Fibonacci and the Golden Ratio
The Mathematics
Mathematicians, scientists, and naturalists have known about the golden ratio for centuries. It's derived from the Fibonacci sequence, named after its Italian founder, Leonardo Fibonacci (whose birth is assumed to be around 1175 A.D. and death around 1250 A.D.).1
But this sequence is not all that important; rather, the essential part is the quotient of the adjacent number that possess 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.
Are you still having trouble believing 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 does that mean it works in finance? Actually, financial markets have the very same mathematical base as these natural phenomena. Below we will examine some ways in which the golden ratio can be applied to finance, and we'll show some charts as proof.
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. Meanwhile, there are four ways that the Fibonacci sequence can be applied to charts: retracements, arcs, fans, and time zones. However, not all might be available, depending on the charting application being used.
1. Fibonacci Retracements
Fibonacci retracements use horizontal lines to indicate areas of support or resistance. Levels are calculated using the high and low points 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, as well as trading ranges.
3. Fibonacci Fans
Fibonacci fans are composed of diagonal lines. After the high and low of the chart is located, an invisible horizontal line is drawn through 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.). Each line indicates a time in which major price movement can be expected.
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