Speculative Bubbles: The Anatomy of One, Phase by Phase

A speculative bubble is a price that has left fundamental value behind and then keeps climbing because it is climbing. The definition names two quantities and only one of them can be seen. A bubble is therefore easy to label afterwards and close to impossible to call while it is running. Blanchard and Watson showed in 1982 that one can persist with wholly rational participants.

The word arrives already familiar and almost certainly never seen defined. The looseness is not accidental. The word carries a strong feeling and a weak test, so a bubble claim needs two things stated: precisely what would have to be true for it to be right, and precisely why nobody can check it at the moment the check would matter most.

What is a speculative bubble, and how is it defined?

Start away from markets entirely. A stretch of farmland sits beside a district road. For thirty years it has changed hands at a price built on what it can grow: so many quintals a season, so much a quintal, less what the seed and the labour cost. Then somebody announces a new station two kilometres away. Now the same field changes hands at a price built on what the next buyer will pay in three months. Both of those are real prices, and money genuinely moves at both of them. Only one of them is tied to something a person could walk out and count.

The shift from what a field can grow to what the next buyer will pay is the whole idea. A speculative bubbleA price that has moved away from what the underlying facts support, and then rises further because it has been rising. is a price that has departed from fundamental valueWhat a thing is worth on the underlying facts. It has to be worked out from assumptions rather than read off a screen. and then keeps rising largely because it has been rising. The definition has two halves and the second half is the one people drop: a price can sit far above value without being a bubble, and a price can rise for years without being one, so long as the rise is not feeding on itself. A rise caused by a genuine change in what the thing will produce is not a bubble however large it gets. A rise caused mostly by the fact of the rise is one however small it stays.

Now the difficulty, and it is a serious one. Of the two quantities the definition names, one can be read off a screen and the other has to be built. Price is a fact about a transaction that actually happened. Fundamental value is a conclusion, and a conclusion needs a model behind it: an assumption about what the thing will produce, an assumption about how long it will keep producing it, and an assumption about what a rupee arriving in eight years is worth today. Change any one of those three and the value changes with it. Two careful people with the same facts can land on different numbers and neither has made an error.

Computing fundamental value is set out under discounted cash flow. Anybody who cannot compute it is standing in exactly the position the definition describes. The task is to reason about a gap whose lower edge cannot be located. The position is everybody's, including the position of the people who sound most certain.

The two conditions are clearer as a grid than as a sentence. Separating them shows how much of ordinary market conversation lives in the other three squares. A price can be high without the rise having become its own reason, and that is not a bubble.

What does a bubble claim rest on?

The joint hypothesis problem, set out under market efficiency, looked like a technicality and turns out to be the shape of half the subject. Testing whether a price is right always means testing two things at once: whether the market got it right, and whether the model used to say what right means got it right. Fama set this out in Efficient Capital Markets, in the Journal of Finance in 1970, and it has never been solved because it cannot be. There is no way to hold one half still while the other is tested.

A bubble claim is that same problem wearing a different coat. Somebody says a price is a bubble. The speaker has made a claim about a market: price sits above value. The speaker has also made a claim about a model: this particular inferred number is what value actually is. When a bubble claim turns out to be wrong there is no way to tell which of the two halves failed, and that is not a shortcoming of the analyst but a property of the statement itself. Somebody who called a rise a bubble and watched it rise for four more years can always say the collapse has not arrived yet, and somebody who denied it can always say the fall that came was something else.

Put numbers on that so it stops being abstract. Take the invented index at its Q2 level of 131.0. One analyst infers a value of 100.0, so the price sits 31.0 per cent above value and the word bubble follows. Another infers 140.0, so the price sits 6.4 per cent below value and the same number looks cheap.

What are the five phases, and what marks the boundary between them?

The phase names are set out under mania, panic and capitulation, and assumed here. Most readers assume the boundary between one phase and the next is a size of move, and it never is. Naming what actually draws the boundary is worth adding. Minsky set out the sequence in The Financial Instability Hypothesis in 1977, and Kindleberger built it into a narrative structure in Manias, Panics and Crashes in 1978.

Take a small town where a new highway junction opens. DisplacementThe new thing that starts the sequence by making a higher price look reasonable to a sensible person. is the junction itself: something genuinely new has happened and a higher price for the land around it is now defensible. The boom is the phase where credit and attention arrive, three plot brokers open offices and the story starts travelling. EuphoriaThe phase in which the rise has become its own reason, and buyers no longer refer to the underlying facts at all. is the phase where nobody mentions the junction any more, only that plots went up last year. Distress is the first Tuesday when two of the three brokers have no buyers and the story stops working. RevulsionThe phase in which holders will part with the thing at any price they can get, and buyers stay away regardless of the price. is the phase where holders will take anything and nobody is interested at any number.

