## A Little History of Fibonacci

Fibonacci is the short name for Leonardo Pisano, also known as Leonardo Bigollo, an Italian mathematician from the 12th century. He was already famous in his time, having been hired by the Emperor of the Holy Roman Empire Frederick II. He is attributed for having first introduced Hindu-Arabic numerology based on the decimal system. However, he is best known nowadays for having invented the Fibonacci Sequence of numbers.

## Fibonacci Numbers

Also known as a Fibonacci Spiral, due to the graphical representation of its sequence.

The Fibonacci Series is created by adding the previous two numbers, where the first two numbers are 0 and 1.

The mathematical formula is:

Fn = F_{n-1} + F_{n-2}

The sequence will be as follows 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on.

These numbers have been found to be repetitive throughout nature, where often the numbers of petals on a flower, segments in a pine cone or seeds in a sunflower are each a Fibonacci number.

In Forex, these numbers are used in a series of technical indicators and ratios. They are also used to create ratios for price movement levels. These ratios can help calculate how much a currency may retrace or extend into the future. The ratios are created by dividing one number of the Fibonacci Series by the next higher number, by the second next higher number and then by the third next higher number.

**Examples**

(11th Sequence Number / 12th Sequence Number
34/55 =0.61818182 (61.8%)

Multiply by 100 and round to two decimal places to get the percentage value.

As the Fibonacci numbers increase, the ratio tends to be closer to 0.618. Dividing a number by the previous (lower) number gives 1.618, known by ancient civilizations as the **Golden Mean**, and often used in architecture.

Dividing a number by the second subsequent number and by the third subsequent number will give ratios that become 0.382 and 0.236.

**Examples**

10th Sequence Number / 12th Sequence Number
21/55 = 0.381818 (38.2%)

10th Sequence Number / 13th Sequence Number
21/89 = 0.235955 (23.6%)

Note: `1 - 0.618 is equal to 0.382`

The most important and commonly used Fibonacci numbers in Forex trading are **38.2%, 50.0% and 61.8%**. These numbers show different depths of how a trend may retrace or extend. The price may not always land exactly on the Fibonacci numbers, so it’s always important to allow a little buffer zone either way. You will see these in the following examples.

## Fibonacci Extensions

Making use of The Fibonacci Series - this extension tool is used to determine how far the next leg of a trend may extend after a retracement. The trend may be an upwards trend or downwards trend. Looking at the chart below, you can see how the line from point A to point B traces the last leg of a significant rally and the line from point B to point C traces the subsequent retracement. The Fibonacci Extension tool calculates the extension of the rise from point A to point B and plots a line exactly 100% above the lowest retracement point, which is point C. That is to say, if the increase from point A to B is equal to 2% then the 100% line will be 2% above the lowest retracement point C.

The 61.8% and 161.8% are also representations of the rise from point A to point B. These lines then represent target price and resistance levels for the continuation of a Bull trend. We can see that price action rises from point C and its first target/resistance level can be set by the 61.8% line at 191.793. If that line is broken and the rally continues, the next target level would be the 100% line at 201.709

The chart below, shows how the first leg of the rally, line A to B, gives way to a retracement, line B to C, then plotting the Fibonacci Extension we can see how the rally continues to the 161.8% line, at which point it meets resistance and retraces close to the 100% line before subsequently breaking the 161.8% line again, which also acts as a support line before continuing the Bull trend.

As the price level breaks one line it is expected that price will continue to the next line. In this example, the price broke through the first two lines before retracing after bouncing off the third line.

## Fibonacci Retracement lines

These lines use the same ratios created with Fibonacci numbers to forecast possible support and resistance levels in a retracement. From the chart below, we can see how the Bear leg that goes from point A to point B then retraces from point B to point C. The price hits the 38.2% Fibonacci Retracement line. It does not manage to break and hold that resistance and regains downward momentum; eventually going past the previous low at point B.

These lines are useful in detecting possible target and resistance or support lines.

These lines can help you avoid getting into a market just before a minor correction, where you might see your stop hit whilst being on the right trend. At the same time they can indicate where the best points may be to get into a trade to begin with.

