# The Explorer's Guide to Fibonacci Principles in Trading

## Executive Brief

• Mathematical sequence developed by Leonardo of Pisa, also known as Fibonacci

• Ratio of each subsequent Fibonacci number pair is approximately equal to the Golden Ratio or 1.618

• Simple method for technical practitioners to identify support and resistance, stop levels, and price targets

• Retracement levels are mapped by connecting extreme low-high or high-low

## Who is Fibonacci?

The accomplishments of Fibonacci, also known as Leonardo of Pisa, are impressive.

Aside from introducing the Hindu-Arabic number system (yes - the conventional number system still used today), this successful 13th-century Italian merchant was also a mathematical revolutionary whose contributions are still apparent today.

## What are Fibonacci numbers?

In his book Liber Abaci or The Book of Calculation, Fibonacci presents a peculiar sequence of numbers which he coins the Fibonacci Summation Series. The series of sums works as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc....

As you can see, each number within the series is a sum of the previous two numbers.

For example:

0 + 1 = 1

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

3 + 5 = 8

5 + 8 = 13

8 + 13 = 21

13 + 21 = 34

And so on....

Now, this is where things start to become interesting.

A number within the sequence that is divided by the number immediately prior will produce an irrational number. This unique number is never-ending and contains an unpredictable string of decimal values that proportionately orbits the figure:

1.61803398875... decimals values continue to infinity

Let's demonstrate this below by taking some numbers in the Fibonacci sequence and dividing it by the preceding number.

Example 1

13 divide by 8 = 1.625

Example 2

21 divide by 13 = 1.615..

Example 3

89 divide by 55 = 1.618..

All results rounded to the third decimal place

This magical quotient guides the Fibonacci number sequence and appears across nature. However, many know its popular name - the Golden Ratio.

## The Golden Ratio in Trading

Present throughout the ages, the Golden Ratio emerges as a far-reaching constant in nature, design and the financial markets.

To avoid confusion, the Golden Ratio may also be known as:

• Golden Mean

• Golden Section

• Divine Proportion

In algebra, the Greek letter Phi designation applies to the Golden Ratio. In other words:

Golden Ratio = Phi = 1.618

Phi is fascinating for scientists, mathematicians - and traders!

To develop an understanding of Fibonacci Principles in trading, technical practitioners must first appreciate the Divine Proportion's significance in the natural world.

One reason for this polytechnic intrigue is the reciprocal value of Phi - commonly denoted as Phi'.

The value of Phi' is calculated by taking a number in the Fibonacci sequence and dividing it by the number that succeeds it. Let's take a look at how this simple calculation works:

Example 1

8 divide by 13 = 0.615..

Example 2

13 divide by 21 = 0.619..

Example 3

55 divide by 89 = 0.618..

All results rounded to the third decimal place

Interestingly, both the Fibonacci summation series and Golden Ratio appear distinctly through nature.

Examine the number of petals on each of the common flowers below:

Technical practitioners can find more proof of the Golden Ratio’s existence in these beautiful natural designs below:

Above: Nautilus sea shell with a Fibonacci overlay

Above: Gaze upon the heavens and discover Fibonacci across the cosmos

Believe it or not - Fibonacci numbers are responsible for these natural patterns, which are innately beautiful and pleasant to the eye.

Take the example of a sunflower, where its petals' curves form the aesthetically pleasing lines shown below.

The geometry of the sunflower's petals is a simple set of equiangular spirals that are superimposed and intertwined - one set turning clockwise and the other anti-clockwise.

Can you guess the number of equiangular spirals?

You might have guessed it... The value of clockwise and anti-clockwise spirals are both Fibonacci numbers!

Interestingly, the order closely follows the theoretical technical basis of Elliot's Wave Principles - the Guideline of Alternation.

Q's Advanced Technical Concept: What is the Guideline of Alternation?

Ralph Nelson Elliott developed the Elliott Wave Theory in the 1930s, gaining popularity after predicting a stock market bottom with incredible accuracy.

At a glance, Elliott's findings conceptualise socio-behavioural mechanics within a market setting - in other words, underlying crowd psychology trends and reverses in distinct patterns.

The Guideline of Alternation offers technical practitioners a rule of thumb, where non-adjacent waves within a trend structure will typically alternate somehow.

For example, the Guideline of Alternation expects Wave 2 and 4 to alternate in a five-way trend structure. According to the rule, the alternate waves within this structure may differ in:

• Formation time

• Distribution pattern

• Strength and depth

Qluster analysts visualise this concept below:

Elliott's Principles broadly interpret the natural constant - Golden Ratio.

Recall, the Golden Ratio governs the design of living creatures and the celestial. Furthermore, Q refers back to the basic definition of a market exchange - where buyers and sellers meet at these market exchanges to determine the fair price of an asset.

Thus, for the technical practitioner, Elliot proposes this divine constant exists inherent within the multitude of dispositions, attitudes and emotions of human psychology en masse in the financial markets.

According to Elliott's Wave Principles, the Golden Ratio perseveres omnipresent in the financial markets - perhaps, the best mirror of mass psychology!

Some traders may reject Elliott and Fibonacci's principles as self-fulfilling prophecies. Instead, they argue that an infatuation or belief in these systems is the predominate driver behind each individual's performance.

However, the empirical evidence and data are clear.

The markets are a near-perfect illustration of crowd mentality that accurately reflects the trends and changes in the psychological states of market participants.

Anyone can observe this manifestation of fluctuating valuations in enterprise and economic productivity by looking at any price chart. The market is generous and candidly describes patterns of progress and regress - quite often with brutal objectivity.

Q muses that one cannot build a strong house on weak foundations.

Fostering an early appreciation for the theory behind Fibonacci Principles is an essential requisite to developing higher level of fluency with this powerful technical indicator.

🤩 Make sure to stay tuned! 🤩

Qluster analysts prepare to continue the Fibonacci Principles deep dive in the next edition to help our readers cement tonight’s understanding of theory into practice.

Subscribe now to be the first to receive Edition #2 of Q’s Almanac of Technical Analysis 👇

See you again for the next update.

- q