The boundaries between the phases are drawn by reasons rather than by magnitudes, and a reason cannot be read off a chart. No phase is defined by a percentage. Euphoria is not a rise of a certain size, it is a rise in which the reason people give for buying has become the rise. Distress is not a fall of a certain size, it is the moment when the reason stops persuading. The reason in anybody else's head cannot be observed, only the price they paid. Drawing a boundary by reason is honest as description and close to useless as a live instrument.

The invented index makes that concrete. The rise from the open at 100.0 to Q1 at 118.0 is 18.0 per cent. The rise from the Q4 low of 104.0 to Q6 at 124.0 is 19.2 per cent. The two rises are 1.2 points apart in size and belong to completely different parts of the story.

Set the three ingredients of the anatomy against the five phases and the difficulty becomes a picture rather than an argument.

Can a bubble exist if everybody involved is behaving rationally?

Here is the part most readers do not expect. The mechanisms set out under the cognitive biases, under prospect theory and under herding all make careful people go wrong in patterned ways. A natural next step is to conclude that a bubble is what happens when enough of those mechanisms fire at once, and that a market of hard-headed people could not produce one. The conclusion is wrong, and the result that kills it is not a behavioural result at all.

Blanchard and Watson set it out in Bubbles, Rational Expectations and Financial Markets in 1982. Suppose a price already sits above what the facts support. Suppose every participant knows this, and also expects the price to be further above value tomorrow by enough to compensate for the chance that the whole thing falls back to value in the meantime. Then buying today at the inflated price is not a mistake. Buying is the arithmetically correct thing to do given those expectations. The bubble is sustained by rational behaviour rather than in spite of it, and that is why it earns the name rational bubbleA bubble kept going by participants who are each behaving correctly given what they expect, rather than by anybody making an error..

Put whole numbers on it so the shape is unmistakable. A speculative holding trades at Rs 1,00,000/- and a careful assessment of the underlying facts puts its value at Rs 80,000/-. Everybody agrees on both numbers. If the rise continues, the price next period is Rs 1,25,000/-, and the chance of that is 80.0 per cent. If it collapses, the price returns to Rs 80,000/-, and the chance of that is 20.0 per cent. The expected price next period is 0.80 multiplied by Rs 1,25,000/-, giving Rs 1,00,000/-, plus 0.20 multiplied by Rs 80,000/-, giving Rs 16,000/-. The two branches total Rs 1,16,000/-. Against a price of Rs 1,00,000/- today, the expected gain of Rs 16,000/- is 16.0 per cent, so anybody whose required return is below 16.0 per cent should buy, and every one of them can be completely rational.

A consequence in that arithmetic keeps the result honest, and it is worth drawing out. Hold the price at Rs 1,00,000/- and the assessed value at Rs 80,000/-, and ask what the surviving branch has to pay for a buyer to break even as the chance of collapse climbs. The answer rises, and then it runs away.

Now connect that to the aggregation step set out under investor and market behaviour. Errors that scatter cancel out against each other, so a mechanism only reaches a market when the errors it produces share a direction. The condition is a demanding one, and it is the reason most individual quirks never show up in a price at all. A rational bubble needs no error at all to clear that bar. The requirement is shared expectation rather than shared error, and shared expectation is a far easier thing to arrange. Everybody expecting to sell higher is not everybody being wrong. The expectation is everybody being right about each other.

Set the three arrangements side by side with the sixty investors of the invented log standing in for a market. Scattered errors cancel and never reach a price. Errors that share a direction survive the aggregation and move one. And a third arrangement moves a price with no error in it anywhere.

Why is a bubble so much easier to name afterwards?

Because the two jobs are not the same job, and they are not done with the same information. Afterwards the peak is available. Where the path turned is known, so the highest price is known, so which part of the rise was never supported is known. The label attaches cleanly. During, there is a rise and nothing else, and here is the difficulty in one line: every bubble looks exactly like an ordinary rise while it is happening, and so does every ordinary rise.

Naming a bubble afterwards uses a fact that did not exist while the decision that mattered was being taken, so the confidence of the retrospective account is borrowed from information the participants never had. A great deal of commentary consists of applying a completed anatomy to an unfinished path and calling the result insight, and it is worth being blunt about that. The anatomy is genuinely good description. The anatomy cannot identify the phase in progress. Doing so would require the peak, and the peak is the one thing a live path never shows.

Watch what the invented path does to somebody standing inside it. The highest level seen so far reaches 131.0 at Q2 and then never changes again for the rest of the sequence. The whole peak is present from Q2 onwards, and at the time it was utterly indistinguishable from a level about to be exceeded next quarter.

Was the invented index path a bubble, and what did three readers get?

