In the previous article, we briefly reviewed the basic principles that Trading Chaos relies on. In fact, Williams improved the Elliott wave theory, supplementing it with specific criteria for identifying the moment of completion and beginning of waves.
But to complete the picture, today we will continue to consider Bill's trading techniques, which significantly increase profits from speculation, and let's start, perhaps, with fractals.
In one of the earlier publications, we have already touched upon the topic of identifying and constructing fractals (including with the help of indicators). Therefore, we will not repeat the theory again, we will only note that a fractal is a formation, the central extremum of which is above (below) the corresponding extrema of four neighboring bars.
The whole logic of fractal analysis in Trading Chaos is based on the search for breakouts of extremes, but unlike later trading strategies developed by other traders, the original Williams model consists strictly of three elements:
- Fractal start - the first extremum preceding the signal;
- Signal fractal - is formed in the opposite direction to the starting fractal;
- A fractal stop is the largest downtrend top (or uptrend bottom) of the last two fractals.
Thus, fractal analysis completely eliminates uncertainty in decision-making and at the same time allows you to weed out a lot of false signals (but only if the prevailing trend is reliably known).
Speaking of trends, in the theory of Chaos Williams, this issue is resolved by itself, since fractals become integral part wave analysis, and the wave (or wave structure) is the trend. At the same time, in order to maximize profits and further create a pyramid, it is permissible to switch to a lower timeframe after the start of the wave.
Pyramiding is an increase in a position in the direction of a trend after the floating profit on the first trade allows you to transfer the stop order on the totality of orders to breakeven, while the volume of each new trade is either equal to a constant or divided by a certain coefficient.
For example, suppose that the market has entered the third wave, which is being hunted by all wavers, in this case the algorithm of the trader's actions will be as follows:
Besides, without fractal analysis any attempt to look for wave structures is doomed to failure - this is a fact that has been verified by several generations of traders, although Bill warned about this. In his "five bullets" outlined in the ninth chapter of Trading Chaos, Williams listed the main signs of the end of a trend:
- There was a divergence on the MACD between the third and fifth waves;
- Current price located in the target area, i.e. the fifth wave, according to the approximate marking, should already begin (but not the fact that it will form completely), as a rule, beginners use Fibonacci levels to build zones, but much more often the situation is assessed visually;
- A fractal has formed at the next top during a bullish trend and at the bottom during a bearish one;
- Among the three maximum (minimum) bars, a “squat” appeared (see previous publication);
- MACD histogram bars crossed the signal line in the opposite direction to the last trend.
In conclusion, we note that, despite the universality and good practical results, Williams' theory has something to complain about. For example, Bill claims that the market does not follow traditional physical laws, but at the same time behaves similarly to the tides of the sea, which, in fact, are associated with the gravitational influence of the Moon and the Sun on the Earth - is this not a law?
Therefore, one should not look for a hidden meaning in Trading Chaos, Williams was simply able to describe the behavior of the market crowd for the first time with technical analysis tools, that is, roughly speaking, mathematics, which deserves respect in any case.
Fractals are quite popular among many traders. Interest in fractal analysis appeared after the publication of several works by Bill Williams on this topic. Fractals were invented before him, but were referred to under a different name. Williams, studying the financial markets, came to the conclusion that the movements of the rates of many financial instruments are chaotic. As a result of research, he proved that the graph of changes in the cost of cotton is similar to the coastline and the movement of blood in the human body.
In his research, Williams came to the conclusion that the markets are chaotic, not linear systems, so the use of indicators based on linear functions is useless. In his opinion, stability in the markets is present only a small fraction of the time, and in all other cases chaos reigns in them.
A fractal is a repeating formation that occurs in one form or another on any price charts. Coastline fractals, like stock market fractals, have the same nature. A fractal consists of at least five bars.
Up and down fractals can be in the same group of bars. Sometimes the upper and lower fractals form simultaneously on the same bar. When a fractal is formed, it is endowed with all properties.
