Learning and Observing the Market: Stocks Love Symmetry

By Divid Waggoner

“Beauty is Truth, truth beauty, - that is all Ye know on earth, and all you need to know.”

-Ode on Grecian Urn, John Keats

“God does not play dice with the universe.” -Albert Einstein

The mathematical basis for the Elliott wave principle is Fibonacci mathematics. Leonardo Fibonacci was a 13th century Italian mathematician who is credited with the sequence of numbers bearing his name: 1,1, 2, 3, 5, 8,13, 21, 34, 55, 89 and so forth. Beginning with the number 1, each new term is the sum of the previous two.

It is believed that Fibonacci learned of the additive sequence while studying with Arabs in North Africa. He introduced it to the Western world in his famous book Liber Abaci (Book of the Abacus). The more relevant contribution of the book at that time was the introduction of the Arabic numeral system, which is now used throughout the world as the decimal system. It replaced the Roman numeral system that was in use at the time in Europe.

The additional mathematical fact of the Fibonacci sequence is that the ratio of any two numbers in the sequence approximates 1.618, or its inverse, .618 after the first several numbers. The higher the number, the closer to .618 and 1.618 are the ratios between the numbers. The Fibonacci sequence can be visualized geometrically as a mathematical grid growing larger (or smaller) in which each new unit always bears a relationship of .618 or 1.618 to its predecessors.

The number .618, or to be more exact, .618034... is an irrational number that is known as the golden ratio or "Phi." The Greeks held this ratio to be divine. Plato establishes it in his Socratic dialog of creation, Timaeus, as the mathematical basis of all creation.

The Golden Ratio In The World

The divine ratio was central to Greek thought and the works of Pythagoras, Euclid and Eudoxus. It governs geometry’s golden section, golden rectangle and golden spiral. In Greek architecture, its proportions are responsible for the incredible symmetry of proportion found in the Acropolis and the Parthenon. 2,000 years before Greek civilization, the Golden ratio is found to consciously be incorporated in the construction of the Great Pyramid of Cheops(2,560 BC) and other structures of ancient Egypt. (This is also explained in Timaeus.)

In nature, the Fibonacci sequence and ratios are found in vertebrate, tree branches, honeybee populations, the flight path of birds, the swimming path of fish, pinecones, sunflowers, shells, pineapples, hurricanes, whirlpools, ferns, clouds, flower petals, ocean waves, spiraling galaxies, lightning, snails, animal horns, DNA (the double helix), and, as depicted in Leonardo da Vinci’s Vitruvian Man and On the Divine Proportion, the human body.

Many great thinkers throughout the ages have been obsessed with the golden ratio. Famous scientists were in awe of how it repeated persistently throughout their work. Famous artists, recognizing its aesthetic quality in nature, reproduced it in their work.

Johannes Kepler, the famous astronomer, believed that the golden ratio described virtually all of creation. Isaac Newton, physicist, had the golden spiral engraved on the headboard of his bed. Pythagoras, mathematician, chose the 5-pointed star, in which every segment is the golden ratio to the next smaller segment, as the symbol of his order. Jacob Bernoulli, mathematician and astronomer, directed the golden spiral be etched on his headstone when he died. Leonardo Da Vinci used the golden ratio in much of his art to enhance its aesthetic appeal; the Mona Lisa employs the golden ratio. Mozart consciously used the golden ratio in his sonatas.

The golden ratio is central to arithmetic, algebra, geometry, trigonometry, proportion, architecture, electronics, and music. (According to H.E. Huntly, author of Divine Proportion, the golden ratio naturally appears in the relationship of the intervals or distance between notes in music.)

Fibonacci numbers and the golden ratio are evidenced and accepted as fact to exist in the progress of the cosmos, botany, physics, geophysics, astronomy and biology.

Therefore, is it too much of a leap to accept that human progress might also have form? And if human progress has form, then isn't it a logical conclusion that the stock market, which is a representation of man's progress on this Earth, would embody that form? And wouldn't that form show up in a chart?

The Golden Ratio in the Markets

R.N. Elliott discovered the golden ratio and Fibonacci sequence of numbers, the same persistent, repeating structure and unity evidenced throughout the universe, in the charts of the stock market.

The golden ratio in the stock market is the proportionate relationship of one wave amplitude to another. There is also evidence to support that these relationships exist in time. In my experience, the proportionate amplitude of waves can be detected more easily and consistently for forecasting than time. (But, it doesn’t stop me from trying to figure out time also.)

The following Fibonacci ratios are the most commonly found ratios in the stock market: .382, .500, .618, 1.00, 1.618, and 2.618. These ratios can be applied as either extensions or retracements of wave patterns to forecast price action.

For example, the structure of a motive or impulse wave is 5-3-5-3-5. The most common expression of the golden ratio in a motive or impulse wave is that wave 3 extends to a 1.618 ratio of wave 1, and, in such cases, wave 5 tends toward a .382 ratio of the entire length of waves 1 through 3. Let's take a look at the primary trend wave count thesis to see if these desired proportions are present.

Using a Fibonacci extension tool available with most charting software, one can determine that the actual proportions of the waves are consistent with my thesis: wave 3 is very close to a 1.618 ratio of wave 1, and wave 5 is close to a .382 ratio of waves one through three. That is a powerful confirmation that we have completed five impulse waves down and an example of how the golden ratio presents in the stock market.

Golden Ratio Present in Stock Market

Continuing with my primary trend thesis, I suggested that we were probably in the process of a counter-trend rally second wave. We will now use Fibonacci ratio analysis to target probable turning points. First I will apply a retracement of the entire move from the top.

The inside band of Fibonacci numbers are the resultant retracement levels. Last week I identified a completed counter-trend double zigzag at the 60min level, and I suggested that the downward move from that point was probably a correction of a correction. I then deduced that since we were almost finished with another double zigzag, and near the .500 Fibonacci retracement level, we had a strong set up for a turn. That was in fact correct. With a confirmed turn, I can now project a Fibonacci extension of the double zigzag from the bottom (W-X-Y).

The double zigzag is now part of a larger combination at one higher level of degree, and I have new information to include in our calculations for probable targets. In doing this I have an overlap of two Fibonacci relationships. Both the .618 retracement level and the 1.00 extension are at the same level. This is now my most compelling target for two reasons: 1) A 1:1 ratio is the most common extension of a corrective combination. 2) A .618 to .81 retracement is the most common retracement for a second wave.

New Probability Target for Retracement

Here is one more example of Fibonacci ratios in the stock market on the same chart. I mentioned earlier that second waves most commonly retrace .618 - .81. Take a look at the ratios of all the second waves down from the top.

Repeating Fibonacci Ratios in Stock Market

The relationship between accurate wave counts and the golden ratio is key. It is the best method for proofing wave counts. If the symmetry isn’t there on some level, the wave counts are probably wrong. Nature loves symmetry and proportion, and so does the stock market. Coincidence? What would Isaac Newton think?