The Rational Investor: The Assumption and Why It Broke

The rational investor is a benchmark, not a description. The benchmark assumes preferences that are complete, transitive and stable, probabilities updated correctly as evidence arrives, and a choice that maximises expected utility over final wealth. Each assumption was made because it made the mathematics work. Behavioural finance begins where a careful, ordinary person predictably departs from it.

The rational investor model rests on a distinction most readers have never been shown. A model can be an excellent standard and a poor description at the same time, and those two jobs are judged by completely different tests. A standard is judged by whether departures from it carry information, and on that test the rational investor has never been beaten. Every effect in behavioural finance is defined as a departure from this model, which is why relaxing the model is not the same thing as throwing it away.

What does the rational investor model actually assume?

The rational investor is not a person, and no economist has ever claimed to have met one. The rational investor is a set of four assumptions about how a decision gets made, written down carefully enough that the consequences can be worked out with arithmetic instead of argued about. The four are these. Preferences are complete, transitiveIf the first is preferred to the second and the second to the third, the first beats the third. and stable. Probabilities are updated correctly when new evidence arrives. The investor maximises expected utilityThe average of the satisfaction each outcome would give, weighted by how likely it is. measured over final wealthThe total a person ends up holding, as opposed to the gain or loss from where they started.. And only the future matters, so what a holding cost is irrelevant to whether to keep it.

Notice what is not on that list. Nothing says the investor is clever, well informed, unemotional, patient or good at arithmetic. Nothing says the investor makes money. The word rational is doing far less work than it sounds like it is doing, and most public argument about behavioural finance is really an argument about those four lines rather than about the word. The four assumptions are separable. A decision can break exactly one of them and leave the other three standing, and that separability is the single most useful thing to know about the rational investor model. Separability is what makes the model diagnostic rather than merely wrong.

What does it mean for preferences to be complete, transitive and stable?

Completeness says that for any two options a person can say which one is preferred, or say that the two are equally good. There is no third answer and no permitted shrug. Being transitive says that the rankings fit together: preferring the first to the second and the second to the third commits a person to preferring the first to the third. Stability says the ranking does not wander while nothing relevant has changed, so the same three options rank at four in the afternoon the way they ranked at eleven in the morning.

Take it out of finance first. A household is choosing between three schools, weighing distance, fees and what the neighbours say. If the first school beats the second on the whole, and the second beats the third, then the household is committed to the first beating the third. If it turns out the household would also choose the third over the first, the ranking has closed into a loop, and no school can be called the best one. A preference ordering that runs in a circle can be pumped: somebody willing to charge a small fee at each swap can walk the household round the loop again and again, and it will arrive back where it started holding less money. The assumption is not stated because circular rankings are common. The assumption is stated because a model containing a circular ranking has no stable answer for anything else to be measured against.

What does correct updating require, and how strict is it?

The second assumption is about evidence. Correct updating means a new belief depends on exactly two things: what was believed before the evidence arrived, and how much more likely that evidence would be if one story were true rather than another. The prior belief and the diagnostic power are the entire input list. Correct updating is indifferent to how vivid the evidence was, how recently it arrived, how easy it was to picture, and how firmly the person had already told somebody else what they thought. The assumption is demanding in a way that is easy to miss. Correct updating does not ask for more information. Correct updating asks that the information already in hand is weighted by its diagnostic power and by nothing else.

The Palash decision log, an invented record of 240 decisions taken by 60 investors over eight quarters, gives a way to see how far real deciding sits from correct updating. A written reason was recorded on 84 of the 240 decisions, being 35.0 per cent. Of the 240, 71 were taken within 48 hours of a news item, being 29.6 per cent. Of the 96 buys in the log, 41 followed a media mention of the holding within three days, being 42.7 per cent, against 11.0 per cent of the eligible list being mentioned at all in a given week. None of those three rates proves that anybody updated incorrectly. The three rates measure something narrower and more useful. Each records how much of the deciding sat close to the moment a news item arrived, and the timing of that arrival is the one thing correct updating is supposed to be completely indifferent to.

