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 Math**

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 . Each number in this sequence is simply the sum of the two preceding numbers (1, 1, 2, 3, 5, 8, 13, etc.).

Its not specifically the numbers that are relative; rather, it is the RATIO between the numbers that possesses an amazing proportion, roughly 1.618, or its inverse 0.618. This proportion is known by many names: the golden ratio, PHI and the divine proportion, among others. What is so special about these numbers? 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.

**Relationships in Nature**

Take honeybees, for example. If you divide the female bees by the male bees in any given hive, you will get 1.618.

pascals-triangle-fibonacciSunflowers, which have opposing spirals of seeds, have a 1.618 ratio between the diameters of each rotation. This same ratio can be seen in many relationships between different components throughout nature.

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.

The markets have the very same mathematical base as these natural phenomena mentioned above.

**The Fibonacci Studies and Finance**

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% etc.. There are four primary methods for applying the Fibonacci sequence to finance: retracements, arcs, fans and time zones.

Retracement Levels

0.236, 0.382, 0.500, 0.618, 0.764

Extension Levels

0, 0.382, 0.618, 1.000, 1.382, 1.61

**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:

**Fibonacci Arcs**

Finding the high and low of a chart is the first step to composing Fibonacci arcs. Then, with a compass-like movement, three curved lines are drawn at 38.2%, 50% and 61.8%, from the desired point. These lines anticipate the support and resistance levels, and areas of ranging.

**Fibonacci Fans**

Fibonacci fans are composed of diagonal lines. After the high and low of the chart is located, an invisible vertical line is drawn though the rightmost point. This invisible line is then divided into 38.2%, 50% and 61.8%, and lines are drawn from the leftmost point through each of these points. These lines indicate areas of support and resistance.

**Conclusion**

Fibonacci studies are not intended to provide the primary indications for timing the entry and exit of a CFD however, they are useful for estimating areas of support and resistance and are excellent when used in conjunction with other technical tools. Investors use combinations of Fibonacci studies to obtain a more accurate forecast. Many use the Fibonacci studies in conjunction with other forms of technical analysis. Such as the Fibonacci studies are often used with Elliott Waves (crowd theory) to predict the extent of the retracements after different waves.

Information, charts or examples contained in this lesson are for illustration and educational purposes only. It should not be considered as advice or a recommendation to buy or sell any security or financial instrument.