Fibonacci Fans
What Are Fibonacci Fans?
Fibonacci Fan lines are trend lines based on Fibonacci retracement points. Rising fan lines extend up from a trough and pass through retracement based on the advance (trough to peak). These fan lines can then estimate support levels or potential reversal zones. Falling fan lines extend down from a peak and pass through retracements based on the decline (peak to trough). These fan lines can then estimate resistance levels or potential reversal zones. This article will explain the Fibonacci ratios and provide examples of Fibonacci Fans to project support and resistance.
Fibonacci Sequence and Ratios
We won't delve too deep into the mathematical properties behind the Fibonacci sequence and Golden Ratio. There are plenty of other sources for this detail. A few basics, however, will provide the necessary background for the most popular numbers. Leonardo Pisano Bogollo (1170-1250), an Italian mathematician from Pisa, is credited with introducing the Fibonacci sequence to the West. It is as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610……
The sequence extends to infinity and contains many unique mathematical properties:
After 0 and 1, each number is the sum of the two prior numbers (1+2=3, 2+3=5, 5+8=13 8+13=21 etc…).
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 1.6180 as the numbers increase.
A number divided by the next highest number approximates .6180 (13/21=.6190, 21/34=.6176, 34/55=.6181, 55/89=.6179 etc….). The approximation nears .6180 as the numbers increase. This is the basis for the 61.8% retracement.
A number divided by another two places higher approximates .3820 (13/34=.382, 21/55=.3818, 34/89=.3820, 55/=144=3819 etc….). The approximation nears .3820 as the numbers increase. This is the basis for the 38.2% retracement. Also, note that 1 - .618 = .382
1.618 refers to the Golden Ratio or Golden Mean, also called Phi. The inverse of 1.618 is .618. These ratios can be found throughout nature, architecture, art, and biology. In his book, Elliott Wave Principle, Robert Prechter quotes William Hoffer from the December 1975 issue of Smithsonian Magazine:
….the proportion of 0.618034 to 1 is the mathematical basis for the shape of playing cards and the Parthenon, sunflowers and snail shells, Greek vases and the spiral galaxies of outer space. The Greeks based much of their art and architecture upon this proportion. They called it the golden mean.
How To Draw and Calculate Fibonacci Fans
Rising Fibonacci Fan
Fan Line 1: Trough to 38.2% retracement
Fan Line 2: Trough to 50% retracement
Fan Line 3: Trough to 61.8% retracement
The chart below shows the SPDR S&P 500 ETF (SPY) with rising Fibonacci Fan lines. The lines are based on the March 2009 trough (low) and April 2010 peak (high). The horizontal pink lines show the Fibonacci Retracements tool extending from trough to peak.
It takes two points to draw a line. The first point for each fan line is based on the low. The second point is based on the Fibonacci retracements. Notice how the Fibonacci Fan lines start from the trough and pass through these Fibonacci retracements (blue arrows).
Falling Fibonacci Fan
Fan Line 1: Peak to 38.2% retracement
Fan Line 2: Peak to 50% retracement
Fan Line 3: Peak to 61.8% retracement
The chart below shows the SPY with falling Fibonacci Fan lines. The lines are based on the April 2010 peak (high) and the July 2010 trough (low).
The horizontal pink lines show the Fibonacci Retracements tool extending from peak to trough. It takes two points to draw a line. The first point for each fan line is based on the high. The second points are based on the Fibonacci retracements. Notice how the Fibonacci Fan lines start from the peak and pass through these Fibonacci retracements (blue arrows).
How To Use Fibonacci Fans
After an advance, the Fibonacci Fan lines can be drawn to identify potential support or reversal areas. Once a pullback starts, the fan lines provide chartists with key levels to watch as prices correct. After a decline, the Fibonacci Fan lines can be drawn to identify potential resistance or reversal areas. Once the bounce starts, the fan lines provide chartists with key levels to watch as prices bounce. As with regular trend lines, support or resistance zones extend as the Fibonacci Fan lines extend, which makes them dynamic, not static.
