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February
2006
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:
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 . Take a look at the chart below, which
illustrates how these arcs do this:
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. Take a look at the chart below:
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.
Conclusion
These Fibonacci 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 studies 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 studies, and add it to
your set of investment tools!
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