Reflexivity: When Belief Changes the Fundamentals

Reflexivity is a two way loop: what people believe about a thing changes the thing itself, and the changed thing then changes what people believe. Belief moving a price is not enough, and that much is ordinary. The loop needs a named route by which the price reaches the underlying facts. Without one, what remains is a correlation wearing a longer word.

Finance normally treats a price as a reading taken from something. Reflexivity is the one idea that says the reading and the thing being read can be joined together. Where they are joined, the price stops being a report on the facts and becomes one of them. The joining is a real structure and it is worth knowing. Reflexivity is also the most abusable word in the subject. A loop can be told about any price move after the move has happened, so what matters is the test that separates the real loops from the told ones.

What is reflexivity, and what makes it different from ordinary feedback?

Start outside markets. A food stall opens outside an office building and a queue forms. People join the queue partly because it is long. A long queue is what a good stall looks like from thirty feet away. So far this is one way feedbackOpinion moving behaviour or price, with no route running back to the underlying facts.: belief moves behaviour, and the stall is whatever it was before. Now add the missing arrow. The takings from the queue let the stall buy better ingredients, cook a second batch and open an hour earlier. The food genuinely improves. The belief that the stall is good has made the stall good, and the better stall pulls a longer queue tomorrow.

Write the loop as three boxes and it becomes much harder to misuse. Belief moves the price. The price moves the underlying facts. The changed facts move belief again. Almost every claim of reflexivity a reader will meet has the first arrow, assumes the third, and never establishes the second. The second arrow is the entire content of the idea. George Soros used the word in exactly this sense for financial markets in The Alchemy of Finance in 1987.

A loop is worth separating from its single pass cousin. A self fulfilling prophecyA single pass version, where an expectation causes the outcome once and then the matter is closed. runs once: everybody expects the early bus to be empty, so everybody takes it, and it is full. The expectation caused the outcome, and then it was over. A loop runs again. The output of one pass is the input to the next, and the interesting question about a loop is therefore never whether it exists but how many more passes it has left in it.

Why does measuring a thing usually leave it alone, and why not here?

The physical sciences can normally assume that measuring something does not change it. A thermometer on the wall reports the temperature of a room and does not warm it by any amount worth writing down. Finance quietly borrows the same assumption. A price is treated as a reading taken from a business, the way the thermometer takes a reading from the room, and the business is treated as sitting there being whatever it is.

The assumption fails whenever the thing measured is partly made of expectations about itself. The cost of raising money is not an independent fact that a share price merely reports on. The cost is partly produced by that price. The reading is an input to the thing being read, and no better instrument repairs that. The problem is structural rather than a fault in the measuring. Notice too what kind of claim this is. Reflexivity is not a claim that anybody is foolish and not a claim about mood. The claim is about the shape of the arrangement, and the people in the third example below are no different from the people in the first two.

What is the channel, and why must it be named?

The whole working test is a single question. Name the route by which the price reaches the underlying facts, in one sentence. If that sentence can be written, the claim is one somebody could go and check, and possibly show to be wrong. If it cannot, what remains is a correlation with a longer word attached to it. The test is blunt, and blunt is what makes it usable at speed.

The word carrying the weight is channelThe named route by which a price reaches the underlying facts, stated specifically enough that somebody could check it., meaning the specific route from price to facts. The sentence has to name a mechanism rather than a mood. Saying that the price went up and people grew excited names no channel at all. Saying that the higher price let the business issue shares and pay for a second plant names one, and names one that can be checked. Either those shares were issued or they were not.

The test is worth having for what it throws out. Applied honestly it kills most claimed instances, including confident ones told by people who have thought about the subject for years. A test that throws out most of what it is given is not thereby a weak test. An idea that survives every application of a test is not being tested at all.

Which routes from price to the facts actually survive the test?

Three do, reliably, and they are worth learning by name because they are the whole surviving list for most readers most of the time. Each one can be written in a single sentence, each one names something a person could go and look at, and each one can be shown to be false. The last property is what separates the three from the crowd of claims the test throws out. A channel that cannot be described specifically enough to be wrong about is not a channel.

The first channel: what it costs to raise money

The clearest of the three runs through cost of capitalWhat it costs a business to raise money, whether by borrowing or by issuing shares. A higher share price is part of what sets it.. A business with a higher share price can raise a given amount of money by issuing fewer shares. The existing holders give away less to get it. Lenders looking at the same business see a larger cushion beneath their loan and price it accordingly. So money becomes cheaper, and cheap money is not a feeling. The rate is a term written into a contract. The price has reached the facts. The business can now afford something it could not afford last month, and it can afford it precisely because of the price.

