## Table of contents

## Who is Fibonacci?

Fibonacci, also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano, was born in 1170 and died in 1250. Fibonacci was a famous Italian mathematician and often referred to as the most talented of the Middle Ages.

He was not commonly known as Fibonacci until many hundreds of years after his death.

Fibonacci is known for two great works in the field of mathematics.

His first achievement was to popularise the Hindu-Arabic numeral system in the Western world. This was done by his composition of Liber Abaci, the book of calculation. This book advocated the use of the numeric digits 0 through 9, as well as a place value. This new method of enumeration replaced the Roman numeral system. It has been instrumental in transforming the global economy by allowing modern finance and accounting methods to flourish.

His second achievement was to bring us the famous Fibonacci sequence. This sequence was also documented in his book Liber Abaci. Each number in the sequence is the sum of the previous two numbers. Today this sequence often starts with 0 but Fibonacci originally started from 1 and continued to the thirteenth position. His sequence is therefore 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.

## What is the Fibonacci golden ratio?

The golden ratio is intimately linked to the Fibonacci sequence. It defines the approximate relationship between any two successive terms of the sequence.

For example; 233 / 144 = **1.61805**

As the Fibonacci sequence extends further the ratio draws closer to the value defined by the golden ratio. For the mathematicians amongst us the value of the golden ratio is 1.6180339887.

The golden ratio can be found in almost all aspects of the natural world, from the smallest atom, to the universe itself.

Our interest though is with the financial markets.

The traders who are familiar with Fibonacci will notice that the golden ratio is a significant value. The value 61.8% is a very common value used for extension and retracement levels. We can also derive the other significant extension and retracement level from the golden ratio. If this number is taken from 100, then we arrive at 38.2%.

We shall be discussing other key levels that are derived from the Fibonacci sequence and golden ration.

## Fibonacci Retracement Levels

When the price of an asset experiences a rally it will often experience a decline before it continues its original advance. When the price declines in this way it is referred to as a retracement.

This is where Fibonacci comes in useful.

Lets take an example. The price of XYZ stock advances from £10 to £20, followed by a decline to £16. The price has retraced £4 of the original £10 increase. The retracement is therefore 40%.

The amount that a price retraces very often coincides with a Fibonacci ratio. The main ratios are described later on this page.

The same principle applies when the price of an asset falls.

The key to Fibonacci retracement levels is knowing how and where to apply them to charts. To be successful the trader must clearly identify a significant high and low. These 2 values then form the original advance or decline. From there you can identify where the key retracement levels are likely to occur.

The above is a weekly chart for the S&P 500. It shows examples of Fibonacci retracements in rising and falling markets.

The left side of the chart shows a decline from A to B, followed by a retracement to C. The high at A is 2940, the low at B is 2603 and the retracement level C is 2816. The price falls by 337 points from A to B and then recovers 213 points to C. The price has retraced by 63.2%.

The right side of the chart shows an advance from A to B, followed by a retracement to C. The low at A is 2315, the high at B is 2958 and the retracement level C is 2728. The price advances by 643 points from A to B and then declines 230 points to C. The price has retraced by 35.7%.

These retracement values of 63.2% and 35.7% are very close to the key Fibonacci levels associated with the golden ratio.

These retracement levels can be seen on all assets and on all time frames. A Fibonacci retracement can also be referred to as a Fibonacci ABC pattern.

## Fibonacci Extension Levels

Once you have mastered Fibonacci retracement levels the next logical progression is to Fibonacci extensions.

Fibonacci extensions always occur immediately after a Fibonacci retracement. If the retracement is a decline then the extension will be an advance. If the retracement is an advance then the extension will be a decline.

You have probably guessed that the amount the price extends corresponds with a Fibonacci ratio.

Lets take an example. The price of XYZ stock advances from £10 to £20, retraces to £16, followed by an advance to £22. The price has therefore extended by £6 from its retracement low. £6 is 60% of the initial advance from £10 to £20.

Just like Fibonacci retracements the key to extension levels is knowing how and where to apply them to charts. Once you have mastered the ABC pattern it is not too much extra effort to apply extension levels.

The above example shows a daily chart for GBP USD. It shows a Fibonacci ABC retracement pattern with three examples of Fibonacci extensions plotted onto the chart. The first horizontal line is a 38.2% extension and coincides with the high at D1. The second horizontal line is a 61.8% extension and coincides with the high at D2. The third horizontal line a 100% extension and coincides with the high at D3.

A Fibonacci extension can also be referred to as a Fibonacci ABCD pattern. As the name suggests this is very similar to the Fibonacci ABC pattern.

## Fibonacci Arcs

To construct a Fibonacci arc you must first draw a straight line between a significant high and low. This forms the base line.

The arcs are then drawn as semi circles with the central point being on the end of the base line. The arcs are drawn so they intersect the base line at 23.6%, 38.2%, 61.8% and 78.6%.

## Fibonacci Time Zones

Fibonacci time zones are drawn as vertical lines on the chart . The chart can be on any time frame. You must first identify a significant high or low. This point then forms the first time zone.

A reminder of the Fibonacci sequence. 1, 2, 3, 5, 8, 13, 21, 34.

For each number in the sequence a vertical line is drawn on the chart. Each line will be drawn the corresponding number of bars outwards from the first time zone.

## Fibonacci Ratios

We have discussed a few different Fibonacci ratios on this page but there are many others that are significant. The following list highlights the major ratios:

- 23.6%
- 38.2%
- 61.8%
- 78.6%
- 100%
- 161.8%
- 261.8%
- 423.6%

Many traders also consider 50% a Fibonacci ratio, although this is not strictly valid according to the Fibonacci sequence.

## Summary

Adding Fibonacci to your trading skill set will be invaluable and you will see charts in a different light.

There are two key Fibonacci ratios. These are 38.2% and 61.8%.

We have discussed the main ways that the Fibonacci sequence is used in trading. Another way that they are used is for the values associated with indicators and oscillators. For example you could use Fibonacci numbers for your moving averages and crossovers.