Fractal market analysis - what is it?
An article about fractal analysis. Lots of theory. My comments are marked in green.
Fractal market analysis is a relatively new direction in the analysis of the currency and stock markets. The founder of fractal market analysis is Benoit Mandelbrot, who described the theory in his book, co-authored with Richard L. Hudson, “(Un)obedient Markets: The Fractal Revolution in Finance.” The next researcher who contributed to the development of fractal market theory is Edgar Peters.
Fractal analysis of markets (Forex) indicates the dependence of future prices on their past changes. Thus, the pricing process in markets is globally determined, dependent on “initial conditions”, that is, past values. Locally, the pricing process is random, that is, in each specific case the price has two development options. Fractal market analysis comes directly from fractal theory and borrows the properties of fractals to produce forecasts.
The main properties of fractals on the market:
Market charts have a fractal dimension. The fractal dimension of a market chart is always 1
Market charts always form a certain structure that has unique properties.
Market fractals have a “memory” of their “initial conditions”.
The first practitioner to apply fractal theory in analyzing financial and commodity markets was Bill Williams. Subsequently, his method of fractal market analysis became widespread in many countries. This was facilitated by his works such as “Trading Chaos”, “New Dimensions in Exchange Trading”, “Trading Chaos Second Edition”.
My opinion is that Bill Williams is a scoundrel. His books contain a lot of water and abstract reasoning. This does not mean that fractal theory is incorrect or ineffective. This means that specifically B. William either does not know how to express his thoughts briefly or does not fully understand the theory, or all his books are PR for himself and his courses.
Over time, many inattentive traders and analysts believed that the beautiful name was more likely to be a clever PR move by the author than the actual use of fractals in the market. The main mistake that leads to distortion of the analysis results is the incorrect interpretation of the concept of “overcoming a fractal.” The ambiguity of fractal analysis ceases if the word “overcoming” is understood not as a puncture by the price of a fractal level, but as a breakdown confirmed by the closing of a price above or below the fractal level.
This is wrong. Often the price closes below the fractal, and the breakout turns out to be false. My practical experience shows that the closing price is not a criterion for the truth (or falsehood) of a price breakout. See picture.
The price broke through the fractal from top to bottom and the closing price of two entire candles was below the level. However, the downward breakout turned out to be false...
In Russia, the first author and follower of fractal theory as a strategy in financial markets is Almazov Aleksey Alexandrovich. He proposed the Weierstrass-Mandelbrot fractal function (this function was not developed by Mandelbrot, but is a component of the mathematical program Fractan) as a real model of price values for identifying graphic cycles (patterns).
Using practical examples, the author reveals in sufficient detail complex mathematical concepts, such as: initial conditions, attractor, non-periodic cycle, dimension and many others, in relation to the graphical structure of the market.
Unlike other authors, Almazov is constantly developing the direction of fractal analysis as an independent tool for analyzing market prices, this is evidenced by new developments and many years of successful experience as an analyst of financial markets.
An analyst, simply put, is a talker. He receives a salary not for the effectiveness of his forecasts, but for the ability to wrap his forecasts in beautiful packaging. If he were a practical “trader”, then this would be a different conversation.
Among the shortcomings of the theory developed by Almazov, one can point out that in this approach the mathematical apparatus for predicting prices is still poorly used.
That is, there is little mathematics and statistics and a lot of “guessing”.
In the Russian forum environment one can find attempts to apply fractal theory in the market. Basically, the legacy of Benoit Mandelbrot and his mathematical apparatus are used.
Many traders use fractal analysis in their trading. Fractals help a trader identify market reversals.
By the way, the first person to look at the market as a nonlinear system was Bill Williams. In his scientific work, he discovered that the market moves chaotically. Bill Williams saw the harmony of chaos in cotton prices, human bleeding, and coastal surf.
Chaos in the work on the foreign exchange market, according to B. Williams, is its basis, therefore the exchange rate cannot be predicted using linear calculations.
Fractal, translated in Latin, means broken, crushed, shattered.
A fractal is a mathematical model that is self-similar. That is, each part of the fractal is similar to the fractal system as a whole. We can also observe the repetition of graphic figures in the foreign exchange market. By looking at the daily, hourly, five-minute and other charts of any currency pair, we will see repeating chart patterns.
Where do fractals come from?
The very concept of fractals appeared in the 19th century, when mathematicians were looking for examples of self-similar patterns in nature.
The word fractal was coined by Benoit Mandelbrot back in 1975, although he wrote the book “Fractal Geometry of Nature” only in 1977.
An interesting fact is that scientists have found fractals in corals, broccoli, sea shells, pineapples, human bronchi, as well as in snowflakes, clouds, lightning, crystals, etc.
