
DRC uses a trading approach based on tools and concepts derived
from fractal geometry, a rich body of mathematics developed by Benoit
Mandelbrot. Fractal geometry has been used
to describe a wide variety of natural patterns and shapes from coastlines
to galaxies and including market prices.
The application of fractal mathematics to market analysis has revealed
both profound insights and useful tools. The primary insight, which
is supported by research conducted by Mandelbrot, Dreiss and others,
is that market prices are not random, but instead exhibit persistence,
the statistical tendency to continue in the same direction over
a wide range of time frames. This conclusion contradicts the standard
academic assumption (known as the efficient market hypothesis) that
markets are random, and provides rigorous support for the notion
that it is possible for dedicated and disciplined traders to profit
consistently from trading.
Since fractal analysis has shown that most markets exhibit persistence,
it is logical to pursue trendfollowing strategies as a means to
profit from this tendency. It seems natural to look again to fractal
geometry for tools to be used in designing these trading systems.
The defining characteristic of fractal patterns is that they are
selfsimilar across scale. For instance, a tree may have large branches
which branch into smaller branches and so forth, where each level
of branching displays the same general pattern as the previous level.
Similarly, it would be difficult to distinguish between hourly,
daily and weekly price charts if they were not labeled as such.
The Fractal Wave Algorithm was developed by Bill Dreiss and Art
von Waldburg to implement this logic of nested patterns in order
to provide a method for identifying trends and turning points which
is grounded in sound mathematical logic. The resulting Fractal Wave
System is free of numerical parameters and is therefore quite different
from numerically based systems, since it cannot be "optimized".
This approach thereby avoids the major danger to effective system
design, and provides a universal approach which is applicable to
virtually any market.
The assumption that the markets are fractal also has implications
for risk measurement and management. Standard statistical measurement
of risk relies on the calculation of the standard deviation of returns.
However, it has been shown that for fractal distributions, the standard
deviation is undefined, which means that it cannot be mathematically
calculated. This is due to the large number of unusually large moves
which occur across all time frames in real markets, a phenomenon
familiar to any market participant. The above reasoning reveals
an interesting paradox: If the markets are random, then risk can
be mathematically measured but there is no possibility of profiting
from trading, except by chance. On the other hand, if the markets
are fractal, it is mathematically possible to profit from trading
over a sustained period of time, but it is not possible to reliably
predict the risk involved in doing so.
