The Magical Numbers of the Fibonacci Series
Optionetics Staff
03/11/03 - 12:40 PM EST
In the 12th century, an Italian mathematician traveled to the Middle East and was introduced to a mysterious set of numbers, which he brought back to the Western world and which now bear his name: the Fibonacci series.
The series is produced by adding any two adjacent numbers to arrive at the next-higher number, or subtracting to arrive at the next lower number. Starting with 1, the series is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 etc., to infinity.
After the smaller numbers, each of the Fibonacci is related to the next-higher number by the ratio of 1:1.618 and to the next-lower number by a ratio of 0.618:1.
The Fibonacci ratios can be used by traders to forecast price and time targets. They're found virtually everywhere in Elliott Wave analysis. One complete cycle has eight waves, five up and three down, all of which are Fibonacci numbers. Two further subdivisions will produce 34 and 144 waves, also Fibonacci numbers.
The mathematical basis of the wave theory on the Fibonacci sequence, however, goes beyond just wave counting. There's also the question of proportional relationships between the different waves. The most common ratios used by market technicians are 0.382, 0.500, 0.618, 0.79, 1.27 and 1.618.
The secret to their proper usage lies in the verification of a price vibration from two totally different price swings. These Fibonacci ratios help determine price objectives in both impulse and corrective waves.
Another important application of Fibonacci is derived from the distinct relationship of the numbers with time. There's no question that Fibonacci time relationships exist. However, some technicians feel they're harder to predict and are less important than the price relationships. Fibonacci time targets are found by counting forward from significant tops and bottoms.
On a daily chart, the analyst counts forward the number of trading days from an important turning point with the expectation that future tops or bottoms will occur on Fibonacci days, that is, on the eighth, 13th, 34th, 55th or 89th trading day in the future.
The same technique can be used on weekly, monthly or even yearly charts. On the weekly chart, the analyst picks a significant top or bottom and looks for weekly time targets that fall on Fibonacci numbers.
Combined with Elliott Wave analysis, these "magical" numbers play a very important role in determining time and price targets. The ideal situation occurs when the wave pattern, ratio analysis and time targets all come together.
For example, suppose that a study of waves reveals that a fifth wave has been completed. Let's say wave No. 5 has gone 1.618 times the distance from the bottom of wave No. 1 to the top of wave No. 3, and that the time from the beginning of the trend has been 13 weeks from a previous low and 34 weeks from a previous top. Suppose further that the fifth wave has lasted 21 days. This type of time and price clustering indicates the odds are really good that an important top is near.
Take the time to test these ratios for yourself. You might be surprised how often they come up in the markets.