When evaluating the upper fractal, it is necessary to pay attention to its maximum. When studying the lower, respectively, the minimum. A fractal start is formed from two successive fractals directed in different directions. The fractal signal appears on the opposite side of the start. The fractal stop is behind the far fractal. If an opposite signal appears, it cancels the previous ones.
This technique allows you to increase the percentage of profitable trades, but the average losing trade will be higher. Since stop losses when using such a strategy will be infrequent, in the end you can count on a good profit. Fractal analysis of the market does not always give 100% profitable trades. For this reason, it should not be used in trading system only him. Other tools are recommended for signal validation or filtering.
When using fractal analysis, it is also important to study data from different timeframes. The system that Bill Williams described in his writings is a trend one. To use it correctly, you first need to determine the dominant trend in the market by referring to the older period.
The system should also take into account the “fractal leverage”. This is the name of the possible amplitude during rollbacks. You can evaluate the "fractal leverage" using the standard Fibonacci lines that are available in MT4. Corrections up to 38% Fibonacci are evidence of a strong trend move. In this case, the fractal leverage is strong. The opposite is true if the rollbacks are 62% fibo or more.
Fractals and wave theory
Fractals can also be used in conjunction with wave theory. Indeed, in its essence, a fractal is nothing more than the beginning or end of an impulse movement or wave. There is some difficulty here, because different periods graphs, different impulses are formed. It is not difficult for traders who have gained experience in using wave theory to accurately identify a specific wave on a specific timeframe.
If several groups of fractals are formed at the same level, then in case of breaking through given level a long and strong trend is to be expected. Fractal analysis of the market gives very good results in the presence of trends. When the price stays in the channels for a long time, the fractal breakout strategy brings losses. The difficulty lies in the fact that it is quite difficult to recognize the emerging flat.
How to apply the fractal strategy in a flat?
You should only trade on a breakout in the direction of a pronounced trend. You should not worry about several losses in a row. The future profit will surely cover all the losses that the strategy received during the fluctuation in the corridor. A good effect is achieved when working at small time intervals. If a trader enters a fractal breakout based on the daily chart, then a stop loss can be set based on H4. Usually, the more fractals are located at the same level and the longer the flat lasts, the stronger and more directed the future movement will be.
To reliably determine whether a fractal breakout is true or false, you can use breakout candle analysis. If the breakout candle is “strong”, that is, it has a large body and its closing level is located far from the clusters of fractals, then there is a high probability that the movement will continue in the chosen direction. Using this conclusion, you can successfully trade on small charts in order to increase profits. For example, if yesterday there was a breakdown on D1, then today we can consider breakouts on the four-hour chart.
If, after the breakdown of the cluster of fractals, a reversal candlestick pattern has formed, then in the future, the market will most likely be flat, new fractals will appear. In this regard, a lot of attention should be paid to the analysis of the breakout candle. To increase efficiency, it is recommended to familiarize yourself with at least the basics of Price Action (candlestick analysis).
Bill Williams recommended not only looking at the reversal candle, but also analyzing the volume. If the candle has a large body, but the volume is small, then the signal is weak. The signals that come from clusters of fractals are strong when they form on longer-term charts (as they do with candlestick analysis). Williams himself recommended watching D1. At the same time, it is necessary to analyze other timeframes. As mentioned in this article, fractal analysis is best combined with something else to increase the profitability of the strategy, because no tool can boast 100% accurate signals.
The video contains useful information on the topic under consideration.
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fractal analysis financial markets is a relatively new way of predicting behavior exchange rates On the market . Instead of mechanical systems and indicators, this species analysis uses a completely new approach based on fractals. Thanks to this, it became not only an alternative to technical analysis, but also allowed to get rid of its shortcomings. Before talking about fractal analysis itself, you need to understand what it is based on:
In fact, he did a great job before declaring that the markets are in fact in constant motion, which is similar to the movement of chaotic systems and is not at all linear, as previously thought. For the same reason, Bill Williams affirmatively stated that when analyzing a chaotic market, it is foolish to draw conclusions from ordinary, linear indicators. After all, chaotic movement in the market is constant, while stability, on the contrary, is changeable. If we give examples, we can say that the prices of grain, cotton or stocks, as well as the movement of water in a pipe or blood, have an identical structure.
