Fibonacci Analysis Read online

  Now you need to go back to the proportional analysis within the Roman Colosseum. Several 0.618 ratios have been marked, but you are going to find many more. Once this diagram is full of pinholes from your proportional divider, you will be a whiz with this tool. I have a beautiful art book of Leonardo da Vinci that is marked with small pinholes from the proportional divider. The book helped me learn how to use the tool and before I realized it my eye was trained to see this ratio with precision without the tool.

  Now, this is where we depart from prior authors on this subject.

  Introducing Rhythmic Wave Diagrams

  To the right of the measured proportions of the Colosseum (Figure 4.4), you will find a rhythmic wave diagram. Rhythmic wave diagrams are being introduced to you now; I believe they are new to our industry, but they are not new to music theorists. This method of proportional analysis is a common way to define harmonic unity. In the chart of the Colosseum, two rhythmic wave diagrams intersect at the 0.382 and 0.618 proportional levels based on internal measurements of the Colosseum. These two wave diagrams are the easiest to relate to in the beginning. As an example, line ad is subdivided into 38.2 and 61.8 at points b and c respectively. In fact, they look similar to the results of a subdivided range into Fibonacci ratios. But the difference with rhythmic wave diagrams is their ability to show you the relationships between the proportional ratios. You will study rhythmic wave diagrams in Chapters 7 and 8 to begin to understand how the Fibonacci confluence zones begin to develop proportional ratios of greater significance. Not every confluence zone of support or resistance will be of equal importance. But some of the clustered zones of Fibonacci ratios will exhibit harmonic intervals in both the price and time axes. A rhythmic wave diagram is the first building block to a much deeper understanding of relationships between ratios, and it will help you trade with higher probability.

  Harmonic analysis and rhythmic wave diagrams will go hand in hand. The rhythmic wave diagram will paint a visual picture of unity between price swings to show that harmonic proportions are not serial. As an example, consider points a, b, c, and d in the diagram of the Roman Colosseum. Arc ac skips over point b. The arc then feeds back into point d. What if all the confluence measurements in a chart fall on points c and d, and b is left standing alone? We would think price b was minor and prices c and d were major resistance or support targets. But in rhythmic wave analysis, what if point b becomes the start of a series of harmonic clusters with more ratios at the confluence points forming further ahead of point d? What would you think about price b then? How would you know to make a future price projection from point b and not level c? You developed the skills in Chapter 2 to prepare for this concept of confluence forming at major price targets. But you need to push this thought process much further as you see me infer from the questions I am asking now. Relationships between a grid of confluence zones impact your thinking about price projections, and they impact your method of defining time cycles. Time cycles are not serial. They plot one after another, but they are not related to one another in a linear simplistic series. You will see that harmonic and rhythmic wave charts can bring a far deeper sophistication to your analysis of price and time. The reason the Fibonacci ratios that define confluence targets work so well within your charts is they identify harmonic proportions developing within your price data. Harmonic proportions are not linear number series. We will develop these concepts in Chapters 7 and 8.

  Geometry in the Nautilus Shell

  The nautilus shell demonstrating the golden spiral is far more meaningful than the architectural proportions of the Roman Colosseum can reproduce. But the architectural analysis taught you how to use a proportional divider and gives you the freedom to study complex figures in books and other works of art. This is strongly recommended. A good place to start is in the artwork of Leonardo da Vinci, and then, study your charts in many time horizons. The purpose is to examine proportional relationships along the horizontal, diagonal, and vertical axes. In Chapter 5, we will apply these proportional relationships in charts. But it is essential to study more than just charts. The extra effort is fascinating and will help you train your eye to see proportional ratios more quickly and with surprising accuracy. Start with the horizontal as you did in the figure of the Roman Colosseum. With the basic skills and concepts you have in place now, you are ready to examine one of the most stunning forms in nature and then to see how the Fibonacci spiral applies to proportional unity within price swings.

