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Understanding The Fibonacci Sequence

Introduction

Fibonacci is probably the most famous tool for traders. In this article, we will explain its origin, how the more common levels are calculated, and how to use retracements and extension tools.

The Fibonacci sequence was discovered and developed by the Italian mathematician Leonardo Pisano “Fibonacci” (son of Bonaci Pisano). The Fibonacci Sequence, published in the year 1202 in his book “Liber Abaci” (Book of Calculus), exposes the problem of growth of a population of rabbits based on specific assumptions. Fibonacci concluded that each month the density of rabbit pairs was increasing from 1 to 2, then from 2 to 3, the next month from 3 to 5 and so on to infinity. In mathematical terms, the Fibonacci Sequence is:

In practical terms, the Fibonacci Sequence is:

 Understanding The Fibonacci Sequence

Now that we have calculated the sequence, we will determine the proportions that are related to this number series. In the first place, we will calculate the “Golden Ratio” or Phi (Φ) = 1.61803 and its inverse phi (1/Φ = φ) = 0.61803. Brown (2008) defines the Golden Ratio as a universal law that explains how everything with a growth and decay cycle evolves. In Table 2, we can see how the Fibonacci sequence converges to ratios 1.618 and 0.618; this can also be seen graphically in Figure 1.

The Fibonacci Sequence

1.618 and 0.618 Convergence

Fig 1: 1.618 and 0.618 Convergence (Source: Personal collection)

Fibonacci Levels Formation

Before calculating the various levels of Fibonacci, it is necessary to expose the concepts of retracement and projection. In figure 2, the US Dollar Index <DOLLAR> began a bearish movement on the 3rd of January 2017, registering a maximum level of 103,785, this move recorded a minimum lower than the previous minimum (99,465), after having reached 99,195 on the 2nd of February 2017, going back to 102,270. Once it reached this level, a new bearish cycle began with a projection that reached 90.985. This example is analogous to the bullish case.

Fibonacci Levels Formation

Fig 2: Retracement and Projection Movements. (source: Personal Collection)

Using the levels Phi Φ (1.618) and phi φ (0.618), we will calculate the different Fibonacci levels, as follows in Table 3:

Fibonacci retracement and projections calculation

Some traders prefer to use the level 0.764 and not 78.6, and vice-versa; this is not a critical factor for analysis and trading, the relevant factor is the decision that could take place when the price reaches this zone. Additionally, it is usual to add some levels in projections, for example, 227.2, 238.2, 3, 327.2, and so on.

Considering the example of the US Dollar Index, in figure 3 the DOLLAR finds resistance at 61.8 level (102.032), where the new bearish cycle takes place in continuation. We do not consider the F(61.8) as a per se rule strictly, sometimes the price finds resistance (or support) on another Fibonacci level, it is essential to follow what the price action is doing.

Fibonacci RETRACEMENT

Fig 2: Fibonacci Retracement (source: Personal Collection)

 

Once we have continuation signals, using the Fibonacci extension tool, we can define a forecast of the price movement target. In figure 4, DOLLAR follows in the bearish direction, the first objective expected is FE(100), FE(161.8) as the second target and third target FE(200). In our example, the Dollar targets are FE(100) 97.672, FE(161.8) 94.83 and finally FE(200) 93.074.

Fibonacci Extension

Fig 4: Fibonacci Extension. (source: Personal Collection)

Notes:

  • F(61.8) means 61.8 Fibonacci Retracement Level.
  • FE(161.8) means 161.8 Fibonacci Extension Level.

 

SUGGESTED READINGS:

  • Brown, C., (2008). Fibonacci Analysis. New York: Bloomberg Press.
  • Carney, S., (2010). Harmonic Trading Volume 1. New Jersey: Pearson Education Ltd.

 

KEYWORDS:

 

Fibonacci, Theory, Retracement, Extension.

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Fibonacci: Analysis of Common Errors

Analysis of errors

There are certain common errors that traders can make when they are using the analysis of Fibonacci.

