The Concept

DRC uses a trading approach based on tools and concepts derived from fractal geometry, a rich body of mathematics developed by Benoit Mandelbrot over the last 30 years. 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 trend-following 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 self-similar 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.