Break out the bubbly

Bubbles are fascinating market phenomena. They often end with a devastating crash – these occasions etch themselves into collective human memory because of the psychological devastation they cause. In retrospect it is almost always obvious that values were inflated, that the market was exceedingly fragile and that the good times would not last. But in the midst of the bubble all except a wise (and ignored) few are blind. It seems a fundamental flaw of human nature dooms us to repeating the same mistake time and again.

Famous bubbles

In order to entrench that what we call bubbles are real events, rather than just an academic construct, I think it is useful to list some of the more famous bubbles in world history.

Tulip mania (1585 - 1650): People invested heavily in tulips, a Dutch export. The price of tulip bulbs shot up as people mortgaged their houses and businesses to trade in tulips. In 1637, bulbs which people used to pay for dearly become nearly worthless when the bubble burst.

South Sea Bubble(1720): It is actually after this episode that the term “bubble” was coined. Here speculation was based on expectations of profitable trade with Spanish colonies in South America. This is a good example financial manipulation. The directors of the South Sea Company deliberately sought to drive up its stock price - this was done by creating an artificial hype around trading possibilities. A number of bogus companies (and some bona fide ones) also tried to cash in and swindled many investors. A famous example was a bogus company “for carrying on an undertaking of great advantage, but nobody to know what it is”. The bubble burst slowly but definitively, bankrupting many.

Roaring twenties (1922 – 1929): The stock market was the place to be. The man-on-the-street started investing in stocks – everyone thought they could make a fortune, and quickly. Many invested in the market with borrowed money. This time it was new industries that were thought be able to bring permanent prosperity. Bankers came under fire after 1929 for manipulating the market and bolstering the speculation. The crash of 1929 and the resulting depression are well known.

Dot com bubble (1995- 2000): With the advent of the internet, speculation in internet and technology companies took place. It was thought the old rules did not apply to this new industry.

These are just the more famous bubbles. There are many more examples of varying devastation. The financial crisis was partly caused by the bursting of a housing bubble in America. The unsavoury lending practices associated with this bubble are by now well known. Not all bubbles end in crashes. In the 1960s there was a bubble associated with electronic manufacturing, which ended less spectacularly than the examples described and as a result it has not earned a prominent place in history.

Bubbles are characterised by some defining features:

1. There is a belief that prices will continue to rise indefinitely
2. There is an overwhelming belief that (1) can be justified as circumstances are somehow different from previous bubbles. In the 1920’s it was “The New Era” of industry, in the 1990’s it was the “New Economy” caused by the internet.
3. People exhibit a willingness to believe bordering on stupidity. People may be fooled by swindlers, by bankers, and, often, themselves. All that’s needed is an excuse to believe. No more.
4. People purchase stocks (or other assets) purely for their resale value – the dividends or income from the asset become secondary and, in fact, may be traded away. For instance in the 1920’s people were willing to pay interest rates on loans far higher than the earnings on stocks hoping to sell the stock later at a higher price.
5. There tend to be high levels of speculation, which can be taken to mean making risky investments with the possibility of a complete loss of capital, usually with borrowed money.
6. The dismissal of “prophets of doom” who forecast the end of the bubble
7. Right up until the end, everything seems good. There seems only to be cause for optimism. The cracks only seem to appear later.
8. People focus on the fact that prices go up, rather than why they go up. Inevitably the why is that people expect prices to go up. So they go up.
9. When the end comes people are reluctant to believe it. But efforts to revive the bubble inevitably fail.
10. There is a “failure to know what isn’t known” as Galbraith puts it. People act is if they are knowledgeable – of course this stock will go up – but they do not know that they do not actually know.

How do bubbles form?

The origins of bubbles are not clear. We can identify some conditions which seem to be necessary and a number of others that help bubbles along.

Looking for a definite cause may be misleading – the structure of the market itself may be the cause. This is, essentially, what the dynamical systems models, as in my earlier post, posit. Here it is a process of contagion of opinion between investors that causes the bubble. People are optimistic because others are optimistic, which causes more people to become optimistic. All that’s needed is an initial spark and enough optimism to be generated from it. This is not deterministic – it’s an inherently random process.

It is clear that optimism is essential. People have to believe the story of the era to be tempted to invest. They need to blind to the risks they are taking. People need to have faith in others – mistrust results in caution, which does not favour speculation.

