Fibonacci For Traders, Truth Or Fib?


by Steven Sarnoff

Since today is Pi Day, and we were honored by our math major nephew dropping by the office during his break from university, I decided this was as good a day as any to get back to blogging with a post about how a trader should regard the influence of a famous Italian mathematician from the Middle Ages on today’s markets.

Leonardo Pisano Bigollo, better known as Fibonacci, published his Liber Abaci (Book of Calculations) in the year 1202.  He is credited with sparking the spread of the Hindu-Arabic numeral system we use to Europe. He also introduced his Fibonacci number sequence, to understand the propagation of rabbits and, which can be used in modern times to mathematically describe and understand certain shapes and patterns in nature, including things from atoms to honeybees, nautilus shells, sunflowers, and spiral galaxies.  Market technicians have learned to manipulate and apply Fibonacci’s thirteenth century principles to the price movement of today’s stocks and commodities.

The ratio derived from his celebrated sequence (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…) is 0.618 (and its reciprocal, 1.618) and is known as the golden ratio for its appearance in nature.  Here’s the rub, though, the series can begin anywhere, even negative numbers as long as the expansion follows the correct formula which is 1 plus the square root of 5, all divided by 2.

Traders translate Fibonacci ratios into percentages to forecast support and resistance targets for retracements and expansions.  They can be expressed in terms of arcs, horizontal lines, and fan lines based on price and/or time.  Common percentages derived for price forecasting include:  38.2%, 50%, 61.8%, 78.6, 88.6%, 1.27%, 1.618%, 2.618%, 3.14%, and others.

Here’s an example of a Fibonacci retracements tool applied to a daily candlestick chart of the S&P 500, together with lines of average price movement, to spot potential underlying support on a correction of the post-election rally.


My study of market price movement seeks to reveal the human behavior, of buying and selling, that ultimately drives price direction.  Because many large buyers and sellers use Fibonacci ratios, it’s valuable to consider them as an indicator in coming to a “weight of the evidence” decision about which side has the advantage, along with where and when the balance of power is likely to shift.

I’ve seen Fibonacci targets hit with great accuracy and I’ve seen them miss spectacularly.  There’s an old saying that the chart is never wrong, only the analysis. Price can blow through one or more levels and stop short of others.  The danger arises for traders when they zealously accept any indicator as the gospel truth.

Traders can also succumb to “paralysis from over-analysis.” No indicator is foolproof.  Fibonacci ratios can be an important addition to your indicator toolbox. My bottom line is to listen to the words of a wise trader who once advised me to, “Pick the indicators you like best and use them.”

I hope you found this article helpful.  Subscribe to Options Hotline today to see how we keep our readers a step ahead of the crowd.

Good luck in your trading!

Best regards,


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