The last of those three rates is the only one with a base rate sitting beside it, and that comparison is what makes it worth reporting at all.

What is being maximised, and what is it measured over?

The third assumption has two halves, and the second half is where the damage eventually comes from. The first half says the investor maximises expected utility, where utilityA number standing for how good an outcome is for a person. It only has to rank outcomes correctly; the size of the number means nothing on its own. is a number standing for how good an outcome is rather than how large it is. The second half says the input to that number is final wealth: the total held afterwards, not the gain or the loss from wherever the person happened to start.

The reason utility is not the same as money is that money is worth less to a person the more of it is already held. The first ceiling fan in a Chennai summer changes the household completely; the fourth one changes a spare bedroom. Because each additional rupee adds a little less satisfaction than the one before it, the utility curve rises quickly at first and then flattens, and that flattening produces caution towards risk automatically, without anybody being timid. A person with a flattening curve turns down an even bet with a positive average, not out of fear, but because the extra satisfaction on the winning side is smaller than the satisfaction given up on the losing side.

Work it through with the measurement in the log. The 60 investors were offered a certain Rs 5,000/- against a half chance of Rs 11,000/-. The expected value of the gamble is Rs 5,500/-, so on money alone the gamble wins. And yet 42 of the 60 took the certain Rs 5,000/-, being 70.0 per cent. Take a utility curve of wealth raised to the power 0.75, a standard flattening shape. The certainty equivalentThe sure amount that would feel exactly as good as taking the gamble. of that gamble is Rs 11,000/- multiplied by 0.5 raised to the power of one divided by 0.75. The certainty equivalent comes to Rs 4,365/-. Preferring the certain Rs 5,000/- is not a departure from the rational investor model at all: it is exactly what the model predicts once the curve is allowed to bend.

Why is what a holding cost treated as irrelevant?

The fourth assumption is the shortest to state and the hardest to live with. A decision is made only on what happens next, so the price already paid for something is information about the past and about nothing else. The past price is sunkAlready spent and unrecoverable, so logically irrelevant to what should happen next.: it has already gone, it will not come back whichever way the decision goes, and it therefore cannot change which future is better. The rational investor model does not say the price paid is unimportant emotionally; it says the price paid appears nowhere in the arithmetic of what to do now.

Everyone has met this outside finance. A hall has been booked and paid for, the wedding party has shrunk, and a smaller hall would now be better and cheaper on the night. The money already handed over does not come back in either case, so it cannot help decide between the two halls, and yet almost nobody can leave it out. Meera Sundaram, an investor in the Palash decision log, holds Kesari Logistics Limited, bought for Rs 3,00,000/- and worth Rs 1,95,000/- at the 30 September valuation. The only question the fourth assumption permits is whether Rs 1,95,000/- is better held where it is or somewhere else. The Rs 3,00,000/- appears in that question nowhere at all.

Setting the two branches beside each other makes the reason plain.

Why did economists build the model this way, and was that naive?

The order in which the pieces arrived explains why they look the way they do. Daniel Bernoulli, in 1738, in the paper later translated into English in Econometrica in 1954, proposed that a person values an outcome by how useful it is rather than by how much money it is. The flattening curve comes from that proposal. John von Neumann and Oskar Morgenstern, in Theory of Games and Economic Behavior in 1944, then proved something much stronger. If a person's preferences over gambles obey a short list of consistency conditions, then a utility number must exist such that the person behaves exactly as though maximising its expected value. The theorem is why the rational investor model is stated as assumptions about consistency rather than as a claim about anybody's psychology: the expected utility calculation is a consequence of the consistency conditions, not an extra belief bolted on beside them.