## Upward Fibonacci Trends

The chart below shows the Fibonacci Fan and the three lines that fan out from the base at point A, which is the beginning of the bull trend. Point B is the highest point after which there is a considerable retracement for the following two bars. Drawing a line from A to B creates the fan shown in the chart, with support/resistance lines at 38.2, 50 and 61.8.

The number 50 comes from the general knowledge of market technicians that support and resistance levels often occur on the 50% line.

Fibonacci Lines Create Both Support & Resistance lines.

We can see that price hits the first fan line, 38.2 at point C, and stalls, eventually breaking it and bouncing off the 50 fan line at point D. Strong price action then breaks through the resistance of the 38.2 fan line and continues upward. At point E, another retracement of the underlying Bull trend is met with resistance on the same fan line. The Bull trend is considered to be intact as long as the 61.8 line is not broken, in which case you would be looking for signs of trend reversal.

## Downward Fibonacci Trends

The Fibonacci Fan works in the same way for a downward trend and creates resistance and support lines for a Bear trend. The numbers used are the same ones created by the Fibonacci Sequence. The chart below shows how the fan is drawn by plotting a line from the peak at point A to the first trough at point B. The first retracement goes through the first two lines and is stopped by the resistance of the third line, point C.

Price then retests the 61.8 line at D and subsequently continues to fall, with price action remaining between the 38.2 and 50 lines for most of the downward movement, as shown by the arrows. The warning of reversal comes first with an initial break of the 61.8 line at point E, for the price to then continue its fall. However this is then met by support at F, the 61.8 line, at which point reversal is complete and price action shows a Bull trend from there.

61.8 is an important break line.

## How is Fibonacci Used With Other Indicators?

These Fibonacci indicators are especially useful when used together with other __Technical Indicators__. You may be using __Simple Moving Averages__, Oscillators, or other combination of indicators at your disposal. The Fibonacci tools can give a great help in understanding better support and resistance points.

Fibonacci should not be used alone.

The Chart below is a combination of __Ichimoku cloud__ and Fibonacci retracement, which is drawn on the rally that goes from point 1 to point 2. We can see how price retraces to point A, the 23.6% retracement line, where it meets some support for 3 candles and then falls further to the 38.2% retracement line, where again it encounters some support for 6 candles before decreasing further in price and bouncing off the support created by the 50% line, point B. Price then rises to point C where it encounters resistance at the 23.6% line and also from being close to the top side of the Ichimoku cloud. Failing to break the 23.6% resistance line price then falls back down to the 61.8% support line before regaining momentum for a rally up to the bottom side of the Ichimoku cloud.

Note how price action gets close to the 76.4% line but doesn’t reach it. This line is not derived by a Fibonacci ratio, simply it is 1 – 23.6% and is often used in a Fibonacci Retracement to give another layer as the distance from 61.8% to 100% is quite large. Both Ichimoku and 23.6% Fibonacci line need to be broken for the Bull trend to continue, creating a strong area of resistance and a strong indicator if the level is broken.

## Fibonacci Clusters

A Fibonacci Cluster is made by creating layers of Fibonacci lines, this is done by drawing various trend lines at key reversal points on a chart.

In the example below you can see three different trend lines, AB, CD and EF which create three different sets of retracement lines. Where lines overlap or are very close together will create stronger resistance and support levels. This may be repeated with a Fibonacci Extension or Fan to obtain the same type of result.

Summary

- Fibonacci numbers are calculated using
`Fn = F`

_{n-1}+ F_{n-2} - Most important numbers are 38.2%, 50.0%, 61.8%
- Identify key levels of support and resistance
- Find how deep a retracement may occur
- Find how long an extension may occur
- Don’t use Fibonacci numbers on their own
- More clusters mean these areas will show stronger support and resistance levels

Actions

- You’re going to identify an existing Fibonacci extension
- Open Meta Trader 4 on the AUD/USD, H1 chart
- Scroll to 13 May 2015
- Find the initial downwards Fibonacci trend
- Draw your Fibonacci lines and see if the price bounces around
- Identify another Fibonacci line further down in the trend
- Do you notice any areas of confluence? (Multiple Fibonacci lines in one place)

Bonus: Try to find any other technical indicators that could help you decide whether there are points that have strong resistance or support.