Subsequently, the method of fractal market analysis became widespread among so many traders, thanks to Williams' books such as "Trading Chaos", "Trading Chaos Second Edition" and "New Dimensions in Stock Trading".
Fractal analysis of the forex market
Despite the positive results of such an analysis, it should be remembered that this analysis does not work out 100%. There are also erroneous signals here, so you should not use it in its pure form - this is, first of all, another method of analysis that can become the main or additional for a trader. Also, a trader needs to take into account that applying this type of analysis, he will need to master the technique of connecting timeframes for his strategy. The synthesis technique was also introduced by Bill Williams, who only applied it to trending positions based on higher timeframe trends.
Besides important point in this type of analysis is the "fractal lever" - the depth of the rollback of the previous movement. To measure this movement (fractal leverage) it is necessary to stretch the Fibonacci grid to the last movement. If the rollback on the grid is less than 38%, this is a strong fractal leverage and a confident movement. If the rollback is larger and is 62% on the Fibonacci grid, then the fractal leverage is small, and the movement is very weak.
Since fractal analysis as it is is not 100% effective, most traders use it in conjunction with Elliot Waves. After all, a fractal is, in fact, a turning point where the beginning or end of the next wave is formed. Bill Williams himself in his book "Trading Chaos" recommends using these waves. But since it is quite difficult to calculate the waves correctly, it will also be very difficult for a beginner to make a correct forecast using fractals without a certain experience in determining waves. Therefore, for beginners, something simpler is needed, for example, trend lines.
How to start using fractal analysis?
A novice trader needs to first learn how to make small, short-term forecasts, as they require less external data. To do this, it is better to use a familiar currency pair, commodity or other asset with which the trader has already worked. A trader needs to make a forecast and see if it was justified or not. If the forecast is incorrect, then the trader needs to understand the reason why this happened. Find out where his mistake lies, perhaps he did not take into account something in his analysis.
If a trader made the correct forecast several times and correctly determined the price change, even before the trend he determined became visible to other participants, this is an excellent result.
Moreover, the novice trader has an advantage. Since brokers offer their clients demo accounts with real market quotes, a novice trader can practice without risking anything.
Also, using fractal analysis, a trader should pay increased attention to the factors that formed the price in a certain period of time. This is done so that the trader can be more confident in his forecast. After all, if social, political and other factors coincide, there is a high probability that the price will behave in exactly the same way as before in a similar situation. Therefore, fractal analysis, in addition to knowledge about the formation of the fractal itself, requires the trader to also know. Accordingly, to learn at least the basics of fundamental analysis would be very helpful.
Fractal analysis of the market is more complicated than it seems at first glance and requires the trader to have knowledge in various areas of financial market analysis: fundamental analysis (which is already difficult in itself), timeframe synthesis, economic and other indicators that work together to filter false signals etc. But at the same time, fractal analysis enables the trader to discover the relationship between past and future prices. Which, in turn, allows you to more accurately determine the future rise or fall in prices earlier than other traders. Since they are basically waiting for the market to confirm its intentions.
Due to its complexity, such analysis is used by already experienced and strong traders. But on the other hand, it is worth understanding this method of analysis, because it is as effective as it is complex.
On October 14, 2010, Benoit Mandelbrot passed away - a man who largely changed our understanding of the objects around us and enriched our language with the word "fractal", meaning "a structure consisting of parts, in a certain sense similar to the whole" 1 . Now it is thanks to Mandelbrot that we know that fractals are all around us. Some of them are constantly changing, like moving clouds or flames, while others, like coastlines, trees, or our vascular systems, retain an evolutionary structure. At the same time, the real range of scales where fractals are observed extends from the distances between molecules in polymers to the distance between clusters of galaxies in the Universe. The richest collection of such objects is collected in Mandelbrot's famous book "The Fractal Geometry of Nature" 2 .
