# Fibonacci tools on the stock market

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In search of profits on the financial markets – be it on the stock exchange or on the Forex market, or elsewhere, we create more and more perfect (at least in our opinion) investment systems, which are assumed to be ever more effective. Although the truth is that in most cases (with appropriate capital and risk management) you can earn well with the effectiveness equal to the toss of a coin, i.e. 50 percent, as we know achieving such effectiveness is extremely difficult – otherwise almost everyone on the market would earn and not just a small fraction of investors. We demand more!

With 50% success, we want 60%, and with 60% we aim for 70%. And if someone says that they are 100% effective, they are 100% lying. When creating newer and newer strategies, we use more and more technical analysis indicators and oscillators, trying to automate our trading as much as possible. While this has many advantages, this approach to trading brings one major problem – the price is often forgotten. We focus so much on AT tools that we forget about the price chart. So why not use tools that focus only on current prices, instead of its derivatives resulting from more or less complex mathematical formulas?

One of the best (if not the best, but it’s a matter of subjective judgment) tools for analyzing price charts are Fibonacci indicators, which you will find by default on most trading platforms – for example on the MetaTrader 4 platform you will find them under the Fibonacci objects category. The six Fibonacci-based metrics are levels, ranges, channels, time zones, arc, and fan. We will talk about how each of them works later in the article. All Fibonacci objects are based on the so-called Fibonacci sequence, i.e. a sequence of natural numbers that is recursively defined as follows:

• the first term is 0
• the second term is 1
• each subsequent word is equal to the sum of the two previous words
• Thus, we get an infinite sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, etc.

The Fibonacci sequence was discussed by Fibonacci in his work entitled Liber Abaci in 1202. It has been operating under the name of the Fibonacci sequence since the 19th century, when it was popularized by the French mathematician Édouard Lucas.

Fibonacci numbers are strongly related to the so-called golden ratio, also known as the golden mean or the golden ratio. Its achievement is that the section is divided in such a way that the ratio of the longer part of the section to the shorter one is equal to the ratio of the entire section to the longer section – for such a relationship to occur, the length of the longer section of the section must be the geometric mean length of the shorter section of the section and the entire section. The ratio between the quotients of two consecutive terms of the Fibonacci sequence is an approximation to the golden number. These dependencies naturally occur in nature and are also used in painting (illustrations by Leonardo da Vinci), architecture (Pantheon), music (drums and Stradivarius violin), and also in financial markets.

## Leonardo Fibonacci

Leonardo Fibonacci, or actually Leonardo Bonacci, also known as Leonardo of Pisa, is an Italian mathematician who lived from around 1170 to around 1250. He is considered the most gifted Western mathematician of the Middle Ages. Young Fibonacci was educated in Africa because his father, a diplomat, was on a diplomatic mission in North Africa. Fibonacci has traveled, inter alia, to Egypt, Syria, Provence, Greece and Sicily. During his travels around Europe and the Eastern countries, he learned about the achievements of Arab and Indian mathematicians – including the decimal number system. He wrote many works, many of which, unfortunately, have been lost – the most famous Fibonacci publications are the aforementioned Liber Abaci from 1202, Practica Geometriae from 1220, Flos from 1225, as well as the lost Di minor guisa and Commentary on Book X.

## Fibo coefficients

We have already established that the Fibonacci sequence is an infinite sequence that begins with the words 0 and 1 and then consists of the sums of the previous two, which gives us the sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 , 55, 89, 144, 233, 377, 610, 987, 1597, etc. There are interesting relationships between the consecutive terms of the sequence, also called the golden ratio mentioned above. If we divide any number of the sequence by the number preceding it, we get a value oscillating around 1.61804, which is the golden ratio known in geometry, denoted by the twenty-first letter of the Greek alphabet – phi (φ or ϕ). The larger the terms we divide, the closer the result will be to the golden ratio.

As a result of a few basic actions, we can obtain the following Fibonacci coefficients, which are used in Fibo tools (this is what Fibonacci tools are called in short):

• 1 / 1.618 = 0.618;
• 0.618 * 0.618 = 0.382;
• 1.618 * 1.618 = 2.618;
• 2.618 * 1.618 = 4.236;
• and:
• 1 – 0.618 = 0.382;
• 1.618 / 0.618 = 2.618;
• 0.618 / 1.618 = 0.382
• 1 / 1.618 ^ 2 = 0.282

There are also investors who, apart from the levels 0.382, 0.618, 2.618 and 4.236, also use the level of 1.272 being the result of the square root of 1.618 and the level of 0.786 being the square root of the quotient of 1 / 1.618. In addition, a retracement of 0.5 is added to the Fibonacci levels, as it is generally assumed that in technical analysis the level of half the traffic is analytically significant. Additional factors are 0.886, which is the square root of 0.786 (and also the fourth-order root of 0.618) and 1.13 being the reciprocal of 0.886. There are several other coefficients, so the division into prime coefficients, coefficients resulting from primary operations on prime coefficients and additional coefficients are established.

