One of the "tenets" of technical analysis is the belief that the movement of the market schedules are subject to certain standard proportions. Among the different variants of such proportions were highest recognition Fibonacci ratio associated with the golden section. For each trader's golden section proportions are an important part of his perception of the market, reliable benchmarks in making trading decisions. But by itself the origin of Fibonacci levels is still a mystery.
The proportions in the analysis of Fibonacci graphs
For each direction the course of the market schedule should roll in the opposite direction. Moreover, between the course and size of rollback, there is a stable relationship: the more progress, the more and the subsequent roll.
Naturally, in such a way that the property still does not give recommendations, needed a trader. Namely, quantitative estimates are needed: what value will roll after the market made a move, the value you measured. The benefits of such assessments will be expressed in specific amounts of profit. Not surprisingly, the attempts to find the exact ratio (ratio) "move / roll" has long been doing a lot of analysts. The first idea was the proportion of 1 / 3, proposed by C. Doe: if the market was some progress in the value 1, the most probable roll will be the value of 1 / 3, 1 / 2 or 2 / 3 (in percent record 33%, 50%; 66%).
The meaning of the recommendations based on the proportions, is as follows: if the trend is formed is strong enough, then 33% - the size of a natural correction of the previous move. Rolling 50% even considered as a normal market correction, but a return of 66% - is already a signal of possible termination of the trends and turn the market. Another set of proportions, the number of multiples of 1 / 8, used in the analysis of markets, W. Gunn. He believed that the major correction in line with the size of 3 / 8 (38%), 4 / 8 (50%), 5 / 8 (62%). As shown, the ratio is close to the proposed Dow.
But the most common approach has been the distribution of aspect ratio on the degree of golden section
proposed by R. Elliott. If the graph, a move (to take the size of the progress of 100%), the most likely level of kickbacks - is the Fibonacci ratio: 23.6%, 38.2%, 50%, 61.8%, 76.4%, 100%, 161.8%, 261.8%.
Here
Figure 1 shows the construction of the Fibonacci ratio in the afternoon schedule of the British pound. Once the schedule has made a strong move down from 1.51 to 1.3680 (oblique line), the height of the stroke (vertical red line segment) is divided into parts according to the Fibonacci proportions, and cross sections are obtained through the horizontal line. These lines in the future will certainly be the levels of consolidation.
Understanding the Fibonacci ratio is the same as it was formulated before: roll from the first level (23.6%) are usually little, the next level (38.2%) is more important, the market almost always makes it a significant rollback.
If the market turns and then continue, the next important level of consolidation will be 50%, and the continued fall-back to 61.8%, as a rule, means the permanent termination of the previous (in this case - down) trend [1].
Proportion, less than 1, estimate the size of kickbacks emerged after the price of progress. Proportions greater than 1 (projection), estimate the consolidation guidance in the event of further progress.
For example, if in figure 1 pound continued to schedule your course below the level of support (1.3680), as a goal of this course was offered to the level that lies below 1.3680 at a distance of 61.8% of the height of the course indicated in the figure the vertical line segment. In addition to constructing of kickbacks, the proportions of a golden section used in a number of methods for analyzing graphs such as the Fibonacci fan (otherwise known as high-speed lines, Fibonacci), an arc Fibonacci golden spiral, etc., as well as a well-known concept of Elliott Wave [2] . The proportions of a golden section - one of the most universal and reliable tools for analysis of market schedules. Regardless of the chosen market, commercial approach and the time scale for the work, every trader has to follow the Fibonacci levels, as they are, as always strong levels often provide a useful benchmark for the opening and closing positions.
The Inevitability of a golden section
On the basis of such unity in the behavior of many different markets? The usual explanation of the Fibonacci ratio in books on technical analysis is based on a vague discussion of the universal laws of nature, drawing on analogies from the fields of biology, architecture, fine arts [2]. Despite the significance of such comparisons in a logical, they do not explain.
Of course, by itself the formation of the consolidation is an inevitable manifestation of the psychological dynamics of speculative forces in the markets. The availability of stable, recurring regularly proportions in the size of turns and setbacks in the graphs - an undeniable empirical fact. But why the golden section? What is worse than, say, the proposed ratio J. Dow, multiple 1 / 3, or multiples of powers? proportions W. Hanna?
