Fibonacci / Golden Ratio
Learn how to use a Fibonacci retracement to identify possible areas of support and resistance and decide when to open and close a position, or when to apply stops and limits to your trades.
Origins of Fibonacci or the “Golden Ratio”
The Fibonacci Sequence or “Golden Ratio” is a powerful number that recurs in nature and can be used to explain relationships in geometry, art, architecture and astronomy. Represented by the Greek letter “Phi” and equal to approximately 1.618, it appears in many natural phenomena, from small strands of DNA to massive galaxies.
The ratio was first discovered by the Italian mathematician Leonardo Pisano Bogollo, who lived between 1170 and 1250. His nickname “Fibonacci” roughly translates to “Son of Bonacci”.
The first two numbers in the Fibonacci sequence are 0 and 1, and 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 mathematically as a rule:
Fn = Fn-1 + Fn-2
Figures 1 & 2: How the Fibonacci series develops and the first 15 numbers in the sequence
|The Fibonacci sequence:|
Figures 3 & 4: The Fibonacci sequence appears in naturally occurring phenomena such as Hurricane Sandy and the curvature of a seashell
How is Fibonacci relevant to financial markets?
Fibonacci numbers can be used in several 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), you can use Fibonacci numbers (21, 55, 89, 144) instead. It’s important to remember that, depending upon requirements, different moving averages will work for different traders and in different markets.
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, you might observe the intersecting points in a combination of Fibonacci fans and resistances.
N.B. 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 but 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.
Figure 5: Fibonacci retracements in use
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%.
It is also possible to use Fibonacci for calculating potential breakout price targets. Fibonacci projections are numbers 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 above GBP/USD chart, 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 note that once consolidation of the 100% Fibonacci projection breaks to the upside in January 2018, the market quickly moves to the 161.8% Fibonacci projection.
Figure 7: Fibonacci Fans on EUR/USD
Fibonacci fans are a less commonly used Fibonacci tool to help gauge 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. You can look to use these lines for consolidation.
- A useful confirmation tool
- Helps to identify supports and resistance areas.
- Can also provide price targets.
- Once the market has traded decisively clear of a Fibonacci level, the next Fibonacci level becomes the near-term target.
- Markets will often consolidate around Fibonacci levels.