Reasonable resemblance. Finances, fractals and technical analysis.

Visual acuity exercise. Here are successive extensions of a graph of a quoted value any. In this case, the IBEX35.

And here are successive extensions of the structure of the Romanescu, a type of broccoli.

Yes, I know, they look just as much like an egg to a chestnut, one is a graph and another is an enlarged picture. However, if you look at the content, both share a common feature: at any scale we take the image, the composition of its parts is very similar. This property is called “Autosimilariedad” or “self-similarity”, and is characteristic of fractal structures.

One of the greatest advantages of technical analysis is that it can be applied to different timescales. It does not do the same if we take a weekly bar graph, daily or per minute, as the technical principles and the identifiable figures maintain their validity. There are times when even a figure is made up of other smaller similar figures, as is the case with the HCH (shoulders-head-shoulders), whose parts are sometimes composed of other smaller HCH.

Also, Dow’s theory and Elliot’s waves are based on this property: both the impulsive and corrective waves are composed of other smaller waves, also of the same type. It is the scheme of the waves of the sea, in short, in which the tide can be assimilated to the main trend, composed of large waves (secondary tendencies) that move in favor and against the tide, and waves or waves smaller (tertiary and successive) , with the same behavior.

This uniqueness of the financial markets, discovered and exploited for more than a century by technical analysts, has its “rational” explanation in which quotation charts are representations of human behavior, which, as part of the Nature, sometimes shares with this certain characteristics. However, the difficulty that people have in accurately capturing complex forms, made tried simplify graphic figures, reducing to Euclidean forms (triangles, rectangles…) to be able to operate with them with some reliability

With the emergence and great development of new technologies, physics and mathematics have experienced a breakthrough, and that has opened up new perspectives for the study of the series of quotes, as I pointed out earlier. On the subject of this post, one of the branches with the greatest development is the chaos theory, and within it, the fractals that we have previously named. Although the interest on these structures is prior to the studies of Benoît Mandelbrot, it was this one who coined the term fractal, of Latin fractus, which means fragmented or fractured. In general, a fractal is a structure composed of small parts, which are similar to the original figure, and that are repeated at different scales, from the micro level to the macro, either in spatial measurements (length or surface) or temporal ( Frequency). That is to say, in Kadanoff’s words, “a fractal contains copies of itself within itself.”

Studies on financial fractals received a great boost in the Nineties with Peters ‘ studies. In particular, it developed the advances of Mandelbrot and related them with the existing theories, managing to converge them in what it called “hypothesis of the fractal market”, or FMH by its acronym in English (Fractal market hypothesis). Assumptions:

The market is stable when there are a large number of investors covering different investment horizons, which ensures sufficient liquidity in the market. From here we extract the most important consequence: the variety of horizons guarantees stability, and this, in turn, the liquidity of the markets.

The set of information relevant to each investment horizon is different. Therefore, the variations in the price of the shares will reflect the relevant information for each investment horizon. Short horizons rely more on information on “market sentiment,” i.e., technical factors of supply-demand fluctuations, while long horizons establish their decisions based on economic or fundamental values.

When all investment horizons are reduced to a single level, the market becomes unstable, as there are no long-term investors that stabilize the market by offering liquidity to the short-term.

As we see, Peters ‘ assumptions combine financial reality and theory from the perspective of fractals, so that such a theory, without completely opposing the EMH (efficient market hypothesis), does try to refine it and adapt it to new developments in various Fields such as physics, statistics and mathematics, to achieve a better understanding of the movements in the financial markets.

The open horizon in this field is immense, since it provides a new scientific basis for the development of studies that confirm or refute, the new FMH, applying the aforementioned assumptions and techniques econometric to different markets and products Financial. If we also look closely at the underlying assumptions and techniques included in the technical analysis, and compared them with the financial fractals, we see that they depart from assumptions and come to similar conclusions, despite the fact that they have left disciplines Different, the fractals, the academic world, and the technical analysis, the observation and the “popular wisdom”.