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So You Wanna Learn Elliott Wave Analysis? Part III
Fibonacci-derived Golden Ratio exists throughout nature: in the DNA helix, in plants… and in financial markets.
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So You Wanna Learn Elliott Wave Analysis?
For more reading on the basics of Elliott wave analysis, please read all parts of the series: Part I, Part II, Part III, Part IV, Part V
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In the first article of this series, you learned about the basics of Elliott wave patterns. The second article introduced you to "alternate counts" and ways to identify the market position in the wave pattern. This article is about the Fibonacci sequence and the ratios within the sequence that guide the shape of Elliott waves. These ratios help traders establish support, resistance, and other price targets in the market.
Leonardo Fibonacci of Pisa was the most important mathematician of the Middle Ages. In 1202, he wrote a landmark book on arithmetic, which popularized the decimal and Hindu-Arabic numbering system that we use today. In that book he referred to an additive numeric sequence derived from the growth of a population of rabbits, known to us as the Fibonacci sequence.
The Fibonacci sequence begins with 1 and 1 (two love struck rabbits) and then progresses by adding each number to the one before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 – and so on. What is important to us as Elliott wave students is not so much the numbers themselves as the ratios between them.
As the Fibonacci sequence progresses, the ratios between adjacent numbers approach closer and closer to .618 – or its inverse, 1.618 (depending on which of two adjacent numbers you divide by). The ratios between alternate numbers in the sequence are approximately .382, and 2.618. In fact, the nature of this additive sequence is such that you can start the sequence with any two numbers, and the ratios will rapidly approach .618. Try these examples with a calculator. For a fascinating list of phenomena relating to the Fibonacci sequence, consult chapter 3 of Prechter & Frost's Elliott Wave Principle – Key To Market Behavior (EWP)*.
Phi (.618034…; don't confuse with Pi) is an irrational number called the Golden Ratio. This ratio exists throughout nature – in population growth patterns, in the DNA helix, in plants, in the structure of the human brain, and in spiral structures from seashells to galaxies. R. N. Elliott's stunning discovery (made in the 1930s, without a computer) was that this universal growth pattern found also shows up in stock market chart patterns. To Elliott, this could only mean that, "man's collectively expressed emotions are keyed to this mathematical law of nature." (EWP)
R. N. Elliott was the first person to use Fibonacci analysis in financial markets. The correct usage of it can only be done within a valid Elliot wave interpretation. Many non-Elliott analysts try to find Fibonacci proportions between market moves that are unrelated to each other in any way, making the approach appear far less valuable than it is when you view the markets through the Elliott wave prism.
Elliott had two main observations about Fibonacci relationships within waves.
One: Corrective waves tend to retrace a Fibonacci proportion of impulse waves of the same degree. Frequent relationships between these waves are 38%, 50%, and 62%. (See the chart from the previous article.)
Two: Impulse waves of the same degree within a larger impulse sequence tend to be related to each other in Fibonacci proportion. (See the chart below.) At large degrees of trend these relationships usually occur in percentage terms. At small degrees, the number of points in each impulse wave reveals the ratios.
These Fibonacci relationships occur in numerous ways in wave patterns, from the numbers of waves in a pattern, to their relationships to each other – and even, in some cases, the relationship between time-spans of waves.
That wraps up a brief introduction to the fascinating world of Fibonacci. Stay tuned for Part IV of the series, where we'll show you how to establish investment strategy and reduce risk in your trading using Elliott wave analysis. In the meantime, you can help yourself by studying the Prechter & Frost's classic text, Elliott Wave Principle*.