Let's try to bring the golden section a logical way. Here are a few certainties are well known in the technical analysis of market-based scheduling features that can be taken as an axiom:
- Each accompanied by a subsequent rise of the market fall (corrected);
- There are some strong (typical, regularly recurring) ratio on the amount of income to subsequent correction;
- This behavior is characteristic of all markets, and it manifests itself on different time scales.
The latter property can be characterized as the fractality of market dynamics: the schedule, considered in the small scale of time (say, a 5-mi-nutnom), quite similar to its behavior on a larger scale (eg, hour or day). Assume now that there was some universal ratio (typical value of the progress schedule to the market value of its correction), typical of all market movements. If there is such a universal proportions, how to find it?
Denote r this universal unknown proportion (0<1). Then each value of H recovery schedule P (t), representing the price of P as a function of time t, will be accompanied by a setback rN values (Fig. 2).
Add now to our axioms another: if the graph P (t) represents a certain market, then figure 1 / P (t) also corresponds to some markets. In other words, all the basic features of market schedules are stored in the inversion transaction price P (t) & 1 / P (t).
It is entitled to such an assumption in the general case, discussed later, while the same can be noted that the foreign exchange market is quite clear: if P (t) - the price of currency, expressed in units of another currency (direct quotation, for example, USD / JPY = yen / $), then 1 / P (t) is simply indirect quotation (JPY / USD = $ / yen).
It quotes on both sides of the money, and so little change as a change of forms of writing quotes, may not significantly affect the behavior of market participants.
But if this is true, the picture of "progress / rollback on the schedule back market must look exactly the same as the original, which means that the typical ratio should form symmetrical levels of consolidation. If in the course up to the value of N is a typical setback reduction on rN, then down during a typical setback will grow in the rN, since the market recovery in the reverse 1 / P (t) corresponds to a drop on the source (Fig. 2).
Further, according to fractal properties of markets, each movement of the market may be, in turn, presented as the implementation and roll. Because of market movements (the small piece submitted to the right in Figure 2) also represents the market movement, and therefore consists of the progress and retrogression. They involve the same proportion of r.
It follows that the segments in Figure 2 are similar and their values associated with each ratio
This is quadratic equation
with the only acceptable solution (r <1): Hence, an additional portion of the line segment has length
And this is nothing like the famous golden section! So, we proved that if you just made assumptions about the properties of market-based scheduling, the universal ratio (if it exists) is bound to the gold section.
Well known for a strong mathematical relationship between the golden section and the sequence of numbers 1, 2, 3, 5, 8, 13, 21, 34 ,..., called the Fibonacci sequence [3] (each number in it is the sum of the previous two). In technical analysis on the Golden Section and the Fibonacci series based concept Elliott wave: the market cycle (for the-No), it seems composed of a standard set of 8 waves (5 impulse waves main course + 3 corrective waves), which, in turn, may be placed on the wave of a lower order, the number of which is subject to the Fibonacci pattern. The relationship of stroke and the price correction in Elliott waves obey the golden ratio.
Also known as the main difficulty in the practical application of Elliott Wave: very often decomposition of market movements on the waves does not coincide with the standard rule Elliott.
For example, instead of the five main pulse wave motion is composed of seven or nine, instead of three corrective waves arise various unpredictable "stretching", composed of several waves, etc. The hypothesis of invariance of market graphs gives natural explanation to these phenomena. Indeed, if the proportion of golden section is related to the Fibonacci series in the wave decomposition of the schedule, the deviation of market behavior of inversion invariance (such as deviations from the ideal model is inevitable in the real life of each market) would mean that instead of an ideal system elliottovskoy waves there is something different picture, geometric proportions that would differ from the golden section. From this perspective, the deviation from the ideal model of graphics elliottovskih waves should be seen as a signal of some place within the market transition process. Perhaps the development of the mathematical methods would allow the use of such signals as the information to make good trading decisions. For example, an interesting manifestation of some type of symmetry is the more famous "harmonic" number:
called the plastic number.
