### The Fibonacci number sequence was brought to the west by Leonardo Pisano Bigollo (1170 – 1250) also known as Fibonacci. Fibonacci was best known for his use of the Fibonacci numbers in his work, Liber Abaci (Book of Calculation). The magic of the Fibonacci numbers and their role in trading is something that has occupied me for some time now, and will be the focus of this article.

Most traders who are familiar with the Fibonacci numbers are likely more acquainted with the ratios that result when they are divided with each other, and how they are applied to trading. Despite how some may feel about the Fibonacci numbers and their use in the financial markets, the evidence stacked up to support the use of Fibonacci numbers, makes it difficult to ignore them.

The Fibonacci numbers themselves are simple to calculate, the calculation of which can be summed up via the following expression:

`Fn+1 = Fn + Fn-1`

This results in a sequence of numbers that starts at zero and continues on forever. The following is the sequence of the first 15 numbers:

`0`

1

2

3

5

8

13

21

34

55

89

144

233

377

610

In order to obtain the Fibonacci ratios we know and use in trading, we must divide the numbers with one another. It’s best to start with one of the larger numbers in the sequence such as 34, as this will ensure a greater degree of decimal point accuracy. If we perform the required division using 34 as a minimum value, we get the following:

`34/55 = 0,618`

34/89 = 0,382

This is how we get the standard Fibonacci ratio values. In order to get the deeper Fibonacci retracement levels, we must obtain the square-root of the value 0.618 (The golden mean – 1) as follows:

`√(0,618) = 0,786`

So now we have the following values:

`0,786`

0,618

0.382

Some of you may be wondering where the 50% and the deeper 88% retracement levels are. The 50% Fibonacci retracement has nothing to do with the Fibonacci number sequence but can be obtained when performing the same division operation on the smaller numbers in the sequence, 1 and 2 (1/2 = 0.50). This value was added, as it made perfect sense to have a mid-way reference point between the high and the low. As for the 88% retracement level, this can be calculated by taking the square-root of the 79% Fibonacci retracement value calculated previously:

`√(0,618) = 0,786`

√(0,786) = 0.88656641037

And this process can also continue on forever:

`Rn = √(Rn-1)`

What about the external retracements and extensions? The Fibonacci retracements 127%, 162% and 262% immediately come to mind as some of the more significant external levels: the square root of the golden ratio (1.27), the golden ratio (1.62), the golden ratio + 1 (2.62), as well as the deeper, more extreme level (4.235):

`√(1.618) = 1.27200628929`

55/34 = 1.618 (golden ratio)

89/34 = 2.618 (golden ratio + 1)

144/34 = 4.235

Fibonacci levels are used by all types of traders, as they provide very clear levels for both stops and targets. For the price action trader, Fibonacci levels can be combined with historically respected levels of support and resistance to help qualify price sensitive levels. For the avid chartist (please read Trading Gartley Patterns at Historically Respected Levels for additional information), Fibonacci levels can be used to identify over extended price levels, areas at which price can be expected to slow down and/or reverse. No matter how you trade, providing you understand how to properly apply them, Fibonacci levels can be used to complement most trading styles.

Many of the top traders I know and respect who use them, do so with great success, as they understand the strengths and application of Fibonacci numbers in trading. I asked three of the most respected names in trading why they use Fibonacci levels in their trading and received their responses. Let’s see what they had to say.

**Chris Lori**

My mentor and friend, Chris Lori, has always emphasised the importance of price action. During his workshops and Pro Traders Club webinars, some of the key points you’ll hear him discuss over and over again are support and resistance and Fibonacci retracement levels. When I asked Chris why he used Fibonacci levels in his trading, he responded with the following:

Fibonacci numbers are the only secondary tool that I use in our trading models, outside of price action. The common thought that price response at Fibonacci levels is the result of a consensus of traders eyeing the same level is a myth. The diversity of traders’ minds and market structure doesn’t work that way. Rather, in my fourteen years using Fibonacci levels, there is a distinct and consistent human rhythm that connects Fibonacci numbers to real market behaviour.