It helps if there is a large supply of savings. If this is the case people will be more willing to risk a part of their savings in the market (Economists would say that the marginal value of savings diminishes with increasing savings). In addition the availability of credit would make speculation easier. It allows people to buy far more stocks, driving prices higher. These are contributing factors, not a causes.

This suggests, then, that speculation-fuelled bubbles are more likely after a period of prosperity, which builds up confidence and savings, and may also result in fewer credit restrictions. The memory of previous bubbles and hardships needs to dull. As such it may be some time before the next bubble after the latest financial crisis appears. But it will come.

Why do bubbles burst?

It is tempting to think that bubbles burst because something happens. In the efficient markets view a huge crash must be caused by some dramatic and unexpected news. This does not seem to be the case. In hindsight, it is always possible to say this event or that caused the selling. But more often than not, there is no good reason why that event should have had such a catastrophic effect.

Dynamical systems theory, as mentioned in my earlier post, gives an alternative explanation. The truth is that after a period of speculation, the market is in an unstable state. A large number of market participants are acting in unison. All that is needed for a crash is for them all to decide to sell at once. The truth is that just about anything can cause this to happen, say slightly worse than expected economic figures. The true underlying cause of the crash is the bubble that caused the market to be in such an unstable state, not the event that bursts the bubble.

Bubbles seem to rely on a supply of new buyers, to whom those who want to cash in can sell. We may call these buyers fools, as they are purchasing an overvalued asset. However, they expect to sell to a “greater fool” who will purchase the asset at an even higher price. When this supply of greater fools dries up (as it inevitably does), prices decelerate.

When confidence diminishes, even just a little, it can cause the bubble to burst. The first wave of speculators sell, causing others to sell as well. Pessimism rapidly infects the market and sellers swamp buyers. If there were sales on margin, this can exacerbate the matter as these generally come with margin requirements. Speculators need to put up money as collateral for the stocks they bought on credit. The lower the price of the stock, the more of this money called margin is needed. Falling prices will cause some margin buyers to be forced to sell when they can no longer put up more margin, which drives prices down further.

Bubbles can be burst by regulatory action. The central bank can raise interest rates, for instance. Even just a statement by the bank that assets are overvalued could do it. But this immediately identifies who ended the bubble and opens up the authorities up for criticism. As such, this is not generally how bubbles burst.

A litany against arrogance

Having now examined history, I may be tempted to think I am immune to the kind of mass deception that characterises bubbles. This would be a mistake. If I have learnt anything, it is that bubbles are complex and subtle, and that human nature being what it is, cannot easily digest subtlety. I am human and have the same flaws. It is, perhaps, even more tempting to think that great minds (through introspection or rational deliberation) may be immune. Few would challenge the greatness of Irving Fisher, whose work pervades economics and statistics even today. In a statement now famous, 14 days before the crash, Fisher said that “In a few months, I expect to see the stock market much higher than today.” Fallibility is pervasive. There is some (cold) comfort if one recognises that markets are random, that some things cannot be explained or predicted, that knowledge is superficial at best.

Some references

An excellent account of the 1929 crash:

• Galbraith, J. K. (1997). The Great Crash 1929. New York: Houghton Mifflin Company.

From a dynamical systems viewpoint:

• Sornette, D. (2003). Why stock markets crash. Woodstock: Princeton University Press.

Wikipedia:

• Wikipedia. (2012). Speculation. Wikipedia. Retrieved February 4, 2012 from http://en.wikipedia.org/wiki/Speculation
• Wikipedia. (2012). Dot-com bubble. Wikipedia. Retrieved February 4, 2012 from http://en.wikipedia.org/wiki/Dotcom_bubble
• Wikipedia. (2012). Economic bubble. Wikipedia. Retrieved February 2, 2012 from http://en.wikipedia.org/wiki/Economic_bubble

Don’t look at my crystal ball: predicting crashes

Stock market crashes seem to hit with a ferocity and suddenness that suggests we cannot possibly predict their occurrence. With previous crashes, including in 1929, there have been those who argued that a crash was coming because speculation could not be sustained. In “Why stock markets crash: critical events in complex financial systems” Didier Sornette argues that he has found a scientific way to predict crashes.

Heisenberg uncertainty for markets

The problem with predicting stock market crashes is that prediction changes the market. If you make your prediction public, either

1. very few people believe you and the stock market crashes on its own, or it does not crash because your prediction was wrong; or
2. a large number of people believe you. They get out of the market or worse, go short. The prediction causes the crash; or
3. a sizeable number of people believe the prediction may be correct. They adjust. Rather than crash, the market merely wanes. The prediction prevents the crash.