Just as the golden section is connected with the Fibonacci sequence, as well as those related to plastic consistency Padovana (named after the Italian architect, to apply these numbers in their projects): 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21 ,....
Figure 4 is an example, the corresponding proportions of the plastic is better than the Fibonacci proportions.
The blue lines show the Fibonacci levels (the upper dotted line corresponds to the projection of 1.618), while the yellow line - levels, relative proportions of plastic:
(1 / p) 3 = 0.324718 = p-1 (1 / p) 2 = 0.56984, 1 / p = 0.754878; p = 1.324718.
It is evident that a satisfactory version of the decomposition of the schedule for the classical waves of Elliott's hard to pick. Using numbers Padovana could suggest other options.
Invariance of charts and market behavior
The tendency of market-based scheduling to form such images as the levels of consolidation, subject to certain sustainable proportions usually seen as a consequence of the psychology of the market crowd. The two main driving forces of the speculative markets - fear and greed - create a constantly boiling atmosphere is extremely unstable and vysokouporyadochennuyu at the same time.
Due to the properties of human memory, past events (from the profit and loss) have a lasting impact on future decisions of market participants and are apparent, therefore, in the new graphic images. The leading role of emotions in trading decisions determine the unique nature of uncertainty in the speculative markets, different from all other forms of human activity. In the normal life of uncertainty is, as a rule, undesirable phenomena (interference, distortion, noise), and it should be fought. But markets can not function without ambiguity, that is their driving force. Delete the uncertainty of speculative market means to destroy it. While the markets are still alive, they are resistant to any predetermined ordering.
Of course, the above inversion invariance property market schedules should be sufficiently plausible explanation in the light of psychology of market behavior, otherwise it will remain a mathematical trick. For the currency market inversion invariance seems quite natural, since the means to replace the signs. But the market shares of P (t) denotes the price of the securities in the currency. Two hand quotes here are not equivalent. The same has occurred and product markets, and for many other assets. However, it can also be seen as adequate psychological and economic reasons for the alleged invariance. Indeed, today all of these markets can not be seen as some isolated areas of activity. Information, financial and business relationships between a large number of individual market participants are united in terms of closely related activities:
... - Currencies - Products - Stocks - Bonds - Futures - ...
This market does not in any way in order for any degree of importance, and neither end nor the beginning of the conversation. This is just an endless series of bilateral exchanges of some assets to the other. Continuity of flow at all levels of the chain is ensured by well-known principles:
- High liquidity assets, which is a consequence of the development of market infrastructure and the availability of permanent incentives to work of a large number of independent members;
- The lack of any dominant parties, who alone can control the market at its own discretion.
Under these conditions, all assets are to a certain extent, equivalent in the sense that an asset could be exchanged for another, and they are all really involved in the ongoing process of movement. Then, any understanding of asset price coincides with the definition of cross-course in the terminology market FOREX: P value is the price a given asset expressed in units of another asset. There is every reason to expect that the price charts of all of these assets will be subject characteristic inversion invariance.
You must still make a clarification regarding the possible existence of such a principle of invariance. The point is that the transformation of inversion P (t) 1 / P (t) is nonlinear, and the relations of similarity (ratio) with a conversion, generally speaking, are not saved. Fig. 3 some market schedule P (t) showed a rise from entry-level m to a new maximum of m + M, followed by a rollback of the achieved level. The size of rollback involves the standard proportion of r to the previous track, so that the roll was completed at the level of m + (1-r) M.
If we consider the reverse schedule of 1 / P (t), then it is the movement began with a level 1 / m, reached a new minimum of 1 / (m + M) and finished rolls back to 1 / (m + (1-r) M). Evaluating the relationship "move / rollback to reverse the schedule provides:
If the property of inverse invariance is indeed true, then the right-hand side should be equal to r. Obviously, this is done (approximately) for sufficiently small M / m. In other words, if all the considered changes in market prices are sufficiently small compared with the initial levels of the markets, the inversion invariance properties of market-based scheduling may take place.