However, fractals burst into trading when scientists began to use computer modeling. At this time, scientists A. Almazov in his work “Fractal Theory. How to change your view of the market" and B. Williams in "Chaos Theory..." suggested using fractal analysis in the foreign exchange market.
How is a fractal constructed?
To build a fractal in the foreign exchange market, you need to find five candles, among which the middle candle must be the maximum or minimum.
In the Forex currency market, everything is the same as in nature: a fractal is somewhat reminiscent of the fingers of a human hand. Put your hand on the monitor, and just as in the definition of a fractal, you will see that your middle finger will show the tip, where the fractal will be outlined.
However, not everything is so simple. Fractal calculations use a continuous sequence of candles. Therefore, it happens that one middle candle will be both the maximum and minimum for a different group of fractals.
Elements of fractal analysis
In the foreign exchange market, there are fractal models that describe the beginning of the movement of exchange rates. For example, a fractal start characterizes the movement of a currency pair, in which an upper fractal is formed first, for example, and the end of the movement closes the lower fractal.
Fractal model: a fractal signal, on the contrary, describes the end of the exchange rate movement, as opposed to the fractal start.
Thus, the impulse movement of the exchange rate begins with a fractal start and ends with a fractal signal.
Fractal stop
A fractal stop is the previous fractal on which an insuring Stop-loss order can be placed.
From the practice of using a fractal stop, it is important to note that sometimes the fractal stop is too close to our entry point. Therefore, it is better to place a fractal stop on a fractal that formed at a key low or high. It’s both safer and more effective.
Fractal analysis is used by traders mainly in the trend area of the foreign exchange market. As you understand, a combination of five candles appears constantly. Therefore, in the case of a flat movement of the foreign exchange market, fractals give many false entry signals.
To effectively apply fractal analysis, traders use time frame overlay. How does this work?
We apply the fractal indicator in the MT4 platform through the menu Insert – Indicators – Bill Williams – Fractals.
Thus, we see the fractal indicator on the D1 chart of the EUR/USD currency pair.
From the figure above, we can see that the maximum of the fractal start was formed on May 8, 2014, when the daily candle closed at a price of 1.3839.
To enter the market more accurately, we are using the tactics of adjusting time frames and looking for an entry on the lower time frame – H1.
As can be seen from the figure, on the H1 chart of the euro/dollar, a flat formed at the price level of 1.3744-1.3774, which lasted until May 13, 2014. We marked a fractal level with a red line, after breaking through which, we expect to sell the pair euro/dollar At 9:00 on May 13, 2014, the fractal level was broken down and we entered a Sell position on the euro/dollar. Naturally, we place a stop-loss order slightly above the upper border of the flat, beyond the level of 1.3774.
In the terminology of fractal analysis, there is another important concept, the fractal lever.
In trading, fractal leverage is the size of the correction. To identify retracements in fractal leverage, traders use the Fibonacci grid.
There is an observation that if the correction reaches 38% on the Fibonacci grid, it means there will be good momentum and the fractal leverage is strong. In the case when the correction reaches up to 61.8% on the Fibonacci grid, then the fractal leverage is weak and you can ignore entering the market.
Let's take a closer look at the fractal level that we used in our example of entering the market above.
As you understand, the foreign exchange market moves in impulses and corrections. So, the fractal level is formed due to the accumulation of fractals, combinations of five candles, during correction.
In fractal analysis, it is important to understand that entering a breakout of a fractal level is safer and more effective than entering at the edges or turning points of the market. Also, you need to take into account the fact that it is better to take breakouts of fractal levels along the trend. Trend is our friend. Everyone who is against the trend is not our friend and, as a rule, quickly loses their deposit and then criticizes the foreign exchange market.
There is an observation that the longer a flat and fractal level is formed, the greater the likelihood of its breakthrough, and the greater the opportunity to make money from it.
Fractal level breakthrough
In the practice of using fractal analysis, difficulties arise in determining a true or false breakthrough of a fractal level. After all, even from our example above it is clear that the fractal level was broken through and tested several times. How to understand where the true breakthrough of the fractal level is and where it is not.
Traders in their work, when determining a breakthrough of a fractal level, use the search for a breakout candle. A breakout candle is a candle that confidently closed outside the fractal level. It can be assumed that the next candle, after the breakout, will also continue its movement towards the breakout.
But it is possible that after a breakout candle there is a return to the fractal level, something similar to the expansion of a flat. To enter the market more accurately in such cases, you should use other methods of analysis, possibly using additional indicators.
Thus, in our short review of fractal analysis in the foreign exchange market, we learned that fractals exist in nature, that human fingers help determine the fractals of the foreign exchange market on your monitor. Also, you already understand what a fractal start, signal and lever are.
