One of the most frequently asked questions we get from subscribers is how we go about determining stop loss and target prices on each day’s stock and ETF trade setups in stock trading report.
In addition to volume, trendlines, and support/resistance levels, one of the technical analysis indicator we sometimes use for predicting anticipated levels of support and resistance is called Fibonacci.
In this article, we will give you a rather unique background on the history of Fibonacci.
Leonardo de Pisa de Fibonacci & Fibonacci Theory
The great Fibonacci was a 13th century Italian Mathematician, who among other things, brought the Western world the Arabic/Decimal system, an explanation of the mathematics contained within the Great Pyramids of Giza, and the Fibonacci Summation series.
Of course, we are most interested in the Fibonacci Summation series and its importance to predicting price movements in the equities markets, which we will cover later in this article.
Fibo here, Fibo there, Fibonacci everywhere!
Fibonacci numbers and ratios are everywhere.
The human body has 2 arms, 2 legs and 1 head which total 5, a Fibonacci number.
Humans also have 5 senses.
The ear is a perfect Fibonacci (Golden) Spiral.
The eyes are located exactly 50% from the top of the head while the nose is approximately 61.8% from the top of the head (both Fibonacci Ratios).
Artists have known and used this knowledge for centuries.
Furthermore, the nautilus shell, galaxies and sub atomic crystals have been found to be perfect Fibonacci (Golden) spirals.
On many types of trees and plants, the branches grow in a spiral fashion. This phenomenon is known as spiral phyllotaxis.
The important point to be made here is that the Golden Ratio and Fibonacci numbers exist everywhere in our universe.
Order out of Chaos: The Fibonacci Summation Series
The Fibonacci Summation Series is derived by:
1) Taking any two numbers and adding them together to get a third number
2) Then adding the 3rd number (next) number in the sequence to the number before it to get the 4th (next) number in the sequence and so on. It can be illustrated as follows: 0+1 =1, 1+1=2, 2+1=3, 3+2=5, 5+3=8, 8+5=13.
Therefore the basic sequence would like this: 0,1,1,2,3,5,8,13,21,34,55,89,144,233.
To mathematicians, this additive series is based on the equation: Phi +1 = Phi squared.
What is absolutely fascinating about this sequence is that if you take any number in the sequence and divide it by the number after it in the sequence (after 8 additions or sequences), you always get the ratio 0.618.
Along the way to deriving the ratio 0.618, you will get a sequence of numbers that oscillate around 0.618 (the first ratio just a bit lower than 0.618 and the next ratio in the sequence just a bit higher than 0.618).
This oscillation around 0.618 is mathematically important to understanding the wave like oscillations found in the expansions and contractions in the markets!
Further, if you take any number in the sequence (after the 8th sequence) and divide it by the number before it in the sequence, the resulting ratio is 1.618.
The number 1.618 is know in geometry as the Golden Ratio and is denoted by the Greek letter phi.
To avoid getting too complicated, suffice it to say that the Golden Ratio is an important number in geometry and from it can be derived the Golden Rectangle and a Golden Spiral which can further be related to geometric characteristics of stock charts as we will soon see.
Its now time to see how Fibonacci ratios inter-relate.