The ULTIMATE Beginner's Guide to FIBONACCI Trading

Welcome to the ultimate beginner's guide to Fibonacci trading. In this guide, you will gain free access to a detailed understanding of how the various Fibonacci trading tools can be used for generating precise and timely trade entries and exits in any market, in any time frame.

We are not going to talk only about the good side. You're also going to learn the nasty pitfalls you will encounter if you decide to use this method. Most trading guides simply don't do that. The nuances and detail of how all this stuff works are not written in technical analysis books; it comes from experience.

Let me briefly go over the table of contents here so you can have an idea of what you're going to learn in greater detail. We start with the origin and mathematics of Fibonacci numbers and Fibonacci ratios. Next, we'll jump right into the many Fibonacci trading techniques. We'll cover price-based tools, time-based tools, and dynamic tools. We'll also observe many examples of these techniques. Throughout the examples, I'll demonstrate certain tricks about these tools and also some of the unknown pitfalls associated with them. We'll talk about how to use Fibonacci trading tools with other trading techniques to maximize results. We'll talk about different chart scales and how that affects certain Fibonacci techniques. We'll also talk about the possibility of using other types of ratios beyond Fibonacci. We'll talk about the most important concept you must keep in mind when trading with Fibonacci tools in order to reduce the confusion that can emerge and keep things as simple as they can be. Finally, we'll talk about advantages and disadvantages in general terms. As I often do in my guides, the idea here is to show you the good and the bad side of trading so you can make more rational decisions, which will ultimately lead you to save time and money in your learning journey. Without further ado, let's begin the course by talking about the origin and mathematics of Fibonacci ratios.

In the year 122, an Italian mathematician called Leonardo Pizano, which later gained a nickname Fibonacci, wrote a book called Liber Abaci, which roughly translated to English means "The Book of Calculation." You can find a modern translation of Liber Abaci written by Lawrence Sigler on Amazon if you're interested. Fibonacci's Liber Abaci is partly known for introducing the Hindu-Arabic numerical system to Europe. The Hindu-Arabic numerical system is the one we are familiar with today, composed of numbers from 0 to 9, which is a lot more efficient than the Roman numerals that were used at the time in Europe. So, part of the reason we used numbers from 0 to 9 nowadays is because of Leonardo Pizano.

Another reason why Liber Abaci is famous is because that's the book where Leonardo Pizano introduced the Fibonacci sequence, which became very famous for reasons that will become clear in a few moments. Let's now dive into the mathematics of the Fibonacci sequence so you can have a better understanding of why this is so important and why it became so famous. The Fibonacci sequence is very simple to understand. It's a sequence of numbers that start with zero and one. To calculate the third number in the sequence, we add the first two numbers. So, the third number in the sequence is equal to 0 + 1, which of course equals to 1. To discover the fourth number, we repeat the same process that we used to discover the third number, but instead of adding the first and second, we add the second and third numbers. In this case, the fourth number is equal to 1 + 1, which equals 2. Of course, using this process, you can find the numbers of the Fibonacci sequence, which is infinite. We can summarize this process using a very simple formula: F(n+1) is the next number in the sequence, F(n) means the current Fibonacci number, and F(n-1) is the previous number in the sequence. So, if you want to find out the next number in the sequence, all you have to do is to add the current number and the previous.

The Fibonacci sequence is closely related to another sequence called the Lucas series. At the end of the 19th century, the French mathematician Edward Lucas published his studies of the Fibonacci sequence, as well as other integer sequences, in a book called "Theory of Numbers." The process to find a Lucas sequence is the same used in the Fibonacci sequence, but instead of starting with zero and one, the Lucas sequence starts with two and one. The reason the awareness of the Lucas sequence is important is that the difference in the initial two numbers leads to a completely different sequence of numbers compared to the Fibonacci sequence, and yet the two series share many mathematical properties. We can calculate any term in the Lucas series using the Fibonacci series using the following formula. Both the Fibonacci series and the Lucas series are used in technical trading tools, as we'll explore in greater detail later on.

The first interesting idea related to the Fibonacci sequence in financial markets is that the method of construction of the sequence shows the unbreakable and ongoing link between past, present, and future. In other words, if we imagine the Fibonacci numbers are a time series, future Fibonacci numbers are a natural consequence of numbers in the present and in the past. That's an interesting parallel with financial markets because future prices are also a consequence of present and past prices, to some degree. This is perhaps one of the reasons why Fibonacci numbers started to be used in trading. The core idea here is that price evolves over time, following some of the same properties of how Fibonacci numbers evolve over time, once we treat them as a time series.

The important feature of the Fibonacci series associated with trading relates to what are called Fibonacci ratios. So, let's dive into that idea. The Fibonacci sequence begins to draw the interest of traders when we look at what are called Fibonacci ratios. These ratios are discovered when we divide adjacent or non-adjacent numbers in the sequence. For example, let's take two adjacent numbers in the Fibonacci sequence and calculate the ratio between them. We'll consider the two adjacent numbers, 144 and 89. If we plug these numbers into the Fibonacci ratio formula, the result will be 1.618.

To understand the importance of this number, let's observe what happens when we calculate the ratios from the beginning of the Fibonacci series up to higher numbers. In this graph, we can see the evolution of the ratios as we go further into the Fibonacci sequence. Notice that the ratios oscillate in the beginning, in the initial and small numbers of the sequence, and then the ratios dampen down to the value of 1.618 in the higher numbers of the sequence. It doesn't matter which pair of adjacent numbers you choose to calculate the ratio; it will always return the value of 1.618. This is known as the golden ratio, also referred to with the Greek letter phi.

As it turns out, the same behavior can be found in the Lucas sequence. This is a unique phenomenon because the Lucas sequence is composed of a completely different list of numbers in comparison to the Fibonacci sequence. In mathematics, this means that the ratios in the Fibonacci and Lucas series asymptotically approach the ratio of 1.618 as we go to infinity after the initial dampening effect. No matter which pair of adjacent numbers you choose to calculate the ratio, either in the Fibonacci or Lucas series, the result will always be 1.618.

Let's now quickly explore a mystery related to this number, 1.618. We saw how the ratios, both in the Fibonacci and Lucas series, approach phi as we move further into the series. However, the golden ratio also has a unique geometric property. The ratio 1.618 is the only ratio that satisfies the following condition: In other words, if you divide the length of the BC segment by the length of the AB segment, you get 1.618. If you divide the length of the AC segment by the length of the BC segment, you also get 1.618. It's this very unique property that has inspired many works of art and architecture that follow a certain pattern of symmetry and proportion related to Fibonacci numbers and ratios. If you want to go deeper into this particular subject, there's a very interesting book about it called "Golden Ratio: The Divine Beauty of Mathematics" by Gary B. Meis.

This course only demonstrates the very tip of the iceberg of how Fibonacci numbers and ratios occur in nature, art, and human behavior. When we recall that price action analysis is the only form of visual market analysis, we can see why the golden ratio began to be used by traders. Price action analysis is a geometric way of analyzing financial markets, so it logically follows that traders will inevitably attempt to find different geometric patterns, ratios, and proportions in the price charts.

The pioneer in the use of Fibonacci ratios in trading is Ralph Nelson Elliott, the man behind the development of the famous Elliott Wave Theory in the 1930s. The golden ratio is known as a mathematical constant. The reason the golden ratio and other Fibonacci ratios began to be used in trading is because mathematical constants capture some sort of fundamental feature of reality. So, let's explore this idea a little more deeply. Mathematical concepts such as phi are tremendously important because they reveal fundamental relationships and structures of various related and unrelated phenomena of the natural world, as well as mathematical theories. And because of that, mathematical constants have predictive power.

