Das Kapital – The three volume set by Karl Marx and Friedrich Engels may contain the theoretical underpinnings for the observations of R. N. Elliott. The fundamental interactions involved in economics via social relationships between commodities lead to the development of Elliott Waves — later expanded upon by Prechter, Sornette, and others. More on this possible connection in a future post. Regardless, based on what I have read so far, I think this will be an interesting intellectual read. The well-worn hardback copy version I am reading, from a Boston library, was published in 1902; I wonder who has read this copy in the past 112 years?

PDF of the price movement:

GIF animation of the model:
Red dots are traders short the stock. Yellow dots are traders long the stock. Orange dots are traders neither short nor long the stock.

online backup storage

I created a blog devoted to exploring these LPPL market signals: LPPL Market Watch

Update: new website devoted to this subject. Visit: The Bubble Index.

Summary of Research

Recent research by Didier Sornette and his colleagues suggests that market crashes are predictable phenomenon. Even though economists debate the existence of crashes and their precursors – bubbles,  there exists historical proof of Log-Periodic Power Law (LPPL) oscillations occurring immediately before all recorded major market declines in all major stock indices. For example, these LPPL oscillations occurred in the Dow Jones Industrial Average and S&P 500 shortly before the crashes of 1929, 1987, and 2000.

With the aide of Sornette’s previous papers on market crashes, a “bubble index” is created. The bubble index displays the likelihood of a market bubble at any given time. With an index like this as a tool, any investment strategy which seeks to time the market will be highly successful. The bubble index indicates when to change asset positions in preparation for an incoming crash. One application of the bubble index is for financial planners and investment managers to change their client’s asset allocations accordingly. As the bubble index spikes, a crash is near. After the crash occurs the bubble index returns to low levels, indicating that the crash is over.

A bubble index for both the Dow Jones Industrial Average and the S&P 500 is formed with the methods presented in this paper. Remarkably, the 1929, 1962, 1987, and 2000 crashes are all predicted at least a week before the actual crash. In the weeks prior to these crashes there is a large spike in the index. After the crash occurs, the index returns to low levels. Interestingly, the bubble index for these indices only spikes during a crash. In other words, given that a spike has occurred, there is a 100% probability that a crash has or will occur. However, some of the crashes are not predicted by spikes in the bubble index. For instance, In both indices the 1968, 1972, and the 2008 crash show no spike in the index before or during the event.

These LPPL signals indicate that crashes are not related to changes in technology, culture, economic policies, etc… In other words, financial markets have patterns which suggest an underlying structural instability during crashes. This supports Sornette’s belief that financial crashes are critical phenomena resulting from the complex interactions of traders. To me, this suggests that the natural sciences have a key place in finance.

The implications of these results are rather enormous, since the index is simple to create and understand. The ability to leave the market before a crash and enter after the event provides a wonderful opportunity to earn excess returns while preserving capital. This bubble index should be run on a daily basis to allow an investment manager or financial planner to gain an awareness of current stability conditions. If the bubble index is widely viewed and accepted as a legitimate and reliable forecast of bubbles and crashes, then crash prevention may be possible at the macro level.

Links to papers:

2. January 15, 1973 — followed by a drop in excess of 23%

3. December 27, 1976 — followed by a drop in excess of 14.7%

4. March 26, 1984 — followed by a 11.8% drop

5. Sept. 28, 1987 — followed by a 31.7% drop

6. July 9, 1990 — followed by a 17.4% drop

7. August 28, 2000 — followed by a 36.5% drop

8. October 1, 2007 — followed by a drop in excess of 42%

9. July 18, 2011 — followed by a 16.5% drop

Figure 2

Figure 2 was produced with C++ code. S&P 500. Six year window of data.

3. April 19, 2010 — followed by a 16% drop

Figure 3

Figure 3 was produced with C++ code. Dow Jones Industrial Average. Six year window of data.
1. December 31, 1909 — followed by a 23% drop
2. October 2, 1929 — followed by a 43% drop
3. March 12, 1937 — followed by a 40% drop
4. January 8, 1960 — followed by a 15.6% drop
5. October 2, 1987 — followed by a 31.7% drop
6. July 27, 1990 — followed by a 17% drop
7. September 8, 2000 — followed by a 36% drop
8. October 12, 2007 — followed by a drop in excess of 42%

Figure 4

Figure 4 was produced with C++ code. Dow Jones Industrial Average. Seven year window of data.
1. December 31, 1909 — followed by a 23% drop
2. October 2, 1929 — followed by a 43% drop
3. March 12, 1937 — followed by a 40% drop
4. September 23, 1955 — followed by a quick 8.7% drop and then recovery
5. January 8, 1960 — followed by a 15.6% drop
6. October 2, 1987 — followed by a 31.7% drop
7. July 27, 1990 — followed by a 17% drop
8. September 8, 2000 — followed by a 36% drop
9. October 12, 2007 — followed by a drop in excess of 42%
10. July 8, 2011 — followed by a 16% drop

Poor Market Forecasting

And as we now know, the true model (for now) of the solar system was introduced by Aristarchus (Copernicus and Kepler helped bring forward this model) and predicts planetary motions with near perfection and represents the actual state of the solar system. I believe that the analogous model for stock returns has been introduced by Didier Sornette, Anders Johanson and others.