Conclusion
Typical declaration of golden section as a consequence of the universal laws of nature, bringing together the Egyptian and Mexican pyramids, the Parthenon, a spiral nautilus shells and spiral galaxy, looks impressive. Unfortunately, it is not clear that the internal mechanisms of such a unity and does not spill over the bridge from the Galaxy to the financial markets. Invariance principle allows for a fresh look at these phenomena. From the viewpoint of modern physics the most fundamental properties of matter can be derived from these or those principles of symmetry. Invariance of physical laws has such important consequences, as the law of conservation of energy law of conservation of momentum and others. Perhaps the fact that the golden section can be deduced as a consequence of the invariance properties of the market charts, tells us something really important about the nature of market conduct. There is no doubt that further studies of symmetry properties of market-based scheduling can lead to the creation of new methods and tools to make trading decisions.
Victor Lihovidov
The proportions in the analysis of Fibonacci graphs
For each direction the course of the market schedule should roll in the opposite direction. Moreover, between the course and size of rollback, there is a stable relationship: the more progress, the more and the subsequent roll.
Naturally, in such a way that the property still does not give recommendations, needed a trader. Namely, quantitative estimates are needed: what value will roll after the market made a move, the value you measured. The benefits of such assessments will be expressed in specific amounts of profit. Not surprisingly, the attempts to find the exact ratio (ratio) "move / roll" has long been doing a lot of analysts. The first idea was the proportion of 1 / 3, proposed by C. Doe: if the market was some progress in the value 1, the most probable roll will be the value of 1 / 3, 1 / 2 or 2 / 3 (in percent record 33%, 50%; 66%).
The meaning of the recommendations based on the proportions, is as follows: if the trend is formed is strong enough, then 33% - the size of a natural correction of the previous move. Rolling 50% even considered as a normal market correction, but a return of 66% - is already a signal of possible termination of the trends and turn the market. Another set of proportions, the number of multiples of 1 / 8, used in the analysis of markets, W. Gunn. He believed that the major correction in line with the size of 3 / 8 (38%), 4 / 8 (50%), 5 / 8 (62%). As shown, the ratio is close to the proposed Dow.
But the most common approach has been the distribution of aspect ratio on the degree of golden section
proposed by R. Elliott. If the graph, a move (to take the size of the progress of 100%), the most likely level of kickbacks - is the Fibonacci ratio: 23.6%, 38.2%, 50%, 61.8%, 76.4%, 100%, 161.8%, 261.8%.Here
Figure 1 shows the construction of the Fibonacci ratio in the afternoon schedule of the British pound. Once the schedule has made a strong move down from 1.51 to 1.3680 (oblique line), the height of the stroke (vertical red line segment) is divided into parts according to the Fibonacci proportions, and cross sections are obtained through the horizontal line. These lines in the future will certainly be the levels of consolidation.Understanding the Fibonacci ratio is the same as it was formulated before: roll from the first level (23.6%) are usually little, the next level (38.2%) is more important, the market almost always makes it a significant rollback.
If the market turns and then continue, the next important level of consolidation will be 50%, and the continued fall-back to 61.8%, as a rule, means the permanent termination of the previous (in this case - down) trend [1].
Proportion, less than 1, estimate the size of kickbacks emerged after the price of progress. Proportions greater than 1 (projection), estimate the consolidation guidance in the event of further progress.
For example, if in figure 1 pound continued to schedule your course below the level of support (1.3680), as a goal of this course was offered to the level that lies below 1.3680 at a distance of 61.8% of the height of the course indicated in the figure the vertical line segment. In addition to constructing of kickbacks, the proportions of a golden section used in a number of methods for analyzing graphs such as the Fibonacci fan (otherwise known as high-speed lines, Fibonacci), an arc Fibonacci golden spiral, etc., as well as a well-known concept of Elliott Wave [2] . The proportions of a golden section - one of the most universal and reliable tools for analysis of market schedules. Regardless of the chosen market, commercial approach and the time scale for the work, every trader has to follow the Fibonacci levels, as they are, as always strong levels often provide a useful benchmark for the opening and closing positions.The Inevitability of a golden section
On the basis of such unity in the behavior of many different markets? The usual explanation of the Fibonacci ratio in books on technical analysis is based on a vague discussion of the universal laws of nature, drawing on analogies from the fields of biology, architecture, fine arts [2]. Despite the significance of such comparisons in a logical, they do not explain.
