THE MAGIC OF FIBONACCI
 
 
 
Many of the technical write-ups mention this curious sounding name quite often. It is one of the more popular trading and analysis techniques used by most people in the market. The popularity of the Elliott Wave led to more detailed study of the Fibonacci number series though Elliott himself never mentioned this in any of his treatise. But the later authors of the wave principles used the number series to relate waves and this led to some renewed interest in the number series.
 
“Liber Abaci “ was a book written back in the late 12th century by a man called Leonardo Fibonacci de Pisa. It is said that he had returned from a trip to Egypt where he came across a set of numbers with many remarkable properties. Apparently, it was his study of the Pyramid of Gizeh that he noticed the "Golden Ratio" that the ancient Egyptians had integrated into its dimensions. This book contained s nu number sequence, which today we refer to as the "Fibonacci Numbers."
 
The numbering sequence follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377… As you can see, each number is the result of adding together the previous two numbers in the sequence. This can be done right into infinity.
 
Since Fibonacci attention had been attracted by what he called as the golden ration, we shall examine that first. He found that the pyramids of Egypt had consistent ratios of 0.618. When this aspect was examined further, it was found that this ratio was prevalent in substantially disparate elements such as the nautical shell, the whorls of a sunflower, within the atom, the arrangement of rings of Saturn, the leaves of certain plants etc etc. The wide presence of the ratio across the universe was what prompted the name “golden ratio”.
 
One may wonder what this has to do with the markets or the Fibonacci number series. Well, we are coming to that. More than the numbers within the series, it is the relation between the numbers that is interesting, leading to its usage in technical analysis. The interesting properties of these numbers, after getting past the first 4, are as follows:
 
Each number in the sequence is approximately 1.618 the previous number. The higher the number, the closer to this ratio it will be. E.g 13 is 1.618 times 8 or 34 is 1.618 times 21.
 
On the reverse, each number is approximately .618 of the next higher number. The higher the number, the closer to this ratio it will be. Eg. 55 is 0.618 of 89 and 144 is 0.618 of 233 etc.
 
Every Alternate numbers will be 2.618 of each other, such as 377 to 144 and 89 to 34.
 
Exactly in the inverse manner every alternate number will be 0.382 of the next higher alternate number such as 21 is 0.382 of 55 and 89 is 0.382 of 233.
 
These ratios also interrelate to each other as follows:
 
  • Square of .618 = .382.
  • Square of 1.618 = 2.618
  • 2.618 x .382 = 1
  • 2.618 – 1.618 = 1
  • 2.618 x .382 = 1
  • 1.618 x .618 = 1
  • 1.618 - .618 = 1
 
The question was, how does one use this in the market? The logic applied was pretty simple. If the golden ratio is prevalent in nature then any man made structure should also reflect this “law” of nature. Since the markets are a human creation, this is applied to the markets also. We have another market mystic, W.D.Gann, who gave us the theory of market “sections” and even the venerated Dow theory talks about a secondary lasting from around one third to two third of the earlier leg which it is correcting. Hence, the Fibonacci principle is mainly applied to the price discovery process by as found in many trading programs today, what is called 'Fibonacci Retracements' are derived by taking a market range, such as a market bottom to a top, and dividing that range by these Fibonacci ratios of .382, .618.
 
There are also other Fibonacci ratios you can use, such as .786 and .236. .786 is the square root of .618, and .236 is from multiplying .382 with .618. Example: Suppose we look on our daily price chart and see an obvious market bottom at 150. Now suppose that price moved up for some days and eventually made a top at 200.
 
We know this to be a top because price has started to move down from that top. All we would have to do to get our Fibonacci static support/resistance prices is to take the top price of 200 and subtract from that the bottom price of 150. Our RANGE would then be 50 points.
 
Take the RANGE (50 Points) and multiply it by the Fibonacci ratios of .236, .382, .618 and .786. We would end up with the following results:
 
  • (50 x .236) = 11.8
  • (50 x .382) = 19.1
  • (50 x .618) = 30.9
  • (50 x .786) = 39.3
 
Since price is moving down from the top price of 200, we would subtract the results of these ratios from 200 to get our SUPPORT prices.
 
  • (200 – 11.8) = 188.20
  • (200 – 19.1) = 180.90
  • (200 – 30.9) = 169.10
  • (200 – 39.3) = 160.70
 
The process is the same for price ranges that go from top to bottom, where price is starting to move up again. In those cases you would simply add the results of those ratios to the bottom price to get your RESISTANCE prices.
 
Fibonacci ratios can also be useful at times for discovering when a top or bottom may form. The process is to simply count the days between two tops or bottoms (or whatever combination you care for) and multiply by .618. Take the result and add to the second top or bottom in your equation to forecast out a possible turn. In the example below, two multiples of a swing (marked by vertical lines) are projected forward. Note that both points worked well. This chart was chosen at random.
 
Another time approach is to take any major top or bottom and then count forward a Fibonacci number worth of days into the future, such as 34, 55, 89 days and so-forth, that will produce a future date in which to look for a possible market top or bottom to occur. The vertical lines in the following chart are time counts by Fib numbers projected ahead from a significant low.
 
 
As with anything else in trading, price will not always find Fibonacci support/resistance nor will it always turn at your Fibonacci time day counts. Other methods and indicators could and should be employed along with Fibonacci ratio work in market analysis. However, due to the frequency of ratios affecting market action, it would be worth your time to further your study in Fibonacci numbers/ratios.