Rabbits, Fibonacci and Market
Rabbits
and Market Behavior
Fibonacci Number & Golden
Ratio
Retracement & Projection
Ever Wonder ….
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How a pair of rabbits, produce baby
rabbits, and produce more next
generation rabbits, … and so on and
so forth, .. And leading to massive
growth of rabbits ..?
How some disease strikes on the
rabbit population resulting in decline
of rabbit population and to almost
extinction, then rabbits population
grows again?
How you calculate the growth and
decay pattern?
Leonardo Fibonacci

Leonardo Fibonacci, a famous
mathematician, born in Pisa, Italy around
1170, figured out the rabbit puzzle.
Fibonacci sequence, or Number
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Add the last two numbers to get the next.
0, 1, 1, 2, 3, what is the next number?
 The answer is 5, and so on and so forth
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610,
987,...
Beginning with a single pair of rabbits, if every month each
productive pair bears a new pair, which becomes productive
when they are 1 month old, how many rabbits will there be
after n months? The answer is in the above number.
Do you enjoy music, with rhythm, notes (numbers) behind?
We will be curious about the number behind that produces music.
Do you react with anxiety, anger, excitement, greediness to these number? They occur
naturally, they emerge naturally also. No need to be reactive, just be patient, observe, enjoy
when the numbers appear.
What has this got to do with investment on market?
Fibonacci in nature
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some plants branch in such a way that they
always have a Fibonacci number of growing
points. Flowers often have a Fibonacci number
of petals, daisies can have 34, 55 or even as
many as 89 petals!
Do you appreciate the beauty of the nature?
We will be curious about the patterns that
produce the beauty.
Do you react with anxiety, anger, excitement,
greediness to these patterns?
What has this got to do with investment on
market?
The Golden Ratio
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Divide any number in the Fibonacci sequence
by the one before it, for example 55/34, or
21/13, and the answer is always close to
1.61803.
Or, divide by one after it, e.g. 34/55, or 13/21,
and the answer is always close to 0·61803...
phi = 1·61803.. Or the inverse (1/1.61803) phi
= 0·61803...
Do you aspire to have well balanced life, with a golden
ratio, a balanced RATIO?
What has this got to do with investment on market?
Fibonacci Fingers?
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You have ...
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2 hands each of which has ...
5 fingers, each of which has ...
3 parts separated by ...
2 knuckles
The Fibonacci Number! Is this just a coincidence or not?????
However, if you measure the lengths of the bones in your finger
(best seen by slightly bending the finger) does it look as if the
ratio of the longest bone in a finger to the middle bone is Phi?
What about the ratio of the middle bone to the shortest bone (at
the end of the finger) - Phi again?
Can you find any ratios in the lengths of the fingers that looks
like Phi? ---or does it look as if it could be any other similar
ratio also?
Fibonacci Credit Card
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Standard sized credit
cards are 54mm by
86mm, creating a
ratio of 0.628, less
than a millimeter off
from a perfect
golden section of
0.618.
A balanced / Golden ratio is pleasing to the eyes.
What has this got to do with investment on market?
Markets may be as geometrically
perfect as a spider's web
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Ermanometry Research shows the
markets to be perfectly patterned,
explaining that humans, being part of
nature, create perfect geometric
relationships in their behaviors, not unlike
a spider spinning a geometrically perfect
web with no conscious awareness of its
amazing feat. Ermanometry applies the
logarithmic spirals found in sea shells
with dynamic ratios in 3D to relate one
market move to others
If you are more curious, refer http://goldennumber.net/stocks.htm
What has Fibonacci got to do with
investment in market?
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So much for the mathematic. Important
message & insight & challenge to us …
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Respect and appreciate the evolving
pattern of the market, the nature, the
manifestation of human beings.
Don’t be reactive, but be cool and calm
and ride along with the up and down of the
sea waves like a good wind surfer.
Market Behavior
[Market = Stock Market, Unit Trust, Currency, Commodity, Future, Option …]
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Observe carefully, market goes up and down, up and down again.
Market goes up “b” in chart “A”, drop a bit “a” (or retrace) and goes
higher up again. The little drop reaches certain level, or ratio, and
climbs up again.
Market declines “b” sharply in chart “B”, up a bit “a” (or retrace) and
come down further. The little up or retracement reaches certain level,
or ratio, and moves downward again.
a/b = Ratio,
Y
a
“A”
b
X
Y
Fibonacci
ratio
(see next slide to
remember some
important ratios”
a
“B”
b
X
Just remember these Fibonacci Ratios
 23.6%,
 38.2%,
 50
%,
 61.8%
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Study carefully the following templates where
the ratios are applied.