The most important class of natural fractals are chaotic time series, or time-ordered observations of the characteristics of various natural, social, and technological processes. Among them are both traditional (geophysical, economic, medical) and those that have become known relatively recently (daily fluctuations in the level of crime or traffic accidents in the region, changes in the number of impressions of certain sites on the Internet, etc.). These series are usually generated by complex non-linear systems of very different nature. However, for all, the pattern of behavior is repeated at different scales. Their most popular representatives are financial time series (primarily stock prices and exchange rates).
The self-similar structure of such series has been known for a very long time. In one of his articles, Mandelbrot wrote that his interest in quotes on the stock market began with the statement of one of the stock market traders: “... The price movements of most financial instruments are outwardly similar, on different time scales and prices. By appearance graph, the observer cannot tell whether the data refer to weekly, daily, or hourly changes. Mandelbrot, who occupies a very special place in financial science, had the reputation of "subverting the foundations", causing a clearly ambiguous attitude among economists. Since the emergence of modern financial theory based on the concept of general equilibrium, he was one of its main critics and until the end of his life he tried to find an acceptable alternative to it. However, it was Mandelbrot who developed a system of concepts, which, with appropriate modification, as it turned out, allows not only to build an effective forecast, but also to offer, apparently, the only one on this moment empirical justification classical theories of finance.
Fractal market concept
The main characteristic of fractal structures is the fractal dimension D introduced by Felix Hausdorff in 1919. For time series, the Hurst index is more commonly used. h, which is related to the fractal dimension by the relation D = 2 – H and is an indicator of the persistence (ability to maintain a certain trend) of the time series. Usually, there are three fundamentally different regimes that can exist in the market: H= 0.5 price behavior is described by a random walk model; at H> 0.5 prices are in a state of trend (directional movement up or down); at H< 0,5 цены находятся в состоянии флэта, или частых колебаний в достаточно узком диапазоне цен.
However, for a reliable calculation H(as well as D) requires too much data, which excludes the possibility of using these characteristics as indicators that determine the local dynamics of the time series.
As you know, the basic model of financial time series is a random walk model, first obtained by Louis Bachelier to describe observations of stock prices on the Parisian stock exchange. As a result of rethinking this model, which is sometimes observed in the behavior of prices, the concept arose effective market ( effectivemarketHypothesis, EMH), where the price fully reflects all available information. For such a market to exist, it suffices to assume that it has a large number of fully informed rational agents who instantly react to incoming information and adjust prices, bringing them to a state of equilibrium. All major results classical theory finance ( portfolio theory, the CAPM model, the Black-Scholes model, etc.) were obtained within the framework of just such an approach. At present, the concept of an efficient market continues to play a dominant role in both financial theory and financial business 3 .
By the beginning of the 1960s, empirical studies showed that strong price changes in the market occur much more often than predicted by the main model of the efficient market (the random walk model). Mandelbrot was one of the first to subject the concept of an efficient market to comprehensive criticism. Indeed, if we correctly calculate the value of the indicator H for any stock, it is likely to be different from H= 0.5, which corresponds to the random walk model. Mandelbrot found all possible generalizations of this model that can be relevant to the real behavior of prices. As it turned out, these are, on the one hand, the processes he called Levi's flight(Levi flight), and on the other hand, the processes that he called generalized Brownian motion(Fractional Brownian Motion). The behavior of a time series for which (quite often observed in the real market) can be denoted using any of these processes.
