Intermediate and Advanced Technical Analysis Series
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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 geometry, art, architecture and astronomy. The phenomenon appears in many natural events, ranging from small strands of DNA to the unimaginably large in galaxies such as the Milky Way.
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”.
The first two numbers in the Fibonacci sequence are 0 and 1, but then 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 a 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
Figures 1 & 2: How the Fibonacci series develops and the first 15 numbers in the sequence
How is Fibonacci relevant to financial markets?
Fibonacci numbers can be used in a number of technical indicators. Some traders use the Fibonacci series to set up their moving average studies. Instead of using round number moving averages (20, 50, 90, 200), traders may look to use Fibonacci numbers (21, 55, 89, 144). It is important to remember that different moving averages will work for different traders and in different markets, depending upon requirements.
Fibonacci is more commonly used for the calculation of potential support and resistance levels in price retracements and projection levels. The key factor is that the quotient of the adjacent terms possesses the golden ratio of approximately 1.618, or its inverse 0.618.
Many traders will use combinations of Fibonacci techniques to obtain a more accurate forecast. For example, a trader may observe the intersecting points in a combination of the Fibonacci fans and resistances.
N.B. The Fibonacci studies should not be used as primary indicators of timing on entry or exit of a position. They can be useful in establishing potential areas of support and resistance, however, they should be used in conjunction with other indicators as a confirmation tool.
Calculating 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.
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 the original direction re-establishes.
What are the popular Fibonacci retracements traders look out for? 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%, 76.4% and 100%.
Figure 5: Fibonacci retracements in use
It is also possible to use Fibonacci for calculating potential breakout 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 initial retracement is then used for deriving targets for breakouts.
Popular levels used will once again be 50%, 61.8%, 100% and perhaps even 161.8%.
Figure 6: Fibonacci Projections
In the chart of GBP/USD, the Fibonacci projection levels can be used once the market breaks above the May 2017 high of $1.3045. A long term 100% Fibonacci projection target is hit and other key Fibonacci levels become key support and resistance points. It is also interesting to notes that once consolidation of the 100% Fib projection breaks to the upside in January 2018, the market quickly moves to the 161.8% Fib projection.
Fibonacci fans are another (less commonly used) Fibonacci 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 7: Fibonacci Fans on EUR/USD