Discovered long before there were stock markets, the Fibonacci method has proved to be useful for traders.
One of the key goals of stock market traders is to find a way out of the maze of the stock market. Toward this goal, traders have resorted to using astrology, rocket science, fundamental analysis, technical analysis, and more to achieve this goal. The Fibonacci method is one such attempt to unravel the mysteries of the stock market, in this case by relating the market's movements to the Fibonacci series. Fibonacci series were discovered long before there were stock markets, but they relate amazingly well to the stock markets and other natural phenomena.
Leonardo of Pisa, a 13th-century Italian mathematician better known by his nickname, Fibonacci, is credited with the creation of the Fibonacci series. The series has its first two numbers as zero and 1. You arrive at the remaining numbers by adding the previous two numbers. For example,
0+1=1
1+1=2
1+2=3
2+3=5
3+5=8
5+8=13
8+13=21
13+21=34
21+34=55
34+55=89 and so on.
Thus, we arrive at a series of numbers: zero,1,1,2,3,5,8,13,21, 34, 55, 89.
These numbers are related to each other by a ratio. Many phenomena in nature, science, and astrology can be explained by using this property of the Fibonacci numbers. Fibonacci numbers also have an interesting relationship with each other. Using the sums from the examples above, we get 21/34 = 0.618; 34/55 = 0.618; 55/89 = 0.618. Similarly, 34/21 = 1.618; 55/34 = 1.618, 89/55 = 1.618. This ratio is known as the golden ratio and forms the basis of the Fibonacci methods in technical analysis.
The other two fractions, 0.382 and 0.5, most commonly used in technical analysis are calculated as follows:
(1 - 0.618) = 0.382 and 0.5 is the mean of 0.382 and 0.618.
FIBONACCI RETRACEMENTS
Fibonacci retracement tools are conveniently available in most software packages. To use it, we must:
Identify a swing high and a swing low in the price action.
Generally, use the 38.2%, 50%, and 61.8% values (Figures 1 and 2). If those values do not hold, 25% and 75% can also be used.
Look for supporting evidence along with Fibonacci retracements, such as extreme values in short-term relative strength index (RSI) or stochastics, or confluence of Fibonacci levels across time frames.
Focus on regions of support and resistance.
In very strong bull and bear markets, look for prices that often do not retrace more than 25-38.2%. In moderately bullish and bearish markets, prices can retrace up to 50-61.8%.
Finally, keep an eye out if prices start breaking the 61.8% to 75% retracement. If this happens, the main trend may be under threat.
Figure 1: Fibonacci retracements in an uptrend