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.