To describe the behavior of prices is usually used fractal market concept (FractalmarketHypothesis, FMH), which is usually considered as an alternative to EMH. The concept assumes that there is a wide range of agents on the market with different investment horizons and, therefore, different preferences. These horizons change from a few minutes to intraday traders up to several years for large banks and investment funds. A stable position in such a market is a regime in which "the average return does not depend on the scale, except for multiplying by the appropriate scale factor" 4 . In fact, we are talking about a whole class of modes, each of which is determined by its own value of the indicator H. At the same time, the value H= 0.5 turns out to be one of many possible and, therefore, equal to any other value (). These and other related considerations gave rise to serious doubts 5 about the existence of a real equilibrium in the stock market.
Price Efficiency
The study of the fractal properties of the prices of Russian (in the MICEX index) and American (included in the Dow Jones Internet Index) companies, together with the corresponding indices over the past ten years, emphasizes the special position of the value H= 0.5. For this, however, it is necessary to use a new fractal index (the fractality index) introduced by the authors of this article in a separate paper 6 . It is related to the index H ratio, but its determination with acceptable accuracy requires two orders of magnitude less data than for the indicator h, therefore, it can be considered as a local fractal characteristic. It turns out that with the help of the fractality index, one can give a rationale for the modern theory of finance, as well as predict strong fluctuations in the stock market.
In the first approximation, the general picture observed in all series is the following. The fractality index (and the fractal dimension of the financial series) makes quasi-periodic fluctuations around the position = 0.5 (this mode corresponds to a random walk). At the same time, the time series continuously changes its mode, moving from the trend (< 0,5) через состояние случайного блуждания во флэт (>0.5) and vice versa. From time to time, for each series, states appear and disappear with relatively stable values other than 0.5. In this case, the mode c = 0.5 occupies a clearly privileged position. For each time series, it is the longest for all intervals containing eight points or more.
It should be noted that the interpretation of price fluctuations based on the description of the behavior of market agents can vary greatly on different scales. So, for example, during the day, where more than half of the transactions are made by trading robots (in the US markets), the behavior of agents, apparently, is very close to rational. On a scale from several days to several months, social psychology plays an important role, which always contains an irrational element. Meanwhile, the invariable nature of oscillations with the most frequently occurring random walk mode is reproduced on all scales, starting from the smallest ones. This suggests that the nature of these fluctuations is based, apparently, on the general mechanism of delay, which accompanies the very way of decision-making by agents in the stock market. At the same time, the main state of prices is still just a random walk, which remains the main mode of attraction on all scales. In other words, despite often occurring long-term local deviations, prices tend to return to the efficient behavior that the random walk model describes.
Prediction Method
The presence of the described fractal properties of the price series, observed in a wide range of scales, allows us to take a fresh look at the possibility of forecasting the stock market. In general, the task of the forecast is to determine the qualitative or quantitative parameters of the future behavior of the time series based on the entire array of historical data. In this case, of particular interest is the determination of the early precursors of the critical behavior of the series.
Let us consider one of the new approaches to solving this problem, based on the fractal properties of prices. It has been rigorously proven 6 that if we introduce the average amplitude of fluctuations as the average difference between the maximum and minimum price values averaged over segments of size t, then the average oscillation amplitude will be related to the observation scale by a power law:
,An index (which, like an index, requires two orders of magnitude less data to define than an index H) coincides with H in those areas where H can be calculated with acceptable accuracy. The dependence of the average amplitude of oscillations on the scale of observations for different values of H is shown in graph 1.
It turns out that knowledge of the law of the dependence of the amplitude of oscillations on time in different modes allows us to substantiate a very curious effect, which can become the key to predicting the emergence of a strong movement in the market. Indeed, suppose that the market is currently in transition from a random walk to a strong trend. This means that after a certain time, the amplitude of fluctuations on large scales (for example, several months) will become significantly larger than the current amplitude (arrow 2 on graph 1 shows the transition from a random walk to a trend on large time scales). This simultaneously means (due to the property of the power function) that on small time scales (hours, days of the week) a decrease in the oscillation amplitude should be observed compared to previous period(arrow 1 in graph 1 shows such a transition on a small scale). Thus, observing the behavior of the amplitude on a small scale, in some cases it is possible to predict a significant increase in the amplitude of price fluctuations in the future.