  1. The first most common mistake that is made when traders use Fibonacci retracements is to start the range in the wrong direction. For example, if you want to find supports, you should start from high prices and go down, and the opposite process to find resistances. Also, when you select the high price and low price for the range, you should be sure that the confluence or support area is below the current price that closes the market, otherwise you would be finding a support which the market has already broken in the past.

how to use fibonacci on charts

If you use the Fibonacci tool like in the graph above to find supports, you will not have the correct supports or confluence zones and the market will be able to easily break these levels in the future because the market does not consider them important. The trader should find important levels of the market but levels that serve to project the future behavior of the market.

fibonacci stock charts

The graph above is taken on the EUR/USD. If you use the tool from high prices to bottom to find resistances, the analysis will be carried out erroneously and these supposed resistances will not be, and the market will continue its rally. This would be a costly mistake because the stop loss zone will be activated removing the trader from the market.

  1. Do not use high or low prices for ranges that have been reached by recent oscillations, because if this is done, the market will have exceeded the Fibonacci levels and this means that the market will have broken zones of resistances or supports so that the market could do it again.

fibonacci charts

forex charts with fibonacci

In these graphs can be observed that if high prices are in a range that has been touched by the market recently at some point, the market will break the resistance and the trade will be closed by a bad analysis running the point of stop loss.

  1. Another common error is to make the ranges for Fibonacci retracements, but without a fixed point. For example, each range has an initial and final point different from each other, so the confluence areas will not be the right ones or there will not even be confluence zones so many people could say that the Fibonacci-based analyses do not serve, but they don’t realize that the exercise is wrong. Below are two graphs that show this problem and why it will lead to erroneous conclusions.

stock charts fibonacci tools

charts with fibonacci

As seen in the graphs, if this were done, the trader would have areas of support and resistance that the market does not respect because it is not a true level so the trader will assume erroneous levels and will not be managing the risks adequately. To finish, it is important to mention that like all the tools, those that use the Fibonacci series can fail in some cases, where the market does not respect areas that the market should and continues its path without rebounding. But by using these tools, most of the time it will be managing the risk correctly and dramatically increase the chances of performing winning trades, so it is important to use all the tools mentioned to confirm that the market signals are correct.

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Fibonacci Complementary Tools

The analysis with rhythmic wave diagrams shows a relationship between the ratios so it will allow traders to further understand the relationship between them and help to make better decisions in trading. To understand the great contribution of the analysis of the harmonic proportions, it should be mentioned that the confluence zones are connected between them by harmonic relations. Also, if you want to know when the market is going to develop a strong movement in a bias you can also apply the harmonic proportions as a relevant indicator.

When the harmonic proportions are plotted, there are points where the harmonic intervals overlap and the market respects these points known as the diatonic Pythagorean scale; As the market respects the areas where different harmonic proportions coincide, this indicates that there are areas of confluence that weigh more than others so that the harmonic proportions will be a complement to the tools already studied, thus giving the trader the information on which major resistances and supports will be more important to the market.

A very important suggestion that must be considered by the trader is never to operate a single index, since in the market there are always assets that are correlated either proportional or inverse, so for certain assets there will be some other index that takes the lead and will serve to predict how the market behaves in the active trading. To see that assets can be correlated with an asset of interest you should analyze assets in the same sector, bonds, global indexes or raw materials.

fibonacci harmonic series

In the graph above the harmonic series is exhibited; There are analyses that apply these series to the market and in the points, that overlap series with others, will be areas that will be more important to the market, as not all areas of supports and resistances weigh the same for the market.

Retaking the Fibonacci analysis, there are certain tips that need to be considered. The highest or lowest prices are not always used to perform the analysis. The market gives the parameter to locate the range such as, the development of a rally in the market, very strong decision bars, gaps or certain technical patterns that indicate a change in the bias. If there are several signs of the market, it is better to draw several ranges to make sure that you are not leaving important areas without analysis, but considering that the ranges and their respective divisions must be areas respected by the market in the past because if this does not happen the drawn range will be irrelevant.

Other tools that serve to support the Fibonacci analysis are the oscillators like the RSI, but it is advisable to use them only when the market is in the confluence areas because otherwise it could give erroneous signals and is not reliable. If the market is reaching areas of confluence that are larger supports or resistances, oscillators will be able to give clues as to how the market behavior will be when it touches these points

Future price projections will be obtained by the projection of boxes where the important is the height of the boxes whose edges will be the ranges that were used for the Fibonacci analysis. If the market does not respect the first box of a small range, you should draw larger boxes that cover larger ranges and oscillations and their respective subdivisions that generate areas of confluence. This is the first step in creating future projections.