Feel it at street level first. A stall outside an office building gets busy, and the landlord watching the queue offers a longer lease at the same rent. A visibly busy tenant is a safe tenant, and a longer lease is worth money. The stall spends it on a second counter and another pair of hands, serves more people in the same lunch hour, and the food comes out fresher because less of it is sitting waiting. The queue is longer tomorrow, and this time it is longer for a reason that would survive anybody checking. The belief made the stall better, and only then did the better stall justify the belief.

The second channel: whether other people will deal with the business

The second route runs the other way and is often the faster of the two. A price that falls a long way and stays down is read by other people as information about the business, whether or not it deserves to be. A supplier who was giving thirty days to pay asks for cash up front. A lender declines to renew a facility on the same terms. A large client, whose own committee has to justify its choices, quietly moves the work elsewhere. None of these people is being unreasonable, and each of them is doing what a careful person does with a signal.

Now look at what has happened to the business. The business is paying earlier and collecting no faster, so less money moves through it and it turns down an order it would have taken. Its results get worse, and they get worse because of the price, not because of anything that was true before the price moved. Confidence is not a mood here, it is a set of terms other people offer, and terms are facts. The household version is unpleasantly familiar: a person whose credit record slips is offered worse terms, pays more for the same borrowing, and finds it harder to recover for exactly that reason. The reputation changed the cost, and the cost then justified the reputation.

The third channel: the people who decide whether to stay

The third is the quietest and the slowest. Where a meaningful part of what people are paid depends on the share, a price move changes what staying is worth to them. A rising price makes leaving expensive for exactly the people a business can least afford to lose, and a falling one makes leaving cheap. The choices those people make over a year or two show up in what the business produces. The route is describable in a sentence, and it is checkable. Either people left or they did not.

Notice the one thing all three have in common, and carry it away. In each case the price altered a term, a decision or a resource, and the altered thing then produced a different outcome that anybody could measure afterwards. None of the three works through anybody feeling more positive; all three work through something changing hands. The practical difference between a channel and a story sits there, and it is why the test asks for a route rather than for an explanation.

How is reflexivity told apart from momentum and from sentiment?

The three words get run together constantly, and the confusion matters because they make different claims about different things. Momentum, in the sense documented by Narasimhan Jegadeesh and Sheridan Titman in Returns to Buying Winners and Selling Losers in the Journal of Finance in 1993, is a pattern in prices: what has risen over some past window has tended, in the periods those researchers examined, to keep rising over the next one. Read the claim carefully and notice what is missing from it. Momentum runs from a price to a price, and the business it belongs to never appears in the statement at all.

The absent business is the whole distinction. A reflexive account has to pass through the business, and the business changing is what is being claimed. A momentum account does not, and does not pretend to. The two therefore differ in kind rather than in strength, and no amount of a momentum pattern turns into reflexivity, however long it lasts or however large it gets. A very long price pattern with no route to the facts is still a price pattern.

Sentiment is the other neighbour, and the confusion there is subtler. In the sense measured by Malcolm Baker and Jeffrey Wurgler in Investor Sentiment and the Cross-Section of Stock Returns in the Journal of Finance in 2006, sentiment is a reading of collective appetite: how willing people currently are to hold the sort of thing that requires optimism to hold. Sentiment is a real measurable quantity, and it is genuinely useful for understanding why a whole class of holdings moved together. But mood, however strong and however widely shared, has no route to the underlying facts unless something else carries it there.

The distinction is worth sitting with. Careful people slip exactly here. A shared mood can move a great many prices at once, and a great many prices moving at once feels like a force acting on the world. The mood is still only acting on prices. If the mood lifts a price and the higher price then lets a business raise money it spends, the loop closes, and it closes through the money and not through the mood. The mood was the starting push. The channel was the borrowing.

Does the Palash decision log contain a reflexive loop?

The log contains something that looks like one at first glance, and that is what makes it worth working through. The invented Palash decision log records 240 decisions taken by 60 investors over eight quarters. Of those 240, 96 were buys. Of the 96 buys, 41 followed a media mention of the name within three days. Dividing 41 by 96 gives 42.7 per cent. Set against it is the share of the eligible list that got mentioned at all in a given week. The log puts that share at 11.0 per cent.

Put those two next to each other and the size of the thing is hard to miss. Buying went to mentioned names at 42.7 per cent where the mentioning itself covered only 11.0 per cent of what was available to buy. Dividing one by the other, 42.7 divided by 11.0 gives 3.9. Buys arrived at names that had just been talked about at close to four times the rate that the amount of talking would suggest on its own. The same log records that 71 of the 240 decisions, or 29.6 per cent, were taken within 48 hours of a news item. The count points the same way.