Of course, by itself the formation of the consolidation is an inevitable manifestation of the psychological dynamics of speculative forces in the markets. The availability of stable, recurring regularly proportions in the size of turns and setbacks in the graphs - an undeniable empirical fact. But why the golden section? What is worse than, say, the proposed ratio J. Dow, multiple 1 / 3, or multiples of powers? proportions W. Hanna?
Let's try to bring the golden section a logical way. Here are a few certainties are well known in the technical analysis of market-based scheduling features that can be taken as an axiom:
- Each accompanied by a subsequent rise of the market fall (corrected);
- There are some strong (typical, regularly recurring) ratio on the amount of income to subsequent correction;
- This behavior is characteristic of all markets, and it manifests itself on different time scales.
The latter property can be characterized as the fractality of market dynamics: the schedule, considered in the small scale of time (say, a 5-mi-nutnom), quite similar to its behavior on a larger scale (eg, hour or day). Assume now that there was some universal ratio (typical value of the progress schedule to the market value of its correction), typical of all market movements. If there is such a universal proportions, how to find it?
Denote r this universal unknown proportion (0
It is entitled to such an assumption in the general case, discussed later, while the same can be noted that the foreign exchange market is quite clear: if P (t) - the price of currency, expressed in units of another currency (direct quotation, for example, USD / JPY = yen / $), then 1 / P (t) is simply indirect quotation (JPY / USD = $ / yen).
It quotes on both sides of the money, and so little change as a change of forms of writing quotes, may not significantly affect the behavior of market participants.
But if this is true, the picture of "progress / rollback on the schedule back market must look exactly the same as the original, which means that the typical ratio should form symmetrical levels of consolidation. If in the course up to the value of N is a typical setback reduction on rN, then down during a typical setback will grow in the rN, since the market recovery in the reverse 1 / P (t) corresponds to a drop on the source (Fig. 2).
Further, according to fractal properties of markets, each movement of the market may be, in turn, presented as the implementation and roll. Because of market movements (the small piece submitted to the right in Figure 2) also represents the market movement, and therefore consists of the progress and retrogression. They involve the same proportion of r.
It follows that the segments in Figure 2 are similar and their values associated with each ratio
Well known for a strong mathematical relationship between the golden section and the sequence of numbers 1, 2, 3, 5, 8, 13, 21, 34 ,..., called the Fibonacci sequence [3] (each number in it is the sum of the previous two). In technical analysis on the Golden Section and the Fibonacci series based concept Elliott wave: the market cycle (for the-No), it seems composed of a standard set of 8 waves (5 impulse waves main course + 3 corrective waves), which, in turn, may be placed on the wave of a lower order, the number of which is subject to the Fibonacci pattern. The relationship of stroke and the price correction in Elliott waves obey the golden ratio.
Also known as the main difficulty in the practical application of Elliott Wave: very often decomposition of market movements on the waves does not coincide with the standard rule Elliott.
For example, instead of the five main pulse wave motion is composed of seven or nine, instead of three corrective waves arise various unpredictable "stretching", composed of several waves, etc. The hypothesis of invariance of market graphs gives natural explanation to these phenomena. Indeed, if the proportion of golden section is related to the Fibonacci series in the wave decomposition of the schedule, the deviation of market behavior of inversion invariance (such as deviations from the ideal model is inevitable in the real life of each market) would mean that instead of an ideal system elliottovskoy waves there is something different picture, geometric proportions that would differ from the golden section. From this perspective, the deviation from the ideal model of graphics elliottovskih waves should be seen as a signal of some place within the market transition process. Perhaps the development of the mathematical methods would allow the use of such signals as the information to make good trading decisions. For example, an interesting manifestation of some type of symmetry is the more famous "harmonic" number:
Just as the golden section is connected with the Fibonacci sequence, as well as those related to plastic consistency Padovana (named after the Italian architect, to apply these numbers in their projects): 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21 ,....