The Palash 100 is an invented index built for teaching, and its nine levels are fixed throughout. The index opens at 100.0 and then records eight quarter ends: 118.0, 131.0, 112.0, 104.0, 116.0, 124.0, 121.0 and 127.0. The peak is Q2 at 131.0 and the low is Q4 at 104.0. From the open to the peak is 31.0 per cent up. From the peak to the low is 20.6 per cent down. The shape is the one everybody draws when they draw a bubble.

Set the label aside for a moment and follow three readers instead. Each buys the whole index once and holds to Q8. The only thing that differs between them is the entry pointThe level at which one particular person began. Two people can live through the same path and start at completely different places on it.. Reader A enters at the open at 100.0, so 27.0 index points on 100.0, and that is 27.0 per cent up. Reader B enters at the Q2 peak at 131.0, so 4.0 points on 131.0, and that is 3.0534 per cent, rounding to 3.1 per cent down. Reader C enters at the Q4 low at 104.0, so 23.0 points on 104.0, and that is 22.1154 per cent, rounding to 22.1 per cent up.

Now the point, and it is the one worth carrying away. Suppose this path was a bubble. The low of 104.0 is 4.0 per cent above the open of 100.0, so Reader A finished 27.0 per cent ahead of where they started and was never below cost at any quarter end at all. Reader C, who bought at the worst-looking moment in the sequence, finished 22.1 per cent ahead. Reader B is the only one down, and by 3.1 per cent. The anatomy of a bubble is not the anatomy of a loss, so a word that describes the shape of a path says almost nothing about what happened to any particular person walking it.

There is a second thing hiding in the same numbers, and it is the sort of thing that quietly misleads people who read only headline statistics. The peak-to-trough fall of 20.6 per cent is a real and correct measurement. The fall is also completely silent about where anybody started. The trough of 104.0 is simultaneously 20.6 per cent below the peak and 4.0 per cent above the open. Both statements describe the same quarter end and the same single number.

The same trap catches Reader B from the other side. Their worst quarter end was Q4, when 131.0 had become 104.0, a fall of 20.6 per cent. Their finish was 127.0, a fall of 3.1 per cent. Both describe the same holding, and they differ by a factor most readers would not guess.

Here are all eight results with their divisions, so the argument survives without the control. From the open, 27.0 on 100.0 is up 27.0 per cent. From Q1, 9.0 on 118.0 is up 7.6. From Q2, 4.0 on 131.0 is down 3.1. From Q3, 15.0 on 112.0 is up 13.4. From Q4, 23.0 on 104.0 is up 22.1. From Q5, 11.0 on 116.0 is up 9.5. From Q6, 3.0 on 124.0 is up 2.4. From Q7, 6.0 on 121.0 is up 5.0. Seven of the eight entries finish ahead and exactly one finishes behind. The word bubble does not remotely prepare a reader to expect that.

What does the turnover overlay add, and what does it not?

The invented log records one more thing about this path. Turnover ran at 3.1 times its eight-quarter median in Q2, the peak quarter, and at 0.4 times the median in Q4, the low quarter. Activity was at its highest near the top and had almost stopped near the bottom. The overlay is satisfying, and it lines up neatly with the phase language: heavy trading where euphoria would sit, silence where revulsion would sit.

Be careful with the satisfaction. An overlay that is consistent with a story is not evidence for that story. The same two observations are equally consistent with information simply arriving unevenly across the eight quarters. A quarter in which a great deal becomes known is a quarter in which a great deal of trading happens, and no crowd behaviour is required to produce that. Two data points cannot separate the two explanations, and that limit is more useful to know than the neat version.

The overlay cannot decide anything, and the reason is worth seeing. The peak quarter ran at 3.1 times median activity and the low quarter at 0.4, a ratio of 7.8 to one. Both explanations predict that ratio, so the number that looks like evidence is the number both sides would have forecast.

Why does naming a bubble license nothing, in either direction?

One conclusion matters more than any other and needs saying plainly rather than being left to be inferred. Everything above is an explanation of why a price path took the shape it took. An explanation of a price movement is never an instruction to buy, sell, hold, wait or avoid, and it is never evidence that acting on it would have paid. The sentence that must never be assembled is: this effect exists, therefore trade on it.

Three separate reasons hold that line, and any one of them would be enough on its own. First, an effect of this kind is almost always measured before costs. The invented log shows the most active turnover group paying 4.1 points a year in dealing charges, spread and tax together, larger than most documented effects in this subject area. Second, a published effect is read by everybody who read the paper, so what it did before publication is not what it does afterwards. Third, the very obstacles that let a mispricing survive are the obstacles that stop a reader capturing it. Shleifer and Vishny set that out in The Limits of Arbitrage, in the Journal of Finance in 1997. The explanation and the obstacle are one fact seen twice.

