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Elliott Wave Theory and Fibonacci Numbers?
The use of characteristics of the mathematical Fibonacci sequence to calculate market price retracement objectives was pioneered by R.N. Elliott when he enhanced his Wave Theory with this concept in the early 1940’s. In doing so, Elliott tied in his observation that mass human psychology was reflected in a classic eight-wave sequence commonly seen in market price action with the natural evolutionary sequence Fibonacci invented in relation to the reproduction of rabbits.
His basic conclusion was that market corrections tended to retrace their preceding trend according to set percentages of the length of that trend, and that those percentages in turn consist of ratios of successive numbers in the Fibonacci sequence. Although many forex traders now use Fibonacci retracement levels regularly when looking to trade market corrections, not all of them know that they are applying an aspect of Elliott Wave Theory in doing so.
The Fibonacci Sequence and Ratios
The now-famous Fibonacci sequence was originally published in the early 13th century and involved a mathematical solution to a question posed about the reproduction of rabbits. A short-cut to calculating the series starts with 1 and 1 and then progresses by adding together the preceding two numbers to get the next number, and so on. This process produces the infinite Fibonacci sequence as follows:
- The ratio of one number in the sequence, when divided by the next, approaches the so-called Golden Mean of 0.618.
- The ratio of one number in the sequence to the number two places further up approaches 0.382.
- The ratio of one number to the number three places down the sequence approaches 0.236.
Fibonacci Retracement Levels
Those observations, when expressed as percentages, result in the classic Fibonacci Retracement levels of 23.6%, 38.2% and 61.8%. Many Elliott Wave Theorists complete this retracement series by adding the 50%, the 100%-23.6% = 76.4%, and the 100% retracement levels, to obtain a retracement series based on the Fibonacci sequence as follows:
When an initial market trend occurs and the market then shows signs of beginning a correction or retracement in the opposite direction, an Elliot Wave Theorist will compute these percentages of the length of the initial impulse to yield a succession of retracement targets for the correction.
In general, once one Fibonacci retracement level has been broken, that sets up the next Fibonacci retracement level as the subsequent target. Also, when the key 61.8% retracement level is broken, the correction will often return to the beginning of the preceding trend. A Fibonacci Retracement level example calculation could involve a scenario where the AUD/USD rate has trended from 0.8000 to 0.9000. Once this initial move corrects over 23.6% of its length or: that would imply AUD/USD has pulled back from its high to a rate of: A forex trader using Fibonacci retracements levels might then reasonably expect that the market will continue to correct lower provided that the market remains below this 23.6% level at 0.8764. If they were then to establish a short position in AUD/USD to take advantage of this correction, they would tend to place their buy stops above this level. This procedure would generally be followed through successive Fibonacci retracement percentages as the exchange rate corrected lower until the market eventually reversed the correction as it began to move higher again and resume its upward trend. This would be signaled by a breach of the 23.6% retracement level at 0.8764. Profits would usually be taken on shorts ahead of each Fibonacci level in the correction sequence.
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