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The Myth Of Fibonacci Numbers
We all have our favourite indicators and, if only we could discover just the right parameter settings, surely the Holy Grail would be within our grasp.
What better place to start than numbers with magical properties from the well-known Fibonacci Sequence.
Fibonacci, or to give him his proper name, Leonardo da Pisa, was born in Pisa in 1175AD. He travelled widely and, in the early 1200s, he returned to Pisa and used the knowledge that he had gained on his travels to write Liber Abaci in which he introduced the decimal number system to the Western world as a replacement for the Roman system still widely used at that time.
Fibonacci is perhaps best known for a simple series of numbers introduced in Liber Abaci and later named the Fibonacci Sequence in his honour.
The series begins with 0 and 1. After that, we add the two previous numbers in order to get the next number in the sequence as follows:
2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, etc.
Divide any number in the Fibonacci sequence by the one before it, e.g. 55/34, and the answer is always close to 1.618. You may also divide any number by the one after it, e.g. 34/55, and the result approximates 0.618. This is known as the Golden Ratio. Hence Fibonacci's Sequence is also called the Golden Sequence.
This sequence of numbers creates some further interesting mathematical relationships. The ratios of alternate numbers, e.g. 21/55, approach a constant 0.382 and those one place further removed, e.g. 21/89, converge upon 0.236. The inverse ratios of alternate numbers, e.g. 55/21, approach a constant 2.618 and those one place further removed, e.g. 89/21, converge upon 4.236.
For those of you who are mathematically inclined, the Golden Ratio is the only number whose square can be produced simply by adding one and whose reciprocal can be produced by subtracting one. You may also have noticed that 0.382 is also the inverse of 0.618, i.e. 1 - 0.618 = 0.362.
By dragging the Fibonacci study on to any of your Metastock charts, you will see the retracement levels displayed in corresponding percentage terms; 61.8%, 38.2%, 23.6%, etc. Fibonacci extension levels are shown as 1.618%, 2.618%, 4.236%, etc. By the way, the commonly used 50% retracement is, strictly speaking, not a Fibonacci level but, hey, if it's good enough for Gann then it's certainly good enough for me.
The Golden Ratio was known to the ancient Greeks and has fascinated mathematicians, philosophers and artists ever since. Geometrically speaking, a rectangle measuring 1 x 1.618 or 1 x 0.618 (it's exactly the same thing) is considered to possess the most aesthetically pleasing dimensions to the human eye. This proportion has been used in many monuments, buildings, industrial designs and works of art. Have you ever wondered why it is so pleasurable to remove your credit card from your wallet? A link from the ancient Greeks to your Amex card? Whatever next?
From the above discussion, it becomes obvious that the numbers contained in Fibonacci's Sequence have special magical properties and, therefore, are ideal candidates to use in our search for the Holy Grail, right?
We will now create another 'sequence' at random. Let's take, say, 6 and 9 as our starting point and by adding the two previous numbers in order to arrive at the next, we get the following sequence:
6, 9, 15, 24, 39, 63, 102, 165, 267, 432, 699, 1131, etc.
By the way, I have taken 6 and 9 for this example from the classic Jimi Hendrix track on Axis Bold As Love so this sequence shall henceforth be known as the Jimi Sequence.
But what do we have here? Divide 267 by 165 and we get 1.618. Divide 267 by 699 and we get 0.382. Doesn't this start looking a little familiar?
If you use the attached spreadsheet, you will discover that you may start the sequence with any two numbers of any size that you wish and you will find that manipulation of the sequence will sooner or later converge upon the Fibonacci ratios. Why not invent your own sequence and sell a trading system based upon the constituent numbers?
But what does appear to come out of all this is that the ratios themselves appear consistently across the universe of numbers and this fact in itself may justify the reverence afforded to the Golden Ratio.
However, seeing 'magical' significance in, say, a 55-day cycle or a 144-period moving average is tantamount to self-delusion. Say NO to Fib numbers.
Unfortunately, Leonardo made the same mistake that many of us continue to make today; he didn't execute his back testing properly. Consequently, the Fibonacci Sequence is probably the earliest known example of curve-fitting. However, this is a minor gripe. Without him, we would probably be coding our trading signals something like this:
Buy: C > Mov(C, L, E) AND Mov(C, L, E) > Mov(C, CC, E) AND Cross(RSI(XIV), XXV)
Were you beginning to think that this would be an MSTT article with no Metastock code? Shame on you. Ducats on margin anybody?
Perhaps the last word should be left to Falstaff, another of Shakespeare's larger-than-life characters, in The Merry Wives of Windsor:
'I hope good luck lies in odd numbers. There is divinity in odd numbers, either in nativity, chance, or death'.
Isn't that where we came in?