In the previous article, we briefly reviewed the basic principles on which Trading Chaos is based. 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 make the picture complete, Today we will continue to look at Bill's trading techniques, significantly increasing profits from speculation, and let’s start with, perhaps, fractals.
In one of our earlier publications, we already touched upon the topic of identifying and constructing fractals (including using indicators). Therefore, we will not repeat the theory again; we will only note that a fractal is a formation whose central extremum is located above (below) the corresponding extrema of four neighboring bars.
The entire logic of fractal analysis in Trading Chaos is based on the search for breakouts of extreme points, but unlike later trading strategies developed by other traders, the original model according to Williams consists of strictly three elements:
- Fractal start – the first extremum preceding the signal;
- Signal fractal – formed in the opposite direction to the starting fractal;
- Fractal stop is the largest top on a downtrend (or bottom on an uptrend) of the last two fractals.
Thus, fractal analysis completely eliminates uncertainty when making decisions and at the same time allows you to weed out many false signals (but only if the prevailing trend is reliably known).
Speaking of trends, in the Chaos Williams theory this issue is resolved by itself, since fractals become an integral part of wave analysis, and a wave (or wave structure) is a trend. At the same time, 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 the trend after the floating profit on the first transaction allows the stop order for a set of orders to be transferred to breakeven, while the volume of each new transaction is either equal to a constant or divided by a certain coefficient.
For example, suppose that the third wave has begun in the market, which all wave traders are hunting for, in this case the trader’s action algorithm will be as follows:
Besides this, without fractal analysis any attempt to look for wave structures is doomed to failure - this is a fact proven by several generations of traders, although Bill warned about it. In his “Five Bullets,” outlined in Chapter Nine of Trading Chaos, Williams listed the main signs of a trend ending:
- A divergence appeared on the MACD between the third and fifth waves;
- The current price is located in the target zone, i.e. the fifth wave, according to the approximate markings, should already begin (but it is not a fact that it will be fully formed), 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);
- The MACD histogram bars crossed the signal line in the opposite direction to the latest trend.
In conclusion, we note that, despite its universality and good practical results, there is something to complain about in Williams’ theory. For example, Bill argues that the market does not obey traditional physical laws, but at the same time behaves similarly to the ebb and flow of the sea, which, in fact, are associated with the gravitational influence of the Moon and the Sun on the Earth - isn't this a law?
Therefore, one should not look for hidden meaning in Trading Chaos; Williams was simply able to describe for the first time the behavior of the market crowd using the tools of technical analysis, i.e., roughly speaking, mathematics, which deserves respect in any case.
Price movement has a fractal nature because the actions and reactions of people in the market are repeated. The challenge is to recognize these repeating patterns on the price chart. In this article we will consider in detail one of the ways to find such models.
The laws of gravity, capacity, inertia and cyclicality are important driving forces in financial markets. All market patterns, behavior and dynamics can be seen as symptoms or results of these laws. These basic forces are easily understood and intuitively perceived. Their presence can be proven using simple, irrefutable logic based on empirical evidence. In this article we will look at the fractal structure of markets, its manifestations and consequences, and the opportunities it presents to the astute and ultimately successful trader.
Fractals in financial markets
Fractals are a natural phenomenon and at the same time mathematical sets. What they have in common is their repeating pattern, which can be observed on any scale of time and space. To put this into financial context, take a look at Figure 1, which shows three candlestick charts. One is a daily chart (one candle represents one day of trading), another is a 5-minute chart (one candle condenses 5 minutes of trading), and the third is a weekly chart (all movements for the week are compressed into one candle). Each chart represents a different type of financial asset - , index and commodity. Additionally, each one covers a different period of time.
Figure 1
But even taking all this into account, it is still impossible to tell which graph belongs to what. Without prices on the vertical axis and/or timestamps on the horizontal axis, it will be impossible to distinguish them. In fact, since these three graphs are shown next to each other, they can be mistaken for one continuous graph. For those who are interested, the left chart is the weekly time frame for gold, the middle chart is the daily time frame for the S&P 500, and the right chart is the 5-minute Google, Inc. (GOOG).
A good analogy here is the concept of numerical infinity. There are two approaches to numerical infinity. One is that for each number there are neighboring numbers - a smaller and a larger one, for which, in turn, there are also smaller and larger neighboring numbers; and so on ad infinitum; this is infinity of size. Another approach is that between any two numbers there is an infinite number of other numbers - this is an infinity of precision. The same can be said for data in financial markets. New quotes are constantly arriving, which can be viewed on timeframes of varying degrees of accuracy. The only exception to this comparison is that the scale (if we are talking about price movement) is not infinite. In practice, the smallest scale is a single operation. But the concept of infinity can still be used to see the fractal nature of price data in financial markets.
