The Golden Section and Elliott's Wave Principle

On the previous pages of our Museum we have considered many different applications of the "golden section" and Fibonacci numbers - in the Solar System, in the Egyptian pyramids, in the art works, in plants and animal morphology, in the cardiac mammals activity, in the modern computers. But on this page we will tell about the rather exotic application of the Fibonacci numbers. The question is about the surprising regularities found by the American engineer and accountant Ralf Elliott still in the 30th years of the 20th century at the market fluctuation research. These fluctuations are called in modern science as the "Elliott Waves".

But who is Elliott and how he came to his discovery?

Ralf Nelson Elliott (1871-1948) was an American renaissance man who excelled in several fields.

Ralf Nelson Elliott (1871-1948)

As an accountant by education he specialized in reorganizing and revitalizing large companies such as export-import houses and railroads in the U.S. and Central America.

In 1924 the U.S. State Department under Coolidge administration chose Elliott to serve as Chief Account for Nicaragua where the U.S. ran at the time.

Elliott subsequently wrote a foreign policy proposal based upon his years of experience in Central and South America and submitted it to the State Department. Its essential ideas were reflected later in efforts such as the "Good Neighbor" policy of the Franklin D. Roosevelt administration and more recent development polices of the World Bank.

After barely surviving a debilitating anemia in his early 60s, Elliott turned his interest to studying the stock market. In 1938, at the age of 67, he published his first monograph on the market's patterns, entitled The Wave Principle. The following year, he published a series of articles detailing his discovery in Financial World magazine. He then moved to New York to establish a stock market periodical and a financial consulting business.

In 1946, he finished a larger book, Nature's Law, in which he expanded upon his 1940 essay on the connection between the Wave Principle and the Fibonacci sequence.

Thus, we have approached to the main Elliott's ideas, namely to connections of Fibonacci numbers with regularities of the stock market.

Elliott wrote:

"Nature' Laws embraces the most important of all elements, timing. Nature's Laws is not a system, or method of playing the market, but it is a phenomenon, which appears to mark the progress of all human activities. Its application to forecasting is revolutionary".

Elliott based his discoveries on Nature's Law. He notes:

"This law behind the market can only be discovered when the market is viewed in its proper light and then is analyzed from this approach. Simply put, the stock market is a creation of man and therefore reflects human idiosyncrasy".

He said:

"All human activities have three distinctive features, pattern, time and ratio, all of which observe the Fibonacci summation series".

In markets, progress ultimately takes the form of five waves of a specific structure.

The basic pattern of Elliott's Waves
Figure 1. The basic pattern of Elliott's Waves.

The Waves of (1), (3) and (5) in Fig.1 actually effect the directional movement. The Waves of (2) and (4) are countertrend interruptions. The two interruptions are apparently a requisite for overall directional movement to occur.

Elliott noted three consistent aspects of the fife-wave form. They are: the Wave 2 never moves beyond the start of the Wave 1, the Wave 3 is never the shortest Wave, and the Wave 4 never enters the price territory of the Wave 1.

Fig. 2 shows the first two Waves of Fig. 1 in greater detail. Notice the difference in their subdivisions, which reflect the two modes of the Wave development: motive and corrective. The two modes are fundamentally different in both their role and construction.

The motive Wave (also called the "five" one) has a five-wave structure. Its sub-waves are denoted by numbers (in this case 1, 2, 3, 4, 5). Both the five-wave pattern of Fig. 1 and its same-directional components, i.e. the Waves of (1), (3) and (5), employ motive mode. Their structures are called the "motive" structures because they powerfully impel the market.

Subdivision of the Waves of (1) and (2)
Figure 1. Subdivision of the Waves of (1) and (2).

The "corrective" Wave has a 3-wave structure. Its sub-waves are denoted by letters (in this case, A, B, C). All countertrend interruptions, which includes the Waves of (2) and (4) in Fig. 1, employ "corrective" mode. Their structures are called the "corrective" structures because each one appears as a response to the preceding "motive" Wave. Thus, the main model of the stock market offered by Elliott is based on the Fibonacci numbers and "Golden Section"!

Elliott wrote:

"Later I found that the basis of my discoveries was a law of Nature known to the designers of the Great Pyramid "Gizeh", which may have been constructed 5000 years ago".

Even if we do not agree with some of Elliott's findings, we must be admired for this idea. And many scientists especially in U.S. are convinced Elliott's supporters.

In 1978 the Publisher "New Classic Library" published the book "Elliott Wave Principle - Key to Market Behavior". The book was written by the Canadian scientist A.J. Frost and American scientist Robert R Prechter, Jr.

A.J. Frost, Robert R Prechter, Jr. 'Elliott Wave Principle - Key to Market Behavior' (1978)Robert Fisher 'Fibonacci Applications and Strategies for Traders' (1993)

In 1993 the other American researcher Robert Fisher published the book "Fibonacci Applications and Strategies for Traders". The book is interesting development of the Elliott Wave Principle by using the "golden" logarithmic spiral for the forecast of market behavior.

However the American scientist Robert Prechter became the most consistent follower of Elliot's ideas. He published in 1999 the book "The Wave Principle of Human Social Behavior and the New Science of Socionomics" and established Elliott Wave International for propaganda of Elliott's ideas.

Robert R Prechter, Jr. 'The Wave Principle of Human Social Behavior and the New Science of Socionomics' (1999)Product Catalog 'Elliott Wave International'

Robert Prechter wrote in his wonderful book:

"(R.N. Elliott's) Wave Principle is to sociology what Newton's laws were to physics".

A time will show: does Prechter be right by comparing Elliot's Wave Principle with Newton's Laws? But one thing is doubtless. Due to Elliott's activities and his followers Frost, Prechter, Fisher the theory of modern sociology and market economics were filled up with the rather steep scientific concept that the Fibonacci numbers and "golden section" determine not only growth of a pinecone and motion of planets of the Solar system, but also determine the laws of human behavior, and through them the laws of the stock market.