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Technical Analysis is the ultimate marriage of art and science, and there is one indicator above all others which embodies this principle; the Fibonacci retracement.

It's named for one of the greatest mathematicians of the middle ages, Leonardo Fibonacci, who discovered a sequence of numbers whose proportionality is so powerful that it has been applied within art, architecture, nature and science for thousands of years. Fibonacci can be found in everything from the Mona Lisa’s smile, the great pyramids, the structure of Human DNA, and most importantly, the stock market.

Yes, even the action of the market itself has for centuries adhered to the patterns of proportionality described in the Fibonacci sequence. Let’s take a look at the basics of the sequence so you can harness its powers and apply it to the stock market to make you a better trader.

The Fibonacci sequence starts like this: 0, 1, 1, 2, 3, 5, 8, and so on, all the way to infinity.

At first glance, that may look random, but it’s not. Fibonacci observed that the sum of any two adjacent numbers in the sequence forms the next higher number. In other words, that sequence is calculated this way:

0+1=11+1=21+2=32+3=53+5=8 8+5=13And on and on.

But the real genius of the sequence is that after the first several numbers, the ratio or proportion of any number to the next higher number is approximately 0.618 to 1. That ratio, 0.618 is more commonly referred to as the Golden Ratio.

You may be wondering how you use this ratio to help make you money. The key lies in the concept of proportionality. Just as the numbers in the sequence display an almost mystical proportionality to each other which approximates 0.618; so do movements in the stock market.

Here's a real world example to better illustrate this concept:

While we can apply Fibonacci to any market movement – short or long term – it helps when we have a well-defined easily recognized trend. The historic decline from the October 2007 high precipitated by the US financial crisis is one such trend.

The first step in applying Fibonacci is to identify the starting point and the end point of the move we want to analyze.

[Fortunately, most basic charting packages provide a tool which takes care of the math for you. All you need to do is click on the start and drag down to the end and let the software plot the Fibonacci levels, ratios or retracements on the chart.]

If Fibonacci was to be believed, once the low was established and the market began to recover, the sequence tells us that we are likely to reclaim losses in the proportion of 0.618 or 61.8% of the entire decline. And that is exactly what happened. As the S P 500 index climbed almost 83% over the next 13 months to roughly 61.8% of the distance from the 2007 top to the 2009 low before experiencing its first meaningful decline.

And, just to further blow your mind, the Fibonacci sequence also called the exact bottom of that 17% pullback, as the 38% Fibonacci level (which is simply the converse of the Golden Ratio) held firm at 1,008 before the Bull Market resumed in earnest.

And we all know how that story ended.

While we have only just scratched the surface, I hope this helped to show you how you can harness the power of a centuries old mathematical sequence to be a better more profitable trader.

Talking Numbers contributor Richard Ross is Global Technical Strategist at Auerbach Grayson.

Glossary of Terms

Double Bottom

A chart pattern in which a stock falls to a trough, rises, and then falls to that same trough again. This is considered to be a bullish indicator.

Double Top

A chart pattern in which a stock rises to a peak, falls, and then rises to that same peak again. This is considered to be a bearish indicator.


The performance of a stock as it falls. A stock in a downtrend will make a series of lower highs and lower lows.

Head and Shoulders

A pattern in which a stock rises to a peak before falling, then rises to a higher peak before dropping, and then rising to a third peak that is not as high as the second before falling. This is considered to be a bearish pattern. (On the other hand, if the pattern is turned upside-down — with the stock falling to three different troughs — then the pattern is considered to be bullish.)

Relative Strength

A stock's performance relative to the overall market.

Resistance Level

A level that a stock is not expected to rise above.


A stock's change in trend. A stock in an uptrend can undergo a reversal and enter a downtrend, and a stock in a downtrend can undergo a reversal and enter an uptrend.

Short Interest Ratio

This number is calculated by dividing the number of short positions in a given stock, or bets that the stock will fall, by the average daily trading volume. It indicates how bearish Wall Street is on a given stock.

Support Level

A level that a stock is not expected to fall below.

Trading Range

The range of price levels that a stock is trading in. The top of the range is typically considered "resistance," and the bottom is "support." If this range is "well-defined," then the stock is not expected to exit this range unless it is impacted by a major catalyst.


The performance of a stock as it rises. A stock in an uptrend will make a series of higher highs and higher lows.

FinanceInvestment & Company InformationFibonacci sequenceLeonardo Fibonaccistock market
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