when the level was lowest. Read that carefully. Turnover of that shape is a statement about when sixty people were busy, not a statement about what was about to happen.

The two series moved together not because sixty people are foolish, but because sixty people were reading the same reports in the same weeks, the plainest available route to a shared direction. Common information and a common trigger are doing exactly what the three routes above describe. One cohort of sixty people over eight quarters is far too small to establish that any rule works. A sample that size can show a mechanism at work and cannot measure how often it occurs.

What does an aggregate reveal about the people in it, and what does it hide?

An aggregate is a sum, and a sum can be reached from an enormous number of different sets of individual positions. Sixty investors could produce a 0.2 point deviation with twelve sharing a direction and forty eight cancelling, or with twenty four sharing half as strong a view, or with six people holding views twice as strong. The level records that something was shared by enough of them. The level records nothing at all about which of those pictures was true, and no amount of studying it will separate them.

The averaging destroys the dispersionHow spread out a set of individual positions is around their average.. Everyone knows this instinctively about an average quoted at them in another setting: the average household on a street can be comfortable while a third of the houses are struggling, and a mean marks sheet says nothing about the child who failed. A level published for a group is the same object with the same silence built into it. The level answers what, at the group scale, and refuses to answer who, or why, or how many.

A movement in an aggregate supports one conclusion, that something was correlated across enough of the people, and honestly not one thing more. A small aligned minority is enough, so the movement does not support the conclusion that most people were mistaken. Common information and common rules produce alignment without any agreement, so the movement does not support the conclusion that the people agreed with each other. The averaging destroyed the individual record, so the movement certainly does not establish which individual did what.

How does this change what a practitioner actually does?

Devika Rao, the adviser at Palash Advisory Services Private Limited, does not use the aggregation rule to forecast anything. She uses it as a sorting rule for her own attention. When she reads a finding about how people decide, she asks one question of it before anything else: was this measured on individuals, or on an aggregate? A finding about individuals tells her what to expect in a room with one client in it, whether or not it has ever moved a level anywhere. A finding about an aggregate tells her that something was shared, and tells her nothing about the person sitting opposite her.

The cohort has a clean instance of the first kind. Split the 60 investors into five groups of twelve by their annual turnover, running 9, 34, 71, 128 and 210 per cent. Their gross returns are 11.2, 11.0, 11.1, 10.9 and 11.0 per cent, all inside 0.3 points of one another. Their costs run 0.3, 0.6, 1.5, 2.5 and 4.1 points, so their net returns are 10.9, 10.4, 9.6, 8.4 and 6.9 per cent, a spread of 4.0 points. The 4.0 point spread is a large, orderly, individual-level regularity about what activity costs the person doing it, and it is perfectly consistent with no visible effect on any published level at all. Terrance Odean, writing in the Journal of Finance in 1998, and Brad Barber with Terrance Odean in the same journal in 2000, studied individual trading records at scale, and their contribution was to measure what individual activity does to the individual's own outcome rather than to any published level.

For a person deciding alone, with no adviser and no committee, the same rule does the same work, and it is cheaper to apply than it looks. Meera puts Rs 25,000/- in by standing instruction every month against an opening holding of Rs 12,00,000/-. When she reads that some behaviour is widespread, the useful next question is not whether she has it too, but whether the cause that produced it in other people is currently reaching her as well: the same segment, the same week, the same round number. Widespread is about a population. Reaching me this week is about a decision, and only the second one is actionable in the ordinary sense of the word.

What lies beyond the aggregation step?

Whether a shared direction, once it exists, produces any of the named market outcomes is a separate subject resting on separate evidence. So is why errors correlate in the first place. The best known account of that involves people inferring from what others do, and it was set out by Abhijit Banerjee in the Quarterly Journal of Economics in 1992 and by Sushil Bikhchandani, David Hirshleifer and Ivo Welch in the Journal of Political Economy in the same year. Inference from what others do is set out under herding, and the aggregation step needs only that correlation happens.

Two older lines sit underneath everything above. Herbert Simon, in the Quarterly Journal of Economics in 1955 and in Psychological Review in 1956, established that decisions get made by people with limited capacity working in a particular environment. A shared environment can therefore produce shared error. Amos Tversky and Daniel Kahneman, in Judgment under Uncertainty: Heuristics and Biases in Science in 1974, established that the departures are systematic rather than scattered. Being systematic is precisely the property that lets some of them survive an average. Systematic at the level of a person is the necessary condition; shared in direction across enough people is the sufficient one, and only the second decides whether a market ever shows it.

An index path invites the wrong kind of statement, so the difference between the two kinds is the last thing to be clear about. Explaining how an aggregate movement was produced is a backward-looking account of a mechanism. Predicting the next movement is a forward-looking claim about the world. The two kinds of statement rest on different evidence, and an account of a movement that already happened supports no claim at all about the next one. The aggregation argument establishes why sixty people were busy at the peak reading of 131.0. Nothing about the reading after Q8 follows from any of it, and no line is drawn past Q8.

Meera Sundaram, Devika Rao, Palash Advisory Services Private Limited, the Palash decision log, the Palash 100 index, Suvarna Chemicals Limited and Kesari Logistics Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.