The golden ratio appears in many different places in nature. For example, the number of petals in flowers are usually Fibonacci numbers. The famous Nautilus shell follows a logarithmic spiral that approximates the golden ratio. The wings on a butterfly also follow a similar spiral pattern, approximating the golden ratio. The family tree of bees follows the Fibonacci sequence. Fibonacci numbers can also be found in the relation of proportions in the human body. We can find the same Fibonacci spiraling pattern in the broader sense in the case of galaxies. Another example of that broader scale is the shape of storms. Interestingly, we can find Fibonacci relationships in the smaller scale, as is the case of the DNA molecule, for example. The list of examples like that is enormous. But the question that emerges here is whether we can find Fibonacci relationships in behavioral phenomena such as the financial markets.

Let's dive deeper into the relationship between Fibonacci and behavior in the financial markets. The reason Fibonacci ratios began to be used in trading is because people like Ralph Nelson Elliott believed that Fibonacci ratios were embedded in the way everything works, and that, of course, includes how human beings behave. This points to the possibility of Fibonacci relationships being some sort of universal truth.

When we talk about financial markets, we have to make a few distinctions. It's a well-known and accepted fact that Fibonacci trading tools can cause market reactions due to the self-fulfilling prophecy effect, and that is a behavioral phenomenon. In other words, Fibonacci techniques can cause market reactions because Fibonacci traders act as if these techniques are true. There is no question about the existence of this type of behavioral effect in the markets. However, there is also the possibility that Fibonacci techniques can describe market reactions due to reasons unrelated to the self-fulfilling prophecy effect. In other words, there is the possibility that such tools describe certain aspects of the market from a mathematical point of view. Even though that is a possibility, we cannot prove that with any degree of certainty due to the way markets work. Trading the financial markets is known as a game of incomplete and asymmetric information, and the market is not just composed of Fibonacci traders; there is a diverse set of market participants. That means that there is no sure-fire way of distinguishing between coincidence and causality. There are only ways of decreasing the chances of certain setups and techniques being a miracle coincidence, and that is through integration.

When Elliott developed his theories about how the market moves following Fibonacci relationships, the self-fulfilling prophecy effect could not be part of the equation because nobody used Fibonacci ratios in trading. So, that's an interesting idea that points to the possible mathematical validity of these tools on top of their behavioral validity. Whether Fibonacci relationships work just because of behavior, or just because of mathematics, or both, is not that important. We know that their behavioral effect is a fact, and that makes it worth learning about them.

The golden ratio is the most important Fibonacci ratio by far, but it's not the only powerful ratio. We can arrive at these other ratios following fundamental mathematical operations with the golden ratio, like you can see here. Once again, the reason why one would do this is not clear, but the fact is that many traders do. In trading, there are also what are called higher-ordered magnitude ratios beyond the 1.618 and the 2.618. Traders also use the 3.618 and the 4.618. It's also common to find ratios such as 0.5 and 1, which occur at the very beginning of the Fibonacci sequence. Another way of arriving at apparently unusual Fibonacci ratios is to calculate the ratio between non-adjacent numbers in the series or to invert the ratio.

Let's take the higher numbers of the Fibonacci series where the ratios stabilize and perform a few calculations with adjacent numbers. We get the 1.618 and 0.618 ratios. Calculating the ratios between one number and two numbers back, we get 2.618 and 0.382. And calculating the ratios between one number and three numbers back, we get 4.236 and 0.236.

One important detail regarding Fibonacci ratios and trading is that these ratios are used in percentage terms. To transform ratios into percentages, all you need to do is to multiply the ratios by 100. In trading, Fibonacci ratios are used to find where significant price reversals will occur. This is useful in two distinct and important ways: to find optimal trade entries and to find optimal trade exits. Fibonacci levels are also seen as types of support and resistance levels.

Now that we have a solid mathematical understanding of Fibonacci numbers and ratios, where they come from, and why we should care about them, it's time to understand how these ideas are applied to trading in more practical terms. Fibonacci trading techniques can be used in three main ways: in terms of price, in terms of time, and also in terms of a combination of price and time. The most common application of Fibonacci tools occurs in terms of ratios and price. In that sense, we have four main variations: the retracement, the extension, the expansion, and the projection. These are also called price-based Fibonacci tools because they only consider the y-axis of the chart.

Before we understand the difference between these four price-based ratios, we need a concept of range. Range is simply the vertical distance between a low and a high in the chart. It's also helpful to define the most common Fibonacci levels used in trading. With that established, let's move on to the most common price-based Fibonacci tool, which is the Fibonacci retracement.

The Fibonacci retracement is a way of measuring the probable price level where a pullback will occur within the price range. It's often the case that pullbacks will happen at well-established Fibonacci levels. One extremely important tip here is that you must observe which Fibonacci retracement ratio price reacts to. That's how you know which Fibonacci level to use; otherwise, you'll be confused since there are many of them. One important idea here is that the depth of retracement can provide some information about the power behind a trend. For example, a shallow retracement generally means that the subdominant market player is weak; therefore, when the trend resumes direction, the movements tend to be more powerful. If a deep retracement occurs, it generally means that the subdominant market player is powerful. When the trend resumes, it's probably not going to be as powerful as in the case of a shallow retracement.

Let's observe some examples of the Fibonacci retracement technique. In this chart, you can see the EUR/USD 1-hour time frame. Notice that price has created an upper price movement and it has started to retrace to the downside. At this point, we can draw the upper price range from the low to the high using the Fibonacci retracement tool, like so. Notice that the current candle is now reacting to the 38.2% retracement level, a very common Fibonacci level used by many traders. Notice that price does seem to be interacting with it. Notice also that this is a rather shallow retracement, meaning that the sellers that are producing it are not very strong in comparison to the buyers against which they are retracing. In this next chart, you can see how price takes off from that retracement level with a lot of power. Once again, the key here is observing which Fibonacci level price responds to and what kind of reaction price produces.

Let's now look at an example of a downward price range in a 10-minute chart of Nasdaq futures. In this chart, you can see a downward price movement and then price retracing to the upside. At this point, we can draw the range by plotting the Fibonacci retracement tool from the high to the low. Notice how price retraces all the way to the 78.6% level, which is considered to be a deeper retracement simply because it's higher than 50%, and then price creates an inside candle, showing that the market has indeed found a barrier at that level. In this next chart, you can see how price went to the downside from that point forward. Even though some would categorize this a strong downward trend, it is not as strong as the upper trend in the last example.

At this point, you might be thinking that this is a sure-fire way of catching pullbacks, but as is the case with any technique, we can find many instances of failure. Take a look, for example, at this 10-minute chart of the Pound/Yen. We see an upper price movement and then price retracing to the downside. At this point, we can draw the Fibonacci retracement based on the upward range, like so, and immediately we see the price reacted to the 78.6% retracement level with a spinning bottom candle formation, and then right after, price produces a candle with a high body percentage, which for all intents and purposes represents high bullish power. In this case, Fibonacci traders would consider this setup as almost perfect. If we move to the future, however, we'll see that it failed. What was seen as the beginning of an upper price movement was actually the beginning of a small retracement to the upside.

This is not meant to discourage you to use Fibonacci ratios; it serves to show you the reality of not just Fibonacci ratios, but the reality of any trading technique. There's no technique that works all the time for reasons that go outside the scope of the course. This is the reason why the most important principle in technical analysis is integration, meaning the combination of as many techniques as possible in order to increase the chances of success in a trade. Even with that, failure cannot be avoided; it can only be decreased.

