Lessons from Leonardo Fibonacci

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 back into Latin.

In researching this story, I learned some interesting things about Fibonacci. He particularly liked ancient math books, and he learned that the Arabs had developed a numbering system vastly superior to the Roman numerals used in Europe. More importantly, they mastered the concept of zero and the placement of digits in addition and subtraction. The Arabs themselves borrowed these concepts from Indian mathematicians as far back as the 6th century.

Now, just think about how significant this was to the world of math. Try multiplying CCVII by XXXIV (The answer is VMMXXXVIII, or 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 over $26 trillion in Roman numerals.

Fibonacci discovered a series of numbers that seemed to have magical predictive powers. 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. I wonder if we could use it today to predict the growth rate of a population of government officials.

Fibonacci ratios are mathematical relationships expressed as ratios and 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 approximately 0.6154, and 55/89 is approximately 0.6180. Got that? We’ll have a quiz in the morning.

Over the centuries, other great mathematicians experimented with numbers and discovered a lot of interesting applications or coincidences. It turns out the Great Pyramid in Egypt was built to the specification of a Fibonacci ratio, and so is the rate of change of the curvature in a seashell, or a human ear. Upon closer inspection, the Fibonacci sequence turned out to be absolutely everywhere. Coincidence or by design? You be the judge.

Fibonacci introduced his findings in a book entitled Liber Abaci, or “Free Abacus” in English, which he published in 1202. In the book, he proposed the 0-9 numbering system, place values, lattice multiplication, fractions, bookkeeping, commercial weights and measures, and the calculation of interest. It included everything we would recognize as modern mathematics.

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 like Fibonacci would have predicted. The bad news was 61 percent 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. Sadly, most people don’t have the stomach for that kind of trading, including me. Needless to say, my Fibonacci trading days are long in the past.

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. It’s also why a lot of technical trading theories of the past are not working so well anymore.

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!