Figure 4 is an example, the corresponding proportions of the plastic is better than the Fibonacci proportions.
(1 / p) 3 = 0.324718 = p-1 (1 / p) 2 = 0.56984, 1 / p = 0.754878; p = 1.324718.
It is evident that a satisfactory version of the decomposition of the schedule for the classical waves of Elliott's hard to pick. Using numbers Padovana could suggest other options.
Invariance of charts and market behavior
The tendency of market-based scheduling to form such images as the levels of consolidation, subject to certain sustainable proportions usually seen as a consequence of the psychology of the market crowd. The two main driving forces of the speculative markets - fear and greed - create a constantly boiling atmosphere is extremely unstable and vysokouporyadochennuyu at the same time.
Due to the properties of human memory, past events (from the profit and loss) have a lasting impact on future decisions of market participants and are apparent, therefore, in the new graphic images. The leading role of emotions in trading decisions determine the unique nature of uncertainty in the speculative markets, different from all other forms of human activity. In the normal life of uncertainty is, as a rule, undesirable phenomena (interference, distortion, noise), and it should be fought. But markets can not function without ambiguity, that is their driving force. Delete the uncertainty of speculative market means to destroy it. While the markets are still alive, they are resistant to any predetermined ordering.
Of course, the above inversion invariance property market schedules should be sufficiently plausible explanation in the light of psychology of market behavior, otherwise it will remain a mathematical trick. For the currency market inversion invariance seems quite natural, since the means to replace the signs. But the market shares of P (t) denotes the price of the securities in the currency. Two hand quotes here are not equivalent. The same has occurred and product markets, and for many other assets. However, it can also be seen as adequate psychological and economic reasons for the alleged invariance. Indeed, today all of these markets can not be seen as some isolated areas of activity. Information, financial and business relationships between a large number of individual market participants are united in terms of closely related activities:
... - Currencies - Products - Stocks - Bonds - Futures - ...
This market does not in any way in order for any degree of importance, and neither end nor the beginning of the conversation. This is just an endless series of bilateral exchanges of some assets to the other. Continuity of flow at all levels of the chain is ensured by well-known principles:
- High liquidity assets, which is a consequence of the development of market infrastructure and the availability of permanent incentives to work of a large number of independent members;
- The lack of any dominant parties, who alone can control the market at its own discretion.
Under these conditions, all assets are to a certain extent, equivalent in the sense that an asset could be exchanged for another, and they are all really involved in the ongoing process of movement. Then, any understanding of asset price coincides with the definition of cross-course in the terminology market FOREX: P value is the price a given asset expressed in units of another asset. There is every reason to expect that the price charts of all of these assets will be subject characteristic inversion invariance.
You must still make a clarification regarding the possible existence of such a principle of invariance. The point is that the transformation of inversion P (t) 1 / P (t) is nonlinear, and the relations of similarity (ratio) with a conversion, generally speaking, are not saved. Fig. 3 some market schedule P (t) showed a rise from entry-level m to a new maximum of m + M, followed by a rollback of the achieved level. The size of rollback involves the standard proportion of r to the previous track, so that the roll was completed at the level of m + (1-r) M.
Conclusion
Typical declaration of golden section as a consequence of the universal laws of nature, bringing together the Egyptian and Mexican pyramids, the Parthenon, a spiral nautilus shells and spiral galaxy, looks impressive. Unfortunately, it is not clear that the internal mechanisms of such a unity and does not spill over the bridge from the Galaxy to the financial markets. Invariance principle allows for a fresh look at these phenomena. From the viewpoint of modern physics the most fundamental properties of matter can be derived from these or those principles of symmetry. Invariance of physical laws has such important consequences, as the law of conservation of energy law of conservation of momentum and others. Perhaps the fact that the golden section can be deduced as a consequence of the invariance properties of the market charts, tells us something really important about the nature of market conduct. There is no doubt that further studies of symmetry properties of market-based scheduling can lead to the creation of new methods and tools to make trading decisions.
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