# Technical Analysis Explained

## The Elliott Wave Theory

Ralph Nelson Elliott (1871-1948) had been an accountant by profession. He retired in 1927 after contracting a serious illness and spent the next several years at his home in California. It was during his long period of convalescence that he developed his theory of stock market behaviour. He apparently was much influenced by the Dow Theory, which has a lot in common with his wave principle. Elliott and Dow, both refer to the tide cycles of the sea and compared the rhythm of the waves to the price fluctuation in the stock market. Two years before his death, in 1946, Elliott wrote his definitive work about his research and entitled it "Nature's law-the secret of the Universe". Elliott was convinced that his theory was a part of a much larger law governing all of human's activity.

There are three basic aspects of the theory - wave pattern, ratio and time (in that order of importance). Elliott claims that the Stock market follows a repetitive rhythm of a five-wave advance followed by a three-wave decline. Figure 26 shows one complete cycle. Wave one, three and five go with the main trend and are called impulsive waves. Wave two and four are corrective waves. After a five-wave advance has been completed, a three-wave correction begins, subdivided in an A-B-C structure. After that, a new five-wave advance can start. In figure 27 you can see the Elliott wave counts, applicable in the "macro and micro" view. Along with the constant form of the various waves, there is the important consideration of degree. Elliott categorizes nine different degrees of trend ranging from a Grand Supercycle spanning two hundred years to a subminuette degree covering only a few hours.

Since computers record every price change of a specific market, the described five wave sequences can even be detected in intra-day moves lasting less than one hour.

## The Fibonacci numbers as part of the wave principle

In "Nature's Law" Elliott stated that the mathematical basis for the wave principle was based on a number sequence discovered (or more accurately rediscovered*) by the mathematician Leonardo Fibonacci who lived in the thirteenth century. In "Liber Abaci" (the best known of his three major works published) the Fibonacci sequence is first presented as a solution to a mathematical problem involving the reproduction rate of rabbits. The number sequence presented is

1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, ...

The sequence has a number of interesting properties. The two most noteworthy ones are first, each Fibonacci number is the sum of the two numbers preceding it, thus it is an additive sequence.

For example, 3 and 5 equals 8, 5 and 8 equals 13, 8 and 13 equals 21 etc; and second, the ratio of each Fibonacci number to its preceding number is alternately greater or smaller than the golden ratio. As the sequence continues, the ratio approaches the golden ratio, 1.6180339..., known also as "phi". For example: 144 / 89 = 1.617977, 233 / 144 = 1.618055 etc. The ratio of any number to its higher number approaches .618, after the first four numbers. For example, 144 / 233 = 0.618025 etc. Notice the values of 1.00 (1 / 1), .50 (1 / 2) and .67 (2 / 3) that area also important retracement levels (see "Fibonacci and phi in nature")

Here is a partial list of other intriguing properties of Fibonacci numbers.

- the sum of any ten consecutive Fibonacci numbers is divisible by 11

- every third Fibonacci number is divisible by 3, every fourth is divisible by 5,

every sixth is divisible by 8, etc. (divisors being Fibonacci numbers).

- consecutive Fibonacci numbers have no common divisor other than 1.

**The knowledge of phi (phi = 1.618...) was known and revered already by the ancient Greeks. Euclid solved the problem of finding the golden section of a line. This knowledge extended beyond the mathematicians and philosophers to the artists and architects. The temples, the most sacred and enduring structures, were based on phi. **

## The geometry of phi

## Fibonacci and phi in Nature

Spirals appear in seashells, pine cones , animal horns and patterns of plant growth. They also appear in non-living natural objects such as galaxies and in non-living natural processes such as hurricanes or ocean waves (see figure 30, the pattern which connects). Virtuous, the Roman architect and author of De Architecture, said, "Nature has designed the Human body so that its members are duly proportioned to the frame as a whole." Studies show the proportions of phi are found in man. The average height for the navel of a man is .618 of the total body height (figure 31 "human body"). The same proportion is found between the bones of the human hand (figure 32 "the human hand"). The human body, including the head, has a Fibonacci five appendages attached to the torso. The hands and feet each have five fingers or toes. Our senses also number five, sight, smell, taste, touch and hearing. The Fibonacci sequence has been found in the solar system. Planets with more than one moon have a Fibonacci correlation in the distance from the moons to the planet. A similar Fibonacci relationship holds true for the distance of the planets to the sun.

The mathematical basis of the Elliott wave theory of the Fibonacci sequence, goes beyond just wave counting as previously described. There is the crucial question of proportional relationships between the different waves. The following are some of the commonly used Fibonacci ratios.

1. A minimum objective for the top of wave 3 can be obtained by multiplying the length of wave 1 by 1.618 and adding that total to the bottom of wave 2.

2. Because only one of the three impulse waves extends, the other two are equal. If wave 3 extends, wave 1 and 5 tend towards equality.

3. Where wave 1 and 3 are about equal, and wave 5 is expected to extend, a price objective can be obtained by measuring the distance from the bottom of wave 1 to the top of wave 3, multiplying by 1.618, and adding the result to the bottom of 4.

4. For a normal zigzag correction, wave c is often about equal to wave a.

5. Another way to measure the possible length of wave c is to multiply .618 by the length of wave a and subtract that result from the bottom of wave a. Another way to determine price objectives is by the use of percentage retracements (corrections). The most commonly used numbers in retracement analysis are 61.8%, 50% and 38.2% but also 67% (2/3) is a frequently used retracement figure.