  The spiral of the nautilus shell holds within its geometry all the Platonic solids, the pentagon, pentagram, the Pythagorean 3-4-5 triangle, and the geometry of the heavens. The Pythagoreans used the pentagram as a sign of salutation among themselves. Its construction was a jealously guarded secret. The pentagon and pentagram are interesting because they are loaded with golden ratios. You will see in the golden spiral illustration (Figure 4.7), how the pentagram star forms from the nautilus shell’s geometry. Few sacred geometry books describe why these forms are deemed so sacred. The pentagram, pentagon, and Star of David within the spiral are points whose angles mark a precise astronomical clock. They are measurements of time when specific planets come into orb or align to precise degrees of separation.

  Everything in the heavens moves around everything else, and this dance to the music of the spheres7 is mapped within the nautilus shell. As an example, every eight years Venus draws a perfect pentagram around Earth. The Moon squares the circle, and the inferior and superior retrogrades of the Sun and Mercury form the Star of David to geometric perfection. The pentagon formed the cornerstone of cosmological thought and represented the five wanderers starting with Mercury. Moving round the pentagon increases the planets’ distance from the Sun. Wisdom keepers from the Rosicrucians of today tracing back to the ancient Pythagoreans, all look upon these forms of geometric perfection as proof there must be a divine creator. To understand how to map the nautilus shell onto a chart requires skills in geometry, harmonics, and astronomy. Without conscious awareness, you too have become a student of the ancient quadrivium. You will begin to develop these skills further in Chapters 7 and 8, and then apply them to your charts. This is the foundation of Gann analysis, and it is hard not to ask why this works so well in markets when you see a major price reversal where price confluence and time objectives merge. But I warn you now, when you begin to seek understanding behind the many whys, you will find a labyrinth of rabbit holes leading to a path many have traveled before you. Together we are seeking the Truth behind the Fibonacci spiral and walk the steps of Plato, the Pythagoreans, and the ancient Egyptians. The pentagrams carved near the Queen’s Chamber of the Great Pyramid of Khufu are shown in the photograph of Khufu’s Pyramid in Figure 4.8.

  FIGURE 4.7 Golden Spiral Geometry

  Source: Niece Lundgren and Connie Brown

  FIGURE 4.8 The Great Pyramid of Khufu

  Source: Private photograph collection of Connie Brown

  CHAPTER NOTES

  1 Cooke, 289.

  2 The British Museum, Room 56: Mesopotamia 6000 BC-1500 BC. Objects on display in Room 56 illustrate economic success based on agriculture, the invention of writing, developments in technology and artistry, and other achievements of the Sumerians, Akkadians, and Babylonians, who lived in Mesopotamia at this time.

  3 Cooke, 43.

  4 Mad05, 3.

  5 The relative mean distance of all planets and the largest asteroid Ceres is 1.618 when calculated in the following manner using astronomical units:

  Planet Mean Distance (in million kilometers) per NASA Relative Mean Distance (where Mercury = 1AU)

  Mercury 57.91 1.00000

  Venus 108.21 1.86859

  Earth 149.60 1.38250

  Mars 227.92 1.52353

  Ceres 413.79 1.81552

  Jupiter 778.57 1.88154

  Saturn 1,433.53 1.84123

  Uranus 2,872.46 2.00377

  Neptune 4,495.06 1.56488

  Pluto 5,869.66 1.30580

  Total: 16.18736
/>
  Average: 1.61874

  Phi: 1.61803

  Degree of Variance: (0.00043)

  During a meeting with Dr. Okasha El-Daly he commented, “Mercury had particular significance to the ancient Egyptians.”

  6 Please see Appendix A for a photograph of the actual drafting tool. I favor the 7½-inch Proportional Divider made by Alvin Company, as it is lightweight aluminum. The 10-inch Proportional Divider is made from steel and very awkward due to its weight. The lightweight 7½-inch duraluminum product is ideal for our use. A company in the finance industry sells this drafting tool under the name precession ratio compass. In my experience, it is not long enough for charts on 8½-inch by 11-inch paper or books. It is also made from steel and too heavy. If you enter “Alvin Proportional Divider 450” into your search engine, several suppliers will be identified. Alvin is a German company and the product is made in South Korea.

