# FOR MATHS FANS: FIBONACCI, GOLDEN RATIO & STOCK MARKETS?

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

This is the Fibonacci Sequence, taking its name from Leonardo Bonacci of Pisa (1170/5 – 1240), known as one of most brilliant western mathematician of the Middle Ages.

Despite its apparent randomness, this mathematical sequence turns out to be closely related to the famous Golden Ratio (symbol “Phi” in greek), also known as the “divine proportion”. The latter has proved to be of utmost important throughout history, given its uses in geometry, art, architecture and so forth.

This brings us to our point: can it be exploited in the financial industry?

> get a brief history back up on the Golden Ratio

> check this full list of art works designed with the Golden Ratio

> finally, here are general myths, facts and misunderstanding about the Golden Ratio

• ###### on the use of Fibonacci in Technical Analysis:

-> There are mainly 4 popular “Fibonacci tools” used among technical traders, which exploit key numbers and ratios in the sequence in order to help predict points of support or resistance in stock prices patterns.

1. Fibonacci Retracements
2. Fibonacci Arcs
3. Fibonacci Fans
4. Fibonacci Time Extensions

-> you can also watch this video for a quick overview of how to trade with the Golden Ratio; or this one for a longer and more advanced webinar on the subject

• ###### Further Considerations: here are 4 mistakes to avoid when applying Fibonacci (investopedia.com)

“1) Don’t mix Fibonacci reference points.

2) Don’t ignore long-term trends.

3) Don’t rely on Fibonacci alone.

4) Don’t use Fibonacci over short intervals.”

##### – Vladimir Lefebvre & Human expectations

Human opinions, valuations and expectations play a prominent role in stock prices changes… In his 1992 Book (A Psychological Theory of Bipolarity and Reflexivity), the mathematical psychologist Vladimir Lefebvre demonstrated that humans exhibit positive and negative evaluations of the opinions they hold in a ratio that approaches the Golden Proportion, with 61.8% positive and 38.2% negative.

##### – Stephen Wolfram & The theory of everything

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 behaviour, computers that think and the future of science.”

##### – William Erman & Ermanometry

This new field of research tries to show that markets may be as geometrically perfect as a spider’s web. One of the main concepts include the fact that market movements are viewed as spherical, following the logarithmic spiral that occurs pervasively in nature (in sea shells for instance).

##### – Elliot Wave Theory & Fibonacci numbers

Phi and Fibonacci numbers define the price movements of stocks in Elliott Wave Theory, used by W.D Gann and R.N. Elliott, pioneers in technical analysis of the stock market.

Nb: Elliott Wave International (EWI) is one of the largest independent financial analysis and market forecasting firm in the world, which specialises in this field.

• ###### Final Caveat:A Cautious Note…

> PaperMagic numbers in the Dow (Batchelor, Ramyar; 2006)

“A few significant ratios appear, but no more than would be expected by chance given the large number of tests we conduct.”

Do not hesitate to share your comments & thoughts (see comment section below).