• The main coefficients are: 0.618 and 1.618.
• The coefficients resulting from the basic activities are: 0.786, 0.886, 1.13 and 1.272.
• The additional factors are: 0.382, 0.5, 1.414, 2.0, 2.236, 2.618, 3.14, 3.618 and 4.236.

While all these numbers may seem quite complex at first glance, they are actually just a few basic steps. In addition, you do not have to count them, but it is worth knowing where they come from, especially bearing in mind that you may be looking for convenient places to conclude and close transactions on their basis. Nevertheless, the most important thing is to know how to plot them on the chart. Fortunately, modern trading platforms help with this. In the charts, the Fibo coefficients look almost trivial, because regardless of the selected tool, it is „only a few dashes”. So there is nothing to worry about. Let’s move on to the next section, i.e. to the available Fibonacci tools.

## Fibonacci tools

There are six core Fibonacci tools available on most trading platforms. These are: Fibonacci levels, also called Fibonacci retracements, Fibonacci ranges, also referred to as Fibonacci expansions, Fibonacci fan, Fibonacci arc and Fibonacci time zones (Fibo cycles) and Fibonacci channels. These tools differ from each other, but they are all based on the Fibonacci sequence and the dependencies between the successive words of the sequence, which you read about above. The most popular tool out of the six listed are Fibonacci retracements.

## Fibonacci levels

The method of measuring price movements by means of Fibonacci levels is based on the assumption that the previously mentioned golden proportions occurring in nature also appear on the price charts of financial instruments – at any time intervals and markets: stock, forward, debt, currency, etc. Of course, the sentences concerning methods are broken down, as is usually the case with technical analysis tools. However, this method is used by a large number of investors, which increases its effectiveness. The simplest application of Fibonacci levels is to set the last significant high and low on the price chart. The problem may be that determining these extremes is quite discretionary, and particular difficulties may arise in consolidations (in a strong trend, determining the last extremes is not a difficult task). The absolute difference between the determined extremes is the so-called unit segment. This segment is then divided in proportions that are Fibonacci coefficients and extended by Fibo coefficients greater than one. These levels are considered significant support and resistance limits for a given instrument.

## Fibonacci ranges

The Fibonacci range tool is very similar to the Fibonacci levels. It is used to determine the theoretical ending points of the movement continuation after correction. It measures not only the last move – as in the case of Fibonacci levels, but the last two moves – trend and correction. By measuring the trend wave, taking into account the correction wave, we can determine the levels at which the next correction or change of the trend may occur. The basic levels of expansion are 61.8%, 100% and 161.8%.

## Fibonacci time zones

Fibonacci cycles, or Fibo time zones, are Fibonacci levels reversed by 90 degrees – they move us from the price axis to the time axis. They also help determine potential turning points on the chart, but not on the basis of the strength and direction of price movements, but their duration. This tool measures how long it took to build the last wave and on this basis determines the moment when the next move should end.

## Fibonacci channels

Fibonacci channels are regular price channels based on Fibonacci coefficients that are parallel to the trend determined by the channel. The tool is therefore suitable for use during a period of stable and prolonged price movement, where clear parallel trend lines can be seen running along both the lows and the highs of the trend. With it, you can define subsequent channels in which the price may move after a change in the strength of the movement.

## Fibonacci fans

Fibonacci fans are a rarely used method of analyzing price charts, which is quite surprising as it is a very useful AT tool. Fibonacci fans are based on trend lines. When measuring a long trend wave, it plots several other trend lines with different slopes originating from the starting point of the trend. These lines indicate possible support or resistance levels. The most frequently used Fibo coefficients in this tool are 38.2%, 50% and 61.8%. Fibonacci fans are a slightly more complicated tool, because they are a method that combines both price and time.

## Fibonacci arcs

The last Fibonacci tool are Fibo arcs. By default, this tool plots 3 arcs relative to the local high or low that cross the trend line between this extreme and the previous opposite extreme at 38.2%, 50% and 61.8%. Like the Fibonacci fans, it is a tool that combines both the question of the price of the instrument and the duration of the price movement.

## Fibo tools – sample measurements

In this section we will discuss sample measurements made with all six Fibonacci tools described. A very important issue is their very precise determination, because otherwise their analytical effectiveness will drop dramatically – wrongly determined price movements, regardless of the chosen tool, lead to the fact that Fibo tools become practically useless.

Fibonacci levels are the easiest thing to do. We must use them to determine the last two extremes – the local minimum and the local maximum. In the case of a downward movement, we determine this movement from top to bottom, and in the case of growth from bottom to top. As in the picture below.

