You would be hard-pressed to find anyone who didn’t recognize the name Leonardo da Vinci, the Italian scientist, inventor, and painter of the Mona Lisa. Same goes for fellow Italian Galileo Galilei, the mathematician who worked to prove that the Earth revolved around the Sun and not the other way around.
But not so many people know about their fellow countryman Leonardo Fibonacci, his work on the golden ratio, and more importantly for traders, the set of technical analysis tools that bears his name.
Fibonacci: Man, Myth, Legend, Sequence
Born in Pisa, Italy, in 1175, Fibonacci is considered to be one of the most gifted mathematicians of the Middle Ages. He spent much of his youth traveling throughout the Mediterranean learning the systems of arithmetic that merchants used to conduct their business transactions. Later in life he discovered what is now known as the “Fibonacci sequence”—a series of numbers (beginning with 1) in which a given number is equal to the sum of the two preceding numbers:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, etc.
For example, 1+1 = 2; 2+3 = 5; 3+5 = 8, and so on.
The sequence of numbers isn’t that significant, but the ratio you get from dividing any adjacent number into the other—for example, 8/13—is. As you move up the sequence, the ratio approaches the number 1.618, or its inverse, 0.618. This is known as the golden ratio.
The golden ratio shows up in patterns throughout nature, including:
- The petals of flowers
- Seed spirals in sunflowers and pinecones
- The branching sequence in trees
- Concentric snail and nautilus shells
- Spiral galaxies
- DNA molecules
- The ratio of male to female honeybees in a hive
If you want to test out this ratio yourself, measure from your shoulder to your fingertips, then divide that number by the distance from your fingertips to your elbow. The results will likely be very close to the golden ratio.
This Is Relevant to Trading Because … ?
Okay, this is all very interesting, you might be saying, but what does it have to do with trading?
Back in the 1970s, some investors theorized that the ebbs and flows—buying and selling—in the stock market might follow patterns similar to those of a natural ecosystem. They began applying Fibonacci numbers to their charts in the form of Fibonacci retracements.
Fibonacci retracements are designed to find areas of support and resistance after a move has been made, based upon numbers from the golden ratio converted into percentages. The levels include 23.6%, 38.2%, 50%, 61.8%, and 78.6%.
Where did these levels come from? Well, 38.2% comes from dividing a number in the series by the number found two places to the right; 23.6% comes from dividing a number by the number found three places to the right. And 50% isn’t a Fibonacci number, but many traders see the 50% retracement as a significant level. See figure 1.
Using Fibonacci Retracements
In the example above for the S&P 500 Index (SPX), you’d first select the time frame you want to analyze, then use the Fibonacci retracement tool to mark both the low and the high of the move. The tool then automatically calculates the corresponding Fib levels based upon percentage retracements.
Suppose you’re looking for potential support levels if SPX were to experience a down move. Notice the top level is 0.0% because that is where price is currently trading; there has been no (or zero) pullback yet. The bottom level is annotated as 100%, which corresponds to the lowest price of the period you’re analyzing. In other words, if the price were to fall from its current level to the lowest price, it would be a 100% retracement of the move you’re analyzing.
The retracement levels in between are areas you can watch for potential technical support, and a potential entry point for the resumption of the upward trend. Fibonacci retracements can be used in the opposite way to find potential areas of technical resistance in a downtrend. In that case you would select the high of the chart first and then the low.
Fibonacci in the Markets
Now, you might wonder how Fibonacci numbers, which are so prevalent in nature, can have anything to do with a manmade system like the stock market. Is there something about the human emotions of greed and fear (which drive buying and selling) that corresponds with Fibonacci numbers?
Maybe; maybe not. But we do know that Fib retracements are accepted and used by many traders, including some who trade for large institutions and hedge funds. This can give them a self-fulfilling aspect, at least in the short term, and in the absence of other technical or fundamental data. Does this mean that they always work? Of course not. But they do provide some objective (though some traders would say subjective) levels to watch.
Later we’ll expand on this idea and see how Fibonacci levels are used in some lesser-known technical tools such as Fibonacci extensions, times series, fans, arcs, and more.