by Jim Woods | April 10, 2009 4:36 am

The investing game is chock-full of esoteric lingo and obscure mathematical and technical analysis models. All too often, the unfamiliar terminology and the complexity of the models leave the neophyte investor perplexed.

I recently received an e-mail from an OptionsZone reader that exemplifies just this state of confusion surrounding one frequently mentioned technical analysis tool.

The reader asked the blunt question: “What the bleep is a Fibonacci?”

To answer this question properly, we have to go all the way back to 13th-century Italy. It was then that a brilliant mathematician named Leonardo Pisano, who was nicknamed “Fibonacci,” identified a sequence of numbers that possessed an unusual relationship.

Here is the famous Fibonacci number sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. The relationship between these seemingly unrelated numbers is that each term in the sequence is simply the sum of the two preceding terms. This relationship persists into mathematical infinity.

The unusual characteristic of this numerical sequence is that each number is approximately 1.618 times greater than the preceding number.

So much for the “what” of the Fibonacci, now we need to know how this sequence of numbers and the relationship between them is applied to an analysis of the financial markets.

Technical analysts use the relationship between every number in the Fibonacci series as the basis for identifying the common ratios used in price retracement studies.

When technical analysts look at price action through the Fibonacci prism, they identify two extreme points (usually a major peak and trough) on a stock chart, and then divide the vertical distance by the key Fibonacci ratios.

And what are those key ratios? They are 23.6%, 38.2%, 50%, 61.8% and 100%. Once these rations are identified, they signify potential areas of support and resistance. The question now is why did the aforementioned ratios become the key ratios?

Well, here is where the Fibonacci ratios become really esoteric. The theory here is that in nature, and in the financial markets, systems will tend to display numerical characteristics that resemble key Fibonacci patterns. Beehives, spiral galaxies, the human anatomy and, yes, the patterns in the equity markets, all display profound and unequivocally non-coincidental Fibonacci patterns.

Applied to the market, this technical tool is used to help identify critical points that cause an asset’s price to reverse. It’s also used to monitor the direction of a prior trend and how likely it is to continue once the price of the asset has retraced to one of the key ratios.

In the chart below provided by the Investopedia Web site, we can see how a Fibonacci retracement is plotted on a stock chart.

Here we see how a stock’s price tends to change direction as it nears key Fibonacci support and resistance levels. The most famous of these ratios is 61.8%, which is also referred to as “the golden ratio” or “the golden mean”.

This ratio is determined by dividing one number in the series by the number that follows it. For example: 8/13 = 0.6153, and 55/89 = 0.6179.

Now I know what you might be thinking right now. Does this Fibonacci thing really work? The answer to that question is yes and no.

Yes, using Fibonacci retracement patterns along with other technical analysis tools can work by giving you the edge when it comes to identifying key resistance and support levels in a stock. But no, relying solely on a Fibonacci retracement pattern or any single technical analysis measurement as the Holy Grail of investing does not work.

So, now that you know what the bleep a Fibonacci is, you can now move on to other simple questions such as the origins of life on earth, the Big Bang and quantum mechanics.

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