Chapter 2: Fibonacci / Swings

In Fibonacci’s Liber Abaci book, chapter 12, he introduces the following problem (here in Sigler’s translation – see below):

How Many Pairs of Rabbits Are Created by One Pair in One Year?
A certain man had one pair of rabbits together in a certain enclosed place, and one wishes to know how many are created from the pair in one year when it is the nature of them in a single month to bear another pair, and in the second month those born to bear also.

He then goes on to solve and explain the solution:

Because the above written pair in the first month bore, you will double it; there will be two pairs in one month. One of these, namely the first, bears in the second montth, and thus there are in the second month 3 pairs; of these in one month two are pregnant and in the third month 2 pairs of rabbits are born, and thus there are 5 pairs in the month;
…
there will be 144 pairs in this [the tenth] month; to these are added again the 89 pairs that are born in the eleventh month; there will be 233 pairs in this month. To these are still added the 144 pairs that are born in the last month; there will be 377 pairs, and this many pairs are produced from the abovewritten pair in the mentioned place at the end of the one year.

Ultimately, this leads up to the “Fibonacci Series”: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, etc. where each number is the sum of the two numbers that precede it.  History is blurry on whether Fibonacci actually invented this problem or series (history points to Indian mathematics).  In any case, it now bares his name.

This Fibonacci series is also illustrated in Pascal’s Triangle.

As these numbers grow in size, the relation of any pair of numbers gets closer and closer to the “golden ratio” (also known as the “golden mean”), which is 1.61803399… In other words, to go forward in the sequence, you multiply the number by 1.618.  To go backwards, you multiply by 0.618.

For example, in the series:

… 55, 89, 144, 233, 377…

144 * 1.618 = 233

144 * 0.618 = 89

 

Primary Ratios:

1.618 = The Golden Ratio

0.618 = Inverse of 1.618 (1/1.618)

These ratios are found in nature, the human body, plants, DNA, the solar system, art, architecture, music, and even the stock market!

 
From this one number, 1.618, we can derive various other important numbers.

Primary Derived Ratios:

  0.786 = Square root of 0.618

  0.886 = Square root of 0.786

  1.130 = Inverse of 0.886 (1/0.886)

  1.272 = Square root of 1.618 (or the inverse of 0.786 (1/0.786))

 

Complementary Derived Ratios:

  0.382 = 0.618^2 (or 1 – 0.618)

  1.414 = Square root of 2.0

  2.000 = Square root of 4.0 (or 1+1)

  2.236 = Square root of 5.0

  2.618 = 1.618^2

Let’s also not forget the series generated by repeatedly multiplying 1.618… 2.618, 4.235, 6.854, 11.09, 17.94, 29.03, 46.97…

Next, we’ll go into the descriptions of the various Fibonacci Swing Patterns we look for on our charts.  You will quickly notice that the above ratios make up most every ratio of every pattern! Coincidence?

For easy reference, click here for a Fibonacci Swing Pattern “cheat sheet” you can easily print!

This formation was outlined by H.M. Gartley in his book Profits in the Stock Market, published in 1935.
 
The pattern is also known as Gartley 222, in reference to the page number the discussion of the pattern occurred.
 

 
There are others who have assigned Fibonacci retracements to this framework. However, they use a variety of Fibonacci numbers at the B and D points. Despite these variations, the Fibonacci retracements that yield the most reliable reversals are the 0.618 at the B point and the 0.786 at the D point. Furthermore, the formation should possess a distinct symmetrical formation that converges in the same area as the 0.786 XA retracement and the BC projection (1.272 to 1.618). The most critical aspect of the Gartley is the B point retracement, which must be at a 0.618 of the XA leg.
 

 
This formation was discovered by Bryce Gilmore. Frequently, the symmetrical formation will possess an extended CD leg that is 1.27 or 1.618 of the AB leg. Although this is an important requirement for a valid trade signal, the most critical number in the formation is the 1.27 XA leg.  The XA calculation is usually complemented by an extreme (2.00, 2.24, 2.618) BC projection. These numbers create a specific D point that can yield powerful reversals, especially when the formation is in all-time (new highs/new lows) price levels.
 

 
The critical aspect of this formation is the tight D point created by the 1.618 of the XA leg and an extreme (2.24, 2.618, 3.14, 3.618) projection of the BC leg but employs an 0.886 retracement at the B point unlike the regular version that utilizes a 0.382-0.618 at the mid-point. The formation requires a very small stop loss and usually volatile price action in the D area.
 

 
The primary difference between this formation and the one above is the retracement of point B.  This has a much deeper retracement, yet keeps the same 1.618 projection of the XA leg to point D.
 

 
The formation incorporates the 0.886 XA retracement, as the defining element in the D area. The B point retracement must be less than a 0.618, preferably a 0.50 or 0.382 of the XA leg. This formation utilizes a minimum 1.618 BC projection. In addition, the symmetrical formation within this pattern is extended and usually requires a 1.27 symmetrical calculation. It is an incredibly accurate formation and requires a smaller stop loss than most formations.
 

 
This formation incorporates the 1.13 XA retracement, as the defining element in the D area. The B point retracement must be a 0.382 retracement or less of the XA leg. This utilizes a minimum 2.0 BC projection. In addition, the symmetrical formation within it is always extended and usually requires a 1.618 symmetrical calculation.
 

 
This formation is what we call a “class 2” formation, where point C exceeds the AB leg.  As you can see, the formation is very similar to others, except for the location of C in relation to AB.
 

These are not all the patterns!
In addition to our PDF cheat sheet of common patterns, we strongly encourage traders to search for new and powerful patterns using our tool’s ability to create CUSTOM patterns!

Shirky Principle: ‘Institutions will try to preserve the problem to which they are the solution.’

Don’t let ANYONE try and tell you there is only one set of patterns and they are the sole keeper. We at UppDnn.com believe in innovation and progress. Don’t let anyone hold you back!

XLS Spreadsheet

The symmetrical pattern is a price structure where each price leg is equivalent. The Fibonacci numbers in the pattern must occur at specific points. In an ideal symmetrical formation, the C point must retrace to either a 0.618 or 0.786. This retracement sets up the BC projection that should converge at the completion of the symmetry.
 

Based on the retracement of point C, there are other extensions of the CD leg to look for.  Namely, either a 1.27 or 1.618. When there is a 0.618 retracement at the C point, then look for a 1.618 BC projection. If there is a larger 0.786 retracement at the C point, then look for a 1.27 projection. The most important consideration to remember is that the BC projection should converge closely with the completion of the symmetry.
 

Although it was not specifically identified, one of the first references to a Three Drives Formation was outlined in Robert Prechter’s book, “Elliot Wave Principle.” He described the general nature of price action that possessed either a three-wave or a five-wave structure. Adapted from this principle, symmetrical price movements that possess identical Fibonacci projections in a 5- wave price structure constitute a Three Drives formation. Also, the price legs should possess clear symmetry with each drive forming over equivalent time periods.
 

If you missed the link earlier, click here for a Swing Pattern “cheat sheet” you can easily print!
 
PDF Swing Pattern Cheat Sheet

Fibonacci and Swing Pattern go hand in hand. These Fibonacci ratios are found in all aspect of nature and throughout the universe.

The market consists of thousands of traders whose bodies and minds also are built around these ratios, so it makes sense that they appear in the stock market as well.

This style of trading makes logical sense and builds upon many existing, proven styles.