The first of those three is the one readers skate over, so it is worth drawing. The five turnover groups in the invented log earned gross returns of 11.2, 11.0, 11.1, 10.9 and 11.0 per cent. After costs they kept 10.9, 10.4, 9.6, 8.4 and 6.9.

There is a fourth reason, and the arithmetic above supplies it. Even if somebody correctly identified a bubble in progress, the label would not have told them what happened to any particular reader. Seven of the eight entry points on that path finished ahead. Selling on the name would require a fundamental value nobody can observe, so naming a bubble is not a reason to sell. A price that has risen is not evidence about the next price, so the name is not a reason to buy either. The name is a description, and descriptions are worth having on their own terms.

Both directions close off for separate reasons, and it is worth seeing them refused side by side rather than one at a time. The label points at a gap nobody can measure in one direction, and at a rise that carries no information about the next price in the other.

What would have to be true for a bubble claim to be testable?

It is worth turning the difficulty around. Rather than asking whether a given claim is right, ask what somebody would have to supply for it to be checkable at all. Three things, and almost no live claim supplies even the first. A stated model of value, written down before the price is judged rather than reconstructed afterwards. A stated size of gap that counts, fixed in advance, to stop the claim being quietly rescaled once the path is known. And a stated window inside which the collapse has to arrive.

A claim that never expires can never be wrong, and that is precisely why the third condition is the one that gets left out most often. Somebody who says a price is a bubble and names no window has made a statement that will eventually be vindicated by any fall whatsoever, in a year or in nine. The three conditions are worth requesting whenever the word is used seriously. Most of the time the request itself is the whole answer, and the interesting thing is how rarely anybody minds being asked.

Count the chances a claim without a window gets on this one path. A fall of 14.5 per cent arrives from Q2 to Q3. Another of 7.1 per cent from Q3 to Q4. A third of 2.4 per cent from Q6 to Q7. Any of the three vindicates somebody who named no date and no size.

Where does the word get used loosely, and what does that cost?

The loose usage is everywhere and it always takes the same shape: a large rise gets called a bubble because it was large. The loose usage collapses the definition into one of its two halves and throws away the half that did the work. A rise of 31.0 per cent from the open to Q2 on the invented index is a large rise. Whether it was a bubble depends on something the size cannot settle, namely whether the price had left value behind and was climbing on its own momentum.

A term that applies to every large move stops distinguishing anything and can no longer be wrong about anything either, so using the word for any big rise empties it. The cost is not pedantic. The cost is that a precise claim, about price against value, becomes a vague expression of unease about a number having got big, and unease is not a finding. The emptying also runs the other way: somebody who calls every rise a bubble will eventually be right, and being eventually right about everything is the same as being informative about nothing.

Run the loose test over the invented path and it convicts almost everything. The climb from the open to Q2 is 31.0 per cent. The rise from the Q4 low to Q8 is 22.1 per cent, and from the low to Q6 it is 19.2. The last two are the recovery, and a test that cannot tell a recovery from a climb is not a test. Shiller wrote Irrational Exuberance in 2000 precisely to give the popular word a stricter spine than size.

How would a practitioner actually use any of this?

Devika Rao, the adviser at the invented Palash Advisory Services Private Limited, is asked some version of the bubble question most weeks. The useful part of her answer is not a view. The useful part is the structure of the question. She separates what a client is actually asking into two. The first is whether a price is above value, and answering it requires a model and stays arguable. The second is what should happen next in the client's own arrangements, and it does not depend on the first question at all. The second is answerable. The first is a conversation.

Meera Sundaram, an invented investor who is 41 and invests on her own account, has a reserve of Rs 1,10,000/- against monthly outgo of Rs 55,000/-. The reserve is two months of outgo, and a standing instruction puts in Rs 25,000/- a month. Nothing in the five phases changes those numbers or what they imply. The practitioner move is to notice that almost every question dressed as a bubble question is really a question about how much a person can survive being wrong, and that one is answerable without knowing anything about fundamental value.

A household-sized version of the whole argument sits in the invented log already. On 19 February a television segment named Suvarna Chemicals Limited and Meera added Rs 1,00,000/- to it the same evening. Nothing about value was computed. The reason was that the thing had been mentioned.

One evening is an anecdote. The same reason held by many people at once reaches a price.

For a reader with no adviser and no committee the same split works and takes about a minute. The first question is what would have to have been believed for the price to make sense, written down. The second is what would have to happen for that belief to change, written down too. Neither of those requires the bubble question to be settled, and both of them survive whichever way the path goes. Where a conduct duty is involved, the Securities and Exchange Board of India at sebi.gov.in is where the requirement is set out and where it must be confirmed.

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.