Financial Markets as Complex Adaptive Systems Part 1

Financial Markets as Complex Adaptive Systems
by Alan Hull www.alanhull.com

The word linear essentially means straight line or straight line progression and in
order to simplify everything we see and observe, mankind has a profound tendency
to view the world from a linear perspective. The main reason we want everything
to be linear, or progress in a straight line, is so we can both easily understand it and
predict what it is likely to do in the future.
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In more recent times, thanks largely to the computational power of modern
computers, we have also pretty much mastered the ability to get our heads around
curvy things as well. Of course this is largely on the proviso that they are either
constantly curvy or consistently changing, such as the case of an exponential curve
like the one pictured below…

We can even project lines and curvy things into the future and with a reasonably
high degree of accuracy, determine if, when and where they’re likely to intersect.
Although there is one proviso…that there aren’t too many variables to consider.
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But there’s another problem that even the scientific community don’t like to talk
about and that’s the possibility of things changing but not doing it in a consistent
way. In others words the rate of change is not consistent….its bad enough that
something can be ‘Dynamic’ rather than ‘Static’ (thus rendering statistical analysis
and the bell curve useless) but when the rate of change itself isn’t linear either then
everyone starts to get really scared. This is known as non-periodic behavior…


But let’s digress for a second and look at the idea of a system being dynamic as
opposed to static. Take the average life expectancy of the Australian population for
example. If you wanted to know the average number of years we’re all expected to
live then you would most likely use data available from the past 10 years or so…
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But what about using recorded deaths from the last 100 years instead of just the
past 10…wouldn’t this give us a more accurate answer? Put simply, no…because
over this time span factors that impact our lifespan have changed significantly
making this sample period non-static and invalidating any averages taken…
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Thus any sample of data that we subject to statistical analysis must be from a static
system or a representative snapshot that allows for the dynamic nature of a system.
Hence using the average lifespan of Australians over the past 10 years to reflect
today’s average is in fact a snapshot approach and a compromise of sorts.
This is a pity because everyone held out so much hope that statistical analysis
would solve what appeared to be problems of randomization. So the Stockmarket
like other supposedly irregular phenomenon gets labeled as being unpredictable
and that’s that. Just like weather patterns and the human heart, the Stockmarket has
too many variables and is a dynamic system that’s not always linear by nature…
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Thus if we can’t get our heads around it then its random or so close to random it
doesn’t matter. Another neat way of dismissing things we can’t get our heads
around is by calling it noise, interference or turbulence. Thus an engineer working
in fluid dynamics works to eliminate turbulent flow rather than try to understand it.
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So you can imagine everyone’s excitement about Chaos theory when it first
appeared back in the early ‘60s because it went a long way towards understanding
what had previously appeared to be random phenomena. (Well actually it was
largely dismissed by the broader scientific community as a stream of pure
mathematics without any real world application and just a good excuse not to
work on more practical stuff like how to eliminate turbulence)
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A brief history lesson (Reprinted with the kind permission of Greg Rae www.imho.com)

The first true experimenter in chaos was a meteorologist, named Edward Lorenz.
In 1960, he was working on the problem of weather prediction. He had a computer
set up, with a set of twelve equations to model the weather. It didn't predict the
weather itself. However this computer program did theoretically predict what the
weather might be, a weather simulator of sorts…
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One day in 1961, he wanted to see a particular sequence again. To save time, he
started in the middle of the sequence, instead of the beginning. He entered the
number off his printout and left to let it run.
When he came back an hour later, the sequence had evolved differently. Instead of
the same pattern as before, it diverged from the pattern, ending up wildly different
from the original. Eventually he figured out what happened. The computer stored
the numbers to six decimal places in its memory. To save paper, he only had it
print out three decimal places. In the original sequence, the number was .506127,
and he had only typed the first three digits, .506.
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By all conventional ideas of the time, it should have worked. He should have
gotten a sequence very close to the original sequence. A scientist considers himself
lucky if he can get measurements with accuracy to three decimal places. Surely the
fourth and fifth, impossible to measure using reasonable methods, can't have a
huge effect on the outcome of the experiment… Lorenz proved this idea wrong.
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This effect came to be known as the butterfly effect. The amount of difference in
the starting points of two variables is so small that it is comparable to the minute
forces created when a butterfly flaps its wings…

The flapping of a single butterfly's wing today produces a tiny change in the
state of the atmosphere. But over a period of time, the atmosphere actually
does diverge from what it previously would have done. So, in a month's time,
a tornado that would have devastated the Indonesian coast doesn't happen.
Or maybe one that wasn't going to happen, does.

This phenomenon, inherent to chaos theory, is also known as sensitive dependence
on initial conditions. Just a small change in the initial conditions can drastically
change the long-term behavior of a system. Such a small amount of difference in a
measurement might be considered experimental noise, background noise, or an
inaccuracy of the equipment.
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Such things are impossible to avoid in even the most isolated lab. With a starting
number of 2, the final result can be entirely different from the same system with a
starting value of 2.000001. It’s simply impossible to achieve this level of accuracy.
For instance just try and measure something to the nearest millionth of an inch!
From this idea, Lorenz stated that it is impossible to predict the weather with any
accuracy…particularly a long way into the future. However, this discovery led
Lorenz on to other aspects of what has become known today as chaos theory.
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Whilst there is no commonly acknowledged fixed definition of what constitutes a
chaotic system, it is generally accepted that the following conditions must be met;

1. The system must be highly dependent on initial conditions
2. The system must employ at least 2 or more interacting variables
3. The initial conditions must be at least partially dependent on output

A good example of a chaotic system is the operation of a roulette wheel which is
probably best understood by analyzing the process step by step…

• An operator picks up a ball from a roulette wheel which he then spins
(the starting position of the wheel is dependent on where the ball landed after
the previous operation…initial condition is dependent on the previous outcome)
• He or she then sets the ball rotating in the opposite direction
(the wheel is the first variable whilst the ball represents the second variable)
• The ball eventually loses enough energy to drop into the spinning wheel
(The outcome is extremely sensitive to the interaction of the 2 variables)

Roulette is an excellent example of a 2 variable chaotic system which would in
fact be predictable to a degree if a machine was used as the operator. The human
operator introduces the random factor but because the system is chaotic it can’t be
manipulated to any practical degree…
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One of the other principle discoveries that Lorenz went on to make was that
systems or models of systems behaving in a chaotic state produced repeating
patterns that could be observed if the outputs were mapped in 2 dimensions. Note
that these repeating patterns were similar in form but never precisely identical…
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