Fibonacci Numbers and Technical Analysis

By Stock Research Pro • April 2nd, 2011

While the relationship between Fibonacci numbers and technical analysis does get a considerable amount of attention, the concept can be confusing at first. As it pertains to stock pricing, the idea behind Fibonacci analysis is that the price changes in stocks (or other market-traded securities) exhibit connections to Fibonacci numbers. For technical analysts, the importance of the relationship lies between the ratios between each of the numbers in the series, rather than in the numbers themselves.

Definition of Fibonacci Numbers

Fibonacci numbers or the “Fibonacci sequence” is a set of numbers that starts with 0 and 1 with each subsequent number being the sum of the previous two. The Fibonacci sequence is often denotes as F (n) where n represents the first number in the sequence. Starting with 0, the sequence is as follows:

F (0) = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34…

Rather than focus on the sequence of numbers though, mathematicians focus on the quotient between each of the adjacent terms, which is about 1.618 or, taking the inverse, 0.618. This proportion, known as the “golden ratio” has proven to be a dimensional property that is consistent throughout nature, from the smallest building blocks (atoms) to the largest celestial bodies known to man. The study of finance and pricing patterns is no exception to this phenomenon.

Using Fibonacci Retracements to Identify Support and Resistance

For technical analysts, identify areas of price support and resistance is key to developing trading strategies.

  • Support- The price level which has proven to be the are where the stock historically has had difficulty falling below. This is what is believed to be an entry point for buyers of the stock.
  • Resistance- The price level which historically is where the stock has had difficulty rising above. This is thought to be the exit or selling point for many investors.

    Fibonacci analysis the ratios provide indications of levels of support and resistance to technical analysts. Fibonacci ratios are determined within the series with the most commonly used ratios of .382%, .50%, .618%, 1.00%, 1.272% and 1.618%.

    A Fibonacci retracement reflects a stock price reversal. When a stock price rises from low to high, the tendency is for that price to correct or “retrace” to some percentage. Fibonacci tools can assist investors in determining the percentage to identify a potential support area and whether to go long on that stock. An extension refers to retracements in excess of 100% and projections help estimate an end point for the current price move.


    The above information is educational and should not be interpreted as financial advice. For advice that is specific to your circumstances, you should consult a financial or tax advisor.

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