Fibonacci ratios are the result of dividing members of the Fibonacci series of numbers with members succeeding or preceding them. Fibonacci ratios are used in technical analysis of equity and other financial and commodities markets as a means of recognizing and forecasting patterns in price movements. More specifically, they are used to identify price support and resistance levels and potential turning points in price trends, as well as to forecast the longer term course of market movements. Dividing one member of the Fibonacci series by the next in the sequence, beginning with 55 and 89, yields approximately 0.618, the inverse of which is known to mathematicians as phi or the Golden Ratio. Succeeding ratios in the series, obtained by dividing one number by the second and third subsequent members of the series, yields 0.382 and 0.286, all of which are used to determine potential turning points in price trends.
The Fibonacci series and ratios were discovered by the 13th century Italian accountant and mathematician Leonardo Fibonacci. Their first application to the financial markets is attributed to R.N. Elliot, a late 19th century telegraph operator, railroad executive, and accountant. Late in life, Elliot used them to analyze trends in stock market prices and came up with what is known as Elliot Wave Theory. Professional stock market trader Robert Prechter popularized Elliott Wave Theory again in the 1980s when he republished all of Elliott's work and used them as the basis for his own investment service.
Elliot Wave Theory stipulates that stock market prices trend up and down in patterns of five waves whose turning points correspond with Fibonacci ratios. The first major wave is followed by a second wave in the opposite direction, typically retracing 61.8% of the initial wave. A third wave in the original direction is typically the largest. The fourth wave again moves counter to the original trend and is followed by a final, fifth wave in the original direction. Fibonacci ratios tend to mark the turning points in the series of waves.
Fibonacci ratios are also used to identify so-called retracement levels. These chart potential price support and resistance levels. They correspond to the Fibonacci ratios 0.618, 0.382, and 0.236 multiplied by values at market peaks and troughs. In addition to the Fibonacci ratios, many traders also use 50% and 78.6% to indicate levels of potential support and resistance.
Adherents of Fibonacci ratios and Elliot Wave Theory tend to be zealous in their belief. They typically attribute failures of the theory on it being applied incorrectly rather than evidence that it is not always or universally valid. Others acknowledge that the Fibonacci and Elliot methodologies are of value and can provide traders with an "edge" but do not place that much faith in them. After conducting research, one investment research group found that Fibonacci support and resistance levels and Elliot Wave Theory will give accurate forecasts only about half the time.