May 19, 2014

Fibonacci series and numbers

Perhaps one of the finest and most beautiful series ever discovered and why there is order in apparently chaotic events.

Fibonacci numbers are named after Leonardo Fibonacci, an Italian mathematician somewhere in the 10th century. These have originally discovered/ researched in ancient Indian mathematics.

Very simply, it is a series of numbers where each number is the sum of the prior two numbers. For eg., 1,1,2,3,5,8,13,21,34,55,89.....

These numbers have some very interesting properties and are ALL inter-related to each other in ratios.

Take any two consecutive numbers. Depending on the order, all numbers are related to the next or previous number by 1.618 or 0.618.

Further, the inverse of 0.618 is 1.618.
Instead of taking 2 consecutive numbers, one can consider alternate numbers. You will always get 0.328 or 2.618.

These numbers occur in nature in several different ways and demonstrates how efficiently nature keeps some control in apparently chaotic situations.

Incidentally, the most visually attractive rectangle is the one where the length is 1.618 the width!

So you have these numbers appearing in the pyramids of Egypt, DNA helix, length of parts of the human body, orbitals of planets or electrons, nuclear physics and now the stock markets.

Stock markets are the best example of mass psychology or collective human behaviour and it is no wonder that stocks when they move or correct tend to stop exactly at certain levels.

The numbers 0.618 or 1.618 are called the "golden mean" or the "golden number".

Application in stock markets

Take the most recent top and bottom of a trend (up or down). Fibonacci retracements will generate targets for rallies and corrections.

UP targets = Support + X *(Resistance-Support)

DOWN targets = Resistance - X *(Resistance-Support)

Where X equals 0.382 or 0.5 or 0.618 or 1.618 or 2.618

In Elliot waves also, all waves (impulse or corrective) are related to each other Fibonacci ratios. In fact, the 5 impulse waves (1-2-3-4-5) and 3 correctives (A-B-C) are also Fibonacci numbers.

So in any correction, expect support near 50% or 61.8% retracement of the earlier rally. Similarly, any rally will meet resistance at 161.8% or 261.8% retracement of the prior correction.

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