Rising Fan Lines
The chart below (drawn using an arithmetic scale) shows Anadarko Petroleum (APC) with the Fibonacci Fan lines extending from the July low to the October high (2009). The stock bounced off the 38.2% fan line in late October and then moved to the 61.8% fan line in December. APC ended its correction at the third fan line and moved back above 65. There was another pullback in February, and the stock reversed near the third fan line.
The chart below shows Sara Lee (SLE) with the Fibonacci Fan lines extending from the March low to the July high (2009). The stock declined sharply in August, but found support at the 50% line later that month. The first bounce of the 50% fan line was short-lived, but the stock found support again at the 50% line in early September. This chart was drawn using an arithmetic scale.
Falling Fan Lines
The chart on the left shows Nordstrom (JWN) with the Fibonacci Fan lines extending down from the April high to the May low. You could draw the lines once JWN began its bounce in late May. JWN subsequently met resistance between the 50% and 62% fan lines. JWN moved to a new reaction low in early June. Once the prior low is taken out, it is usually necessary to redraw the Fibonacci Fan lines based on the new low. The chart on the right shows new fan lines with JWN again hitting resistance between the 50% and 62% lines. These charts were drawn with a log scale.
Log versus Arithmetic Charts
Wondering whether to use log or arithmetic scaling on your charts? The following are the main differences:
Scaling choice can change the slope of the Fibonacci Fan lines and alter potential support, resistance, and reversal levels.
Log scaling treats price changes as percentage moves. For example, a 10% move from $6 ($0.60) looks the same as a 10% move from $60 (six points).
Arithmetic scaling focuses on the absolute change. A $1 move from 6 to 7 (+16.66%) looks the same as a $1 move from 12 to 13 (+8.33%), even though the percentage change is double. On a log scale, the 16.66% advance would appear twice as large as the 8.33% advance.
The charts below of Alcoa, Inc. (AA) compare an arithmetic and log scale. The chart on the left uses an arithmetic scale. The price grid is equally spaced. The distance between $6 and $7 is the same as the distance from $12 to $13.
Log scaling is generally preferred for longer periods to depict big price movements accurately. Alcoa advanced from about $5 to $12 in less than four months. This move appears sharp on the log scale because the percentage move from low levels is large. The move looks less steep on the arithmetic scale because the absolute change from low levels is the same.
The scaling difference does not change the starting point for the Fibonacci Fan lines or the retracements. The horizontal pink lines show retracement equality. However, because of the scaling, the Fibonacci Fan lines on the log chart are steeper, and Alcoa broke the 50% line in mid-April. The Fibonacci Fan lines on the arithmetic chart are less steep, and Alcoa broke the 50% line in the beginning of May.
So, which scale should you use? There's no right or wrong answer. Arithmetic versus log scaling has been a heated debate for many years. It boils down to a personal preference. Scaling makes little difference with relatively small price movements over short periods. There is, however, a clear difference with big price movements over longer periods. Log scaling is generally preferred for long-term charts.
Extending the Dateline
There may be times when you need to see future support or resistance levels. You'll need to add extra time to your chart to do this.
The chart below shows Fibonacci Fan lines extending from the April high to the July low. These lines are valid as long as the July low holds. An extra 70 bars were added to extend these lines and see future resistance levels.
In SharpCharts, under Chart Attributes, enter the number of extension periods in the Extra Bars box. Notice how the resistance lines steadily work their way lower. The opposite happens with rising Fibonacci Fan lines. Support levels steadily work their way higher.
Concluding Thoughts
Fibonacci Fans identify potential support, resistance, or reversal points. As with the Fibonacci Retracements Tool, these reversal points assume the move is corrective. A pullback after an advance is deemed a correction that will find support well above the initial trough. A bounce after a decline is deemed a counter-trend rally that will hit resistance well below the initial peak. Fibonacci Fan lines allow users to anticipate the ending points for these counter-trend moves.
Like all annotation tools, Fibonacci Fan lines are not meant as a standalone system. Just because prices approach an arc does not mean they will reverse. Prices move right through these lines in many cases. No indicator is perfect. This is why chartists must use other tools to confirm support, resistance, bullish reversals, and bearish reversals.
Using Fibonacci Fans With SharpCharts
Fibonacci Fan FAQs
Further Study
Elliott Wave Principle Robert Prechter
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