Fibonacci numbers seem to occur in nature, and it has been suggested that our brains are hardwired to find Fibonacci progressions naturally pleasing, Where they occur in investing is technical analysis, where the "fibs" are suppose to predict the behavior of the stock market. The theory is that the collective "investor mind" must also be hardwired so that interesting things happen at Fibonacci numbers and retracements.
The first person known to use Fibonacci Retracemnets was R.N Elliot, an interesting character born around 1870 who spent the first 60 years of his life as a telegraph operator, railroad executive, and an accountant. While working in Guatemala in 1927 he became seriously ill with an amoebic infection which developed into anemia. There followed five year convalescence. It was during this period, often sitting alone on his porch, that he developed his wave theory of the markets. The Fibonacci series was key to this theory.
Elliot theorized that all major markets could be described by a five-wave series. The Classic Wave series would consist of an initial up wave, a second wave down (often retracing 61.8% of the initial move up), then the third wave (usually the largest) up again, then another retracement, and finally the fifth wave, the last gasp, which would exhaust the movement. He described all sorts of Fibonacci relationships which would occur among these waves. Each wave had its own "character", describing a certain psychological condition of the market. In addition, there was a recursive quality to the system. Each of the major waves (1, 3 and 5) could themselves be separated into five individual sub waves and so on.
The problem with this "theory" was that it was a characteristic attempt to force what were true insights into a grand theory of everything. During the 1980's, the Elliot Wave Theory was popularized by Robert Prechter.
, who republished all of Elliot's works in 1980 ("The Major Works of R.N. Elliot" Classic Library). Pretcher fell from grace when he failed to foresee the 1987 stock market crash. The irony about this was in 1978 Pretcher had written book a book on "Elliot Wave Theory" in which he predicted that the Dow Jones Average, then ~ 700-800, would undergo a massive rally in the next decade, topping around 2700-2800, and then undergo a significant decline. Unfortunately, in 1983 he issued a revised estimate for a top ~ 3600, so that in 1987 when the market did top out ~ 2750 and then plunge 1000 points, his many followers, trusting his revised forecast of a top ~ 3600, got their asses kicked and developed a very unfriendly attitude towards Prechter. Since that time the market has of course more then doubled, to high ~ 5800. Having undergone the trauma of disgraced gurudom, Prechter has developed into a pessimistic guy, and most of his writings in the past decade have used Elliot Wave Theory to predict the impending end of Western civilization.
The best modern Theorist is Tony Plummer, a bond trader in London. He wrote in 1989 ("Forecasting Financial Markets") in which he acknowledges the great insights of Elliot and Prechter, but discards the orthodoxy of their systems. Plummer brings the theory down to earth by describing crowd behavior as a cyclic continuum of sentiment expansion and contraction. His Model is in many ways more elegant than Elliot's. He describes something he calls a "price pulse". Where a contraction of energy builds up from a base, then a breakout or energetic pulse is the result. This can take prices to levels which usually have a Fibonacci relationship to the size of the previous move. Plummer is refreshingly modest about his understanding of the markets. Probably because he's a real Trader, dealing with real markets where real money can be lost and bring theoretical flights of fancy down to earth quickly.
I believe that the "price pulse" is the basic building block to any wave series. These pulses can be positive or negative and consists of at least three waves, with one of the waves being a side or consolidation wave.
The key to capitalizing on this knowledge is to know when a price pulse is building and knowing when these pulses are overextended and ready to consolidate and break higher or where it may revert to some sort of mean again consistent with a Fibonacci retracment.
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