In summary, Fibonacci retracements are used to pinpoint the end of a pullback, but that assumes the trader already knows the overall trend direction. Knowing the trend direction is dependent on other modes of market analysis, such as Elliott Wave Theory, Dow Theory, Wyckoff Method, or a combination of these three. I have three courses here in the channel for each one if you want to go deeper into these subjects. Fibonacci tools work remarkably well with Elliott Wave Theory, for example.

Let's now move on to the second price-based Fibonacci tool, which is the extension. Observe that in the retracement, we use Fibonacci ratios to determine a price reversal within the range. In the Fibonacci extension, we attempt to pinpoint important levels of support and resistance, and therefore reversal points, below an upward range or above a downward range. Another way of thinking about this tool is that it is an extension of the retracement tool. Let's observe some examples of that.

In this 45-minute chart of Bitcoin versus the US Dollar, we can see an upward price movement and then a downward retracement. By plotting the retracement tool following the upper price range, we can see the price reacts to certain levels like the 38.2% and the 50% as support and end up failing to initiate an upward price movement afterwards. Notice also that price produces reactions to the 23.6% level but has resistance moving price into the future. We can see that it goes outside the retracement zone into the extension territory, and it clearly reacts to the 100%, 127.2% extension level by producing a massive high-wave pattern. The high-wave is basically a high volatility version of the spinning top or bottom formation. The self-fulfilling prophecy effect would really kick in in a situation like this when most Fibonacci traders look at the massive lower shadow reacting to the 127.2% extension level. After that, we can see that price indeed continues to the upside. The lesson here is to notice the failure of the retracement tool and the success of the extension tool.

This is, of course, not the easiest of examples, especially when you realize that you can be too focused on the minor details of how price reacts to every single Fibonacci ratio. What you need to keep in mind is that most traders react to the obvious. So, if you want to take advantage of the self-fulfilling prophecy effect built into this method, we should also try to put the obvious at the top of the hierarchy of what should be considered. Once again, this cannot be stressed enough: to really trust these Fibonacci ratio levels, you must integrate them with other tools. A quick example of that is when we plot a modified Schiff Pitchfork using the upper price range as the B and C anchoring points of the Pitchfork, and in a previous important high as point A, and then we duplicate the Pitchfork to the downside. That would be a simple type of integration with the 127.2% ratio. In this case, notice how the lower shadow of the high-wave candle pattern touches both the Fibonacci ratio and the lower line of the modified Pitchfork simultaneously. As you're probably able to tell, there is science and art in identifying precise market edges.

Let's take another example now in the 4-hour chart of Light Crude Oil Futures. We can see price making a downward price movement and then retracing to the upside. By plotting the retracement tool from the high to the low of the range, we get the following ratios. Notice that price already went into extension territory. Recall that the extension territory is above the retracement zone when the range is plotted in an upward price movement; in other words, the extension tool uses a downward price movement to project an upward price movement, in the same way that an upward price movement can be used to project a downward price movement. As we saw in the previous example, in this next chart, you can see the price ends up going to the upside and producing a reaction to the 200% extension level. The reaction is outlined by a shooting star candle formation, which also happens to be a fractal candle. In this case, this can definitely be used as a short trade setup by Fibonacci traders, especially because price has produced five waves to the upside. However, moving into the future, we see that it would be a failed setup because price continues to rise after forming an expanding pivot formation that goes back to the initial demand zone. The good news is that price stops at the 261.8% ratio and produces a reaction with a spinning top formation that is also an outside candle and a fractal candle. Looking at this from this point of view, we can reimagine the Elliott wave count, although Elliott wave traders would disagree that this is a valid wave count because wave 4 retraces back into the territory of wave 1.

In the next chart, you can see that the Fibonacci extension does work as intended. You can even see that price starts to go down and retraces back up to the 200% extension after encountering this demand zone. It goes down even further after that. Once again, there is nothing special about the 261.8% ratio in relation to the 200%; price reversed at a 261.8% level because that was the level where there were enough factors to put price into a self-reinforcing cycle. A lot of times, you'll find that other ratios will work. This is why we need to focus on the intersection of techniques instead of getting too worried about specific techniques. Notice that the setup that failed initially is basically the same setup that worked a little bit later. This is why you need to understand how and why these techniques work, otherwise you quickly lose confidence, and you'll hesitate too much. Failure is definitely part of trading; there is no way of avoiding it.

Let's now move on to the third price-based Fibonacci technique called expansion. Previously, we saw how the extension occurs below the retracement territory if the range is plotted in an upper price movement, and above the retracement territory if the range is plotted in a downward price movement. The expansion simply represents the opposite side. So, in an upward price movement, the expansion will occur above the retracement territory, and in a downward price movement, the expansion will occur below the retracement territory. That also means that to use an expansion, we must invert the way of plotting the range, otherwise we would have to work with negative Fibonacci ratios, which is certainly possible, but it can be unnecessarily confusing. In TradingView, to measure the range in an upper price movement, we plot the retracement tool from the high to the low of the movement. To measure the range in a downward price movement, we plot the retracement tool from the low to the high. That's when we're dealing with expansions.

Let's take a look at an example of expansion in the 4-hour chart of the S&P Futures. We begin by plotting the expansion in the price movement that originates the uptrend, like so. Immediately, we can see the price went to the 200% ratio and returned to the 78.6% ratio in a suggestive way. Moving price into the future, we can see the price reverses significantly at the 423.6% ratio, and we can also see the price found a strong resistance that was later used as support in the 261.8% level. Recall that all these levels are based on that little upward price movement at the beginning of the trend.

In this other image, we have the 5-minute chart of PayPal. By plotting the Fibonacci expansion in the downward price movement at the top of the chart, we find a similar situation to the previous example. By moving into the future, we see price reacting to the 200% ratio, finding support and resistance at a 261.8% ratio, and exhausting its power at the 423.6% ratio. Recall that this ratio is not arbitrary; it's the ratio that occurs when we divide one Fibonacci number by a number three positions back into the series. Once again, it's not really possible to prove if this type of thing happens because Fibonacci ratios underlie the behavior of prices, or because there is a behavioral element at play, or a combination of both. The fact is that these relationships can be frequently found in all markets, in all time frames.

The fourth price-based Fibonacci tool is the projection. The projection depends on two opposite ranges. In other words, to use a Fibonacci projection, we need an upward price movement followed by a downward price movement, or vice versa. The projection works exactly like the expansion, but the ratios are shifted by the difference in size between two ranges. On TradingView, the projection is called Trend-Based FIB Extension. The term "trend-based" means that the Fibonacci tool is based on two opposing ranges.

In this chart of the 5-minute USD/Yen, we can see a normal expansion based on this downward price movement, and we can see that price reaches the 361.8% level and transitions into a sideways market. However, we can also see that right after the price movement being used to plot the expansion, there is a small pullback to the upside, meaning an adjacent and opposing range. We can use this pullback in alignment with the previous down movement to plot a Fibonacci projection, like so. By doing that, the 361.8% projection ends up being more precise because it's based on more price information. Still in the USD/Yen, but now in the 1-minute chart, we can see an instance where using the projection would be a worse alternative. In this image, you can see the expansion working well with the 361.8% ratio. If we shift the expansion to a projection by considering the adjacent and opposing price range, like so, we can see that the 361.8% ratio would fail to capture price.