Paul Samuelson, writing in Economica in 1938, came at the same target from the other end with revealed preference: instead of asking what a person wants, infer the ranking from the choices actually made, and check whether those choices hang together. Revealed preference made the whole apparatus measurable from behaviour rather than from introspection, and measurement from behaviour is precisely what a science needs. None of the three authors claimed to be describing a mental process. Read them as engineering rather than as psychology. An engineer assumes a beam is uniform, not because beams are uniform, but because the assumption makes the bridge calculable and the error it introduces can be bounded and checked afterwards. The four assumptions were chosen on the same grounds, and calling that naive misreads what the authors thought they were doing.

How can one model be an excellent standard and a poor description?

A normative modelA model of how a decision should be made, used as a standard to measure against. says how a decision ought to be made and is judged by whether measuring against it teaches anything. A descriptive modelA model of how decisions are actually made, judged by whether it predicts them. says how decisions are actually made and is judged by whether it predicts what people do. The rational investor model passes the first test emphatically and fails the second one just as emphatically, and the two tests are separate enough that a verdict on one says nothing about the other.

A clock that runs four minutes fast every single morning is a poor description of the time and an excellent standard. Four minutes is a number that can be named, measured and corrected for. A clock that is wrong by a different random amount each morning is useless as both, because there is nothing to learn from it and nothing to correct. Departures from the rational investor model are the first kind. Departures of the first kind repeat, they run in the same direction, and they are large enough to measure. Each of them therefore ended up with a name and a literature rather than being filed as noise.

Where did the assumption first break, and who broke it?

Maurice Allais, writing in Econometrica in 1953, set out a pair of choices and then watched what people did with them. In the first pair, most people take a certain amount over a gamble with a slightly higher average. The flattening curve is behaving there exactly as designed. In the second pair, built by scaling every probability down by the same common factor, most of the same people switch and take the gamble. The switch is the problem. The common part is shared and cancels out, so the consistency conditions of von Neumann and Morgenstern imply that scaling both sides by a common factor cannot reverse a ranking. Maurice Allais did not show that people are bad at arithmetic; he showed that a consistency condition the theory treats as too obvious to argue about is one that most people violate deliberately, and go on violating after the violation has been explained to them.

Daniel Ellsberg, in the Quarterly Journal of Economics in 1961, attacked a different joint. Offer a bet on a container whose composition is stated, and the same bet on a container whose composition is not stated, and people pay to stay with the stated one. People do it on both colours at once, and that is the part no assignment of probabilities can absorb. Preferring the known container on red and also on black implies two incompatible beliefs about what is inside the unknown one. Frank Knight had already separated risk, where the odds are known, from uncertainty, where they are not, in Risk, Uncertainty and Profit in 1921. Daniel Ellsberg turned that distinction into a measurement by showing people will pay real money to avoid not knowing, and the expected utility calculation has nowhere to put that payment.

What does one real decision look like when all four are checked against it?

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 a gain of 15.0 per cent. She kept Kesari Logistics Limited, then worth Rs 1,95,000/- against a cost of Rs 3,00,000/-, and said she would sell it when it got back to Rs 3,00,000/-. Both entries come from the Palash decision log. Now run the four assumptions down that pair, one at a time, instead of reaching for a verdict about the person.

Both entries sit inside a holding of four positions, and the shape of that holding is worth seeing before the assumptions are checked against it.

Her preferences are complete and transitive: she can rank the four holdings against each other and does so without hesitating. She updates on evidence: she reads every statement she is sent, and she read both of these before deciding. She is not indifferent to risk, which the third assumption expects rather than forbids. The Rs 3,00,000/- doing all the work in her sentence is a purchase price, and a purchase price is a fact about the past, so the fourth assumption is the only one that fails and it fails completely. Three assumptions held and one broke. One broken assumption out of four is what a relaxation looks like from the inside, and it is the reason the whole model does not get discarded when a decision like this one turns up.

What does avoiding the risk cost, stated in money?

The certainty equivalent turns caution into a number instead of a mood. The certainty equivalent is the sure amount that would feel exactly as good as taking the gamble, so the gap between the certainty equivalent and the expected value is what somebody pays to be rid of the uncertainty. At a curvature of 0.75 the certainty equivalent of the half chance of Rs 11,000/- is Rs 4,365/-. The expected value is Rs 5,500/-. The gap of Rs 1,135/- is the price of avoiding the risk, and once it is written as a figure it can be compared with the price of avoiding some other risk instead of being argued about.

