When something sounds esoteric – like Fibonacci trading – the brain sometimes goes into avoidance mode. "Don't make me think that through," it says, "just let me get it quickly." Many people who come to Elliott wave analysis understand the concept of the underlying patterns of 5 waves in one direction and 3 waves in the other, but they stop short at what they perceive to be a strange Italian name for difficult math. For a quick and easy lesson on the Fibonacci [pronounced fib-oh-notch-ee] sequence and why the golden ratio (also known as 'phi') is important for trading, we turn to Bob Prechter in a question-and-answer session with a reporter from his book,
Prechter's Perspective.
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Question: Who was Fibonacci and why is his mathematical sequence so important?
Bob Prechter: Leonardo of Pisa was the son of a successful merchant named Bonacci, thus "fi" for "son of" Bonacci. Fibonacci introduced the Arabic number system to the Western world and was the most famous mathematician of his time. In the 13th century, he would entertain royal courts with mathematical problems. One of those problems was the famous rabbit problem [that is, How will a pair of rabbits multiply in an enclosed space?], the answer to which is the sequence named after him: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on.
The Fibonacci sequence is a self-generated sequence obtained by adding two adjacent figures to obtain the next. Start at the number 1 and add the preceding number. There isn't any, so you get another 1. Add the preceding number, 1, to that 1, and you get 2; take 2 and add the preceding number, which is 1, and you get 3; take 3 and add the preceding number, which is 2, and you get 5; take 5 and add the preceding number, which is 3, and you get 8, and so on to 13, 21, 34, 55, etc. Actually, Fibonacci re-discovered the sequence and the ratio that governs it, which had been known by the Greeks and as far back as the ancient Egyptians. It has been treated as a very special thing by mathematicians and scientists that far back, and to this day.
Then take a look at our brand new webinar, called
How You Can Identify Turning Points Using Fibonacci (Parts 1 & 2). In this new two-part online course, EWI's Senior Tutorial Instructor, Wayne Gorman, presents you with valuable tools to help you trade using a combination of wave analysis and Fibonacci relationships. It's the second webinar listed on our webinar page.
Q.: How does this sequence relate to the market?
Bob Prechter: In the stock market, the simplest description of a bear market is a straight line down, one wave. The simplest description of a bull market is a straight line up. R.N. Elliott found that bear markets most often subdivide into three waves: down, up, down. Bull markets subdivide into five: up, down, up, down, up. It takes one complete bear market and one bull market to make a cycle. At the simplest level, that is 1 rise and 1 fall, for a total of 2 waves. The bear market subdivides into 3 waves, the bull market into 5, and the total is 8. When you drop to the next subdivision, you find that a bear market has 13 waves, a bull market has 21, and the total is 34. And so on to infinity: each new number is the sum of the previous two. That is the Fibonacci sequence.
Q.: Can you explain what the Fibonacci ratio is?
Bob Prechter: As the Fibonacci sequence progresses, the ratio between adjacent numbers is always 0.618, called phi [pronounced "fie"], which has an inverse of 1.618; that is, .618 times 1.618 equals 1. It is the only ratio whose inverse is itself plus 1. This ratio governs all additive progressions of this type, no matter what number you begin with. [Editor's note: So, for instance, take 34 and divide by its adjacent number, 55. You get 0.618 – the golden ratio.]
Q.: Wait a minute. Start with three instead of one.
Bob Prechter: Sure, The result is 3, 3, 6, 9, 15, 24, 39, 63, 102, and so on to infinity. What always remains constant? The Golden Ratio between the numbers after the first few terms. Let's hit the calculator and see. In this example, 63 divided by 102 = 0.61765
Q.: So, in essence, nine is a Fibonacci number, also.
Bob Prechter: While the specific numbers making up the Fibonacci sequence may be more natural in that they begin with the number 1, they are not essential to the ratio, which governs a basic law of geometric progression.
Q.: What's the significance? Why is this relationship so critical?
Bob Prechter: The fact that the ratio governs all additive sequences derived by adding a term to the previous to get the next makes it ideal mathematics for growth patterns. That is undoubtedly why it is found in growth and decay patterns and in expansion and contraction patterns throughout nature. Many things – plants, animals, spiraling galaxies, cloud formations, hurricanes – display characteristics of motion, growth, and, in some rare cases, decay in ways that reflect the workings of the Fibonacci ratio. As a result, this ratio has fascinated scientists and mathematicians for centuries.
Q.: Why should it be this particular ratio?
Bob Prechter: Phi, or 1,618…, governs spirals, such as those seen from the nautilus shell to galaxies. In contrast, pi, or 3.1416…, another irrational number, governs the geometric shape known as the circle. The circle is a static shape. It doesn't imply motion; it implies stasis. A spiral, on the other hand, implies expansion and contraction, progress and regress. The stock market, as a direct reflection of the popular valuation of mankind's productive enterprise, is a record of man's progress or regress in that regard. Like other things in nature, then, human history seems to be following a pattern that conforms to a natural law based upon the same ratio. That mankind is producing a natural, spiral growth pattern throughout history may be a grand concept, but it is hardly fantastic.
Q.: So how do you use the ratio in markets to do Fibonacci trading?
Bob Prechter: One example of the use of the Fibonacci ratio in the Elliott Wave Principle is to establish targets based upon common relationships among waves. Ralph Elliott pointed out one example of when an impulse was likely to display a Fibonacci relationship among its components. I have catalogued a whole lot more.