You might be asking yourself how you are supposed to know which Fibonacci tool to use if sometimes they work and sometimes they fail. The trick about this is quite simple: the Fibonacci ratios that have a higher chance of working are the ones that happen in clusters. In other words, when you see ratios from different ranges and/or different tools happening roughly in the same price level, there's a higher chance that these levels will work well as support and resistance. The reason is simple: different Fibonacci traders look at different places in the chart to plot these tools. When you act at their intersection, there is a higher chance that price will enter a self-reinforcing cycle at these clusters, which is what you're after. This is the same principle we see across different methods within technical analysis and outside technical analysis as well. This can be confusing because sometimes one ratio is enough to produce that effect, but if we want to maximize the chances of reliably using Fibonacci ratios, we must think about what has the greater chance of working over many iterations. Needless to say, observing Fibonacci clusters is harder than observing single ratios, but that's what happens when you increase the quality of the signals you observe; they happen with less frequency.

Let's observe a few examples of how price-based clusters work. Here we have the 15-minute Euro/USD. One obvious projection we can draw here is this one. We can see that a significant reversal ends up happening at the 61.8% projection level. However, like I said previously, different crowds of Fibonacci traders will look at different places to plot price-based tools. One example is this projection on a small set of price ranges. Observe how the blue 161.8% level roughly correlates with the black 61.8% level. It also correlates with this other projection plotted on small price ranges just before, with a 361.8% level. In this case, it also correlates with the 127.2% extension level plotted on this large upper price movement, and also with a 261.8% extension level plotted on a smaller price movement, and in the 261.8% extension in this older upward price movement. You get the idea: many powerful Fibonacci ratios happening roughly in the same level. That's how you increase the power of these Fibonacci ratios. Needless to say, everything has a price; it can be very confusing if you plot all these ratios at the same time in the chart.

Let's move on to a different example now in the 1-hour chart of the US Dollar versus the Canadian Dollar. Notice that we have a well-defined downtrend. In this example, by plotting a Fibonacci projection at the beginning of the trend, like so, we can observe a few interesting things. We can perceive that the market gravitates around the 100% projection level for a while, often treating it as support and often treating it as resistance. We can also see a reaction at the 161.8% projection level. At the end of the trend, we can see something that really draws the attention of any trader, which is a high volatility candle with a very large lower shadow, giving the impression of finding very strong support. Notice how that shadow touches the 261.8% projection level almost exactly.

In this next chart, you can see that I plotted a Fibonacci extension in blue using the upper price movement that was used to plot the black Fibonacci projection previously. The level 127.2% of the projection happens near each other, and price sort of gravitates around it for a while. The more pronounced effect can be seen in the lower ratios on the chart. The 261.8% projection in black happens almost exactly in the same level of the 361.8% extension in blue. In this next image, you can see that I plotted a Fibonacci expansion tool in red in the second downward price movement at the beginning of the trend. Notice how in the lower part of the chart, two clusters of different Fibonacci tools form. The lowest zone being one that projects the end of the trend.

You may be wondering how you can know which cluster to trust. One of the answers is that you can use a phase analysis method like Elliott Wave in combination with Fibonacci in order to clarify that. For example, in this chart, you can see a clear example of five waves to the downside, in such a way that the third wave is the largest, which is a common phenomenon in Elliott Waves. In this next image, you can see five clear waves within wave three as well. My point here is that Elliott Waves and Fibonacci go hand in hand. I have a full Elliott Wave course for free here in the channel; I'll leave it in the video card if you want to go deeper into it. Elliott Waves can also work well for navigating the market with Pitchforks, like you can see in this picture. That's a modified Schiff Pitchfork plotted on waves one and two, providing a very reliable channel for the rest of the trend.

A final example, still in the realm of price-based Fibonacci ratios, is when we look at Fibonacci tools going in opposite directions. In this picture, you can see the 3-hour time frame of the New Zealand Dollar versus the Canadian Dollar. We can see that price has moved to the upside and is now starting to retrace. One obvious thing here is to draw the retracement tool in the upper price movement, like so. A less obvious idea would be to draw the projection tool in the retracement. Recall that a retracement in the home time frame can be seen as a full trend in the lower time frame. We can plot the projection tool based on the small highs and lows already formed in the retracement, like so. Notice here how the 61.8% retracement in black clusters with the 100% projection level in blue, providing a stronger support for price in comparison to the other Fibonacci levels. Moving price into the future, we can see that indeed the retracement went to the cluster, formed a small consolidation in there, and then went with full power to the upside. And by the way, here's the Elliott Waves combined with the Fibonacci analysis. Once again, notice how the range captures the five waves, and the projection aims to capture the end of wave C based on waves A and B.

At this point, we have studied the four major price-based Fibonacci tools: the retracement, the extension, the expansion, and the projection, and also a few examples of how they work individually and integrated with one another. It's time now to move on to the time-based Fibonacci tools. Just like price-based Fibonacci tools only consider the vertical aspect of the chart, time-based Fibonacci tools only consider the horizontal aspect of the chart. In other words, in the same way we can find Fibonacci relationships in the way price moves up and down, we can also find Fibonacci relationships in the way price moves over time. We have four main time-based Fibonacci tools: the Fibonacci Time Zone, the Trend-Based Fibonacci Time, Fibonacci Number Counting, and Fibonacci Wave Counting. Two of these are ratio tools, and the other two are simply counting tools.

Let's begin by the Fibonacci Time Zone technique. The Fibonacci Time Zone is a very simple idea. We measure the length of time that it takes for a significant price movement to form. The Fibonacci Time Zone tool will then show future projections in time based on Fibonacci ratios. These future time points are likely to show the moments where other significant reversals might occur. It's worth noting that this tool by itself is very weak; it serves more as a complimentary tool to other stronger techniques in the toolkit. As usual, it's better to observe how this works in real charts.

In this picture, you can see the 45-minute chart of Copper Futures. As a parenthesis, notice that I'm giving you examples in different financial instruments and in various time frames so you can see the market and time frame don't matter; technical analysis tools work in the same way in all of them, for the most part. If we plot the Fibonacci Time Zone tool in the two first significant price movements of this uptrend, we'll notice that the very end of the trend occurs at the 423.6% ratio. You can also see that the 38.2% and the 361.8% ratios also pointed to small retracements in the middle of the trend. Like I said previously, this is a weak tool, and you should not make trade decisions solely based on it. One of the many ways to confirm the bigger reversal at the top would be a simple channel at the later stages of the trend, like you can see in this picture. The angle of the channel is determined by two important lows, and the upper limit of the channel is determined by duplicating the same angle to a high in between the lows that generated the angle in the first place. Notice how the upper line of the channel intersects almost perfectly with the high outlined by the 423.6% ratio in the Fibonacci Time Zone tool. Notice also that plotting these two in a different price movement led to the same conclusion: the end of the trend happens roughly at the 423.6% ratio. In this case, there's nothing special about this ratio; it just happens to be the Fibonacci ratio that works in this case. Notice that unlike price-based ratios, there isn't a clear way of seeing if time-based ratios are being respected, and that's part of the reason why they tend to be weaker on their own.