Now apply the test, and watch it fail

The temptation at this point is to reach for the word. Attention drove buying, buying moved prices, higher prices attracted more attention, and there is the loop. The account sounds right, it uses the right shape, and it is wrong. Ask the question the test asks: name the route by which the buying reached the underlying facts of the businesses bought. An attempt to write that sentence finds there is nothing to put in it.

Here is why. When somebody buys an already listed holding on an exchange, the money goes to whoever sold it. The holding moves from one person to another and the business whose name is on it receives nothing at all. Its cash does not change, its costs do not change, its customers do not change, and its ability to pay for anything is exactly what it was the day before. The first arrow is there, and it is a strong one. The second arrow, the one that carries the price into the facts, has nowhere to run. There is no channel, so there is no loop, and what the log actually records is a large attention effectBuying that follows a name being noticed rather than anything learned about it. The route runs one way, from notice to purchase, and stops there. running in one direction only.

What would have had to be different for it to count?

The useful way to fix this is to change one thing and see what happens. Suppose the same money had gone into a fresh issue of shares by the business rather than into buying existing ones from another holder. Now the money arrives at the business. The money pays for a building, or a line, or thirty people. Results afterwards are different from what they would otherwise have been, and they are different because of the price. The price is what set the terms on which that money was raised. The identical enthusiasm, pointed one step to the left, becomes a genuine channel, and it is the destination of the money and not the strength of the feeling that makes the difference.

Notice how little of the story had to change. The people are the same people, the mention is the same mention, the feeling is the same feeling, and the sum is the same sum. One structural fact moved, and a correlation turned into a loop. Reflexivity is a claim about the arrangement rather than a claim about the participants, and that is why nothing about how convinced anybody was will ever settle the question.

What weakens this comparison, and why it has to be said out loud

The 3.9 figure deserves an honest health warning. The two numbers going into it are not measured over the same stretch of time. A buy counted as following a mention if it came within three days. The 11.0 per cent share of the list being mentioned was measured across a whole week. Three days and seven days are not the same window, so the numerator and the denominator are not describing the same period of exposure. The mismatch means 3.9 is an indication that the effect is large, not a measurement of how large, and quoting it as a measurement would overstate what the log can support.

The warning is not a technicality tacked on at the end. A reader who takes 3.9 away as a hard number will use it as a hard number, and the log cannot carry that weight. The honest reading is that the effect is plainly there and plainly big, that its exact size is not established by this comparison, and that neither of those facts has any bearing at all on whether a channel exists. Base rateHow often something happens anyway, before the cases of interest are examined. Without it, any share of anything sounds impressive. comparisons are worth making and worth qualifying in the same paragraph.

Where does reflexivity stop, and what stops it?

Loops get described as though they run until something dramatic ends them, and that is the wrong picture. Most of them stop quietly, and they stop for a reason that can be stated in advance. The facts are not infinitely responsive: there is only so much a business can usefully do with money it did not expect to have. The word for that is elasticityHow far the underlying facts can actually respond to a change in price before they stop responding at all. Elasticity decides whether a loop settles or continues., and it is the property that decides everything about how a loop behaves.

Take the first channel again. A higher price makes money cheaper, and cheap money is spent on the best available use first, as anybody sensible would. The second batch goes to the second best use, worth less than the first. By the fifth batch there is no obvious use left, and the money sits, or it goes into something that does not improve results at all. The route from price to facts is still open, but nothing much is travelling down it any more. The loop has not been broken by an event. The loop has simply run out of things to change.

The household version is immediate. A person who gets a raise fixes the leaking tap, replaces the shoes that were falling apart, and settles the borrowing that was costing the most. The three purchases genuinely improve life. The eighth thing on the list improves it much less, and the fifteenth barely registers. Nobody had to intervene. The response simply flattened out.

Now put a number on the shape. The arithmetic makes a point prose cannot. Suppose a first push lifts a price, and suppose the facts respond to half of whatever the last push delivered. Start the illustration at 100.0. The first pass adds 10.0, the second adds half of that at 5.0, the third 2.5, the fourth 1.25, the fifth 0.625 and the sixth 0.3125. Add them: 10.0 plus 5.0 plus 2.5 plus 1.25 plus 0.625 plus 0.3125 is 19.6875, so the level reaches 119.6875, or 119.7 to one decimal. Keep going forever and the total approaches 20.0 exactly, so the level approaches 120.0 and never reaches it. A self-reinforcing loop with a realistic response settles at a level rather than running away, and settling is the normal case rather than the exception.