Using this Fibonacci analysis with the boxes starting from points of confluence to prices where a strong movement has been triggered and its subsequent subdivision with the Fibonacci ratios can be projected future prices in the oscillations that are formed. Many people do not know how to project in this way so they resort to Fibonacci expansions, a topic discussed in the article “Foundations of Fibonacci Extensions” (Foundations of Fibonacci Extensions) which is just as valuable and perhaps a little easier.

Another form of analysis is the Fibonacci channels. The channels are a variation to the Fibonacci retracements in which separate trendlines are drawn from a base price channel at distances provided by Fibonacci ratios. As a result, you get parallel trendlines that form channels used to estimate resistance and support zones as well as a Fibonacci retracement, only projected on a different axis. To create a parallel channel, it is observed first pivots that are confirmations of confluence zones that were analyzed in the horizontal axis, the lines of support or resistance in the channels must be respected where there are areas of confluence using the Fibonacci retracements. The pivot points will serve to create the channels are made in such a way that they respect important areas encountered previously.

The first step is to draw a channel where there are important pivots and based on this main channel are projected the Fibonacci percentages. This type of analysis also creates support areas and resistance and the knowledge becomes more robust because traders not only have the areas of horizontal confluence also have important areas diagonally. On many occasions, the intersections between different axes mark the entry point, but you should keep in mind that the stop loss points must be beyond the confluence zones and outside the Fibonacci channel.

Fibonacci channels

In the previous graph you can see some Fibonacci channels having as the basis of the channel the trend line of the market and then based on this project the Fibonacci ratios It’s important to have in mind that to be projected based on this trend line, the pivot points must have respected this trend line and the confluence areas that have been encountered with the Fibonacci retracements.

Fibonacci retracements

In this second graph, you can see the horizontal Fibonacci levels and the Fibonacci channels. As mentioned in this article, areas where support is intercepted or resistances with the channels will be areas that respect the market with greater determination and will be interesting areas to analyze. If you add this to the analysis with harmonic series, it will be a well-done analysis with enough tools to make no mistakes.

Summarizing, regardless of the asset, you should follow the same steps to analyze your important areas. First, it should be determined whether the areas you want to find are support or resistance zones, and depending on this you will proceed to stipulate the range to use Fibonacci retracements and other tools. There may be many ranges. They will always have the same starting point, but it will be carried at different price levels to obtain different ranges and several confluence zones. After identifying these areas, you should verify that the market has respected them in the past in different time horizons and be clear that the areas that have been found as major supports do not serve as resistance, that is another stage in the analysis. When you have identified the most relevant areas of the market it is advisable to shade them and eliminate those areas irrelevant to make the graph easier to interpret. Using the channels, retracements and Fibonacci expansion, oscillators, and Elliot’s principle, you will have the necessary tools to project the future direction of the market and thus make the best decisions of entry and exit.

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Foundations of Fibonacci Extensions

Introduction

A very popular application of Fibonacci deals with the projection of levels up to where price is expected to further develop. In the article “Foundations of Fibonacci Retracements” (https://www.forex.academy/training/technical-analysis/beginner/foundations-of-fibonacci-retracements/) we covered how to use Fibonacci to locate price areas where impulses could bounce in every wave of a given trend, as well as to its application for risk management (i.e. where to set the Stop Loss). In the following article, we will introduce readers to the basic Fibo extensions as a good set up to exit winning positions.

The first step of the analysis is to draw boxes on the price chart that represent the distances between the top of the range and the closest which Fibonacci retracement level, and from that point to the closest low or high and so on. Priority must be given to the height of the boxes and not to the width. Each box will be subdivided between the Fibonacci retracement levels to determine the percentage ratios within the boxes; these levels may be a guide to fix a target price. However, the problem with the projected boxes is that we won’t know exactly whether such subdivisions are resistances or major supports, i.e., we don’t know how likely it is for the price to reach such levels.