Another time-based Fibonacci tool is called the Trend-Based Fibonacci Time, and it's similar to the Fibonacci Time Zone with the added detail that you can shift the ratios into the future based on specific price points that you judge to be relevant to the trend. To use this technique, you will use two price movements that are relevant in the trend, meaning that there are three anchoring points to choose. If you anchor the first and third anchoring points in the same high or low, the Trend-Based Fibonacci Time tool is the same as the Fibonacci Time Zone tool. For example, in this 10-minute chart of Apple, I grounded the first position in this high, the second position in this low, and the third position in the same high of the first position. That gives us the Fibonacci Time Zone. Notice that the projections in this case are very rough and don't provide timely signals. However, by moving the third grounding position to a different height, like so, we shift all the ratios into the future by the same distance we have from the first high to the second high. That's why it's called Trend-Based Fibonacci Time; it considers the trend element of different price movements. Notice that by shifting the ratios, they end up becoming timely signals and certain reversals that occur in the future, as it is highlighted by the green circles. Of course, in hindsight, this is easier to see, but then again, this is exactly what you must look for when looking at this in real time. The trick here is that you usually don't start with this tool, just like you don't start with the Fibonacci Time Zone. These are more confirmatory tools than anything else, in my opinion. For example, at the lowest point in the chart, there is a very clear V-bottom formation happening. That would be something that would stand out immediately to any classic chart pattern trader. If you happen to know about the Trend-Based Fibonacci Time tool in the way I just described, you will be able to use it as a confirmatory tool. That goes to my other point, which is that you don't start the analysis with the weaker techniques; you usually start with the stuff that really stands out, and then you refine the analysis with the more subtle techniques. The fact that the V-bottom happened exactly at the Fibonacci time projection increases the possibility of the V-bottom working as intended, even if it's just a small increase in probability. Any increase is more than welcome since we are dealing with the unknown. Recall also that trading is always about speculating about the future; there are no guarantees.

The third time-based Fibonacci tool is a surprisingly simple one. The Fibonacci counting technique proposes that the number of candles between significant reversals can approximate numbers in the Fibonacci sequence. This is very simply understood with an example. This is the daily chart of the E-mini Russell. Notice that I have marked a low and a high in the chart with green circles. If we measure the number of candles between this low and this high using the date range tool in TradingView, we'll see that there is a total of 89 candles. 89, of course, is a number in the Fibonacci series. When price moves away from significant reversals following a Fibonacci number, like so, there is a slightly higher chance of reversal. Once again, this might be because Fibonacci relationships do underlie the markets, or because there is a self-fulfilling prophecy effect, or maybe a little bit of both. We'll never truly know, unfortunately. Another point here is that the reversals don't have to occur exactly at a Fibonacci number; a reversal occurring near a Fibonacci number already helps quite a bit. By the way, this technique would have worked with the previous market extreme as well. In this image, you can see that the distance in terms of numbers of candles from this high to this low is 35, just one candle shy of the Fibonacci number 34. If we add a simple resistance line here, we'll see that the market reversed in that high much more because of the resistance, but the fact that the high occurred at the 89th candle from the low makes the signal a little bit stronger. That's the point: nobody would dare to trade just with the Fibonacci counting tool, as it would be too loose, in a sense. While we're at it, if we throw a Fibonacci expansion in this small upward price movement, we see how the 261.8% level correlates with the resistance line and the Fibonacci counting point. The more techniques you add here, the less likely it is that all of this is just a mere coincidence. That's what integrated trading is all about.

The fourth time-based Fibonacci technique in the toolkit is the Fibonacci wave counting, which is similar to the simpler counting technique, but instead of counting candles, you count waves or whole price movements. In fact, the core of the Elliott Wave Theory, one of the most renowned theories in technical analysis, is based on the fact that the market moves in waves that follow a Fibonacci pattern. The 5-3 wave pattern in Elliott Wave Theory works under numbers in the Fibonacci sequence. Five and three are Fibonacci numbers, and of course, the sum of five and three is also a Fibonacci number. This is also true when we look at Elliott Waves from the fractal perspective: impulsive waves are composed of five waves on a smaller degree, and corrective waves are composed of three waves in a smaller degree. So, if you sum the number of waves within the 5-3 wave cycle, you will reach 34 waves, which is also a Fibonacci number. You get the idea. The most famous way of performing Fibonacci wave counts, therefore, is the Elliott Wave Theory.

Let's observe some simple examples of the Elliott Wave Theory integrating with other Fibonacci tools we have studied previously. In this 2-hour chart of the Australian Dollar versus the US Dollar, we can see that after five clear waves to the upside, the market produces a larger reversal. In the second chart, you can see the three-wave count for the retracement. Let's now observe how the integration of one price-based and one time-based Fibonacci tool aligns with Elliott Waves in this case. In this chart, you can see how an extension plotted on Wave 2 led to the determination of Wave 5 at 423.6%, and in this next chart, you can see how the Fibonacci Time Zone plotted from the beginning of Wave 1 to the end of Wave 2 shows that Wave 5 occurs at the 461.8% ratio. Of course, the problem here is knowing that these are the waves and tools you should be using in real time. One way of knowing that is by observing how the tools behave throughout the trend. Notice in this chart how the Fibonacci extension on Wave 2 provides several instances of reliable support and resistance throughout the trend. Notice also how the Time Zone tool also pointed to the end of Wave 4, roughly around the 361.8% ratio. Another clue here is the plot of a Schiff Pitchfork on Waves 3 and 4. Wave 5 exhausts at the median line. Recall that the axis of the Schiff Pitchfork dwells at the vertical midpoint of Wave 3, so it's not curve-fitted. Once again, observe how price reacts to the Pitchfork lines before exhausting its energy at the median line. That's the clue you need to see if a Pitchfork or any other type of line is indeed in tune with price action. These previous reactions are an indication that you can trust the lines in the future.

Another example now in a downtrend is in the 1-hour chart of DAX Futures. Notice the clear five waves to the downside, leading to a more significant reversal at the end. Notice also on a smaller degree, Wave 5 is composed of very clear five waves. Another interesting thing about this Wave 5 is that it is 36 candles long, which is close to the Fibonacci number 34. In terms of price-based ratios, we have a projection using the beginning of Wave 1 and the beginning and end of Wave 4, pointing to the termination of Wave 5 at...

The 61.8% ratio. Using a projection on a smaller degree, we can see that by plotting at on waves 1 and two of the larger wave 5, we see the 261.5 ratio clustering with the 61.8% ratio previously found. An extension of the larger Wave 2 points roughly to the same level at the 4618 per ratio. In an extension of the smaller Wave 2 of Five also clusters in that region with a 361.00 ratio.

In terms of time-based ratio, there is absolutely nothing useful going on. A perhaps simpler and more practical technique here, unrelated to Fibonacci, is one of the variations of an Elliot channel. The angle of the channel is determined by connecting highs two and four, and then the same angle is duplicated to the low three. The channel points exactly to the determination of wave five of five. We could keep going here for a while and finding more intersections using tools with a known logic. This is what good old technical analysis can do. Recall that even though some of these techniques, such as the Elliot channel, are not directly related to Fibonacci, Fibonacci underlies the whole idea behind Elliot waves, so it's indirectly related.

This finishes off the study of time-based Fibonacci tools. Let's now turn our attention to the dynamic Fibonacci tools, which use the element of price and time simultaneously. There are many options in this realm. Let's begin with the simple Fibonacci channel. The Fibonacci Channel works similarly to a common Channel. You find the angle between two extremes of the same kind, like two lows or two highs, and then you duplicate this angle to the extreme of the opposite kind that happens in between. The difference lies in the fact that Fibonacci channels are not equidistant. They obviously follow Fibonacci ratios. For example, in this 30-minute chart of gold future, we can see a standard equidistant Channel plotted using the anchors highlighted in green. The angle is determined by the lows and then it's duplicated to the high in between. The red channel is duplicated equidistant to the upside. However, price continues to the upside, breaking the upper boundary of the channel.

In this next image, we can see one use of the Fibonacci Channel. Price exhausts its energy at the 2618% Channel extrapolation to the upside. If the lower black Channel represents 100%, the sum of the red and Upper Black channels represents 161.8%. Unsurprisingly, at this point, we can see a Fibonacci expansion pointing to the same price level at a 261.5 price-based ratio, based on the same price movement that generated the Fibonacci channel in the first place. The 361 8% extension of the downward price movement related to the channel also clusters in the same price level.

