BALTIMORE (Stockpickr) -- One of the most frequently mentioned -- and perhaps most frequently understood -- concepts in technical analysis is the Fibonacci ratio. Technical traders use Fibonacci ratios to determine key buying and selling points, as well as to predict a stock’s upcoming price action. But what exactly do numbers developed by a 13th-century Italian mathematician have to do with today’s complex financial markets?

Today, we’re going to look at how Fibonacci levels work, and how you can trade off of them.

In his 1202 A.D. tome, Liber Abaci, an Italian mathematician named Fibonacci identified a sequence of numbers whose patterns frequently appear in nature. Today, the Fibonacci sequence is taught to most middle-schoolers, but its more complex applications take place in the world of finance. Simply put, the Fibonacci sequence is a pattern (starting with 0 and 1) in which each subsequent number is the sum of the previous two.

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    It starts off like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 …

    In the sequence above, the third number is the sum of the first two -- and the 10th is the sum of the 8th and the 9th, the two numbers that preceded it. What makes the Fibonacci sequence significant is its existence in nature: The arrangement of leaves on a stem, the spirals of a shell and the arrangement of a pine cone are all examples of naturally occurring items that exhibit Fibonacci patterns.

    For traders, the real significance comes from the behavior of tradable instruments, such as stocks, commodities and bonds, at key Fibonacci levels.

    Finding Fibonacci Ratios

    To adapt the Fibonacci sequence to trading, technicians use the Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8% and 100% (these ratios are found by dividing a Fibonacci number by the series of numbers that follow it in the sequence -- it’s worth noting that the 61.8% ratio, known as the Golden Ratio, is the most critical). By converting Fibonacci levels to percentages, they become relative and can be applied to stock charts.

    So what does a Fibonacci ratio (or Fib ratio) tell us?

    Market technicians use Fib ratios as support and resistance levels for the instruments they’re trading. In other words, those percentages can act as a sort of price floor or price ceiling for a stock.  Take a look at the chart below to see an example:

    Above: The USD/CAD currency pair retracing, with resistance at 38.2% (Source: Wikipedia)

    With all of that in mind, let’s take a look at how you actually apply Fib ratios to stocks.

    Types of Fibonacci Indicators

    There are a handful of ways that traders apply Fibonacci ratios to charts, but the most popular is the Fibonacci retracement (see chart above). Fibonacci retracements are predicated on the idea that broad trends are formed in a series of big moves, followed by pullbacks (known as retracements). Fibonacci ratios are used to determine just how far a retracement is likely to go.

    First a trader finds the relevant high and low for a stock’s movement, then plots 5 horizontal lines that correspond with the Fibonacci ratios between that high and low. Today, nearly any charting software package is capable of drawing Fibonacci retracement levels -- all the trader is required to do is point out the high and low that he or she is focusing on.

    But Fibonacci ratios are used to define more than just horizontal support and resistance – other indicators, such as Fibonacci arcs, Fibonacci fans and Fibonacci spirals, can give suggestions for support and resistance. As with retracements, applying them to stock charts is simply a matter of plotting your high and low -- your charting software will do the heavy lifting.

    Which Fibonacci indicator should you use? In my experience, the most effective way of picking an indicator is to overlay each of them over the chart’s previous price action, and see which is the best predictor of support and resistance. Typically, issues that behave within the bounds of a given indicator will continue to take cues from it in the future.

    Not all Fibonacci indicators are designed to show support and resistance levels -- others have been created to break up time zones on charts and determine where crucial movements (like reversals or breakouts) are likely to occur.

    Few traders use solely Fibonacci levels as a primary indicator for placing a trade. Even so, they’re an important tool that can help you identify key upcoming levels on your existing positions -- and a well-known element of your technical toolbox.

    We’ll continue to add tools to your technical repertoire with more primers that will bring you closer to implementing technical analysis for your portfolio. In the mean time, do you have a burning technical analysis question? Get it answered by heading to Stockpickr Answers.

    -- Written by Jonas Elmerraji in Baltimore.

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    Jonas Elmerraji, based out of Baltimore, is the editor and portfolio manager of the Rhino Stock Report, a free investment advisory that returned 15% in 2008. He is a contributor to numerous financial outlets, including Forbes and Investopedia, and has been featured in Investor's Business Daily, in Consumer's Digest and on MSNBC.com.