Fibonacci (downward) Retracement with
continuing upward trend
a
b
23.6%
38.2%
50%%
61.8%
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a/b ratios : 23.6%, 38.2%, 50%, 61.8%
When Fibonacci behavior applies, price “a” may drop 23.6% of “b”, or
38.2%, or 50%, or 61.8%, before it continues its upward trend.
Again we use this as Guide for our investment decision later.
Fibonacci (upward) Retracement with continuing
downward trend
61.8%
b
a
50%%
38.2%
23.6%
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a/b ratios : 23.6%, 38.2%, 50%, 61.8%
When Fibonacci behavior applies, price “a” may rise 23.6% of “b”, or
38.2%, or 50%, or 61.8%, before it continues its downward trend.
Again we use this as Guide for our investment decision later.
Fibonacci Retracement with change in trend
direction
61.8%
a
b
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50%%
38.2%
23.6%
a/b ratios : 23.6%, 38.2%, 50%, 61.8%
When Fibonacci behavior applies, price “a” may rise 23.6% of “b”, or
38.2%, or 50%, or 61.8%, before the trend changes its direction from up to
down.
Fibonacci Retracement with change in trend
direction
b
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a
23.6%
38.2%
50%%
61.8%
a/b ratios : 23.6%, 38.2%, 50%, 61.8%
When Fibonacci behavior applies, price “a” may drop 23.6% of “b”, or
38.2%, or 50%, or 61.8%, before the trend changes its direction from down
to up.
Our Challenges
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Pattern and beauty occur in nature. At time, we
also see distortions: disfigured fingers, diseased
flowers, …
A lot of time Golden Ratio & Fibonacci number
occur in market behavior, other time, not
happening.
Never use any of the technical analysis tools as
absolute truth, but as guides for our
investment decisions, and with sharp eyes to
identify the “beautiful” pattern.
Exercises..
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I have one example on calculation of
retracement.
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Locate “b”, and multiply by the ratios and draw
horizontal lines
Please do the same exercise on the stock that
you were involved with. I.e. copy the chart
and find retracement shape and do the
calculation.
Horizontal lines with Fibonacci ratios
b
a
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Choose two horizontal lines of peak $11.5, and low $8.20
Hence b= 11.5-8.20=3.30
Ratio 23.6 % of 3.30=0.78, 38.2% of 3.30=1.26, 50%=1.65, 61.8% of 3.30=2.04
Hence for “a” with 23.6%, it is a= 8.20+0.78=8.98, for 38.2% a=9.46, for, 50% a=9.85 & for
61.8%, a=10.24
We draw horizontal lines of these 4 no. of “a”.
Horizontal lines with Fibonacci ratios
b
a
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Hence for “a” with 23.6%, it is a= 8.20+0.78=8.98, for 38.2% a=9.46, for, 50% a=9.85 & for 61.8%, a=10.24
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Do you observe that these 4 horizontal lines touch nicely some of the significant
points or prices?
Are Fibonacci ratios still co-incidentally happening? Rather, market is a Pattern of
behavior for us to recognize and take advantage of.
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Horizontal lines with Fibonacci ratios
b
a
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Acting like an artist, I draw smooth curve in red, which resemble the text-book graph, I.e.
remove the small up & down saw-teeth.
My purpose to draw the smooth curve is a) help us to visualize pattern of graph shape
easier, b) later we will be studying MOVING AVERAGE, a form of smooth graph to help us
to visualize market movement and behavior.
Horizontal lines with Fibonacci ratios
b
a
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The above is Tenaga stock, a blue-chip company, a component of KLCI. Since May 2003,
KLCI has been going uptrend till recently, a time many people get very excited, newspapers
had many good and promising news, all bullish sentiment.
Looking at the above with guided framework and tools, is there any particular reason to be
so reactive, emotional and excited about?
Later, we will learn another Fibonacci
Ratios for projection
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0.618, 1, 1.618
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On Time and Price
23.6%,
 38.2%,
 50 %,
 61.8%
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End of this lesson.
If you have questions or comments, please email to the
class 360qBC03@yahoogroups.com, or post at
http://groups.yahoo.com/group/360qBC03/ or post your
question in the “Database” on Question file.
All students are encouraged to participate, share your
view, or teach those you think you have some
knowledge.
PLEASE USE YOUR STOCK GRAPH AND DO THE
EXERCISE.