  7 Godw, Taylor, Hall, Kap, Lev, Pin, Stroh.

  CHAPTER 5

  Fibonacci Channels, Angles, and Cycles with Oscillators

  IN CHAPTER 4, we analyzed the Roman Colosseum to see proportional ratios within the horizontal, diagonal, and vertical axes. It is important that we think about all three axes when applying this proportional geometry to technical charts. Figure 5.1 is an overlay between China’s Shanghai Composite Index and the Australian All Ordinaries Index. As 2007 comes near to a close, it is clear that North American equity indexes and Europe have lagged far behind China and its benefactors of Australia, India, and South African stock markets to name a few. But in North America, few traders monitor global equity indexes daily or even weekly, though it is essential in trading today’s markets. North American equity markets lag; they are impacted by these global crosscurrents and cash flows.

  In my library are many old and rare books. One small book by William Atherton DuPuy from a series called Factual Reading is simply titled Money (D.C. Heath and Company, 1927). It is rich with old photographs and clearly well researched, but of great interest now are pages 52 and 53. The nations of Europe were buying great quantities of war supplies during WWI from the United States, and they were required to pay at least part in gold bullion. By 1916, enough gold bullion bars had crossed the Atlantic that America housed $2 billion worth of it in this country. It was thought a huge sum for one country to house $2 billion in gold. But the war went on and nations were forced to borrow and buy more and more from America. The next year, America physically housed one third of the entire world’s total gold reserves used for monetary purposes. The $3 billion in gold bullion continued to grow as the nations of Europe turned to America to rebuild after WWI. By 1923 the nation housed $4 billion of the metal in its coffers. The physical gold bullion peak came in 1924, but as we know, the country’s equity bubble and the Roaring Twenties continued into 1929. People have long forgotten why the Roaring Twenties occurred.

  FIGURE 5.1 China Shanghai Composite and Australia All Ordinaries Indexes

  Connie Brown, www.aeroinvest.com. Source: Copyright © 2008 Market Analyst Software

  Today, America is a debtor’s nation and China has cash pouring into its coffers. The equity explosion in the China indexes is being fueled by this rapid influx of cash. History is repeating itself again on a different continent; the outcome will be no different. But technically, we can determine the levels of risk when fundamentals have historically never been able to time the end of a runaway bull market. In this chapter, we will cover how to forecast major market pivots in such an environment.

  The first step is to recognize there is always a market that leads in the global arena. As an example, Japanese Government Bonds (JGBs) have led U.S. Treasuries for years. As JGBs moved so too did U.S. Treasuries move, weeks and sometimes months later. In Figure 5.1, the monthly chart showing an overlay of China’s Shanghai Composite (bold bars) and Australia’s All Ordinaries Index, you can see Australia bottomed in 2003 while China’s market bottomed two years later in 2005. As you study the corrective swings between these two markets, you find Australia has been ahead of the moves in the China index. As a result, the momentum indicators you add, regardless of the formulas selected, will show a more mature pattern in the Australian charts than in the China equity indexes.

  Some will look at this overlay chart and ask the question, would I use logarithmic scaling on the y-axis for such parabolic moves? The answer is no. In Chapter 8, you will learn the Fibonacci confluence zones you are uncovering now are subsets within a harmonic proportional series. Harmonic ratios are derived from prime numbers raised to an exponential number and therefore they become logarithmic. For that reason, I do not want to ever use a log scale within my price axes distorting the raw data. This will not be clear to all readers at this point, but some with a background in this area may have found it difficult to move forward if the question was not at least acknowledged at this point. Not to worry, as the foundation needed for all readers new to the concept of harmonics will be discussed in Chapters 7 and 8.