Market conditions with increased amplitude of fluctuations are usually observed in corners (sharp rises in prices in the market) or crashes (sharp collapses). The effect of an increase in large-scale fluctuations with a decrease in small-scale ones was theoretically substantiated by the authors of 6 . Testing across the above financial database has shown that this effect appears with a probability of 70-80%. In cases where it is possible to minimize the impact external factors, this percentage is even higher.
Prospects-2011
The most interesting, of course, is the forecast using this method not of local movements in individual stocks, but of global events such as the world financial crisis 2008. When analyzing this kind, in addition to the behavior of individual country indices, one should also take into account the flow of capital in the global financial market, which has been heavily liberalized over the past 20 years. Therefore, we have selected the nine largest stock markets 7 , both developed markets and emerging markets, built instability indicators for them and calculated the average for all markets.
The calculation results are shown in Chart 2. Here, country indicators for different markets are shown as lines of different colors. The indicator, averaged over all markets, is shown as a wide red line. An increased value of the indicator means the market is moving to a flat mode. Decreased and upward reversal - a possible increase in the future amplitude of fluctuations and the transition to a trend mode. The figure clearly distinguishes two types of behavior. From April 2001 to April 2004, individual country indicators behaved quite independently from each other, which led to the fact that the average indicator fluctuated around zero. In the language of microeconomics, this apparently meant that participants in individual markets made decisions without significant consideration of what was happening in neighboring markets. After April 2004, synchronization of individual indicators begins: they all decrease and increase at about the same time, which leads to rather strong fluctuations in the average indicator. From May 2009 to May 2010, there is also a rather weak synchronization, and since May 2010, all country indicators simultaneously begin to decline synchronously. What happened at the same time in the stock markets?
In Chart 3, the average indicator plotted above (red dotted line) is presented together with the average aggregated index of the original series (solid blue line), which includes the stock indices of these markets. This approach excludes the factor of influence of stock markets various countries each other, which is associated with the flow of capital in the global financial market. It can be seen from the graph that the indicator showed a sharp decrease in small-scale fluctuations, starting from 2001, two times. The first time was in December 2004, after which, six months later, a rapid growth of all indices followed, which lasted for about two years. The second time was in April 2008, after which, also about six months later, due to the crisis, there was a sharp drop in all indices.
In addition, the chart shows that at the moment a new signal is actively forming, which is a harbinger of strong fluctuations in the stock market in the medium term (from six months to one year). And although the indicator does not say anything about the direction in which the movement will take place, the information received may be quite enough, for example, to build a successful asset management strategy in the stock market. If we define the forecast more precisely, then based on it, it turns out that the recovery will be either fast with a possible entry to the historical highs of the stock markets as early as next year ( minimum value the RTS index, which in this case will be reached, is 2150 points), or the stock markets will cover something similar to the second wave of the crisis (in this scenario, the minimum target for the RTS index will be 1050 points). It should be noted that the forecast is in clear contradiction with the generally accepted expectation of a “slow exit from the recession”.
From the point of view of the theory based on the fractal properties of prices, a decrease in the amplitude of fluctuations on a small scale should be accompanied by two most significant effects: a general decrease in trading activity in the markets and a special adjustment of participants to each other's actions. The second, alas, is currently not possible to verify by methods independent of fractal analysis. But trading activity has really decreased. Thus, the average weekly volume of trading in Russian shares, according to the MICEX, fell to 230 billion rubles. for January-November 2010 from 253 billion rubles. in the same period in 2009. In the US, the decline is even more significant, from $5.5 billion to $4.7 billion over the same periods.