These scientists have expounded the idea that market returns are a function of individual agents in a complex system. Just as the human body is a collection of individual cells which make “decisions” based on communications with neighbours through chemical processes, traders make their own decisions based on communication with neighbours. With this perspective the market is a complex system of interacting agents. Thus, returns should be a function of these interactions. Under this complex system model, bubbles and crashes which dot the history of finance (which are not explained fully by independent returns/martingales) are straightforward results. In addition, these models still explain why returns are close to normal “most” of the time.

So, it seems that we need to modify or throw away the old models in favour of these new complex system models. These complex models offer better prediction of the overall market and more fully represent reality.

There is the interesting possibility of this: the stochastic volatility model referred to as the Ornstein-Uhlenbeck process represents the physical process of a “noisy relaxation process.” The Wiener Process represents Brownian motion or motion of a particle through a gas or liquid. So, if we consider the movement of a stock through a virtual container of many stocks (these stocks are the atoms in the Brownian motion) then we need to ask ourselves: What does the price, interest rate, returns, etc. mimic? It is NOT the equations! BUT the physical processes themselves.  Why is an interest rate in a state of disequilibrium in the first place… that it must try to relax? Who put the stock in swarm of human hands all independently moving… It more correctly seems that the traders are following its movement at every second, waiting to grab it when the time if right (thus not independent)?

My question is this: If market agents realize the instability and expect a crash, will the crash be avoided?

Perhaps there exists a critical proportion of agents who must expect the crash for it to be avoided. If a small number of agents expect the crash, then it will still occur. If more than the critical number of agents expect the crash, it will be avoided. But, if so many agents share the same attitude, doesn’t that make  the market even more unstable? With all this order, there will be opportunities for arbitrage. As attitudes flip-flop and cascade through the system, this arbitrage opportunity will occur again and again; faster and faster; this creates the observed log-periodic oscillations. Eventually, the crash occurs. My conclusion seems to be that a crash can not be avoided.

People say that in reality there is no arbitrage. They believe that any pattern which arises will be quickly removed. BUT, isn’t the removal of a pattern a pattern itself? Perhaps similar to Hofstadter’s Figure and Ground? Caution: some Grounds are not themselves Figures. I believe that the ideas presented by Sornette may be the pattern of pattern removal. Perhaps there can be strategies based on the removal of a pattern, which is based on the removal of a different pattern… and so forth.

The potential for crash prevention has applications in societal collapse. My intuition tells me that the two are related. If we can answer the question: Can we prevent the crash of a market? Then we will know the answer to the question: Can we prevent the collapse of a society? To me this seems deeply connected with Isaac Asimov’s Foundation Series. In this series Hari Seldon develops psychohistory (from Wikipedia):

Using the laws of mass action, it can predict the future, but only on a large scale; it is error-prone on a small scale. It works on the principle that the behaviour of a mass of people is predictable if the quantity of this mass is very large (equal to the population of the galaxy, which has a population of quadrillions of humans, inhabiting millions of star systems). The larger the number, the more predictable is the future.

It seems that Asimov is once again ahead of his time!

Interestingly, the book Why Stock Markets Crash, by Didier Sornette, mentions the same phase transition, or critical point as he refers to it, occurring due to an increasing rate of population growth and dependence upon technology. The rate of population growth implies the occurrence of a finite time singularity. Upon reaching this critical point, a change from one regime into another will occur. What this change will be is unknown.

There have been numerous large civilizations of the past whose existence was relatively brief on the face of the Earth. Will modern civilization have the same fate? These two books suggest an impending change. However, there is a chance that this time could be different. No other society in history has been able to predict its own demise. Is this the key? The knowledge of one’s own collapse could be sufficient to prevent it.

I believe to at least postpone the arrival of this phase transition requires only that we have a full dependence on renewable resources and find a revolutionary way to produce and distribute fresh water. Once these are accomplished, other issues which could lead to collapse can be fixed in due time.

Surprisingly, there already exist potential solutions which I believe can solve the problem: Algae Oil and Water Cavitation. Growing algae in deserts near the ocean seems like a terrific idea for generating fuel. Not to mention the fact that the algae remove CO2 from the air. However, I can foresee that this could actually create a problem, since too little CO2 in the atmosphere is also a problem.

Water Cavitation, as mentioned in the link above, provides a reliable mechanism for removing chemicals and organisms from water. A perfect source of clean, fresh water for the world. However, there still exists the problem of water availability. Perhaps there are good ideas for this, I am not sure.