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Part I: Introduction

Wed, Jun 14 2006, 12:00 GMT
by Facundo Molina

MolFX - Management

Leonardo Pisano, better know as Fibonacci, explained the development of natural growing phenomenon through his famous numerical sequence. He proved that this series was highly connected with the growing of dynamics structures, and the most important use is relationated with its ratios.
The objective of the present work is to demonstrate that the application of these rules, have an important probability of success in financial markets, and principally in FOREX.

We start with the premise that the human society is a dynamic system, and its behavior is represented in financial markets through prices.

That is the reason why we will try to prove that there is an important probability to predict the behavior of prices in Forex, joining Fibonacci numbers with Zig Zag Oscillator.

So, we will try to determine the objectives zones, or where the prices tend to go using Fibonacci. We will study the prices corrections against the major trend.

The Method: Fibonacci, and his legacy

In the beginning, we start using the most important correction ratios discovered by Fibonacci. These ratios came from the famous Sequence.

Many contributions were applied to mathematics science by Fibonacci, but the most relevant discover was denominated by the French mathematician, Edouard Lucas, as Fibonacci Sequence in the XIX Century.

The sequence. Properties and principal characteristics

This sequence is a rule that explain the development of natural growing phenomenon. Formed by adding the last two numbers to get the next one.

The formula is:

The Fibonacci Sequence is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, etc.…

Fibonacci proved that this sequence could be found in the evolution of many natural phenomenons. He used as example the rabbit reproduction process. He wanted to know how many rabbits will be born in a year, knowing that:

1. A couple of rabbits could birth since the fist month, but the others couples just can do it since the second month.
2. Each labor brings two new rabbits as result.

If we suppose that any rabbit die, the process will be the like this:

1. In the first month there will be born two rabbits. So, we will have two couples.
2. During the second month, the initial couple will born another couple, and then will be three pair of rabbits.
3. In the third month, the initial couple, and the second one, will produce new couples. Then, there will be five couples.

Continuing with the present analysis, we could see in the next table the results of the rabbit’s couples forming the Fibonacci Sequence.



Despite all this, we find the major utility of the sequence in these fundamentals properties:

1. If we divide two consecutives numbers, 1/1, 1/2, 2/3, 3/5, 5/8, 8/13, etc. We could find that the results tend to 0.618.
2. If we divided two non consecutive numbers from the sequence, ½, 1/3, 2/5, 3/8, 5/13, 8/21, etc. We could see that the result obtained tend to 0.382.
3. If we calculate the division between any numbers of the sequence to the next lower, 21/13, 13/8, 8/5... the results tend to 1.618, which is the opposite of 0.618.
4. If we calculate the division between any numbers of the sequence to the higher low non consecutive, 21/8, 13/5, 8/3... the results tend to 2.618, which is the opposite of 0.382.

E.g.; 144 / 233 = 0,618 144/89= 1.6179

The ratio 1.618, or the opposite 0,618 were denominated by the Old Greeks “Golden ratio” or “golden section”, and they are represented with the Greek letter phi, referenced by the greek author, Phidias. Chirstopher Carolan mentions in his book that Phidias was the author of the Athens statues in the Parthenon and The Zeus in Olympus. He considered very important the phi number in Art, and in nature.

This ratio, who’s opposite is the same number more the unit, characterize all the progressions of this kind, where ever it is the initial number.

The most important ratios are 0,618 and it’s opposite 1,618, but not the only ones. We can continue on the ratios derivation of the Sequence, just increasing or decreasing the distance between the Fibonacci numbers.

So, each number is relationated with the higher next trough the 0,382 ratio, and with the lower next with the opposite ratio, 2,618.

E.g.: 144/377=0,3819 144/55=2,618

In the same way, the division between a number and the third next, bring as a result, 0,236, and the proportion between a number and the third lower next is 4,236.

E.g.: 89/377=0.236 144/21=4,238

The same occurs with 0,618 and 1,618, these ratios are more exactly, when we use higher fibonacci numbers. The next table shows some examples:

Ratios de 1,618	Ratios de 0,618
1,618 2 = 2,618	0,618 2 = 0,382
1618 3 = 4,236	0,618 3 = 0,236
1,618 4 = 6,854	0,618 4 = 0,146

Carolan emphasized that the Fibonacci ratios could be order as follows: 0,146, 0,236, 0,382, 0618, 1, 1,1618, 2,618, 4,236, and 6,854. Then we could find and additive sequence with the properties of the Fibonacci Sequence, because each number is the sum of the immediately two before, and moreover, each number is 1,618 times the number before.

Published on  Wed, Jun 14 2006, 12:18 GMT