Fibonacci was a mathematician in Europe around 1175 to 1250. In the investing community he is famous for the series of numbers and the ratios of those numbers to which technical analysts pay close attention. The number series is formed by adding the previous number to the current number, starting at 0 and adding 1. Thus the numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 and so on. If we divide a number by the number before it we find that the answer settles down to a constant with a value approximately 1.618034. That is after the sequence progresses beyond eight numbers, for example 144 / 89 = 1.618. The other way round, the answer to 89 / 144 is 0.618. Dividing one number by the second later number, such as 89 / 233, the answer is 0.382. The square root of 1.618 is 1.27, and the square root of 0.618 is 0.786. It has been found that Fibonacci ratios occur in a wide variety of natural situations, for example, in astronomy.
Fibonacci numbers are important to us because investors take note of the key ratios 0.382, 0.50, 0.618, 0.786, 1.00, 1.27, 1.618, 2.618. They expect retracements to find support when the price drops 38.2%, 50%, 61.8%, 78.6%, 100%, 127%, 161.8%, 261.8%. Similarly, when a stock price has dropped it may retrace to an extent related to these Fibonacci ratios. Other ratios can be derived from the Fibonacci series but those ratios are not as popular as the major ones. Most charting software will display Fibonacci retracements and Fibonacci fans when we mark a top and a bottom point.
The argument for this phenomenon is that the Fibonacci series occurs often in nature so similar rules should apply to human behavior. Furthermore, it becomes a self-fulfilling prophecy if people are expecting the Fibonacci ratios to apply.
The difficulty with applying Fibonacci is that there are many ups and downs on charts of a stock’s price movement. Which should be used to calculate the Fibonacci retracement?
Some experts solve this problem by going beyond a single Fibonacci retracement and look for Fibonacci clusters, which they claim are much more powerful. Logically it makes sense that they should be so.
Some experts also apply Fibonacci numbers to time intervals but the results we have seen have been less reliable than the application to price movements.
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http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html has more than we need to know about Fibonacci Numbers.
http://www.fibonaccitrader.com/ has articles on Fibonacci in the 15 issues of the Fibonacci Trader Journal that it has online.
http://www.protradingsystems.com/ has articles on using Fibonacci levels for investing.
http://www.elliott-wave-theory.com/ has articles on using Fibonacci levels for investing.
http://www.fibotrader.com/ has Fibonacci trading information in the Tutorial section.
http://www.harmonictrader.com/ explains Fibonacci Ratios and chart patterns such as The Bat, The Crab, The Gartley and others.
http://www.stockta.com/ provides charts and Fibonacci numbers for any symbol entered.
http://www.enthios.com/ has a free basic tutorial including a Fibonacci Primer, and access to its chat room. It also has a collection of trading techniques, such as 30/34, 40pma Cross, 3 Hills and a Tail, and a dozen more.
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