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The mathematical sequence was discovered by mathematician, Leonardo Pisano Bogollo, who lived in Italy between 1170 and 1250. His nickname “Fibonacci” roughly translates as “Son of Bonacci”.

By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two. The relevance of the Golden Ratio to the Fibonacci sequence is that the further into the sequence you go, the closer the numbers increase by the ratio of 1.618. In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation and can be written as a rule mathematically: Fn = Fn-1 + Fn-2

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INTERMEDIATE

10. Fibonacci: A Key Forex Concept

Origins of Fibonacci – The “Golden Ratio”

The “Golden Ratio” is a special number, represented by the Greek letter “Phi” that is equal to approximately 1.618. The ratio can be used to explain many things in areas such as geometry, art, architecture and astronomy. The phenomenon appears in many natural events, ranging from as small as the strands of DNA to as large as galaxies such as the Milky Way.

Figure 4: The Fibonacci sequence appears in naturally occurring events such as a shell

Figure 3: The Fibonacci sequence appears in naturally occurring events such as Hurricane Sandy

Figures 1 & 2: How the Fibonacci series develops and the first 15 numbers in the sequence

The Fibonacci sequence: 0 - 1 - 1 - 2 - 3 - 5 - 8 - 13 - 21 - 34 - 55 - 89 - 144 - 233 - 377

What are the popular Fibonacci retracements traders look out for?

The Fibonacci retracement is the potential retracement of an original move in price. Fibonacci retracements use horizontal lines to indicate areas of support or resistance at the key Fibonacci levels before it continues in the original direction.

These levels are created by drawing a trendline between two extreme points and then dividing the vertical distance by the key Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8% and 100%.

Figure 5: The Fibonacci retracements in use on Euro/Dollar

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Calculating the Fibonacci levels

• A number divided by the next highest number approximates 0.6180

(13/21=0.6190, 21/34=0.6176, 34/55=0.6181, 55/89=0.6179). The approximation nears 0.6180 as the numbers increase. This is the basis for the 61.8% retracement.

• A number divided by another two places higher approximates 0.3820

(13/34=0.382, 21/55=0.3818, 34/89=0.3820, 55/144=0.3819). The approximation nears 0.3820 as the numbers increase. This is the basis for a 38.2% retracement, however also note that 1 - 0.618 = 0.382

• A number divided by the previous number approximates 1.618

(21/13=1.6153, 34/21=1.6190, 55/34=1.6176, 89/55=1.6181). The approximation nears 1.618 as the numbers increase. This is the basis for a 161.8% projection.

Some traders use the Fibonacci series to set up their moving average studies, however Fibonacci is more commonly used to indicate price retracements and projections. The key factor is that the quotient of the adjacent terms possesses the golden ratio of approximately 1.618, or its inverse 0.618.

The Fibonacci studies are not intended to provide the primary indications for timing the entry and exit of a position; however, they are useful for estimating areas of support and resistance. Many traders will use combinations of Fibonacci studies to obtain a more accurate forecast. For example, a trader may observe the intersecting points in a combination of the Fibonacci fans and resistances.

10. Fibonacci: A Key Forex Concept

How is Fibonacci relevant to financial markets?

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6. Bollinger Bands

Fibonacci Projections

It is also possible to use Fibonacci for calculating potential price targets. Fibonacci projections are numbers that are calculated when there has been an initial move followed by a retracement and a subsequent move above the first peak. This is used for deriving targets for breakouts. The popular numbers used will once again be 50%, 61.8%, 100% and perhaps even 161.8%.

In this chart of Euro/Dollar, the upside target is calculated once the price moves back above the December 2012 high at $1.3308. The first target is the 61.8% projection at $1.3397, followed by the 100% projection at $1.3645. Notice also how the Fibonacci levels continue to provide the basis of support and then resistance during the February 2013 decline.

Fibonacci Fans

Fibonacci fans are another tool to help provide a gauge for support and resistance levels. The fans are measured by calculating the Fibonacci retracement levels on the vertical distance between two key levels; and then drawing the three lines out from the first point to dissect the 38.2%, 50% and 61.8% retracements on the vertical line. Again traders look to use these lines for consolidation.

Figure 6: Using Fibonacci Projections

Figure 7: Fibonacci Fans on Euro/Dollar

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10. Fibonacci: A Key Forex Concept

Summary Trading with Fibonacci:

• Helps to identify supports and resistances.

• Can also provide price targets and forecasts.

• When the market approaches Fibonacci levels expect a consolidation - which might be an opportunity to either enter a position or take profits

Figure 4: Range trading using the Bollinger Bands on Silver

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