Many of the technical write-ups mention this curious sounding name
quite often. It is one of the more popular trading and analysis
techniques used by most people in the market. The popularity of the
Elliott Wave led to more detailed study of the Fibonacci number series
though Elliott himself never mentioned this in any of his treatise. But
the later authors of the wave principle used the number series to
relate waves and this led to some renewed interest in the number series.
“Liber Abaci”
was a book written back in the late 12th century by a man called
Leonardo Fibonacci de Pisa. It is said that he had returned from a trip
to Egypt where he came across a set of numbers with many remarkable
properties. Apparently, it was his study of the Pyramid of Gizeh that
he noticed the “Golden Ratio” that the ancient Egyptians had integrated
into its dimensions. This book contained s nu number sequence which
today we refer to as the “Fibonacci Numbers.”
The
numbering sequence follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,
233, 377… As you can see, each number is the result of adding together
the previous two numbers in the sequence. This can be done right into
infinity.
Since Fibonacci’s attention had been attracted by what
he called as the golden ration, we shall examine that first. He found
that the pyramids of Egypt had consistent ratios of 0.618. When this
aspect was examined further, it was found that this ratio was prevalent
in substantially disparate elements such as the nautical shell, the
whorls of a sunflower, with the atom, the arrangement of rings of
Saturn, the leaves of certain plants etc. The wide presence of the
ratio across the universe was what prompted the name “golden ratio”
One
may wonder what this has to do with the markets or the Fibonacci number
series. Well, we are coming to that. More than the numbers within the
series, it the relation between the numbers which is interesting and
leads to its usage in technical analysis. The interesting properties of
these numbers, after getting past the first 4, are as follows :
Each number in the sequence is approximately 1.618
the previous number. The higher the number, the closer to this ratio it
will be. E.g. 13 is 1.618 times 8 or 34 is 1.618 times 21 |
On the reverse, each number is approximately .618
of the next higher number. The higher the number, the closer to this
ratio it will be. E.g. 55 is 0.618 of 89 and 144 is 0.618 of 233 etc |
| Every Alternate numbers will be 2.618 of each other, such as 377 to 144 and 89 to 34 |
Exactly in the inverse manner every alternate
number will be 0.382 of the next higher alternate number such as 21 is
0.382 of 55 and 89 is 0.382 of 233 |
These ratios also interrelate to each other as follows :
| Square of .618 = .382. |
| Square of 1.618 = 2.618 |
| 2.618 x .382 = 1 |
| 2.618 – 1.618 = 1 |
| 1.618 x .618 = 1 |
| 1.618 – .618 = 1 |
The
question was, how does one use this in the market? The logic applied
was pretty simple. If the golden ratio is prevalent in nature then any
man made structure should also reflect this “law” of nature. Since the
markets are a human creation, this is applied to the markets also. We
have another market mystic, W.D.Gann, who gave us the theory of market
“sections” and even the venerated Dow theory talks about a secondary
lasting from around one third to two third of the earlier leg which it
is correcting. Hence, the Fibonacci principle is mainly applied to the
price discovery process by
As found in many trading programs
today, what is called ‘Fibonacci Retracements’ are derived by taking a
market range, such as a market bottom to a top, and dividing that range
by these Fibonacci ratios of .382, .618.
There are also other
Fibonacci ratios you can use, such as .786 and .236. .786 is the square
root of .618, and .236 is from multiplying .382 with .618. Example:
Suppose we look on our daily price chart and see an obvious market
bottom at 150. Now suppose that price moved up for some days and
eventually made a top at 200.
We know this to be a top because
price has started to move down from that top. All we would have to do
to get our Fibonacci static
Support/resistance prices is to
take the top price of 200 and subtract from that the bottom price of
150. Our RANGE would then be 50 points.
Take the RANGE (50
Points) and multiply it by the Fibonacci ratios of .236, .382, .618 and
.786. We would end up with the following results :
| (50 x .236) = 11.8 |
| (50 x .382) = 19.1 |
| (50 x .618) = 30.9 |
| (50 x .786) = 39.3 |
Since
price is moving down from the top price of 200, we would subtract the
results of these ratios from 200 to get our SUPPORT prices.
| (200 – 11.8) = 188.20 |
| (200 – 19.1) = 180.90 |
| (200 – 30.9) = 169.10 |
| (200 – 39.3) = 160.70 |
The
process is the same for price ranges that go from top to bottom, where
price is starting to move up again. In those cases you would simply add
the results of those ratios to the bottom price to get your RESISTANCE
prices.
Fibonacci
ratios can also be useful at times for discovering when a top or bottom
may form. The process is to simply count the days between two tops or
bottoms (or whatever combination you care for) and multiply by .618.
Take the result and add to the second top or bottom in your equation to
forecast out a possible turn.
Another
time approach is to take any major top or bottom and then count forward
a Fibonacci number worth of days into the future, such as 34, 55, 89
days and so-forth, that will produce a future date in which to look for
a possible market top or bottom to occur. |