The Stock Market and the Fibonacci Series

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Human expectations occur in a ratio that approaches Phi

Changes in stock prices largely reflect human opinions, valuations and expectations. A study by mathematical psychologist Vladimir Lefebvre demonstrated that humans exhibit positive and negative evaluations of the opinions they hold in a ratio that approaches phi, with 61.8% positive and 38.2% negative.

Phi and Fibonacci numbers are used to predict stocks

Phi, the Golden Mean and Fibonacci numbers have been used with great success to analyze and predict stock market moves. Forbes ASAP recently featured a story on the work of scientist Stephen Wolfram in cellular automata (underlying rules that determine seemingly random phenomenon) stating "This seashell may hold the secret of stock market behavior, computers that think and the future of science."

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.

Phi, or Golden Ratio, patterns often define the timing of highs and lows and price resistance points

The golden ratio, or phi, appears frequently enough in the timing of highs and lows and price resistance points that adding this tool to technical analysis of the markets may help to identify key turning points. The photos below illustrate how the Golden Mean Gauge and Phi-based analysis software can be used to identify these turns in the market. The middle arm of the gauge keeps the phi point of the outer arms as the gauge is opened and closed. The lines of the phi-based software are all in phi relationship to one another. The ratios of Fibonacci numbers, commonly used in technical market analysis, converge on phi as explained on the Fibonacci Series page.

Phi and Fibonacci numbers define the price movements of stocks in Elliott Wave Theory

Fibonacci numbers were used by W.D Gann and R.N. Elliott, pioneers in technical analysis of the stock market. In Elliott Wave Theory, all major market moves are described by a five-wave series, adding to the potential to identify the turns described above. The classic Elliott Wave series consists of an initial wave up, a second wave down (often retracing 61.8% of the initial move up), then the third wave (usually the largest) up again, then another retracement, and finally the fifth wave, which would exhaust the movement. In addition, each of the major waves (1, 3, and 5) could themselves be separated into subwaves, and so on, and exhibit other Fibonacci relationships.

A sample stock price wave analysis could look something like this:

Major, minor and sub waves are shown in RED, YELLOW and GREEN and the total number of increases and decreases (2, 5 or 8) is a Fibonacci number. Note too that the predicted end result is based in the Fibonacci series as well as the end price is 61.8% of the high and 0.618 is equal to 1/ and 0.382 is 1/².