Leonardo Fibonacci was a
mathematician who was born in Italy around the year
1170. It is believed that Mr. Fibonacci discovered
the relationship of what are now referred to as
Fibonacci numbers while studying the Great Pyramid
of Gizeh in Egypt.
Fibonacci numbers are a sequence
of numbers in which each successive number is the
sum of the two previous numbers:
1, 1, 2, 3, 5, 8,
13, 21, 34, 55, 89, 144, 610, etc.
These numbers possess an
intriguing number of interrelationships, such as the
fact that any given number is approximately 1.618
times the preceding number and any given number is
approximately 0.618 times the following number. The
booklet Understanding Fibonacci Numbers by Edward
Dobson contains a good discussion of these
There are four popular Fibonacci
studies: arcs, fans, retracements, and time zones.
The interpretation of these studies involves
anticipating changes in trends as prices near the
lines created by the Fibonacci studies.
Fibonacci Arcs are displayed by
first drawing a trendline between two extreme
points, for example, a trough and opposing peak.
Three arcs are then drawn, centered on the second
extreme point, so they intersect the trendline at
the Fibonacci levels of 38.2%, 50.0%, and 61.8%.
The interpretation of Fibonacci
Arcs involves anticipating support and resistance as
prices approach the arcs. A common technique is to
display both Fibonacci Arcs and Fibonacci Fan Lines
and to anticipate support/resistance at the points
where the Fibonacci studies cross.
Note that the points where the
Arcs cross the price data will vary depending on the
scaling of the chart, because the Arcs are drawn so
they are circular relative to the chart paper or
The following British Pound chart
illustrates how the arcs can provide support and
resistance (points "A," "B," and "C").
Fibonacci Fan Lines are displayed
by drawing a trendline between two extreme points,
for example, a trough and opposing peak. Then an
"invisible" vertical line is drawn through the
second extreme point. Three trendlines are then
drawn from the first extreme point so they pass
through the invisible vertical line at the Fibonacci
levels of 38.2%, 50.0%, and 61.8%.. (This technique
is similar to Speed Resistance Lines.)
The following chart of Texaco
shows how prices found support at the Fan Lines.
You can see that when prices
encountered the top Fan Line (point "A"), they were
unable to penetrate the line for several days. When
prices did penetrate this line, they dropped quickly
to the bottom Fan Line (points "B" and "C") before
finding support. Also note that when prices bounced
off the bottom line (point "C"), they rose freely to
the top line (point "D") where they again met
resistance, fell to the middle line (point "E") and
Fibonacci Retracements are
displayed by first drawing a trendline between two
extreme points, for example, a trough and opposing
peak. A series of nine horizontal lines are drawn
intersecting the trendline at the Fibonacci levels
of 0.0%, 23.6%, 38.2%, 50%, 61.8%, 100%, 161.8%,
261.8%, and 423.6%. (Some of the lines will probably
not be visable because they will be off the scale.)
After a significant price move
(either up or down), prices will often retrace a
significant portion (if not all) of the original
move. As prices retrace, support and resistance
levels often occur at or near the Fibonacci
In the following chart of Eastman
Kodak, Fibonacci Retracement lines were drawn
between a major trough and peak.
You can see that support and
resistance occurred near the Fibonacci levels of 23
Fibonacci Time Zones are a series
of vertical lines. They are spaced at the Fibonacci
intervals of 1, 2, 3, 5, 8, 13, 21, 34, etc. The
interpretation of Fibonacci Time Zones involves
looking for significant changes in price near the
In the following example,
Fibonacci Time Zones were drawn on the Dow Jones
Industrials beginning at the market bottom in 1970.
You can see that significant
changes in the Industrials occurred on or near the
Time Zone lines.