To establish the robustness of the boxes´ subdivisions, i.e., how strong price will be contained, the last range of the box should be subdivided if it is in a bearish trend market to the line ending the box using Fibonacci retracements. And the strategy would be to wait for these areas to respect the market and rebound the price or continue to fall. Using this strategy to draw boxes from the Confluence zone to the limit of the range either higher or lower and replicate this box in the opposite direction, and then subdivide the box into Fibonacci levels does not always ensure that there is a successful trade, so you should use more analytical tools; and the first step is to have the confluence areas analyzed before and from this, project the boxes.

In some cases, the boxes will not share the same edges as the confluence zone due to, for example, gaps between both boxes. To find out which prices are areas of resistance or larger supports, inner boxes of other boxes must be carried out between the current price and the nearest percentage that would be of 38.1% and in this inner box are made the subdivisions with the Fibonacci levels which create areas of confluence that show that zones are supports or greater resistance.

To make this concept clearer, two examples will be presented below. The first example will be NOK/SEK. It is a market with a bearish tendency so you want to find supports that the market could respect and bounce, or find supports to where the market could reach if you continue lowering. At the beginning of the confluence zones were determined and from there, the graph of the upper table was created. This box is then replicated at the bottom of the confluence zone and the Fibonacci levels are determined within this. Having these three boxes you can see the smaller supports that the market has before reaching the minimum price. To find out which of these are areas of larger supports would have to draw another box in the smaller one to have areas of confluence. After having the three boxes drawn, you can see a blue line where a major support is located because it is a zone of confluence and the market should respect these levels of prices.

Foundations of Fibonacci Extensions

The second example is the USD/CHF asset, which is at a similar stage to the first example. The procedure is the same, being the first step to find the confluence zones with the Fibonacci retracements because it gives more strength to the analysis of price projection to be achieved with the boxes.

Fibonacci Extensions

As mentioned in the previous articles, the market gives clues on where to draw the ranges and boxes that at the end show areas of confluence. Care should be taken with graphics that have gaps as this will generate the drawn boxes do not share the same edges.

 

Introduction to Fibonacci Expansion

Another method used by traders is the Fibonacci expansion and the objective of this tool is to determine the third oscillation. Unlike Fibonacci regressions, this tool uses the market fluctuations instead of the bias for its construction. With the Fibonacci expansion, traders will be able to obtain signals of how the waves evolve, and with the analysis of the waves could be projected where the end of the bias is and the following rebounds that will suffer the price.

The important percentages used by the tool are 0618, 1,382.1, 1.5 and 1,618; These percentages must be expanded along the graph to touch the axis and to verify that they are important areas that the market has respected in the past. Several ranges have created starting from the same starting point to find zones of confluence and thus to see zones that are resistances or supports. It is important to keep in mind that if you are going to trade on long horizons of time, you should observe more data from the past that will allow for a clearer picture.

As in the article “Foundations of Fibonacci Retracements”, with this type of analysis, if you want to find a major support, you must start from a high price and go down in the graph to a low price where there is a market signal that shows significance at this level. To know where the high price should be located, a market correction point should be chosen. After having a certain range for the analysis, a box is drawn from the higher price chosen to where the bias is triggered. Then a second range will be drawn starting from the highest point, which was used for the first box and lowered in the graph to where the Fibonacci ratios seem significant. When both boxes are subdivided into the Fibonacci ratios, there are confluence areas which represent larger supports or resistances, which will be added to the confluence areas analyzed above. The short-term confluence zones will serve in the long term and vice versa, so it`s suggested to observe different horizons of time to appreciate various important levels. Using the Fibonacci expansion as given by the various trading programs and programming correctly, the graph of the market should be seen in the following way where, as with Fibonacci retracements, areas of confluence should be found to know that Fibonacci ratios are higher supports for the market.

Forex Academy: Foundations of Fibonacci Extensions

Elliot Wave Principle

Elliot’s principle is based on the discovery of Ralph Elliot who discovered that the price of the action was not random, on the contrary, it follows a certain logic and order. Elliot saw the same patterns repeating in different cycles, which reflected the prevailing emotions of investors. The movements were called waves. The basic interpretation of Elliot’s principle is that every action has its reaction. When there is a bullet market there are 5 waves moving in the direction of the bias and after this is exhausted there is a three-wave movement. In the next graph, you can see the waves that compose a bull market. The waves numbers 1,3 and 5 are impulse waves and numbers 2 and 4 are correction waves. While the bias exemplified by the letters shows the correction of the whole upward bias.

