CHAOS AND THE STOCK MARKET

Background

It started off with an assignment to do extrapolations when I was still under-graduate. I used some of the Johannesburg Stock Exchange (JSE) data as basis for input, and the regression methodologies. It soon turns out that these methodologies have some inherent shortcomings regarding extrapolations. This triggered off the development of my own extrapolation algorithm. After 6 years of development and refinement I had a workable methodology. It worked fine, except every so often my predictions were wrong - I did not know at the time that it was chaos that hit me, I called it investor madness! This was something that I could not wish away, so some 8 more years of development and refinement follows in which the accuracy went up from 30% to 90%, with the occasional 100%.

With this accuracy I decided to invest some of my own money on the JSE, using my algorithm. That was January 1996. During 1996 the JSE had a disman performance, ending the year on -4% for the year. By using my algorithm I was able to make more that 37% net profit during the same period. We all know that in a declining market there are always individual shares that will rise, the algorithm was therefore quite successful in picking out the correct shares to buy and sell at the right time. From the beginning of this year until the end of June, net profit is more that 43%.

Development and Application

It is common knowledge that share prices run in cycles, with each share having its own individual cycle or set of cycles - almost like the fingerprints of a human being. This is the base of the algorithm - given the closing prices of any share oer a time period, the algorithm finds all the possible cycles that exist in the given data by using my own developed fractals. Once the cycles have been found, the strongest cycle identified (which I call the chaos cycle, as all shares and indices follow this cycle), extrapolation becomes a trivial Algebra exercise. This this, the behavior of each individual share is predicted a day, a week, a month, or even a year in advance.

As once-offf exercise, I used the terminal of a local stockbroker and feed in prices for 50 randomly selected shares on an hourly basis. After each input the extrapolation algorithm was run to predict what will happen in the next hour. Success rate was a staggering 95% correct. As rules and regulations on the JSE prohibits this kind of activity (for a member of the public to use the terminal of a stockbroker) I could not repeat this - I had to deal with a lot of angry people when they "caught" me, but my joy with the success I had overshadowed my problems with several orders of magnitude!

As I could not repeat the above exercise, I turned to some other (I thought, more accessible!) data. I changed the input and output format, keep the algorithm the same, and feed in data about aircraft accidents. After accumulating some input, the algorithm was able to predict that kind of accident (i.e. a flat tire), can be expected, what kind of aircraft (i.e. twin engine, prop) will be involved, geographically where this accident will occur, and in what time window (i.e. between 10h00 - 11h00) it will occur, with more than 90% accuracy. Unfortunately I had to stop that too as all these data are considered sensitive and not for public consumption. So the Air Traffic Controller (ATC) that supplied me with the data and gave me feedback and myself were persona non grata for months.

The Future

As many investors use the so-called conventional indicators (moving average, overbought/oversold and a host of others) for decision making in buying and selling, stock markets all over the world react to this kind of behavior. In an effort to push up the success rate of the algorithm, several of these indicators are currently used in conjunction with the extrapolations. Initial success rate increased from one-day-in-a-week 100% correct to two days-in-a-week 100% correct. However it is early days, as the new set of indicators are only installed for 2 months, and we only had one bad month (May) thus far on the JSE.

As proof of the algorithm and of the work I'm doing, the following graphs are of the Dow Jones on Wallstreet, as well as MACMED (some other share on the JSE in the parmaceutical sector). The entire system is PC-based and written in PASCAL by myself. The graphs are screendumps from my program.

The first graph is the Dow-Jones extrapolated to the end of July 1997. The second graph is the last 20 trading days, extrapolated to the next 20 trading days of the Dow Jones. The two graphs that follow are of MACMED extrapolated to the end of July 1997, and a zoom-in on the last 20 trading days of MACMED. These graphs are VERY BUSY graphs, but follow the thin red sinus-curve-like line on the zoomed-in graphs as this is the chaos line. All calculations are done every time new input is received, and it usually changes the extrapolation curves significantly. So these graphs are only valid for one day, in this case for June 30, 1997.

Graph 1 Graph 2

Graph 3 Graph 4

In the graphs of the Dow Jones, the chaos cycles are not very well developed (of low prominence) which indicate instability as it is approaching an upper-trend line (not shown for clarity). The graph of MACMED is included as an example to illustrate well developed chaos cycles.