welcome to the ultimate beginners 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 examp 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 training 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 in 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 aachi which roughly translated to English means the book of calculation you can find a modern translation of Liber aachi written by Lawrence Sigler on Amazon if you're interested fibonacci's liberachi is partly known for introducing the Hindu Arabic numerical system to Europe the Hindu Arabic numerical system is the one we are familiar to 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 aachi 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 use 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 subn + 1 is the next number in the sequence f subn means the current Fibonacci number and F subn minus one 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 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 between 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 to 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 f as it turns out the same behavior can be found in the Luca sequence this is a unique phenomen phenon 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 five 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 at 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 Meer 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 the 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 Elliot 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 fi 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 of 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 phenoma 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 Elliot believ that Fibonacci ratios were embedded in the way everything works 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 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 Surefire 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 Elliot 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 fibon relationships work just because of behavior or just because of mathematics or both is not that important 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 FIB 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 magnet itude ratios beyond the 1.618 and the 2618 Traders also use the 3618 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 FIB 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 2.61 18 and 0.382 and calculating the ratios between one number and three numbers back we get 4.236 and 0.236 one important detail regard regarding Fibonacci ratios and trading is that these ratios are used in percentage terms to transform ratios in 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 FIB 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 fib fibbonacci levels used in trading with that established let's move on to the most common price-based FIB 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 wellestablished FIB levels one extremely important tip here is that you must observe which FIB retracement ratio price reacts to that's how you know which FIB 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 1H 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 to the 38.2% retracement level a very common FIB 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 FIB level price for responds to and what kind of reaction price produces let's now look at an example of 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 we can see how price went to the downside from that point forward even though some would categorize this a strong downward trend is not as strong as the upper Trend in the last example at this point you might be thinking that this is a Surefire 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 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 is dependent on other modes of market analysis such as Elliot wave theory Dow Theory wov method or a mod combination of these three I have three ques here in the channel for each one if you want to go deeper into these subject Fibonacci tools work remarkably well with Elliot 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 highwave pattern the highwave 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 Fibber racial levels you must integrate them with other tools a quick example of that is when we plot a modified shift Pitchfork using the Upper price range as the B and C anchoring points of the Pitchfork in a previous important High Asda a point 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 highwave candle pattern touches both the FIB ratio and the lower line of the modified pitch fork 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 we ground the retracement in a downward price movement in other words the extension to 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 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 261.5 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 Elliot wave count although Elliot 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 we can see the 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 261.5 ratio in relation to the 200% price reversed at a 2 61.8% 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 trading view 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 dollar 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 423.15 ratio and we can also see the price AC found a strong resistance that was later used as support in the 261.5 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 5minute chart of PayPal by plotting the FIB 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 261.5 per ratio and exhausting its power at the 4 23.6% 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 underly the behavior 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 fit 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 trading view the projection is called trend-based FIB extension the term Trend based means that the FIB 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 300 and 61.8% 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 fit projection like so by doing that the 361.00 projection ends up being more precise because it's based on more price information still in the USD yend but now in the one 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 361.00 ratio if we shift the expansion to a projection by considering the adjacent and opposing price range like so we can see that the 361.00 ratio would fail to capture price you might be asking yourself how you are supposed to know which FIB 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 FIB ratios we must think about what has the greater chance of working over many iterations needless to say observing FIB 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 15minute 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 FIB 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 movements just before with a 361.00 level in this case it also correlates with the [Music] 127.2% extension level plotted on this large upper price movement and also with a 2 161.8% extension level plotted on a smaller price movement and in the 261.5 extension in this older upward price movement you get the idea many powerful Fibber ratios happening roughly in the same level that's how you increase the power of these Fibber 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 1hour chart of the US dollar versus the Canadian dollar notice that we have a well-defined downtrend in this example by plotting a fit 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 261.5 per projection level almost exactly in this next chart you can see that I plotted a fib extension in blue using the Upper price movement that was used to plot the black FIB 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 lowest ratios the chart the 261.5 per projection in Black happens almost exactly in the same level of the 361.00 extension in blue in this next image you can see that