Elliot Wave Principle

Having explained the principle of Elliot’s wave can be related to the Fibonacci expansion. As mentioned before, the Fibonacci expansion will allow projecting an objective price to where the market price will reach, the Fibonacci projections are calculated after an impulsive phase is produced with its subsequent correction. The projection of 0.618 and 1 is usually used for the waves 5 once the waves 3 and 4 are located, the projection of 1,618 is usually given in the waves 3 once we have located the waves 1 y2. Finally, the projections of 1 and 1,618 usually appear in corrective waves C when the waves A and B are already located.

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Foundations of Fibonacci Retracements

As it shall be further developed throughout this article, the first step when applying the Fibonacci method to construct support and resistance levels of a broader price trend is to identify and connect lower and higher points of wave impulses before a bullish move, and higher and lower points when the move is bearish.

It is important to notice that Fibo percentages of any range when taken from high to low and from low to high correspond to 100. For example, as it is shown in the graph below, if one connects the higher and lower price levels of a bearish wave, the distance between the highest point and the 61.8% retracement equals 38.2% retrace if the connection was to be made from the lowest to the highest points in an inverted symmetric wave. In other words, Fibonacci retracements determine portions of the wave that coincides to 100 when summed up, so that the high price is to 61.8% as the lowest price is to 38.2%. The observation described above has immense implications when attempting to predict the strength of price after a breakout of a given cluster in concordance with other analytical tools. For instance, a 61.8% retracement would indicate that the counter-move is deep enough for us to regard price as losing steam in a broader trend so that a break higher or lower is more likely to complete the 38.2% extension. After all, Fibo ratios are, like any other technical tools, instruments of price prediction and not written-in-stone dogmas.

Foundations of Fibonacci Retracements

The graph above is taken on the USD/CAD and shows the simplest process of connecting the highest and lowest price points of a bearish wave in order to determine resistance levels of a possible retracement move.

When applying Fibo techniques to determine support and resistance price levels, it is important to avoid the following very common mistakes:

  1. Not any High or Low should be plugged with every Low or High to construct resistance or support levels respectively. The reason for this is that;
  2. Not every time interval has the same robustness, i.e., faster time-frames could see the complete counter-move as profit-taking without negating the impulse of a broader trend while a smaller counter-move of a broader time-frame could also be the completing of a broader wave.
  3. Depending on the chosen time-frame of the graph, a wave can be completed or not, thus the Fibo levels are correctly or incorrectly constructed. For example, some authors suggest that it is best to build Fibonacci retracements levels in ranges that include strong price impulses; or ranges when a subsequent sub-wave marks the final thrust of the price.
  4. The time validity of any Fibo setup depends on both the underlying time-frame of the graph and the degree with which a charted range has developed. Put it differently, when considering price as a “living entity”, it is relevant to notice that every technical setup is valid to a certain point and time.

Consequently, constructing Fibo retracement is far more complex than simply connecting some random Highs with Lows or Lows with Highs. Albeit the popularity of Fibo techniques, mainly due to its predictability power, they are only a method that should, in fact, be combined (better to say, completed) with other techniques. The cornerstone of Fibo retracement (and extensions) relates to the degree of robustness of the resulting pivots in terms of the strength with which such price levels succeed in preventing price breakouts, i.e., how well they serve as thresholds that manage to “hold” price within a given range in time and frequency.

It is typically assumed that robust support and resistance levels are the results of using Fibo tools from different divisions and sub-divisions of a certain price range. In other words, any price wave (i.e., oscillation) can be circumscribed in broader waves when observing the chart in a slower time-frame. For example, an 800-pips wave on a monthly chart could easily contain 10 sub-waves on a daily chart and 100 mini-waves. By incorporating slower charts, i.e., wider ranges, we achieve more robustness to the analysis. Adding multiple time-frames allows us to transform simple price levels into clusters and when such areas prove to consistently contain price, they become pivots.

A multi-dimensional approach is belonging (in its simplest form) to a third analytical methodology known as relational. Every trader must print robustness to the price levels he constructs so that a faster and more frequent scalper would combine the 5, 15 and 60 minutes charts while a long-term and more fundamental oriented trader would consider the 4 hours, daily and weekly charts. That leads us to the assumption that there is no “correct” or “incorrect” way to apply Fibo when building up supports and resistance levels; a construction is better or worse depending on how much it fulfills the needs of the trader.

