The Tribune Democrat, Johnstown, PA


December 29, 2012

NICK MASSEY | Leonardo Fibonacci was the original numbers guy

— When I was a young stockbroker and commodities trader in the late 1970s, I became aware of a mathematical formula called Fibonacci ratios.

What a great Italian name! It just rolls off the tongue like it should be a great Italian dish or a fine wine instead of mathematics.

Actually, it is a theory or formula developed by Leonardo Fibonacci in the 12th century, and he unleashed a body of knowledge that would change the world and how people looked at it.

Leonardo was a world-class geek by the standards of his day, with a passion for mathematics. He also learned to read books in Arabic and translated them into Latin.

In a recent piece written by my friend and hedge fund trader, John Thomas, I learned some interesting things about Fibonacci.

He particularly liked ancient math books. There he learned that the Arabs had developed a numbering system vastly superior to the Roman numerals then in use in Europe. More importantly, they mastered the concept of zero and the placement of digits in addition and subtraction.

Now, just think about how significant this was to the world of math.

Try multiplying CCVII by XXXIV. (The answer is 7,038). Try designing a house, a bridge, a computer software program, or just balancing your checkbook with such a cumbersome numbering system. Imagine our national debt of $16 trillion in Roman numerals.

Fibonacci discovered a series of numbers that seemed to have magical predictive


The formula is extremely simple. Start with zero, add the next number, and you have the next number in the series. Continue the progression and you get 0,1,1,2,3,5,8,13,21,34,55 ... and so on. Not surprisingly, the sequence became known as the “Fibonacci sequence” or “Fibonacci ratios.”

The great thing about this series is that if you divide any number in it by the next one, you get a product that has become known as the “Golden Ratio.” This number is 1:1.618, or 0.618 to one.

Fibonacci’s original application for this number was that it could be used to predict the growth rate of a population of breeding rabbits. I guess that was a valuable skill back then.

Fibonacci ratios are mathematical relationships, expressed as ratios, derived from the Fibonacci sequence. The key Fibonacci ratios are 0 percent, 23.6 percent, 38.2 percent and

100 percent. The key Fibonacci ratio of 0.618 is derived by dividing any number in the sequence by the number that immediately follows it. For example: 8/13 is about 0.6154, and 55/89 is about 0.6180. Got that? We’ll have a quiz in the morning.

In the early 1980s, I used the Fibonacci ratios to come up with trading patterns and I used it to day-trade commodity futures contracts for myself and clients. When I saw a certain pattern, I would use the ratios to find the ideal potential trade entry point, the ideal target to sell and the ideal point to bail out if things went wrong. I thought I had discovered the magic formula for all times.

The great news was that it worked almost exactly 61 percent of the time, just as Fibonacci would have predicted. The bad news was the percentage was the average over a one-year period or longer. The short term results were all over the place. When it was hot, it was incredible.

When it got on a losing streak, the drawdown was so bad it took an incredible leap of faith to hang in there.

Today, Fibonacci ratios are used by many technical traders as they try to find support and resistance levels for stock and option prices.

High-frequency traders have developed computer models to take advantage of it.

Knowing where the Fibonacci traders would likely place their buy and sell orders, they place stop-loss orders just under that price to go short and then enter large, rapid-fire sell orders above it to try and drive the price down and trigger the stops. This is not a game for the faint of heart.

So what does all this mean for most of us today? Probably not much. But it’s a great story and perhaps you learned a little about some of the methods Wall Street traders use. Now you know the rest of the story. As for me, I’ll just have a glass of that Fibonacci wine please.

Nick Massey is a columnist for The Edmond (Okla.) Sun.

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