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Elliott Waves And The Fibonacci Sequence

02/24/06 10:54:05 AM PST
by James Maccaro

Though his theories have been criticized, Ralph Nelson Elliott broadened the field of stock market analysis with his insight into how economic waves reflect our history and existence.

Born in 1871 in Marysville, KS, Ralph Nelson Elliott lived for much of his childhood in San Antonio, TX, and became an accountant in the closing years of the 19th century. He worked for several Western railroads as well as other businesses over the years, eventually carving out a successful career in Mexico and Central America, auditing railroads and other enterprises for their US investors. In the 1920s, he returned to the United States and gained experience advising restaurant owners on business matters. He wrote a column on the subject for many years for a trade journal, Tea Room And Gift Shop magazine, and wrote a well-respected manual, Tea Room And Cafeteria Management, published in 1926.

In the late 1920s, Elliott developed anemia, probably as a result of an infection sustained during his time in Latin America. He was apparently bedridden for several years, and during this period he began his study of the stock market. Elliott subsequently declared that he had deduced "a law-abiding rhythmic pattern of waves," which he explained in the late 1930s in articles for Financial World (a leading stock market magazine at the time) and in a book published in 1938 titled The Wave Principle. From 1938 to 1945, he wrote a newsletter issued on an irregular basis, which he initially called Educational Bulletins but later retitled Interpretive Letter. He died in 1948.

In common with fellow Texan William Gann, a contemporary and the developer of "Gann angles" and other technical concepts, Elliott believed in spiritualism and mysticism. Both men developed trading methods that are complex and at times difficult (if not impossible) to fully understand, and they also both asserted that they had uncovered broad philosophical insights into the meaning of life. While Elliott was successful in building a career as a market analyst late in his life, however, he did so to a more limited extent than Gann, who was significantly more adept at self-promotion.

Elliott believed that the stock market moves through a "Super Cycle" of from 15 to 20 years, which in turn moves within a "Grand Super Cycle" of at least 50 years, which moves within an even longer cycle of approximately 200 years. Each cycle contains smaller cycles, ending in the "sub-minuette," which lasts only a few hours. A cycle, according to Elliott, is formed by movements of stock prices, which he called waves; hence his approach is known today as the Elliott wave theory (although the title used by Elliott was the wave principle).

Each cycle contains eight waves, declared Elliott, five of which are dominated by "impulse waves" — that is, waves that push prices up, and three of which are bearish, dominated by "corrective waves," during which gains are lost to varying degrees.

To anticipate waves, Elliott cited the Fibonacci sequence of numbers, which begins with zero and "1," followed by the sum of the two preceding numbers: that is, zero, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 133, 233, 377, 610, 987, 1,597, and so forth.

Scattered references to this sequence can be found in the literature of ancient India, but a 13th-century Italian mathematician named Leonardo of Pisa, better known by his nickname, Fibonacci, introduced the concept to Western civilization. He put forth the concept to predict the growth of a hypothetical population of rabbits! Over the past century, by contrast, Fibonacci's discovery has found many uses in high-level mathematics and the sciences.

Elliott wrote that stock prices follow the pattern set forth by the Fibonacci sequence, but his explanations of the process are contradictory in many details and do not strictly adhere to a Fibonacci analysis.

As noted, Elliott asserted that a price cycle will have five waves that are primarily bullish (dominated by "impulse" waves) and three waves that are bearish (with "corrective" waves predominating). This does not mean that the first five waves will be uniformly upward and followed by three downward waves. Rather, the first waves will consist of a sequence of upward movements followed by relatively shallow pullbacks. The market will then peak, to be followed by a period of price declines with temporary bear rallies during which prices will regain some lost ground, only to return to the downside.

By writing in terms of waves within cycles, which in turn are in larger cycles, and by introducing Fibonacci numbers into the discussion, Ralph Elliott broke new ground. However, his general idea was not new. In fact, it is standard Dow theory, in that a bull market will have a series of peaks that reach new highs, interspersed by declines that stay above previously lows, until such point that the bull market peaks.

At this point, some of the gains of the bull market will be surrendered (there will be a correction) as prices drift down, but with the decline interrupted by a bear rally of limited duration (reaching a point below the previous high). While traditional technicians explain this phenomenon by speaking in terms of market psychology inducing changes in the supply and demand of stocks, Elliott cited "the laws of nature" as reflected by, among other factors, Fibonacci numbers.

Years later, Robert Prechter popularized the wave theory in the early 1980s as the author of an investment newsletter that made headlines when he correctly anticipated the start of the bull market in 1982. However, he was blindsided by the market crash of October 1987 and further damaged his reputation when he subsequently became firmly bearish, going so far as to predict that the Dow Jones indexes would bottom out at levels not seen since the Truman administration. Thereafter, Elliott's renown has been essentially limited to committed technicians.

Elliott took a very long-term view of cycles, which might be easy to dismiss; after all, 200 years seems beyond the concern of even the most steadfast of buy & hold investors. Nonetheless, he must be given credit for introducing a broad historical approach to stock market analysis. An extensive literature now exists around the idea that price movements and other historical trends move in cycles of years, generations, and even centuries.

The leading proponent of this idea as it applies to economics was clearly Elliott's contemporary, Nikolai D. Kondratieff, a brilliant Russian academic, but his research was stunted by Soviet authorities. They used Kondratieff's work to promote the idea that capitalism's days were numbered and, to prevent any contradiction, silenced him in 1930 by imposing a prison sentence of eight years. Shortly after Kondratieff's release from confinement in 1938, he was executed by firing squad at Josef Stalin's direct orders.

A more recent proponent of very long-term cycles is the historian David Hackett Fischer. In a recent book, The Great Wave: Price Revolutions And The Rhythm Of History, Fischer reviewed the historical literature on the subject and argued that the rate of general inflation (and the health of an economy) can be predicted through a study of cycles dating back to the 14th century.

Although his analysis is flawed in that it does not provide a clear roadmap as claimed (and I would argue that any such roadmap is an impossibility) and, moreover, his writings are nebulous, contradictory or nonobjective on many points, Ralph Nelson Elliott broadened the field of stock market analysis and deserves credit for introducing Fibonacci numbers to the field, which subsequently has developed into a fertile ground for investment research.

Frost, A.J., and Robert R. Prechter Jr. [1985]. Elliott Wave Principle, New Classics Library.
Hackett, David Fischer [1996]. The Great Wave: Price Revolutions And The Rhythm Of History, Oxford University Press.

James Maccaro

James Maccaro is an attorney and freelance writer. He has written articles for Newsday, Ideas on Liberty, The Massachusetts Law Review, and other magazines. His law journal articles have been cited in several legal decisions, including by the US Court of Appeals for the DC Circuit and by the US Supreme Court. James A. Maccaro is an attorney and freelance writer. He has written articles for Newsday, Ideas on Liberty, The Massachusetts Law Review, and other magazines. His law journal articles have been cited in several legal decisions, including by the US Court of Appeals for the DC Circuit and by the US Supreme Court. He may be reached at

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