Here's another example of Fibonacci Channel, this time in the 30-minute time frame of Bitcoin Futures. The channel was grounded in the highs and lows highlighted by green circles. Notice how the following price section ends up exhausting its energy at the channel lines that represent common ratios and not so common but very logical ratios as well. We can see price reaction in the 261.5 and 361.506 and in the 6854 per ratio. The last two ratios are the ratios that emerge when we divide one number by three and four numbers back in the Fibonacci series, respectively.

In this next chart, we can see another FIB Channel pointed to the same major reversal Point by using different grounding positions highlighted in Green. From this perspective, the reversal occurred at the 161.8% ratio. This would be a way of integrating two Fibonacci channels for a slight increase in the probability of reversal.

The next Dynamic FIB tool will study is called Fibonacci speed resistance fan. Even though it might seem like a complicated tool, it's not. Imagine that we select a price movement, just like we would do with a retracement tool. We have a vertical space and a horizontal space forming a rectangle. The fences are drawn by connecting a straight line from the lower left corner of the square in the case of an upper price movement, connecting to the points where the various Fibber retracement levels intersect with the right part of the square. That provides a fan that can be used for future points of support and resistance. Take a look at this 3-hour chart of the pound Yen. I plotted the speed resistance fan on this upward price movement, and later we can see how some of the lines worked well as slope support and resistance lines, as it is highlighted in the green areas.

In the three-hour chart of the New Zealand Swiss, we can see an example for a downward price movement. It's interesting to observe how price interacts with these non-obvious lines later down the road. The fact that not too many Fibonacci Traders use this tool makes it weaker to some degree, since the self-fulfilling prophecy effect is diminished in this case. But even with that, we can find many instances where these lines work in a way that it becomes hard to believe that it is just a coincidence.

Another Dynamic FIB tool is known as the pitch fan. Similarly to an Andro Pitchfork, the pitch fan is drawn using three axis in the chart, which are three alternating highs and lows. Let's call these three pivots A, B, and C. The BC line is divided using Fibonacci ratios. The pitch fan lines are drawn from the origin of the pivot A to the points in the BC segment that correspond to FIB ratios. In reality, using FIB ratios within and or outside the BC segment in this tool is a terrible idea. The best results can be obtained by using the simplest lines, which are the ones that connect to the 100% and 0% levels. For example, in this 4-Hour chart of the Euro USD, we can see a pitch fan grounded on pivots A, B, and C. Later on, we can see reactions to two of the lines. The interesting thing here is that the lower line, the one that connects pivots A and B, is not obvious if you're not aware of the pitch fan.

In this other image, you can see the counterpoint between a standard Pitchfork and the pitch fan drawn in the same pivots. Notice how the Pitchfork provides a channel that doesn't expand nor nor contracts, but the pitch fan does. They share a center line, though. One simple example of integration between these two tools here is by doubling the Pitchfork down. You can see that the lower line of the lower Pitchfork intersects with the lower line of the pitch fan.

Another point of integration here is this other red Pitchfork, but now plotted on different anchors and using the modified shift version instead of the standard version. We can keep going here. Let's use some price-based FIB ratios. Here you can see a projection using the black price movements. This is probably the point that most Fibonacci Traders would be looking at. In this case, price encounters lines from two different pitchforks, one pitch fan, and the 361.00 projection ratio.

In this other chart, a projection plotted on the green price movements shows how the 100% projection clusters in the same area. As you can see, integrating too many Fibonacci tools has the disadvantage of making the chart confusing after a certain point, so let's stop right here. However, we could keep going with this, and we would find other Fibonacci tools pointing to the same area. Let's erase the pitchforks and the two projections. By plotting a simple extension of this upward price movement in blue, we see there are another fibal clusters in that area. Now it's the 461.8%. Notice that it's not about the specific FIB ratios; it's about the clustering of the ratios. The pitch fan in this case is more a confirmatory tool to the more powerful price-based Tools in my opinion. A tool like the pitch fan only adds unnecessary confusion to the Chart. It's much better to stick just with the pitchforks because they are much more powerful than a pitch fan by a large margin.

Next in line, we have a tool called FIB Fork. The FIB Fork is not originally a Fibonacci tool; it's a modification of another tool called the Android Pitchfork. You might have heard about it somewhere. The FIB Fork simply adds extensions to the Pitchfork Channel, and these extensions are based on Fibonacci ratios. For example, in this image, you can see a standard Pitchfork plotted on the anchoring points highlighted in green. The standard Pitchfork lines are gray. The 161.8% extension is light orange, and the 261.5 per extension is light blue. Notice how the 2 61.8% Channel captures the end of the trend on the top of the chart, and much later price comes back to flirt with the 161.8% and the 261.5 per lines on the downside.

In this other chart, you can see another example, but this time we have what is called a modified share sh Pitchfork, and the 4618 extension was used. The Pitchfork is grounded in the green circles, and the FIP Fork ends up projecting the end of the trend at the red circle much later. Of course, you cannot simply choose ratios arbitrarily, as there are too many of them. You need to choose the ratios that interact with other tools in a suggestive way. In this other chart, for example, we have a Fibonacci expansion plotted in the same price movements that originated the fit Fork. As you can see, price meets the 423.15 ratio in the 4618 FIB Fork extension in the same price level. We can also see a Time based tool working here, the trend based FIP time tool plotted in the black arrows, which are significant reversals in this trend, point to the intersection we found already at the 661.pbp. Seems like an exotic ratio, but it's not; it's just a higher order ratio like 361.5061.8. Once again, integration of tools is the recurring theme here. That's what's going to make all these tools work in a reliable way. We can also see an extension tool in the blue price movement here. The 200% ratio falls into the cluster we had already. Notice that we have two price-based tools, one time-based tool, and one dynamic tool intersecting. That's considered to be high-level Fibonacci trading, which is based on the integration of various types of FIB tools. Most traders in the market only look at Fibonacci retracements, but there is a whole world of tools beyond that.

As you can see, traders must understand that trading is a game of asymmetric information. Capital flows to the hands of those who have an information advantage. Fibonacci tools generally blend numerical calculations with geometry in the charts, which is one of the characteristics of fractal tools. However, we can find an unorthodox use of Fibonacci ratios within technical indicators that are fundamentally numerical, such as moving averages and Binger bands. One trick you can use in this context of using fiber ratios within technical indicators is to change the period of moving standard deviations of of the Binger bands. For example, as a default, the number of standard deviations is two, but we can change it, for example, to 2.618, which is a Fibonacci ratio.

Let's look at an example. This is the 4-Hour chart of NASDAQ mini Futures. I plotted Binger bands with two sets of bands. One is the standard set of bands with two as the period of standard deviations in black, and the other is a set of bands with a period of 2.618 in red. A couple of interesting details here is that the Fibonacci-based bands seem to hold price action more precisely, as we can see here. In other contexts, the Fibonacci base bands will provide additional confirmation for a reversal. On the right, we can see how a highwave candle pattern, which is the high volatility version of a spinning bottom, touches the Fibonacci-based band almost to the tick and then leads to a significant reversal to the upside.

