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Fibonacci: the Wanderer's Conundrum
or What is Behind One of Today's Most Popular Trading Concepts
The Fibonacci studies still remain popular trading tools and the understanding of how they should be used and to what extent they can be trusted is important to any trader who wants to benefit from the ancient mathematician's scientific legacy. For its no secret that whilst some traders unquestionably rely on these tools for decisions that may become momentous to the whole of their lives, others reckon the Fibonacci studies to be a sort of exotic scientific baubles, toyed with by such a gargantuan number of traders that it cannot but influence the situation on the market. These are two opposing views, each of which has its adherents among successful traders. In this article we will try to prove that the Fibonacci studies influence the market situation by winning the hearts and minds of traders and not due to their presumed divine nature.
Being one of the most popular technical analysis methods, the Fibonacci studies offer a view of the market situation that is shared by a large number of traders when the turning points on their charts are clearly defined. It is exactly this that makes Fibonaccibased forecasts come true. Besides, the Fibonacci numbers define the underlying laws of nature, and it looks like Mother Nature has done its best to make this understanding of its workings appealing to the subconscious of its children.
The Famous Italian
Today, many centuries later, it's pretty hard to say what turned that modest Italian lad, who often referred to himself as Bigollo, which, along with 'wanderer," can also mean "a goodfornothing, a layabout", into a figure so much venerated by thousands and thousands of our contemporaries who concern themselves mostly with matters of purely practical nature. It is most likely to be owing to Leonardo Pisano's (yes, that's the guy's real name) extensive travel alongside his father, a diplomat, who represented the Republic of Pisa in the small 12th century world beyond its borders. It is exactly during these travels that the now renowned Fibonacci picked up the ancient Indian system of nine symbols and some other mathematical skills to further develop and formalize the teachings he was initiated into when he was past traveling and back home in 1200.
One of the Italian's works, Libre Abaci, contained some practical tasks that were related to merchant trade, price calculations, and other problems that needed to be solved by the trading folk as a matter of their everyday activities.
An attempt to solve a sum about the propagation ability of rabbits gave birth to the system of magic numbers Leonardo Pisano Fibonacci is revered for today as much as he was almost eight centuries ago. A sequence whereby each number is the sum of the two numbers that precede it seems to be nature's underlying principle behind life's many events and phenomena.
Leonardo Fibonacci had also applied his lifeinspired theory in conjunction with geometrical constructions. And strange as it is, the nuptials, assumingly performed by a pair of the creatures in the 12th century, still help a quite a bit of folks to cash in. At least, they claim that to be so. So what are the chances in the Fibonacci game?
The Enigmatic Legacy
So let us first look more closely at what the Fibonacci numbers are. The Fibonacci sequence is as follows:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,..
This sequence, asymptotically (more and more slowly), moves toward a certain constant ratio. However, this ratio is irrational, i.e. it represents a number with an endless, unpredictable sequence of decimal numbers in the fractional part. This number cannot be expressed precisely. If any of the Fibonacci sequence members is divided into its preceding member (for example 13:8), this action will result in the value, fluctuating around the irrational value 1.61803398875..., and, intermittently, either exceeding this value or falling short of it. However, even having spent the eternity, it's impossible to determine the sequence precisely down to the last decimal figure. For the sake of brevity, we will quote it as 1.618. At present, the sequence is often referred to as the Golden Section, Golden Average or Rotating Squares Algorithm. In algebra, it is commonly indicated by the Greek letter Phi (Phi = 1.618).
The asymptotic behavior of the sequence and the fading fluctuations of its ratio around the irrational F number can be better understood if the relations between several first members of the sequence are shown. The following example illustrates the relationship of the second member toward the first one, the relationship of the third member toward the second one, and so on:
1:1 = 1.0000, which is less than phi for 0.6180
2:1 = 2.0000, which is more than phi for 0.3820
3:2 = 1.5000, which is less than phi for 0.1180
5:3 = 1.6667, which is more than phi for 0.0486
8:5 = 1.6000, which is less than phi 0.0180
One of the main combinations in which the Fibonacci ratios are used along with other TA methods is the Elliott Wave theory.
As the Fibonacci sequence moves on, each new member will divide the next one approximating more and more to the unreachable phi. Fluctuations of the ratio around the value 1.618 for a lesser or greater value can also be found in the Alteration Rule of the Elliott Wave theory. Thus, any human subconsciously looks for the Divine Ratio: it is indispensable for filling his need for comfort and convenience. With traders, this need for psychological comfort is combined with other stereotypes and comfort zones. For instance, the Moving Average with 13 periods is replaced with MA(14),due to the established European perception of the number 13, and instead of MA(21), MA(20) is used as one reflecting the accustomed decimal system.