We set the Fibonacci ranges just like the Fibo levels, with the difference that we have to use this tool to capture both the latest trend and its correction. We set the upward trend from the bottom up, and its correction from the top down, and vice versa – we set the downward trend from the top down, and the correction of this movement from the bottom up. Here is an example.

We determine Fibonacci cycles in the same way as Fibonacci levels, with the difference that regardless of whether the last move was an upward or downward move, we mark the move from the earlier extreme to the later extreme. It should look like the chart below.

Fibonacci channels follow the prevailing trend, as long as, of course, the price is moving in a clear channel – otherwise there is no point in using this tool. With the first click, you set the angle of inclination of the channel, and with the second, parallel line, you set the width of the constructed channel. One of the lines must therefore run through the successive peaks, and the other line through the successive holes. Below is an example of determining the Fibonacci price channel.

Fibonacci fans are also determined after two consecutive extremes – successively the minimum and maximum in the case of an uptrend and the maximum and minimum in the case of a downward trend. This gives a fan below the North trend and above the south trend, as shown in the image below.

We designate Fibonacci arcs in the same way as Fibonacci fans – from bottom to top in an uptrend and from top to bottom in a downtrend. One small note here when it comes to the use of Fibonacci arcs on the MetaTrader 4 platform – to determine them well, it is necessary to select the appropriate scale in the tool parameters settings. Below is an example of the use of the Fibonacci arc.

## Fibonacci tools – summary

The investment decisions we make and the speculative transactions we make do not rely on predicting the future, reading tea leaves, guessing or tossing a coin. They are all based (or at least should be) based on probability assessment and appropriate risk and capital management. Anyone who has spent some time in the financial markets knows perfectly well that the smallest risk is taken at the points of changing the trend. Successful traders try to catch price movements at the very beginning, regardless of whether they are scalpers wanting to „catch” a few seconds of movement, whether they are day traders hoping to „tear” several dozen pips in tens of minutes, or are long-term investors who want to buy shares for the coming year. Everyone wants to buy in the proverbial hole and sell at the top. Unfortunately, this art is very difficult – if it were otherwise, everyone in the financial markets would earn a fortune, and we all know what the reality is.

The huge popularity of Fibonacci coefficients and technical analysis tools based on these coefficients is due to the fact that this method, as one of the few, allows to estimate with a high probability the place where the trend will stop, or at least start a correction. Of course, there are no strategies that give 100 or even 90 percent effectiveness – but here the Fibonacci ratios come in handy too. Their high accuracy allows for the setting of relatively close hedging orders, which greatly increases the ratio of potential profit to the total risk incurred. The negation of the signal generated by the tools based on Fibonacci coefficients is a quick and clear signal to retreat, i.e. close a lossy position. Speed ​​is key here, as the quicker admission of a mistake means much lower losses. However, it should be remembered that low losses in case of mistakes can only be achieved if the risk is properly managed. Too much capital involved in one transaction can (almost certainly) lead to large losses, which will have a negative impact not only on your account balance, but also on your attitude to trading on the financial markets and your willingness to continue learning.

Fibonacci ratios are truly excellent technical analysis tools. They are one of the most popular analytical tools in the arsenal of investors for a reason. Their popularity is probably only matched by support and resistance levels, price channels and moving averages, and maybe possibly also the MACD and RSI. Fibonacci tools can be used both on the stock market, for example in stock trading, and on the Forex market, bond market and all derivatives – futures, options, CFDs and other financial instruments. What’s more, they can also be used on all timeframes – from one minute scalping to weekly charts for long-term traders. There are few such universal tools in the world, and even fewer such universal tools, which additionally, despite their universality, do not lose their quality.

However, remember to use the Fibonacci coefficients with caution. Any trading signals – regardless of the tool, interval, time, instrument and market condition, should not be taken for granted. Introducing Fibonacci tools to your own investment strategies is very time-consuming, because properly drawing them on the chart requires a lot of experience – it is not enough just to set parameters and put them on the chart, as is the case with most indicators and oscillators. Besides, before you even proceed to the actual tests on your demo account, you need to decide which Fibonacci tools suit you best – whether you want to focus more on the last move, or the entire sequence, the strength of the predominant side or the duration of a given situation. Of course, you can change your mind later, but it will be good if you understand what best fits your investment system. Absolutely do not follow what others have said, what you read on internet forums or what you read in an internet ad. The tool that appears in your hands must be tested personally by you and based on your experience you must decide whether you want to risk your hard-earned money based on the indications of this tool, because if you make a mistake, you will have to make up for your losses – no one unfortunately another one won’t do it for you. Be careful, be suspicious, but don’t give up and give up.