Here's another example, still in the same market and time frame. We can see price touching the standard black band and producing a reaction only, but when it touches the Fibonacci-based band almost to the tick, it produces a more significant reversal right after. You may look at this and think that Fibonacci-based standard deviations take full responsibility for the reversal, but in this chart, you can see price exhausting its energy at the median line of a modified shift Pitchfork in the same level, which is a spinning bottom. Also, in this case, if you think this Pitchfork is the missing link here, notice that there is also another one. The blue modified shift Pitchfork is drawn using the highs and lows highlighted in blue. Notice how the spinning bottom formation, which is also a fractal candle, by the way, touches the upper line of the Blue Fork as support at the same time that it touches the median line of the black Pitchfork in the Fibonacci base moving standard deviation in red. I'm sure we can find other intersections here, but you get the point. Notice that there's a big difference between curve fitting the analysis, which is simply inventing a technique on the spot to justify what you want, and using tools that have a well-established logic. The known logical framework of these tools is precisely what gives them their predictive power.

Another example of this trick using Fibonacci numbers within technical indicators is simply using a Fibonacci number as the period of a moving average. For example, in this 1-hour chart of Bitcoin, we can see an 89-period exponential moving average. 89 is a Fibonacci number. Notice how the EMA provides good examples of dynamic support and resistance levels. When it's deeper, as it is highlighted in the green circles, the EMA loses that capacity when it's relatively flat, as it is highlighted in the rectangle. Recall that when you use moving averages as dynamic support and resistance, which is one way of avoiding the problem of lag in moving averages, you must pay attention to two important factors: the angle of the MA and the reaction produced by price action when it meets it. Moving averages are absolutely useless without these two factors.

Now notice that choosing a Fibonacci number for the moving average period is an unpopular method, so it loses a lot of the self-fulfilling prophecy effect as associated with common moving average periods. Still, we can find instances where it works. You can simply say that this is a coincidence, and you might be right. The way we have to assess whether this is a coincidence is by finding other techniques pointing to the same level. Integration is the only thing that allows a Trader to differentiate between coincidence and causality. Just for illustration's sake here, we can see the modified shift Pitchfork providing additional comfort for one of the setups found in the Fibonacci-based EMA. Recall that this is a 1-hour chart, so you have eons of time to reach these conclusions.

Here's a cool trick you can do with Divergence. In this chart, you see two money flow index indicators based on Fibonacci numbers, 8 and 55. Although you could pick any relatively small and large FIB numbers, this low MFI 55 is providing a bullish continuation Divergence signal, and at the same time, the fast MFI 8 is providing a bullish reversal Divergence signal. As you might be expecting, the reversal is also a result from an expansion tool in blue and a projection tool in black. Coincidentally, both price-based FIB tools cluster at 200%. In this case, we can keep going with tricks and secrets about technical indicators, but this is a Fibonacci trading course, so let's return our focus to the FIB tools.

Let's now talk about the problem of price charts scale invariance and FIB tools. Some traders correctly worry about the reliability of tools when chart scales change. That's an issue because if we're going to take advantage of the self-fulfilling prophecy effect associated with these tools, all traders must be able to see the same tool in the same way, regardless of the chart scale. Certain Fibonacci tools will behave differently when you change from linear to logarithmic chart scales, when you zoom in and out the chart, or even when you scroll the chart left and right. That's a problem because for tools to have the self-fulfilling prophecy effect, they must be scale invariant. Scale invariance is the ability to preserve properties regardless of changes in scale. For example, moving average is scale invariance because its values are calculated numerically before being plotted geometrically. However, certain geometric tools are drawn purely based on geometric relations of proportion, size, symmetry, and angle. In that sense, they can be scale variant, which is a problem. The solution to this is to calculate the tool numerically before plotting it geometrically, just like what happens with moving averages, Binger bands, and most tools you can draw on a chart. However, not all charting platforms do this.

There's another trick to dealing with this problem, which is to lock the price to bar ratio of the chart. In that way, the tool will not change if you scroll or zoom in and out of the chart. However, this is a suboptimal solution because the analysis is still dependent on the initial condition that you determined, meaning the scale that you decided to lock the price to art ratio in. Let me give you an example of this. In this chart, I drew the Fibonacci spiral tool in this black upward price movement. Notice that in this scale, the price movement on the right is above the spiral. However, if I simply zoom out a little bit, now the spiral will change so that price action is now below the spiral. Like I said, one way of dealing with this problem is to lock the price to bar ratio of the chart. You can do that by right-clicking the scale of the chart on the left in Trading View and choosing the option "lock price to bar ratio." In this chart, you can see the spiral once again, but this time I locked the price to bar ratio. Notice how price action is above the spiral in this point. If I zoom out, the spiral is still the same. The tool did not become scale invariant; it's the scale that got locked. This is a way of dealing with it, but it's not optimal because you are still locking the scale in an arbitrary position. The optimal solution is to use a platform that calculates the geometric tools numerically before plotting them geometrically. That would indeed make this tool scale invariant.

I say that locking the price to bar ratio of the chart is suboptimal because of the arbitrary scale value. That arbitrary decision makes the self-fulfilling prophecy effect disappear or at least decrease significantly. However, the purely geometric validity of these tools, if there is any, is still intact. In this case, if you lock the ratio, on the other hand, it's not like Fibonacci spirals, wedges, and arcs have a strong self-fulfilling prophecy effect anyway. You don't have to worry about the most common Fibonacci tools if they are calculated numerically before being plotted geometrically, which is the case in most reliable charting platforms. Because of this problem, I'm not going to waste time with the Fibonacci tools on Trading View that have this problem of scale variance. They are the Fibonacci speed resistance arcs, Fibonacci wedge, and Fibonacci spiral. Theoretically, you can pursue the purely geometric validity of these tools, but if that's the goal, I believe there are better options out there. In any case, this is a discussion for a different course.

There's another tool called FIB circles that is indeed calculated numerically and then plotted geometrically on Trading View, but even with that, the tool is simply too unreliable to spend any effort with it. It will simply clutter the chart and provide almost no value to the analysis, if it provides any value at all. In my humble opinion, if you're going to use Fibonacci tools, you should stick to the most powerful ones, which are the price-based ratios. You can use the time-based ratios for additional confirmation in a dynamic tool like Fibonacci channels or FIB Forks, but I would not go further than this. Sticking to price-based ratios alone provides the best value.

Let's now talk a little bit about using Fibonacci tools as a confirmation for other well-known tools such as chart patterns and harmonic patterns, which also have a strong behavioral element to them. In this 1-hour chart of McDonald's, you can see a powerful chart pattern called double top, which is a bearish reversal pattern that worked very well in this case. By plotting a Fibonacci extension in this downward price movement, we can see that the double top occurs roughly in the 161.8% level, which helps confirm the chart pattern. We can go a step further here and plot a time zone in this upward price movement, which represents the first part that forms the double top, and we'll see that the second top occurs roughly in the 261.5 per ratio. A third and final tool that could be used here is a Fibonacci Channel with the 50% ratio grounded in the points highlighted by the circles. Notice how the double top terminates exactly when price touches the 50% ratio channel line. In this case, the Fibonacci Channel uses the same lines and angles of a modified shift Pitchfork plotted on the same anchors.

Fibonacci tools can also be used with other types of patterns, such as harmonic patterns. In this three-hour chart of the Euro USD, we can see one of the simplest harmonic patterns that exist called bullish ABCD. The retracement of the first leg must be between 38.2 and 88.6%. In this case, it is 48.8. The third leg must extend between 113% and 2 161.8%. In this case, it is 142.5, so it also falls within the optimal range. Harmonic patterns only provide a rough estimate of where price will reverse, and that's where more precise Fibonacci tools can help. By plotting a Fibonacci expansion at the downward movement in the beginning of the pattern, we can see that price terminates the ABCD pattern exactly at the 423.15 ratio. Notice also how price seems to be reacting to that level, which is the important thing here, and how a small double bottom forms in there. You can see that price indeed goes to the upside with a lot of power afterwards. Good opportunities like this are not about this or that technique; it's about the combination of them. Notice also the fractal quality of markets happening here. We have a small double bottom happening inside a larger harmonic pattern.