This same need for comfort dictates the turning points. Traders aren't psychologically comfortable with too long trends. The excessive length of a trend is determined, on the one hand, by the history of the given security, and, on the other hand, by the inborn feeling of harmony, based on the Golden Section. Chart analysis has a lot in common with nature, where things that are based on the Golden Section are beautiful and shapely and things that don't contain it look ugly and seem suspicious and unnatural. That is why when the distance from the Golden Section becomes excessively long, the feeling of an improperly long (or short) trend arises.
Nowadays, there are five types of trading tools that are based on Fibonacci's discovery: arcs, fans, retracements, extensions and time zones. The lines created by these "Fibonacci studies" are believed to signal changes in trends as the prices draw near them. Today, Fibonacci studies are a wellknown technical analysis method that has numerous followers. And, yes, this method does work rather often. However, the following simple question arises, answering which is key to trading profitably with Fibonacci studies: why, when, and how does that happen? Answering this question will help us answer another not less important question: how much trust can one really put in the Fibonacci tools, for, after all, even the most ardent of the admirers will most certainly agree that the theory does not give a 100 % guarantee?
Created by Tradecision
Figure 1  Fibonacci Times Zones give you general changes in the trend areas in relation to time. Time Zones are most appropriate to a longdated analysis of price variation and are very likely to be of limited value while studying shortdated charts.
How It Works
Many traders believe that Fibonacci studies are a relatively easy to understand trading tool that is based on a simple, trenchantly defined principle and has been proven effective over the time by a large number of successful market players. It is a popular opinion that when correctly applied, the Fibonacci tools can successfully predict the market behavior in the 70% of cases, especially when a specific price is predicted. Others reckon that computations for multiple retracements are a real drag and after a while all you have and can use is a mess. The opponents of the method also believe it to be too timeconsuming. But, probably, the greatest disadvantage of the Fibonacci method is the complexity of the results for reading and the ensuing inability of very many traders to really understand them. One should not rely on the Fibonacci levels as "heavensent," compulsory support and resistance levels. Rather, they are the levels of psychological comfort and just another angle from which a chart can be viewed (which is, actually, done by the majority of traders). The Fibonacci levels are a sort of a frame through which traders look at their charts. This "frame" neither predicts nor contributes anything, but being drawn on the charts of the majority of traders it influences the trading decisions they make.
The difficulty of correctly understanding the Fibonacci levels lies in the ability to learn to regard the studies as an artificial means, created by the human mind in an attempt to dispel the uncertainty, and not as something that can serve as the basis for one's trading decisions. Most often, Fibonacci studies work when no real marketdriving forces are present on the market. It is obvious that the levels of psychological comfort and the "frame" which they make up and through which the majority of traders look at their charts, are by no means the determining factors in those situations, when more important reasons for the prices' growth or reduction exist.
Created by Tradecision
Figure 2  The Fibonacci Fan is a threeline guide, originated from the Fibonacci number series, which, as some traders believe assist in identifying the next areas of support and resistance. The zones, indicated by the fan, can forecast areas of retraction in market trends.
Of course, the "nature's Golden ratio," discovered by the brainy 12th century Italian, does hold true in many instances. There is no denying it either that as far as trading the market is concerned, the famous cosmic law oftentimes holds true as well. However, think of the number of those who are at least aware of the Fibonacci tools, let alone rely on them heavily. Used by a vast number of traders, the Fibonacci studies themselves become a very major factor influencing the market. Most of the time, the Fibonacci studies work due to the cascade effect, which arises because of the huge number of traders (up to 80 % of all the market players when the pivots are clear enough) drawing about the same kind of thing on their charts, thus artificially creating support and resistance levels.
The market is a complex system, and the realization of the true nature of Fibonacci studies as a "selffulfilling prophecy" (well, at least to a great extent it is so) will help you use the tools more efficiently. How? Very simple it will help you avoid any perilous overreliance on them. Your trading will become more versatile and, thus, more efficient.
Conclusion
The more popular Fibonacci methods, such as Fibonacci retracements and extensions, are of more practical value than the more exotic timezones and circles. In any case, the Fibonacci method should only be used in a combination with other methods, and the results derived should be considered just another point in favor of a decision if they coincide with the results, produced by the other methods in the combination.
And that's when the magic will begin to work.
Resources
Tradecision (www.tradecision.com)  fullfeatured trading software enhanced with portfoliolevel backtesting, proprietary studies and neural networks.
Alyuda Research (www.alyuda.com) is dedicated to developing cuttingedge trading and forecasting software solutions for active and professional traders worldwide.



