Rabbits, Fibonacci and Market Rabbits and Market Behavior Fibonacci Number & Golden Ratio Retracement & Projection

Ever Wonder …. 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 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 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 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 Or, divide by one after it, e.g. 34/55, or 13/21, and the answer is always close to 0· phi = 1· Or the inverse (1/ ) phi = 0· 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? You have... 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 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 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 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 Ermanometry Research If you are more curious, refer

What has Fibonacci got to do with investment in market? So much for the mathematic. Important message & insight & challenge to us … 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 …] 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, Fibonacci ratio (see next slide to remember some important ratios” Y X a b “A” Y X a b “B”

Just remember these Fibonacci Ratios 23.6%, 38.2%, 50 %, 61.8% Study carefully the following templates where the ratios are applied.

Fibonacci (downward) Retracement with continuing upward trend 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. b a 23.6% 38.2% 50% 61.8%

Fibonacci (upward) Retracement with continuing downward trend ba 23.6% 38.2% 50% 61.8% 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 b 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 rise 23.6% of “b”, or 38.2%, or 50%, or 61.8%, before the trend changes its direction from up to down.

b a 23.6% 38.2% 50% 61.8% Fibonacci Retracement with change in trend direction 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 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.. I have one example on calculation of retracement. 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 Choose two horizontal lines of peak $11.5, and low $8.20 Hence b= =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= =8.98, 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”. b a

Horizontal lines with Fibonacci ratios Hence for “a” with 23.6%, it is a= =8.98, for 38.2% a=9.46, for, 50% a=9.85 & for 61.8%, a=10.24 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. b a

Horizontal lines with Fibonacci ratios 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. b a

Horizontal lines with Fibonacci ratios 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? b a

Later, we will learn another Fibonacci Ratios for projection 0.618, 1, On Time and Price 23.6%, 38.2%, 50 %, 61.8%

End of this lesson. If you have questions or comments, please to the class or post at 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.