Dynamic Symmetry Inherent in Financial Markets

Existence of Fibonacci Numbers in Markets Modeled by Elliott Waves

Feb 19, 2009

Dynamic symmetry is suggestive of life and movement and is evidenced mathematically in botany, art and architecture. Elliott discovered it even 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. He published his findings in an article entitled, “Nature’s Law – The Secret of the Universe”, in which he describes his Wave Principle, modeled entirely from empirical evidence.

The Wave Principle's basic tenets are important for counting the progression of markets waves, with the purpose of timing a trading entry or exit, and for forecasting.

The American artist Jay Hambridge (1867 – 1924) 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 Figure 1, a sunflower head displays florets, well-known to be spirals of 34 and 55, around the outside – both 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:

Each member of this series is obtained by adding together two preceding numbers.

Taking any two consecutive 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. Dividing by any second consecutive numbers in the series yields 0.382.

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

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 2, obtained as: (21 x 5) + (13 x 3) = 144 waves.

Figure 3 shows a breakdown of the total number of waves, number of waves in the bull market and bear market for each of the Major, Intermediate, and Minor waves types. Note:

Trading Markets Using Fibonacci Numbers

The number of waves in Figure 2 and 3 is modeled empirically after the markets. Not only is such wave count observed in the stock market but in all financial markets, such as commodities, forex, or financials.

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. When familiar ratios are obtained, this provides an increased probability that a turning point has being reached.

The copyright of the article Dynamic Symmetry Inherent in Financial Markets in Investment is owned by Harry P. Schlanger. Permission to republish Dynamic Symmetry Inherent in Financial Markets in print or online must be granted by the author in writing.