Such a prediction has very little hope of being credible. If the market crashes either you caused the crash, or you were probably just lucky. Preventing the crash, a social good, necessarily destroys your credibility. The only way to make a prediction, then, is to do so in secret. Leave the prediction with a notary who will reveal it after the fact. This is what Sornette did.

There seems to me to be another problem with prediction and that is with the methods used. If you choose to publish your method, this is essentially the same as making very many future predictions public, provided of course people actually use the model. In this case, either the model becomes a good approximation of reality or, quite the opposite, it fails to predict crashes because people adjust correctly whenever the model predicts a crash will occur. The former case is likely to be unstable. It will create a pattern from which traders could profit.

In any case, if you want to make money from your model, you should probably keep it secret. And Sornette has done this as well, not publishing his latest models. The ones I relate here were probably published with some delay.

The mathematics

Sornette tries very hard to describe his models without heavy mathematics and to explain things in a way that a lay man would understand. He fails miserably in this task. With the talk of spontaneous symmetry breaking, goldstone modes, and log-periodic behaviour (concepts from physics and dynamical systems), I was entirely lost. I am no physicist, but I consider myself to be a sophisticated reader and I got no more than the gist of things.

Sornette’s method is based on identifying the log-periodic signature associated with a speculative bubble. Such a bubble, characterised by rapidly rising prices, must eventually burst or wind down. Prices cannot continue to rise at a super-exponential rate forever, as then they will reach infinity in a finite amount of time. There is a point in time at which a crash is then most likely to occur and this is what Sornette tries to find.

Inherent in this is the idea that there is something special about a crash, and the events that precede it. Crashes are not just price drops on a larger scale. They have special properties. If this were not the case, prediction would be impossible.

Here is a horribly simplified version of the model (which I will present without a proper justification for why markets should follow such a pattern). We can suppose that during a speculative bubble the logarithm of prices follows, roughly, a power law of the following form

log(P(t)) = A + B(t_c – t)^D

With 0 < D < 1 we see that the gradient of the function becomes infinite at t_c and the log-price reaches a maximum value of A at this point. t_c is the most likely point for the bubble to burst and a crash to ensue. However, the crash can occur earlier and it need not occur at all, if prices wind down more gently. The figure plots one example of such a power law for the 1987 crash with t_c = 87.65.

The above figure plots the power-law formula as fitted for a period just before the 1987 crash of the Dow Jones index. (Created using Wolfram Alpha)

Ad absurdum

It is one thing to predict stock market crashes. When the economy is in a speculative frenzy, there are always a few sober individuals who realise it cannot last. It is another thing to predict the course of world events. Sornette applies his techniques to population statistics and other figures to conclude that something, the singularity, is going to happen around 2050. What will it be? Who knows? Sornette provides some fluffy speculation. I suspect this last chapter was added merely to increase sales and should not be taken seriously.

Track record

Sornette reports a small number of actual predictions (made before the events took place). Five crash predictions were made. Two were false alarms, and two (or three, depending on how loosely you define ‘crash’) were successes. This is, of course, a terribly small sample. But even predicting two crashes correctly is something. One can do some math to say whether it is really significant (and Sornette does), but I mistrust such endeavours. Needless to say, I need more convincing.

What is the use?

You can do two things with your ability to predict crashes. You can make money, or at least avoid losses, and you can help prevent future crashes. If people believe the model works, when a crash seems likely to be coming, speculation should slow. The market could become more stable (in fact, it is not clear that it might not rather cause the opposite). Authorities could use the model to decide when to step in. The problem is, if this works, the model will now be a bad predictor of crashes.

It is also precisely when action is needed the most when the model is least likely to be trusted. In a speculative orgy, people want to believe the good times will continue. The model would have failed before. Perhaps it is wrong this time too. I do not believe the Sornette model is likely to have this effect, merely because it does not appear to have been widely adopted. Even if crashes do not occur as predicted by the model, this does not mean they will not occur. They may develop a new pattern, one the model cannot account for.

Final word

Stock market prediction is a perilous business. At best it is imprecise, unreliable. At worst it attracts charlatans and those who would manipulate markets for their own ends. In the midst of a speculative frenzy it seems that we should know better; we should know things cannot last. We seem to be unwilling to predict the end. We can neither trust our models nor our instincts. The former are too simple, the latter too susceptible to fallibility.

References

Sornette, D. (2003). Why stock markets crash. Woodstock: Princeton University Press.