At a response of 0.50 the six passes add 10.0, 5.0, 2.5, 1.25, 0.625 and 0.3125. The running level goes 100.0, then 110.0, 115.0, 117.5, 118.75, 119.375 and 119.6875, or 119.7 to one decimal. The limit is 120.0 and it is never reached. At a response of zero the level never leaves 100.0. Raise the response to 0.80 and the six passes add 16.0, 12.8, 10.24, 8.192, 6.5536 and 5.24288, reaching 159.0. The limit sits far above at 180.0, and the loop is still climbing hard at pass six. Only a response that refuses to decay produces something that looks like running away, and a response that does not decay is the thing the previous figure showed does not happen.

Why does an idea that explains everything explain nothing?

So what does the test actually do to a working stack of claims? The test sorts them quickly and without much argument, and the sorting is uncomfortable because the ones that fail are often the ones people are most attached to. Five claims of the kind an analyst actually meets make the pattern clear. The claims that survive all name something that moved between people: money, terms, or a person walking out of a building. The ones that fail all substitute a description of the price, or a description of how people felt, for the route the word requires.

Why is a reflexive account still not a trading signal?

An explanation of why something moved is never an instruction to buy, to sell, to hold, to wait or to avoid. Establishing that a loop exists gives no entry, no exit and no view on how long anything lasts. A mechanism being real does not make acting on it a good idea. Three separate reasons hold that line, and any one of them would be enough on its own.

The first reason has numbers behind it in this very case. The Palash decision log sorts its 60 investors into five turnover groups of twelve. Annual turnover runs 9, 34, 71, 128 and 210 per cent across them. Gross returns run 11.2, 11.0, 11.1, 10.9 and 11.0 per cent, a spread of 0.3 points from top to bottom. Costs run 0.3, 0.6, 1.5, 2.5 and 4.1 points. Net returns therefore run 10.9, 10.4, 9.6, 8.4 and 6.9 per cent, a spread of 4.0 points. The picking was indistinguishable across all five groups and the outcomes were not, so the whole difference was what the activity cost. Brad Barber and Terrance Odean reported the same shape in Trading Is Hazardous to Your Wealth in the Journal of Finance in 2000.

The third reason is the one that makes reflexivity the sharpest case of all. To know whether a loop is running right now, an observer would have to know what the underlying facts would have been in the absence of the price move, and then compare. The comparison is not available. The path where the price did not move is not a path anybody gets to see. The very feedback that makes a loop self-sustaining is what makes its remaining length unknowable, so the explanation and the reason it cannot be acted on are the same fact looked at twice.

How would a practitioner actually use any of this?

Devika Rao, the adviser at the invented Palash Advisory Services Private Limited, gets asked a version of the loop question most months, usually phrased as whether something is being held up by belief. Her useful move is not to answer the question but to split it. One half of the question needs a path nobody can observe and stays a conversation; the other half is about a person's own arrangements and can be settled in ten minutes. Splitting it is not a dodge. The half she answers is the half that changes what anybody does.

Meera Sundaram, who is 41 and invests on her own account, is the test of that claim. Her standing instruction puts in Rs 25,000/- a month. Her reserve of Rs 1,10,000/- covers monthly outgo of Rs 55,000/- exactly twice. She holds a deposit of Rs 2,40,000/- at 6.5 per cent while carrying Rs 1,80,000/- of card borrowing at 36.0 per cent, and clearing the borrowing out of the deposit would save Rs 64,800/- while forgoing Rs 11,700/-, so keeping them apart costs Rs 53,100/- a year. Not one of those figures moves whether or not a loop is running anywhere, and the Rs 53,100/- is a larger and more certain number than anything a loop argument could produce.

For a reader with no adviser and no committee, the same discipline fits into four questions and takes about a minute. The four questions work on any claim anybody puts forward, including the reader's own, and the first one does most of the work.

What are the three words, side by side, one last time?

Most of the trouble with this subject is vocabulary rather than reasoning, so it is worth ending with the three terms laid out together. The three terms differ in how many times the circuit runs and in whether the circuit touches the business at all.

Reflexivity reduces to one picture: a circuit with two things attached to it, a gate on the way in and a valve on the way round. The gate is the channel test and the valve is the response of the facts. Most claimed loops never get through the gate, and the ones that do run until the valve closes rather than until something dramatic happens. Neither the gate nor the valve tells anybody what to do.

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