Common Retracements
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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