Fibonacci Retracements

In the graph, you can see how the Fibonacci retracements should be applied if you want to find market resistance. Also, you can see that the market respects on several occasions important Fibonacci percentages such as 38.2%, 50% and 61.8% over the monthly period.

In the second example, you can see how Fibonacci retracement should be plotted to find market supports. The range was drawn from the bottom to the top of a bullish trend before subdividing the range to find market supports.

Foundations of Fibonacci Retracements - FA

How to find the range to apply Fibonacci if the market is constantly expanding and shrinking continuously and the oscillations are not symmetrical? To start creating the ranges, there are occasions where the market gives the starting points to locate these ranges. For example, when there are gaps in a bearish market, you can locate the 50 Fibonacci percentage right in the middle of the gap trying to get it aligned. But it is not enough to align the line of 50% with the gap, it is necessary to observe that the high and low prices and the subdivisions are respected by the market in different horizons of time. For this, the subdivisions must be plotted to the axis so will be easier to see if the market has respected these points in its various oscillations. In addition, some points of the subdivision although they have not generated a rebound of the market, can be areas where it begins to develop a strong trend whether bullish or bearish.

After the correct range is selected, the question arises as to whether Fibonacci subdivisions within the range are major resistances or supports. To answer this, you must define a second range with the same starting point of the previous range, but with a different length. When these two ranges have been created, an entry goal will be generated that is called a confluence zone (i.e., price cluster). This area of confluence is formed when different Fibonacci ratios of several ranges overlap each other, showing that there are areas where Fibonacci levels fall at the same market price, it should be clarified that they are not necessarily the same percentages of the ranks.

The confluence areas are tipping points in the price and these areas determine higher supports or resistances. Already knowing the areas or prices that are major resistances or supports, it will be possible to project the direction of the market in the future because it will be known which areas will generate a rebound in the market, or if it is the case that the market breaks it will trigger a strong movement when the market continues its tendency without rebounding. With this knowledge of important points, you can put stop loss points if the market rally takes an unexpected direction or if it exceeds areas of confluence.

To be more confident which will be the correct direction of the market, we need to create a third rank with their respective subdivisions. When the third rank is made in the market, we must be sure that its subdivisions have been respected by the market in the past more than once to ensure that they are not minor resistances or supports. With the third range already made, it will be possible to see sometimes that there is more than one zone of confluence between the subdivisions of the ranks. A key element will be to locate the stop-loss outside of the confluence zones because if it is located between these will not achieve the goal of stopping the losses but possibly stop the gains if a rebound is generated in the areas of confluence. It is also important to mention that Fibonacci ranges should be larger when the trade is long term to be able to observe the entire market panorama than in a short-term position and therefore also the stop loss point will be farther away in long-term horizon operations.

For example, the following graph shows the EUR/USD with three ranges traced with Fibonacci retracements. As you can see, there is a confluence zone around the price 1,19949 since several of the subdivisions of the ranks coincide at this point, forming a major resistance as it began to trace from a low price to different high prices. Another example to see the stroke of the three ranges and their confluence zones is the next graph of the AUD/USD, where you can see several areas of confluence that will be major supports given the way the ranges were plotted from a high price to different low prices. Below the area of 0.89870, there is a major support as well as the level of 0.69470.

Fibonacci Retracements Chart

Fibonacci Chart

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Introduction to Fibonacci Analysis

Fibonacci analysis: A mathematical ground to construct support and resistance price levels.

One of the most complex aspects of trading certainly has to do with risk. How to measure and manage it regardless of any given set up or market environment or direction of the price (i.e., whether it is bullish or bearish). Potential profit and risk are thus correlated concepts; consequently, higher yields imply higher risks and vice versa. The main objective of any sound price analysis is then to maximize profit by keeping risk tightly under control; or, in practical terms, to preserve profit from running off in the long-run. However, the complete elimination of risk is nothing more than an illusion, what truly matters is to make it compatible with the preferred profit-generating setup, and it all starts with recognizing such risks and controlling them through the application of a wide range of tools. Despite the complexity of risk management, novices should not be discouraged; after all, even the most experienced traders still fail when applying their preferred tools, sometimes due to a know-it-all attitude, and because such tools are not comprehensive enough to account for all market conditions.

