As market practitioners, we wake up every day with a hunger to find order in the markets. And to Benoit Mandelbrot’s (the Father of Fractals) point above, order does not come by itself. Global markets are complex and to some seemingly unpredictable.
In the Early Look today, we wrote:
“Across asset classes, global markets have revealed themselves as being as interconnected across a multiple of interacting fundamental factors as they have ever been. Mathematicians call this chaos theory.”
It is our fundamental belief that while markets are complex, they are neither random, nor uniformly unpredictable.
Our idea of applying chaos theory to markets was probably first and most widely used by Bruce Babcock, a Yale graduate, former State attorney in California, and prolific trader of commodities. He wrote as it relates to chaos theory and markets:
“According to respected authorities, the markets are non-linear, dynamic systems. Chaos Theory is the mathematics of analyzing such non-linear, dynamic systems. Chaos analysis has determined that market prices are highly random with a trend component. The amount of the trend component varies from market to market and from time frame to time frame. A concept involved in chaotic systems is fractals. Fractals are objects which are "self-similar" in the sense that the individual parts are related to the whole.”
As outlined in Bruce Babcock’s quote above, chaos theory is used to describe the behavior of a system that is constantly evolving, a dynamic system. The stock market is, for its ever evolving nature, the perfect system for utilizing chaos theory as a framework to analyze and forecast.
When we make a market call, it is based on a proprietary 27-factor model, in which the primacy of the factors evolve, much like a chaotic system, with time. But the basic organization, the 27-factors, remains largely constant, even as certain factors become more important over different market periods. While we don’t disclose our proprietary methods, or all 27 factors, clearly we are focused on both the US dollar and volatility currently as primary deterministic factors.
In some sense, the term chaos is at contrast with the theory. Chaos suggests disorganization, while chaos theory itself implies that there is a pattern, or initial deterministic conditions, behind the seeming randomness. That is, there is actually a method and reason to the madness.
In 1890, while studying the three-body problem, Henri Poincare found “that there can be orbits which are non-periodic, and yet not forever increasing nor approaching a fixed point.” As result of this discovery, Poincare is considered the father of chaos theory. If Poincare is considered the father, then Edward Lorenz would have to be considered the person most responsible for inserting the theory back into modern scientific thought.
Lorenz was studying weather prediction in 1961. He was using a basic digital computer to run his simulations. In an attempt to see a prior sequence of data, he started a simulation in the middle by entering data from a print out. In contrast to the prior simulation, this simulation produced a completely different set of data outputs. The key difference was that the revised simulation used only printouts, which had 3-digit numbers versus the original simulation which used 6-digit numbers. The key conclusion was that small changes in initial conditions can lead to large changes in the long-term outcome.
As a start-up business, we have also applied chaos theory to internal organization. When Keith, Michael, and Brian started Research Edge over a year ago now, the Company was much less complex, in fact it was a concept on a whiteboard. In less than a year’s time, we have evolved to three offices and over thirty full and part time employees, and a great client base of savvy investors who continually keep us challenged and add to our research network.
A key way in which we try to differentiate ourselves is to be first to market with information that is meaningful on the margin. As we say repeatedly at Research Edge, when the things change that matter, they change on the margin, so this is where we want to focus. Marginal changes will predict much larger changes in the future, which is consistent with chaos theory.
Only time will tell whether we will be proven right on the ability to make stock market calls based on a foundation of chaos theory or whether our internal organization based on a fractals is as effective as we expect it to be, but as the Father of Fractals also said:
“When the weather changes, nobody believes the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed.”
Daryl G. Jones