## The Fibonacci Retracements

The topic of Fibonacci retracements is quite intriguing. To fully understand and appreciate the concept of Fibonacci retracements, one must understand the Fibonacci series. The origins of the Fibonacci series can be traced back to the ancient Indian mathematic scripts, with some claims dating back to 200 BC. However, in the 12th century, Leonardo Pisano Bogollo, an Italian mathematician from Pisa, known to his friends as Fibonacci discovered Fibonacci numbers.

The Fibonacci series is a sequence of numbers starting from zero arranged so that the value of any number in the series is the sum of the previous two numbers.

**The Fibonacci sequence is as follows:**

0 , 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610…

**Notice the following:**

233 = 144 + 89

144 = 89 + 55

89 = 55 +34

Needless to say, the series extends to infinity. There are few interesting properties of the Fibonacci series.

Divide any number in the series by the previous number; the ratio is always approximately 1.618.

**For example:**

610/377 =

1.618

377/233 = 1.618

233/144 = 1.618

The ratio of 1.618 is considered as the Golden Ratio, also referred to as the Phi. Fibonacci numbers have their connection to nature. The ratio can be found in the human face, flower petals, animal bodies, fruits, vegetables, rock formation, galaxy formations etc. Of course, let us not get into this discussion as we would be digressing from the main topic. For those interested, I would suggest you search on the internet for golden ratio examples, and you will be pleasantly surprised. Further into the ratio properties, one can find remarkable consistency when a number is in the Fibonacci series is divided by its immediate succeeding number.

**For example:**

89/144 = 0.618

144/233 = 0.618

377/610 = 0.618

At this stage, do bear in mind that 0.618, when expressed in percentage is 61.8%.

Similar consistency can be found when any number in the Fibonacci series is divided by a number two places higher.

**For example:**

13/34 = 0.382
21/55 = 0.382

34/89 = 0.382

0.382, when expressed in percentage terms, is 38.2%

Also, consistency is when a number in the Fibonacci series is divided by a number 3 place higher.

**For example:**

13/55 = 0.236

21/89 = 0.236

34/144 = 0.236

55/233 = 0.236

0.236, when expressed in percentage terms, is 23.6%.

Relevance to stocks markets

It is believed that the Fibonacci ratios, i.e. 61.8%, 38.2%, and 23.6%, finds its application in stock charts. Fibonacci analysis can be applied when there is a noticeable up-move or down-move in prices. Whenever the stock moves either upwards or downwards sharply, it usually tends to retrace back before its next move. For example, if the stock has run up from Rs.50 to Rs.100, it is likely to retrace back to probably Rs.70 before moving Rs.120.

‘The retracement level forecast’ is a technique that can identify upto which level retracement can happen. These retracement levels provide a good opportunity for the traders to enter new positions in the trend direction. The Fibonacci ratios, i.e. 61.8%, 38.2%, and 23.6%, help the trader identify the retracement’s possible extent. The trader can use these levels to position himself for trade.