Fibonacci and The Golden Ratio


There is a special ratio that can be used to describe the proportions of everything from nature’s smallest building blocks, such as atoms, to the most advanced patterns in the universe, such as unimaginably large celestial bodies. Nature relies on this innate proportion to maintain balance, but the financial markets also seem to conform to this ‘golden ratio’. Here we take a look at some technical analysis tools that have been developed to take advantage of it.


The Mathematics

Mathematicians, scientists, and naturalists have known this ratio for years. It’s derived from something known as the Fibonacci sequence, named after its Italian founder, Leonardo Fibonacci (whose birth is assumed to be around 1175 AD and death around 1250 AD). Each term in this sequence is simply the sum of the two preceding terms (1, 1, 2, 3, 5, 8, 13, etc.).


But this sequence is not all that important; rather, it is the quotient of the adjacent terms that possesses an amazing proportion, roughly 1.618, or its inverse 0.618. This proportion is known by many names: the golden ratio, the golden mean, PHI and the divine proportion, among others. So, why is this number so important? Well, almost everything has dimensional properties that adhere to the ratio of 1.618, so it seems to have a fundamental function for the building blocks of nature.


Prove It!

Don’t believe it? Take honeybees, for example. If you divide the female bees by the male bees in any given hive, you will get 1.618. Sunflowers, which have opposing spirals of seeds, have a 1.618 ratio between the diameters of each rotation. This same ratio can be seen in relationships between different components throughout nature.


Still don’t believe it? Need something that’s easily measured? Try measuring from your shoulder to your fingertips, and then divide this number by the length from your elbow to your fingertips. Or try measuring from your head to your feet, and divide that by the length from your belly button to your feet. Are the results the same? Somewhere in the area of 1.618? The golden ratio is seemingly unavoidable.


But that doesn’t mean that it works in finance… does it? Actually, the markets have the very same mathematical base as these natural phenomena. Below we will examine some ways in which this ratio can be applied to finance, and we’ll show you some charts to prove it!


The Fibonacci Studies and Finance

When used in technical analysis, the golden ratio is typically translated into three percentages: – 38.2%, 50% and 61.8%. However, more multiples can be used when needed, such as 23.6%, 161.8%, 423% and so on. There are four primary methods for applying the Fibonacci sequence to finance: retracements, arcs, fans and time zones.


1. Fibonacci Retracements

Fibonacci retracements use horizontal lines to indicate areas of support or resistance. They are calculated by first locating the high and low of the chart. Then five lines are drawn: the first at 100% (the high on the chart), the second at 61.8%, the third at 50%, the fourth at 38.2%, and the last one at 0% (the low on the chart). After a significant price movement up or down, the new support and resistance levels are often at or near these lines. Take a look at the chart below, which illustrates some retracements:


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