Leonardo Pisano Bogollo (1170-1250), an Italian mathematician from Pisa, is credited with introducing the Fibonacci sequence to the West. Leonardo of Pisa, nicknamed, Fibonacci was one of the best known mathematicians of his time. His greatest find was Fibonacci series.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, ...
This sequence is constructed by choosing the first two numbers (the "seeds" of the sequence) then assigning the rest by the rule that each number be the sum of the two preceding numbers. This simple rule generates a sequence of numbers having many surprising properties, of which we list but a few.
- Take any three adjacent numbers in the sequence, square the middle number, multiply the first and third numbers. The difference between these two results is always 1.
- Take any four adjacent numbers in the sequence. Multiply the outside ones. Multiply the inside ones. The first product will be either one more or one less than the second.
- The sum of any ten adjacent numbers equals 11 times the seventh one of the ten. Mesoamericans thought the numbers 7 and 11 were special.What can we get out of these numbers. Try picking any number and divide it by the next number in the series and see what you get.
Or the 62% retracement level. Similarly, if you take the previous number and divide it by the next number you get another important retracement level 38%.
For example: 21/55 = 0.382 or 34/89 = 0.382
And you can go on like this. But the most important retracement levels are 38% and 62%.The sequence extends to infinity and contains many unique mathematical properties.
- After 0 and 1, each number is the sum of the two prior numbers (1+2=3, 2+3=5, 5+8=13 8+13=21 etc…).
- A number divided by the previous number approximates 1.618 (21/13=1.6153, 34/21=1.6190, 55/34=1.6176, 89/55=1.6181). The approximation nears 1.6180 as the numbers increase.
- A number divided by the next highest number approximates .6180 (13/21=.6190, 21/34=.6176, 34/55=.6181, 55/89=.6179 etc….). The approximation nears .6180 as the numbers increase. This is the basis for the 61.8% retracement.
- A number divided by another two places higher approximates .3820 (13/34=.382, 21/55=.3818, 34/89=.3820, 55/=144=3819 etc….). The approximation nears .3820 as the numbers increase. This is the basis for the 38.2% retracement. Also, note that 1 - .618 = .382
- A number divided by another three places higher approximates .2360 (13/55=.2363, 21/89=.2359, 34/144=.2361, 55/233=.2361 etc….). The approximation nears .2360 as the numbers increase. This is the basis for the 23.6% retracement.
- The 50% retracement is not based on a Fibonacci number. Instead, this number stems from Dow Theory's assertion that the Averages often retrace half their prior move.
1.618 refers to the Golden Ratio or Golden Mean, also called Phi. The inverse of 1.618 is .618.
Practical Significance of Fibonacci levels on charts. Focus will be on moderate retracements (38.2-50%) and golden retracements (61.8%) :
38.2% Retracement on Nifty. After taking the support at 38.2% retracement, nifty continues it's uptrend.
50% Retracement on Nifty - Corrective Pullback only to fall after that.
61.8% Retracement on Nifty - After decline from 6111.80 to 5663, Nifty bounces back to 61.8% (corrective Pullback) to face a stiff resistance around those level, only to fall after that.
50% Corrective Advance in Bear Market on Gold
Fibonacci retracements are often used to identify the end of a correction or a counter-trend bounce. Corrections and counter-trend bounces often retrace a portion of the prior move. While short 23.6% retracements do occur, the 38.2-61.8% covers the more possibilities (with 50% in the middle). This zone may seem big, but it is just a reversal alert zone. Other technical signals are needed to confirm a reversal. Reversals can be confirmed with candlesticks, momentum indicators, volume or chart patterns. In fact, the more confirming factors the more robust the signal.