New traders are always after the Holy Grail, meaning that strategy that will give them perfect results every time. That doesn't exist. Again, trading is not about this technique or that strategy; it's about the convergence of good tools. This is a principle that exists not only in technical analysis but across many types of market analysis.

Let's take a moment here to learn a little bit about the realm beyond Fibonacci ratios. The golden ratio is a mathematical constant, but there are several mathematical constants, many of which describe fundamental aspects of reality. The fact that mathematical constants describe fundamental aspects of reality is the reason why Fibonacci ratios began to be used in trading in the first place. The self-fulfilling prophecy effect associated with the infusion of such tools in the technical analysis culture came later because it requires that many traders trust the tools in the first place. This leads us to think that other mathematical constants can be used in trading. For example, Euler's number, denoted as E, is also a mathematical constant that appears in many natural phenomena. It appears in the way exponential growth and decay occurs, being used in the calculation of continuous compounding in finance. It appears in different fundamental aspects of statistics, such as the probability density function of the Gaussian distribution. In thermodynamics, more specifically in statistical mechanics, it appears in what's called the Boltzmann factor. We could spend a very long time describing where mathematical constants appear. This is just a very small sample. The point is that mathematical constants occur in many unexpected places. It's for this reason that using Fibonacci ratios and mathematical constants in the financial markets is not a crazy idea.

One particular detail about Euler's number, which is 2.718, is that it's very close to the Fibonacci ratio 2.618. So, based on the same idea that led to Fibonacci ratios in trading, we can also use Euler's number. I've talked about this in a previous video where I demonstrated the Euler Fibonacci Zone. Perhaps the advantage here is that since it's so close to the 261.8% ratio, you can make it a little bit stronger. For example, in this chart, you can see that the small zone formed between 261.5 and [Music] 271.50, but it's an interesting thought.

Another example of this is the fan bounce number, which is a constant that appears in the study of nonlinear dynamics, a field of mathematics that studies chaotic behavior. It appears in the phenomenon of period doubling bifurcations leading to chaos. If you want to understand more about this in the context of financial markets, I have a whole course on it called Advanced Training Course Volume One. This first course is simply theoretical. If you want to understand how to apply chaos theory and fractal geometry in price action trading, I have another course called Fractal Trading: Mastering Price Action and Beyond.

Going back to what I was talking about, Feigenbaum's number, which is 4.669, is very close to a Fibonacci ratio, the 4618. In this chart, for example, you can see that these two numbers form a small zone, and in this case, they pointed to a very significant bearish reversal. All of this based on the small upward price movement at the very beginning of the trend. This is an interesting idea. If we recall, the Fibonacci clusters are one of the most powerful ways of using price-based ratios. If there are other mathematical constants that cluster with certain FIB ratios, perhaps these ratios become slightly stronger. From a mathematical point of view, once again, this is just speculation, but there are many instances where we can see several tools from Chaos Theory converging in time and price in the charts, and the more tools there are, the less likely it is to be just a coincidence. Once again, you can learn more about this in my premium courses.

Let's now move on to the most important insights about Fibonacci trading, and then we'll finish the course with the advantages and disadvantages.

Number one: Integration. The father of all principles in technical analysis is integration. No tool is strong enough by itself, so the combination of tools is what increases the chances of success. Fibonacci trading tools are not an exception. Another way of thinking about this is that integration is the only way of differentiating between coincidence and causality, since trading is a game of incomplete and asymmetric information.

Number two: Price reactions. One of the most important things in trading with support and resistance lines, such as Fibonacci ratios, is to observe the price reaction to it. That can be the difference between a good and a bad trade. The price reaction is the best filter in this case. Otherwise, it's virtually impossible to know which Fibonacci level to trust. You can only observe price reactions in a meaningful way in price-based tools and dynamic tools. Time-based tools are trickier.

Number three: Hierarchy of tools. By far the most powerful Fibonacci tools are the price-based tools. In second place, the time-based Tools. In third, the dynamic scale-invariant tools, and in last, the dynamic scale-variant tools. This last set of tools is not really worth paying attention to in my experience. The opportunity cost is too high.

It's time now to move on to the notion of advantages and disadvantages of Fibonacci trading tools. Let's begin with the advantages.

Number one: Fibonacci trading provides a wide array of different tools. That means it provides the possibility of vertical integration, which is when you trade on the intersection of various tools from one single method. In other words, it's possible to build a whole strategy using the integration of Fibonacci tools only, but that's not optimal. Horizontal integration, meaning the use of techniques across different types of methods, is more powerful than vertical integration.

Number two: Some FIB tools are deeply infused in the technical analysis culture and therefore can lead to self-reinforcing, self-fulfilling cycles when integrated properly.

Number three: The most powerful FIB tools are extremely simple to use.

Number four: Fibonacci tools are trusted by a wide array of market participants, including professional ones, which helps in the confidence in using these tools. We know that professionals use them because Fibonacci trading is part of the technical analysis certifications that are required for individuals to work in the institutional domain.

Number five: When used in the right way, Fibonacci tools are leading tools; they don't have the built-in lag that occurs in most technical indicators.

Number six: The use of Fibonacci tools can provide insight into the level of power behind a trend. The depth of retracements is an indicator of how strong a trend is. The shallower the retracements, the greater the power of the trend.

Number seven: Fibonacci tools can be used as powerful types of confirmation for other tools that have a strong behavioral element, such as the Elliot wave theory, or tools that derive their power from other fields, such as mathematics and physics. The Pitchfork and the linear regression channel are good examples.

Let's now move on to the disadvantages.

Number one: The correct use of Fibonacci tools through integration can generate confusion, since the price chart can easily become cluttered with too many lines. That's one of the reasons why vertical Fibonacci integration is not optimal, despite being valid.

Number two: Certain FIB tools have scale variance, meaning that the tool changes if the trader zooms in and out of the chart, moves the chart from left to right, or changes the scale from regular to logarithmic. The solution to that is to use a charting package that calculates the FIB tools numerically before plotting them geometrically, or as a suboptimal solution, to simply lock the price to bar ratio of the chart.

Number three: The placement of FIB tools is subjective. It's not clear which highs and lows should be used as grounding positions. This is one of the reasons integration is important. Different FIB Traders will consider different placements. When they intersect, there's a higher chance of reversal.

Number four: The mathematical validity of Fibonacci ratios in the financial markets is questionable, and it's impossible to prove due to the way markets evolve dynamically over time. In other words, the mathematical aspect of Fibonacci ratios cannot be proven, but the behavioral effect of Fibonacci ratios is an undeniable fact.

Number five: Despite the mathematical connotation, Fibonacci tools tend to work because of a behavioral motive, the self-fulfilling prophecy effect. That is a bad thing when FIB tools are used in isolation, but it's an advantage when the tools are integrated.

This is it for this course. If you want to learn how to use Fibonacci Tools in a method that integrates other powerful tools to find the highest quality trades possible, check out my course called Fractal Trading: Mastering Price Action and Beyond in the video description. If you have any questions, you can send me an email at support@fractalflowpro.com. You can support the channel by clicking the like button, subscribing to the channel, activating the notifications, leaving your feedback in the comment section, and sharing this guide with your trading community. Thank you very much for watching, and I hope to see you in the next videos. Take care.