The curvature is the only thing being changed. Straighten the curve to 1.00 and the certainty equivalent rises to Rs 5,500/-, the expected value itself. Being indifferent to risk simply means having a straight line. Bend the curve to 0.50 and the certainty equivalent falls to Rs 2,750/-, which is a quarter of Rs 11,000/- rather than a half. The certain Rs 5,000/- on offer wins for every curvature below about 0.88, and that crossing point is the whole content of the choice that 42 of the 60 investors in the log made.

Does departing from the model mean somebody decided badly?

No, and this is where the whole subject area turns. The same 60 investors in the log were asked a second question on the same afternoon. In gains, 42 of the 60 took a certain Rs 5,000/- over the half chance of Rs 11,000/-, being 70.0 per cent, and a flattening curve predicts that exactly. In losses, 39 of the 60 took a half chance of losing Rs 11,000/- over a certain loss of Rs 5,000/-, being 65.0 per cent. Hold the same curvature of 0.75 that explained the first answer and it predicts the certain loss should have been preferred. The curve that gets the gain question right gets the loss question wrong, and it is the same 60 people, the same room and the same afternoon.

How does an adviser use a model that describes nobody?

Devika Rao, the adviser at Palash Advisory Services Private Limited, does not use the four assumptions to decide whether Meera Sundaram is rational. She uses them as a locator. A client who says she will sell when it gets back to what she paid has said something precise about the fourth assumption and nothing whatever about the other three, and the useful next question follows from that: what would have to be true about the next twelve months for holding Rs 1,95,000/- here to beat holding it anywhere else? Inside an advice conversation the model converts a vague worry about somebody into a located one, and a located worry is the difference between a conversation that can go somewhere and one that cannot.

For a person deciding alone, with no adviser and no committee, the same four lines work as a private check. The sentence that is actually driving the decision is written down, in the words it would take when spoken to a friend, and then matched to whichever of the four assumptions it is about. A sentence about ranking is about the first. A sentence about news is about the second. A sentence about how much it would sting is about the third. A sentence containing a price once paid is about the fourth, every time. The check takes a minute and it does not require calm, information or unusual discipline, which is the only reason it survives contact with a real week. Where somebody is deciding on behalf of other people, conduct and suitability duties apply on top of all of this, and the source for those is the Securities and Exchange Board of India at sebi.gov.in.

What survives the relaxation, and what does not get replaced?

The relaxation is narrow. The second half of the third assumption goes: the input to the utility number stops being final wealth alone and starts including where the person began. Nothing in Allais or Ellsberg or the Palash log gives any reason to abandon the idea that preferences should hang together, or the idea that evidence should be weighed by its diagnostic power, so everything else on the list stays exactly where it was. Relaxing an assumption means replacing one line and keeping the rest, and a reader who hears that the rational investor model was overthrown has been told something that is not true about any of the papers involved.

The benchmark survives for a reason that is easy to state and easy to forget. Every finding in behavioural finance is defined as a departure from this model, so discarding it would leave the findings with nothing to be findings about. The word that does get retired is the word rational used as a verdict on a person. The word was never doing that job. The word named a short list of consistency conditions, and a person can fail one of them while being thoughtful, well informed and entirely reasonable about their own life.

One more test decides whether a departure is worth naming at all, and it is not the size of the departure. A departure that happens once and in no particular direction is scatter. A departure that happens in the same direction every time is a mechanism, and only the second is worth a name. One decision by Meera Sundaram on 12 October is therefore an illustration and not evidence. One case is never evidence that a rule works. The departures turned into a subject because they repeated, in the same direction, across many people who had never met each other.

Meera Sundaram, Devika Rao, Palash Advisory Services Private Limited, the Palash decision log, the Palash 100 index, 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.