As the series of Fibonacci numbers continues, it's interesting to not that any given number is 1.618 times greater than the preceding number and 0.618% of the next number. For example:
(34/55 = 55/89 = 144/233 =0.618) (55/34 =89/55 =233/144 =1.618), and 1.618 =1/0.618.
These same properties of the Fibonacci series occur throughout nature, science and math. The number 0.618 is often referred to as the "golden ratio", since it is the root of the following polynomial: x^2+x-1=0 which can be rearranged to x= 1/(1+x).
So, that's were the fib 0.618 comes from. The other fibs 0.382 and 0.5 commonly used in technical analysis have a less impressive background, but are just as powerful when used in a Technical analysis.
0.382=(1-.618)=(0.618*0.618)
and 0.5 is the mean of the two numbers.
Other neat fib facts (0.618*(1+0.618)=1 and (0.382*(1+.618))=0.618.
Use of Fibonacci Studies in Technical Analysis
Technical Analysis commonly involves the use of Fibonacci numbers with or without any knowledge of the Elliot Wave to help determine potential resistance or support and price objectives. Retracements of 38.2% commonly suggest that the prior trend will continue, 61.8% retracements, generally mean a brand new trend has began to establish itself. Indecision is implied with a 50% retracement, while during healthy trends, 38.2% is considered natural retracements.
ABC's
To determine the price objectives for a natural retracement at 38.2% you simply add the magnitude of the previous trend to the retracement during an upward trend in the market. And, subtract it during a downward market trend. Usually, after a retracement at 38.2%, the stock should peak the prior swing point (B) on heavier volume. It there is no volume, the magnitude of the move is usually diminished, especially if the volume is very low.
A-B =C-D when B-C =38.2% of A-B
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