  Never trade an index alone, as there is always a market that is slightly ahead and correlated to the market of greatest interest to you. You might not ever trade the leading or correlated market but if it is leading, you can use it as a bellwether indicator. In the book Breakthroughs in Technical Analysis (Bloomberg Press, 2007), you will see I used the 3-month Eurodollar in an inverse relationship to crude oil, as the 3-month Eurodollar is leading oil. Expect the inverse relationship to uncouple as the parabolic rise in oil matures. You will then lean on a different market. Consider stocks within a sector, similar bond maturities within Government yield charts as a global comparison, global equity indexes compared, but never analyze a single market alone. In this chapter, we will detail how to project a market bubble using Fibonacci geometry. Our goal is not to define the final top of a parabolic market; we need only find the significant pivots of resistance that a market will give a high degree of respect toward. Once we are short, we will be able to see from our indicators when the market will not hold major zones of support after a rebound from our targets. As Australia is leading China’s Shanghai Composite, and China is fueling the global rally, we will focus on the Australian SP/ ASX 200 market.

  In Figure 5.2, the Australian SP/ASX 200 is charted in a weekly time horizon. As we want to identify support to begin your task, we must start from a price high and work down to multiple price lows. We need to give greater care now when selecting price levels for defining a range, as most spike reversals will never be used to start a range. We will not truncate double-top directional signals, but key reversals or railway tracks rarely display an internal price close higher than a previous bar near the highs. That’s the nature of a key reversal. Tight bar formations that develop head-and-shoulder patterns are often truncated so that the start of the range bisects the matching shoulder pattern. As this chapter unfolds, be aware that the internal subtleties are of greater significance than the blatant swing highs and lows in many cases. Why use data where an emotional trap has developed? The market will mathematically ignore the few trapped in a false breakout as well, and this can be proven.

  Figure 5.2 shows the first range selected in the weekly chart of the Australian SP/ASX 200 Index. It is then subdivided into the ratios 38.2 percent, 50 percent, and 61.8 percent, as was done in Chapter 2. The range begins from a price that is not the final high. The internals within the chart will explain in a moment why the actual high was not used. The low of the first range is an internal low that begins a strong market move up. Always look for the bottom of these strongest bars to end a range. Conversely, when you are developing resistance levels, the highs of the strong price bars are used to end the ranges selected. (We used gaps in Chapter 2 as well. Gaps are always significant points to end a selected range for subdivision or to mark a mid-point within a swing.) It is better to have too many ranges than too few at first. But eventually you will save yourself the extra work and just select the bars that start strong moves. If you know the Elliott Wave Principle, use the start of third wa
ves and wave iii of 3. If you are unfamiliar with this methodology, I have an objective way to count waves within this chapter you will like a lot.

  FIGURE 5.2 Australian SP/ASX 200—Weekly Chart

  Connie Brown, www.aeroinvest.com. Source: Copyright © 2008 Market Analyst Software

  Meaningful ranges will guide you by showing the subdivisions within the range have been respected before by the market. Take the time to look because you want to select ranges that help you account for underlying market expansion and contraction changes within the price data. If you look for the strong bars within a move, you are using the same milestones the market is using to create future highs in this case. The price bar at point a rests on a 61.8 percent retracement. If you had started the range at the exact price high, the internals within this range would not have shown any respect to the Fibonacci grid that resulted. I cannot emphasize the importance of this next point strongly enough. Do not select a range to make the look-back price internals fit the resulting Fibonacci grid; select the range first based on the market pivot that fits the criteria that is the strong start of a move.

  The Composite Index in Figure 5.2 is an oscillator for which I released the formula in the book Breakthroughs in Technical Analysis (Bloomberg Press, 2007). It is used to identify divergence failures in the Relative Strength Index (RSI). The formula breaks the normalization character of RSI that forces the oscillator to travel between zero and 100. In this chart, you see the Composite Index has topped at the same price bars I used to start the range. Line b will guide your eye to the points being compared. Every additional range that follows will use the exact same start as the first range that ends at ‘a’.