I plotted a fib 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 FIB 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 Elliot 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 Elliot waves in this next image you can see five clear waves within wave three as well my point here is that Elliot waves and Fibonacci go hand in hand I have a full Elliot wave course for free here in the channel I'll leave it in the video card if you want to go deeper into it Elliot waves can also work well for navigating the market with pitchforks like you can see in this picture that's a modified shift Pitchfork plotted on ways 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 is when we look at FIB 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 FIB 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 elite 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 in the ually and integrated with one another it's time now to move on to the time based Fibonacci tools just like price-based FIB tools only consider the vertical aspect of the chart time based FIB 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 FIB tools the the FIB time zone the trend based FIB time Fibonacci number County and Fibonacci wave County two of these are ratio tools and the other two are simply counting tools let's begin by the FIB 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 F 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 we 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 FIB time zone 2 in the two first significant price movements of this uptrend we'll notice that the very end of the trend occurs at the 423.15 ratio you can also see that the 21.8% and the 361.00 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 Outline by the 423.15 ratio in the fif time zone two 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 423.15 ratio in this case there's nothing special about this ratio it just happens to be the FIB ratio that works in this case notice that unlike price based ratios there isn't a clear way of seeing if time Pace ratios are being respected and that's part of the reason why they tend to be weaker on their own another time based FIP tool is called the trend based FIP time and it's similar to the FIP 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 points to choose if you anchor the first and third anchoring points in the same high or low the trend based FIP time tool is the same as the FIB 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 FIB 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 FIB 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 FIB 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 FIB time tool in the way I just described you will be 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 happen 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's 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 Emin 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 trading view 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 underly 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 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 261.5 level correl Ates 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 FIB 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 elite wave theory one of the most renowned theories in Tekken coin analysis is based on the fact that the market Moves In Waves that follow a Fibonacci pattern the 53 wave pattern in Elliot 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 fib number this is also true when we look at Elliot waves from the fractal perspective impulsive waves are composed of five waves on a 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 53 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 Eliot wave theory let's observe some simple examples of the Elliot wave theory integrating with other Fibonacci tools we have studied previously in this two-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 FIB tool aligns with Elliot waves in this case in this chart you can see how an extension plotted on Wave two led to the determination of wave 5 at 423.15 and in this next chart you can see how the FIB time zone plotted from the beginning of wave 1 to the end of wave two shows that wave five occurs at the 4618 per 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 FIB extension on Wave 2 provides several instances of reliable support and resistance throughout the trend notice also how the time zone two also pointed to the end of wave four roughly around the 361.50 ratio another clue here is the plot of a shift Pitchfork on waves three and four wave five exhausts at the median line recall that the a axis of the shift Pitchfork dwells at the vertical midpoint of wave three 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 1hour 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 five 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 four pointing to the termination of wave five 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 361.50 6 and in the 6854 per ratio the last two ratios are the ratios that emerg 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 fence 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 nonobvious 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 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 show 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 movement M ments 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 361.50 61.8 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 a 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 tacnical 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 perod of 2.61 eight 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 context 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 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 wellestablished 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 1hour 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 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 1hour 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 deal 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 toart 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 section is above the spiral in this point if I zoom out the spiral is still the same the tool did not became 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 two 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 1hour chart of McDonald's you can see a powerful chart pattern called double toop 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 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 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 Oilers numbers denoted as e is also a mathematical constant that appears in many natural phenomena it appears in the way exponential growth and the K 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 Gan distribution in thermodynamics more specifically in statistical mechanics he appears in What's called the boltzman 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 Oilers number which is 2.718 is that it's very close to the Fibonacci ratio 2.68 So based on the same idea that led to Fibonacci ratios in trading we can also use Oiler number I've talked about this in a previous video where I demonstrated the oiler 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 feud 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 F M's number which is 4.66 n 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 Fe 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 canver merging 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 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 fibbonacci 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 professional 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 indicat 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 placement 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 fractal flowpro docomo 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