One look at Chris Lori’s charts and you’ll quickly notice what he finds most important in his trading: support and resistance, and Fibonacci levels:

If you’re looking for intensive, high quality training, then Chris Lori is your man. If you have any questions for Chris Lori or wish to learn more about how he can help you, please visit any of the following resources:

**Larry Pesavento**

If you’re familiar with H. M. Gartley’s work in his book “Profits in the Stock Market” which he wrote in 1935, then you’ll know Larry Pesavento. Larry has done a tremendous job in documenting the details required to properly understand and identify Gartley patterns in his latest book, *Trade What You See: How To Profit from Pattern Recognition*. This book is a true gem as Larry goes into great detail in order to effectively explain how Fibonacci ratios are used to qualify Gartley patterns (e.g. AB=CD, Butterfly patterns, three drives). If Gartley patterns are of interest to you then this book should be on your shelf.

When I asked Larry why he uses Fibonacci levels in his trading, he responded by sending me some videos, two of which are presented below.

In the first video, Larry provides an analysis of the EURUSD cross, where his primary focus is on Fibonacci levels and Gartley patterns.

In this next video, which focusses on Gold, his focus is again on Fibonacci levels and Gartley patterns.

For more information about Larry, please visit his website: http://www.tradingtutor.com/

**Carolyn Boroden**

Another great and very thorough trading book about the effective use of Fibonacci retracements is, *Fibonacci Trading – How to Master the Time and Price Advantage*, written by Carolyn Boroden.

When I asked Carolyn why she used Fibonacci levels in her trading, I received the following response:

Fibonacci analysis enables you to identify high probability, relatively low risk trade setups where the risk is clearly defined along with the targets. Compared to using indicators which are lagging, this method is predictive. Fibonacci works on any time frame and essentially any good market data. I have applied this method to stocks, ETFs, Futures, and the FOREX markets.

For more information about Carolyn Boroden, please visit her website: http://www.fibonacciqueen.com/

**How do I use Fibonacci Levels**

My interest in Fibonacci levels in trading started when I began programming the Price Action Pro indicator. I was looking for patterns and levels that would benefit the price action trader especially, with the following requirements:

- Must work on any time-frame
- Must not be based on any lagging indicators
- Must work with any currency pair
- They should enable me to project them as far as one year into the future

So my quest began. I performed automated analysis on all time-frames and multiple currency pairs and very quickly, I began to see price levels that price would respect over and over again. What were these levels? Fibonacci retracement levels calculated using data from the period previous to the current. As an example, assuming that the December 2013 high was established before the low, if you draw Fibonacci levels from the high to the low and project the Fibonacci retracement levels onto price action one month into the future, which in this example would be January 2014, you’ll find that price will respect these levels to the point that it almost looks manipulated. I know this sounds silly so let’s have a look at a recent example of the EURUSD H4 chart that illustrates what I’m talking about:

The levels shown above in purple are the monthly Fibonacci retracement levels. The thick black line at the top is the 127% external retracement level of 2013. A single day of trading and a 200+ pip bullish rally moved through this level by 16 pips before closing roughly 150 pips below it. You’ll get the same results on any time-frame but I find the greater time-frames, the lowest being the daily to be the most effective. I programmed this functionality into the Price Action Pro indicator but chose not to go any lower than the hourly to ensure more superior results. The power of these levels still amazes me.

**Conclusion**

To me, the Fibonacci number sequence is fascinating, not only because of its use in trading but because it exists in so many things. Found in the petals of a flower, the heads of a seed, pine cones, tree branches, sea shells, hurricanes, faces, DNA molecules and so much more, why would the currency markets be left out? When I first fixed my eyes on a Forex chart I remember thinking:

Wow what a mess!

Now, looking back, all I can say is that nothing could be further from the truth. While the currency markets are indeed about as random as anything else man-made I can think of, there is indeed a structure, a structure that will reveal itself to those who are willing to look a little closer.

Special thanks for Chris, Larry and Carolyn for their contributions.

Thank you.

**References**