Chart Analysis Using Fibonacci Retracement Lines
How to Perform Technical Analysis on Stocks Using Fibonacci Numbers
Oct 20, 2009
Though Leonardo da Pisa probably never envisioned that investors would apply the principles of his Fibonacci number discovery, their principles have found a place (even if an esoteric one) within the financial world. A small number of technical traders have applied certain aspects of the Fibonacci sequence to a stock's chart, allowing them to accurately forecast a chart's likely highs and lows.
What Are Fibonacci Numbers?
In simplest terms, Fibonacci numbers are a sequence of numbers that build upon themselves by adding themselves together starting with the number 1.
Consider the sequence 1, 2, 3, 5, 8, 13, 21, 34, and so on. At first glance they may just seem to be a random string of larger and larger numbers. A closer inspection reveals that any number in the sequence is actually the sum of the prior two numbers.
Leonardo da Pisa- also called Fibonacci- developed the model sequence when he observed that nature consistently created patterns with those same numbers (or multiples thereof).
For instance, nearly all flowers have a number of petals that is a Fibonacci number, and practically no flowers have a non-Fibonacci number of petals. The ratio of the distance between a human navel and the knee, and the distance between the knee and the end of a foot are also of the same proportions as Fibonacci number ratios. Even the dimensions of a strand of DNA are proportional to two consecutive Fibonacci numbers.
How do Traders Use Fibonacci Numbers?
Obviously investors and other individuals that have an interest in stock charts aren't interested in Fibonacci sequences or their appearance in nature. These individuals are, however, interested in another aspect of Fibonacci number...the ratio of any two Fibonacci numbers. The belief is that these 'organic' ratios also materialize- unknowingly to most- in the ebb and flow of a stock's price.
Revisiting the sequence posted above, divide any of the numbers greater than 5 by the next higher number and note the results. For example, 5/8 = 0.62, 21/34 = 0.62, 13/21 = 0.62. The result will always be a figure very close to 0.62, or 62%.
The phenomenon works when performing the same math for numbers that are one or two places away in the sequence... in either direction. For example, 34/13 = 2.62, 8/21 = 0.38, 21/8 = 2.62, and 5/13 = 0.38.
But aren't 0.38 and 0.62 (or 38% and 62%) clearly different figures? Yes, and no. The number 1 minus either of those figures yields the other number: 1 - 0.62 = 0.38, and 1 - 0.38 = 0.62.
Those two numbers, or any ratio of two Fibonacci numbers, are also expected by technical analysts to play a role in a chart's progress...or lack thereof. For instance, a stock chart is expected to 'retrace' either 62% of a major move, or to retrace 38% of a major move.
More than that, Fibonacci analysts expect a stock to move 38% or 62% beyond a prior trend's high and low levels. Again, any ratio of any Fibonacci numbers is a potential reversal point or target level.
Example of Fibonacci Analysis
As an example, take a stock chart that has rallied from a low of $3.93 to a high of $14.58. Once it was clear a pullback was in motion, a Fibonacci trader would project one of two possible targets.... either a 38% retracement to $10.32, or a 62% retracement to $7.73. At the same time, Fibonacci analysis would suggest the next upside target above the peak of $14.58 would be $20.12 (or 1.38 multiplied by $14.58).
The fact that either Fibonacci line could be a valid target price underscore the reality that Fibonacci analysis isn't perfect, and open to multiple- and sometime conflicting- interpretations. It is, however, a powerful strategy that can be added to a trader's list of analytical tools.
Fibonacci line analysis works equally well at spotting turning points for rising as well as falling charts. And, despite some drawbacks, they often offer a target/stop trading framework when no other tool can.
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