The Fibonacci Retracements Tool at StockCharts shows four common retracements: 23.6%, 38.2%, 50%, and 61.8%. From the Fibonacci section above, it is clear that 23.6%, 38.2%, and 61.8% stem from ratios found within the Fibonacci sequence. The 50% retracement is not based on a Fibonacci number. Instead, this number stems from Dow Theory's assertion that the Averages often retrace half their prior move.
Based on depth, we can consider a 23.6% retracement to be relatively shallow. Such retracements would be appropriate for flags or short pullbacks. Retracements in the 38.2%-50% range would be considered moderate. Even though deeper, the 61.8% retracement can be referred to as the golden retracement. It is, after all, based on the Golden Ratio.
Shallow retracements occur, but catching these requires a closer watch and quicker trigger finger. The examples below use daily charts covering 3-9 months. Focus will be on moderate retracements (38.2-50%) and golden retracements (61.8%). In addition, these examples will show how to combine retracements with other indicators to confirm a reversal.
Fibonacci retracements are often used to identify the end of a correction or a counter-trend bounce. Corrections and counter-trend bounces often retrace a portion of the prior move. While short 23.6% retracements do occur, the 38.2-61.8% zone covers the most possibilities (with 50% in the middle). This zone may seem big, but it is just a reversal alert zone. Other technical signals are needed to confirm a reversal. Reversals can be confirmed with candlesticks, momentum indicators, volume or chart patterns. In fact, the more confirming factors, the more robust the signal.
Fibonacci Retracements are ratios used to identify potential reversal levels. These ratios are found in the Fibonacci sequence. The most popular Fibonacci Retracements are 61.8% and 38.2%. Note that 38.2% is often rounded to 38% and 61.8 is rounded to 62%. After an advance, chartists apply Fibonacci ratios to define retracement levels and forecast the extent of a correction or pullback. Fibonacci Retracements can also be applied after a decline to forecast the length of a counter-trend bounce. These retracements can be combined with other indicators and price patterns to create an overall strategy.
The Sequence and Ratios
This article is not designed to 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
A number divided by another three places higher approximates .2360 (13/55=.2363, 21/89=.2359, 34/144=.2361, 55/233=.2361 etc….). The approximation nears .2360 as the numbers increase. This is the basis for the 23.6% retracement.
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 .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.
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