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Fibonacci and Golden Ratio

Aug 17, 2007
The Fibonacci numbers Golden ratio can be used to describe the proportions of everything from nature to the 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 the Fibonacci Numbers "golden ratio." Here we take a look at some technical analysis tools that have been developed to take advantage of the Fibonacci Numbers Golden Ratio.

The Mathematics
Mathematicians, scientists, and naturalists have known the Fibonacci Numbers Golden ratio for years. It is 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
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.

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. The results the same, somewhere in the area of 1.618. The fibonacci numbers golden ratio is seemingly unavoidable.

So we then transalate this to finance and stocks. 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 Numbers Golden Ratio Studies and Finance
When used in technical analysis, the fibonacci numbers 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.

2. 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.

3. 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.

4. Fibonacci Time Zones
Unlike the other Fibonacci methods, time zones are a series of vertical lines. They are composed by dividing a chart into segments with vertical lines spaced apart in increments that conform to the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, etc.). These lines indicate areas in which major price movement can be expected.

Fibonacci Numbers Golden Ratio studies are not intended to provide the primary indications for timing the entry and exit of a stock; however, they are useful for estimating areas of support and resistance. Many people use combinations of Fibonacci Numbers Golden Ratio to obtain a more accurate forecast. For example, a trader may observe the intersecting points in a combination of the Fibonacci arcs and resistances. Many more use the Fibonacci studies in conjunction with other forms of technical analysis. For example, the Fibonacci studies are often used with Elliott Waves to predict the extent of the retracements after different waves. Hopefully you can find your own niche use for the Fibonacci Numbers Golden Ratio, and add it to your set of investment tools.
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