Figure 1 is an example of the never-ending stream of empirical evidence. Is it possible to put forward a sound explanation, or a universal law, that would take this phenomenon into account? If so, that might explain how . We believe that it is possible to formulate a universal law. Any chart depicting the behavior of financial markets, regardless of its time frame or location in time, is the result of past transactions. We mean operations performed by people in response to various impulses. The diagram in Figure 2 provides an external view of the financial market. The financial market consists of external impulses new to the system (news, reports and other fundamental data), as well as an output signal that is internally returned to the system (people reacting to price movements).
Figure 2
Charts are nothing more than the cumulative result of the past actions of all traders or executed orders. Because people act and react to what the market does in the same way and in the same way across all time frames, their behavior ultimately manifests itself in the same patterns, regardless of scale.
Human emotions are constant, no matter what time frame we consider. The same applies to the behavior resulting from these emotions.
Focal points
Traders use the same methods and indicators to search for the same type of signals, regardless of the timeframe on which they work. Knowing this, it is worth monitoring several time frames during the trading process. Something similar was done by Alexander Elder, who developed his three-screen trading system, which suggests that the trader needs to look at one time frame below and one time frame above the one on which he is trading.
Just as a perfect storm begins as an innocent breeze that eventually develops into a hurricane, so too can one try to profitably pick up on the points where signals on different time frames begin to agree. The greater the number of signals (different or identical) on all timeframes, the greater the importance of this particular point in time.
The number of charts that simultaneously contain similar signals determines the importance and depth of understanding market dynamics. Think about how many people are watching this chart and this signal at this moment, looking at different time frames. The computer is an ideal tool for processing such a large amount of information. For example, you could look at 50 possible formations or signals on 20 different time frames for a particular stock, and then repeat this for several thousand more stocks.
We will then come to understand that the future of any chart is determined by the cumulative execution of orders that have not even been placed yet. It is impossible to know in advance whether a given intraday trade will be short-term, lasting a few days or weeks, or will become a long-term trade that you will hold for several weeks to several months. Each transaction develops from the embryonic stage - this is the smallest form on the smallest time scale. This is why fractals play an important role in trading.
Atoms of Trade
Every trend, regardless of its length, starts from the lowest Low (in the case of an uptrend) or from the highest High (in the case of a downtrend). Each bottom, when close enough, has a V-shape consisting of three bars. Likewise, each vertex should look like an inverted V when viewed at its highest point with sufficient magnification. This means that at the most basic level, regardless of the time frame in question, there are always three bars present that make up this atom - the building block of any chart. Trends and reversals will always end or begin with three bars, the middle of which represents the extreme high or extreme low. Take a look at Figure 3. On the left chart you can see a three-bar pattern called a "single-bar down fractal." "With one bar" means that on each side of the middle bar there is one bar with higher Highs.
Figure 3
Next to this model in the diagram there is an up fractal with two bars, i.e. there are two bars on each side of the middle bar. It is necessary to be aware of some of the nuances of these definitions found in the trading literature. For example, for an up fractal with five bars, most sources require that there must be at least two bars on each side of the top or bottom for the formation to be called a fractal. There is a difference of opinion as some believe that surrounding bars do not necessarily have to show a sustained upward or downward trend, and some believe otherwise. You can see an example of this situation in the third diagram in Figure 3. The red bar is an up fractal with three bars, because to the right of the red bar there are actually three bars with lower Highs, despite the fact that the third is higher than the second. In some literature this is called a three-bar up fractal because the fourth bar from the right again has a lower High. Likewise, if you look at the bars to the left of the green, you will notice that the third bar from the left has a higher Low than the green bar, although its Low is lower than the second bar to the left of the green. There is quite a bit of confusion in the literature regarding the definitions of fractal patterns and how to use them. Therefore, in this matter we need to go one step further.
Fractal continuum
In addition to all classifications that take into account neighboring bars, each bar can be assigned a set of four numbers. The number of bars to the left and right of the bar in question that exhibit higher Lows than the bar in question is called the Chartmill number of left/right support for that bar (CLS and CRS, respectively). Likewise, a given bar's Chartmill Left/Right Resistance number (CLR and CRR, respectively) takes into account the number of bars to the left and right of a given bar with lower Highs. These numbers are clear and avoid confusion. The time frame you use for your analysis should not affect how you define and analyze the fractal nature of the market. It is important to have objective indicators and signals. Moreover, these indicators and signals must ignore any characteristics of visual perception, for example: time scale on the horizontal axis or linearity/logarithmicity of the axis. Only then can objective, chart-independent indicators be created that can be applied algorithmically, scanning for focal points.
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