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Dynamic Symmetry in Financial Markets
Existence of Fibonacci Numbers in Markets Modeled by Elliott Waves
Feb 19, 2009 © Harry P. Schlanger
Dynamic symmetry is suggestive of life and movement and is evidenced mathematically in botany, art
and architecture. Elliott discovered it also exists in the stock market.
Ralph Nelson Elliott (1871 – 1948) was an accountant who studied stock market data in order to find price
patterns and predictability in US markets.
Elliott first published his findings in an article entitled, "Nature's Law –
The Secret of the Universe", in which he describes his wave ideas, known as
Elliott's Wave Principle
, modeled entirely from empirical evidence.
The American artist, Jay Hambridge (1867 – 1924) originally coined the term "dynamic symmetry", meaning
the type of
orderly arrangement of members of an organism, such as found in shell growth, or the adjustment of leaves
on a plant. In his monograph, Elliott also writes about a general rhythm of nature as expressed by the
dynamic symmetry enumerated by Fibonacci numbers.
Dynamic Symmetry in the Sunflower
Elliott was particularly fascinated by the dynamic symmetry in the sunflower. In the above image, a
yellow sunflower head displays florets, well known to be in spirals of 34 and 55, around the outside –
both of these are Fibonacci numbers.
Elliott noted that the spiral was a definite kind of curve, quite like the curve of shell growth. It is
regular and possesses certain mathematical properties governed by the Golden Ratio.
Fibonacci Numbers and the Golden Ratio
Elliott referred to Fibonacci numbers as the summation series, since each number represents a sum of preceding numbers of the series:
1, 2, 5, 8, 13, 21, 34, 55, 89, 144, 233, …
Each member of this series is obtained by adding together two preceding numbers.
Taking any two members of the series and dividing one by the other, say 34 into 55, a ratio is obtained,
and this ratio is constant throughout the series. That is, any lesser number divided into any greater
number, which immediately succeeds it, produces the same value, known as the Golden Ratio.
And this ratio is 1.618 – a number with a never-ending fraction. Conversely, if dividing by the greater
number, the irrational number 0.618 is obtained.
It should be noted that when making the division using the smaller numbers in the series, there is a slight
error. However, if numbers involved in the division are large, say 144 into 233, the error is reduced.
Fibonacci Numbers in the Markets
Figures 1 and 2 below show a breakdown of the total number of waves, into the number of waves in the bull
market and bear market for each of the Major, Intermediate, and Minor waves as stipulated by Elliott's wave model.
Figure 1. Wave Structure Model of the Markets
Figure 2. Number of Waves in Market Cycles
Elliott stated that 144 is the highest number of practical value. In a complete cycle of the stock market,
the number of Minor waves is according to the lower curve in Figure 1, obtained as: (21 x 5) + (13 x 3) =
144 waves.
Note:
- All numbers obtained are members of the summation series
- The entire series is employed
- The length of the waves may vary but not the number
Trading Markets Using Fibonacci Numbers
The number of waves in Figure 1 and 2 are modelled empirically after the markets. Not only is such wave
count observed in the stock market but in all financial markets, such as commodities, forex,
financials, etc.
Traders know that there are price and time swings, which frequently relate to each other in terms of the
golden ratio. They use this information in developing their trading systems.
Today traders are able to purchase specialized Elliott Wave software that is able to track the wave count
as the market develops. When market swings are complete, the software can provide additional information
about swing ratios. The presence of familiar ratios in markets, indicate an increased probability that a
turning point has being reached.
References:
- "The Major Works of R.N. Elliott". Ed. Robert R. Prechter, Jr. New Classics Library. NY, 1990.
- "The Elements of Dynamic Symmetry", Jay Hambridge, Dover Publications, 1953.
The copyright of the article Dynamic Symmetry in Financial Markets: Existence of Fibonacci Numbers in
Markets Modeled by Elliott Waves is owned by Harry P. Schlanger. Permission to republish in print or
online must be granted by the author in writing.
smart-koala.com © 2009 All Rights Reserved
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