Fibonacci-based techniques are powerful enough to dedicate a complete set of articles; they will cover the conceptual basics, some easy-to-digest mathematical grounds, and of course, practical ways of applicability.

The Fibonacci sequence is an infinite sequence of natural numbers, which begins as follows –

0,1,1,2,3,5,8,13,21,34,55,89,144, 233, 377….

Starting with 0 and 1, the following numbers are the sum of their two predecessors. The golden ratio, on the other hand, is a universal law that explains that everything that grows and decays, evolves. Trading in financial markets is just one of the varied ways to apply the sequence. The golden ratio is a continuous geometric ratio resulting from a straight line between two number A and B. The straight line is divided into a segment longer than the other, and the total A + B segment has the same ratio to the more extended segment A as the long segment A has towards the shortest segment

Introduction to Fibonacci Analysis

The relationship would be written as follows: A + B: A: A: B. The golden ratio is an irrational number and the positive solution to this relationship is 1.61803398874989 … This relationship is found in some geometric figures and in nature, as for example in the shell of Nautilus, a species of mollusk.

Fibonacci

This golden relationship is viewed as an aesthetic and even divine character for some people. When a Fibonacci number is divided by its predecessor, a ratio is created, and, as those numbers become larger this ratio will approach the golden ratio.

The power of Fibonacci when added as an extra tool of market analysis lies in the fundamental observation that price does not move in a linear fashion; instead, it progresses in oscillations that can match natural ratios therein described. Put it differently, Fibo ratios describe the way price naturally moves in either direction, so that every new “step” higher or lower (regard such moves as waves) generates price clusters known as pivots; such “barriers” if you will follow patterns where levels are “stationary” areas usually categorized as supports and resistance if price has a bearish (low) or bluish (high) bias if you will.

Through the Fibonacci analysis and Phi ratios, you can test the laws that follow the market and therefore if we follow these principles (instead of going against them), we will be able to anticipate future movements of the market in a more precise fashion. Here is precisely where Fibonacci becomes relevant, either to predict retracement of extension price levels.

It comes as straightforward that Fibonacci belongs to what traders categorize as “technical analysis” as complementary to “fundamental analysis”. As for the retracement appliance of Fibo, the anticipated price levels are setbacks that refer to the possible support areas where buyers re-enter long positions if the dominant trend is bullish; or resistance levels where sellers re-enter short positions if the dominant trend is bearish. These levels are constructed by drawing ranges between the extreme points of the analyzed movement and the distance between the limits of the range there are subdivisions that will be vertical distances and the key percentages of this distance will be 38.2%, 50%, 61.8%, etc.

Why are we talking about retracements? Because in the technical analysis it is known that the prices of an asset move in “tendencies” (waves) either bullish or bearish, but that trend is not continuous; on the contrary, it has levels where the price stagnates due to such resistances or supports levels, simply because the market does not have completely vertical movements but oscillations within that trend.

Given the confirmation of a setback in the price of an asset, Fibonacci retracements will seek to calculate the magnitude of this movement. To achieve this, the Fibonacci tool available in the trading platforms is used and the percentages are applied which are obtained from the Fibonacci series on the magnitude of the previous trend. The percentage of 61.8% is known as the golden ratio and is the limit of the quotient that is obtained from the division of an element of the Fibonacci series with its previous number as the series tends to infinity. The percentage of 50 is equivalent to half the advance of the main trend and the percentage of 38.2 is the result of the subtraction of the unit and the percentage of 61.8%. The above can be seen reflected in the following graph, which shows how a regression would look depending on the Fibonacci percentage.

Fibonacci Analysis

Needless to say, this article introduces the very basis of how Fibonacci ratios can be applied as means to anticipate price retracements (or extensions) in the simplest form; such a tool is nothing but a mathematical approach to the natural ways price develops in any given trend. Being able to draw support or resistance levels by connecting the highest and lowest levels of a certain wave is, however, the first step of the process of charting. More advanced applications refer to the construction of price clusters by, for example, relating different waves from a varied array of time-intervals. To put it differently, Fibonacci is the keystone of more complex methods of technical analysis, but that will be the subject of other articles.

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