At the end of this article, we will say a few words about the effect of an increase in large-scale fluctuations with a decrease in small-scale ones. In essence, this effect means that trends in complex systems (natural, social, technological), which are formed very slowly and imperceptibly, but have increased steadiness, often become global over time, determining the main vector of development of such systems. Note that the well known calm effect(suppression of the high-frequency noise component), which usually precedes natural disasters (for example, earthquakes), is a particular manifestation of this effect. Thus, many global trends in their evolution actually resemble mustard seed from gospel parable, “which, although smaller than all seeds, but when it grows, is larger than all cereals and becomes a tree, so that the birds of the air fly and take refuge in its branches” (Matt. 13: 32).
1 The history of the emergence of fractal geometry was described in sufficient detail by one of the authors in the article “From MA to FRAMA through EMA and fractal”, published in D' No. 15 of August 23, 2010 (algoritmus.ru/?p=2638).
2 Mandelbrot B. The Fractal Geometry of Nature. San Francisco: W. H. Freeman, 1982.
3 See Shiryaev A.N. Fundamentals of stochastic financial mathematics. T. 1M.: "Phasis", 1998.
4 See Mandelbrot B. Journal of Business. № 36, 1963; Mandelbrot B. & Van Ness SIAMRev. № 10, 1968.
5 See V. M. Polterovich “ Economicthe sciencecontemporaryRussia» . №1, 1998.
6 See Dubovikov M. M., Starchenko N. S., Dubovikov M. S. Physica A 339 591, 2004.
7 USA, Germany, France, Japan, Russia, Brazil, China, Korea.
The behavior of the average stock index (blue line, right scale, starting value in April 2001 is taken as one) and the average instability indicator (red dotted line, left scale)
The author devoted this book to the presentation of the fractal market hypothesis. The book states that this hypothesis is an alternative to the efficient market hypothesis. Fractals are everywhere in our world. At the same time, they play a significant role in the structure of financial markets, which are globally determined, but locally random. So says the author of the book. This edition will also consider methods for analyzing the markets for stocks, currencies and bonds in a fractal way. The author will tell about the methods of distinguishing an independent process.
In addition, from the book "Fractal Analysis of Financial Markets" you will learn about the methods of a stochastic non-linear process, as well as a non-linear and deterministic process. This book explores the impact of such differences on user investment strategies and modeling capabilities. Such abilities and strategies are closely related to the user's investment horizon and type of assets. For financiers, risk managers, market technical analysts, investment strategists and, in addition, for currency speculators and individual investors who enter financial markets around the world on their own. Among such markets are Forex and the markets of our country.
The work of markets according to the book "Fractal Analysis of Financial Markets"
When the time comes to look at how markets work more holistically, necessary recognition greater heterogeneity that underlies such markets. All investors do not participate here for the same reason, and they do not use their strategies on the same investment horizons. Strongly linked to the heterogeneity of investors and the stability of the markets. As a rule, a mature market is quite heterogeneous. Instability would rule everywhere if all participants invested their capital for the same purpose, had the same investment horizon and reacted the same way to information.
Mature markets, according to the book "Fractal Analysis of Financial Markets" for quite a long time have amazing stability. Anonymous trading with pension fund can be carried out by a day trader. The fund trades for long-term financial security and does so infrequently, while the day trader trades frequently and aims for short-term profits.
Goals of the book "Fractal Analysis of Financial Markets"
The first purpose of this edition is the need to present the fractal hypothesis of the market. It talks about how and why markets function. The second goal can be called the desire to provide the necessary tools for analyzing markets within the boundaries of the fractal structure. Many existing tools can be used for this purpose. The author presents the reader with new tools that analysts can add to their own set. In addition, the author reviews existing tools in this edition.
The book "Fractal Analysis of Financial Markets" is not a story, despite the fact that the main emphasis is on conceptual aspects. Analytical methods are scrupulously studied within the boundaries of the conceptual structure. Everyone, according to the author, who has a solid knowledge of business statistics, will find a lot in this book. useful information. The main emphasis here is not on dynamics, but on empirical statistics. In other words, on the analysis of the time series to find what each of us is dealing with. After reading this book, you will no longer be able to think in the same way. Your vision for this area will change forever.
