Fibonacci Analysis Read online

  FIGURE 3.6 Centex 3-Day Chart

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

  An Introduction to Fibonacci Expansion Price Targets

  Another method widely used by swing traders is to select a range, as you see in Figure 3.7, and then project the 0.618, 0.50, and 1.618 relationships from a key price pivot. Figure 3.7 shows the 3-day Centex Corporation chart and the selected range from the high at point A and the now familiar price low at point B. Most people will use the price low to the right of point B where it appears to be the end of the swing. You are not going to use that lower pivot because of the important relationships we uncovered earlier in this chapter at B. The high of the corrective rally that follows into X is then used to start a Fibonacci expansion price projection. The 0.618, equality (1.0), and 1.618 proportional relationships are the industry standard ratios created from the range AB. Most books use diagonal lines to mark the swings being created; however, this is mathematically incorrect. You never give the slope or measurements on a diagonal axis any consideration. The projections are always parallel to the y-axis, as you see in Figure 3.7.

  The equality, or 1.0 target, appears to be a confluence target, but it is really the same measurement as the one made in the last example in Figure 3.6 where the gap was used. The real confluence target is missing from Figure 3.7 because people generally only use 61.8, 1.00, and 1.618 for Fibonacci expansion projections. They often miss the confluence zone because the 1.382 and 1.500 relationships should have been included. Figure 3.7 introduces you to the concept, but you will soon make a more thorough study of how Fibonacci expansion targets are used to differentiate between major and minor target areas.

  Now we need to study Centex’s longer-horizon data in Figure 3.8 that leads into the price highs. We will need to define additional confluence zones within this data. All the charts from Figure 2.8 to Figure 3.7 kept us from seeing this data so it was clear we couldn’t be influenced by the historical data behind the most recent downtrend. As I created the charts, I deliberately kept myself from looking back as well. Therefore, I am looking at the long-horizon data myself for the first time in this analysis discussion. The first thing you know: to start a support calculation, you must start from a price high and drag down to a price low. The question is where do you start the high? There is a key reversal next to point c. I normally truncate the starting key reversals for these range selections. But I have to stop myself in this example. There is a double top and both tops produced key reversals. Strong directional signals should not be truncated. So this chart demands you start the range to be subdivided from the price high.

  FIGURE 3.7 Centex 3-Day Chart—Creating Fibonacci Expansion Price Targets

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

  FIGURE 3.8 Centex 3-Week Chart—Longer-Horizon Data

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

  In Figure 3.8, the box corners of the selected ranges are marked. The first range is from the price high aligned near c to the lower price range at d. Why d? I find in my seminars everyone understands the concepts and then they get confused before the computer to do this. Nearly everyone has trained their eye to look at the price extremes that form the major swings, but they have never looked at the internal details of the data. So I know this is new for the majority of readers. We are looking to select a price low that starts a major price move. The price low that aligns with d is clearly the start of something strong, forceful, and relentless. The data that immediately leads into this explosion shows a period of higher highs and higher lows that form a back-and-fill coil. Take the low that finally breaks away from that preparation. These are the areas that let us adjust and stay in sync with the different contraction and expansion proportions developing within all markets. They are unique. They require us to read the data.

  Behind the market high, I see lots of price lows with strong forceful moves within the rally, but you are trying to find the first levels of confluence that may be near price low B. The second range will again start from the high. Always begin from the same level. Then the price low for the second range stops at f. As I dragged my mouse down to look at the swings under the low of the first range at d, I found that the Fibonacci ratios were just noise within the chart. This is why you have to start from a price high to define support. If you start from the bottom, you have no other option than to pick the final high. If you stay with your vendor’s thinking, you will always remain a beginner. I never complained when I managed a fund, as I knew most vendors locked the majority of traders out of using these methods. But later I learned from writing a report for investors and institutions, that you can advertise your exact price target and still be able to use it. Everyone has to tweak his or her results. It is amazing to me that exact price zones never seem to be messed up when large trading firms have been notified of their location.

  In Chapter 5, we will study how to create price objectives when markets are moving into new market highs. You will see that the confluence zones we are developing within Figure 3.8 will be used to project future price targets for new market highs.

  A smile came across my face when the second range was completed in Figure 3.8. The subdivided ranges cd and ef define a confluence zone right along the price level that intersects the much referenced price low B. No surprise to me as this will happen all the time. Use any time horizon, any Fibonacci projection method correctly, and the most significant milestones within the data set will always reappear. But if you never create multiple projections, you’ll never know where they are hiding. You now know you were correct to use the price low at B and not the actual low that fell just to the right of it in all your prior calculations. This area is marked with a horizontal line that runs across the entire chart. It is also an exceptional chart to show why short-horizon traders must work with long-horizon charts as well and vice versa. There will come a day when the short-horizon trader’s data will tell the trader point B is important. But just how important is unknown unless you work with this longer-horizon data as well.

  One last comparison has been added for you in Figure 3.8. The confluence zones developed earlier at levels h1 and g1 have been extended to the left at h2 and g2. I want to use this opportunity to reinforce an earlier comment that markets will show respect to these confluence zones in the future and in the past. In this chart, a major spike reversal developed just to the confluence zone g2. The spike reversal is just to the right of the label g2. Notice also the lengthy consolidation that developed along h2 into the 1998 and 1999 highs.

  Figure 3.9 shows Centex in a 6-month bar chart and becomes a rather dramatic clarification how confluence zones, derived from shorter time horizons that appear multiple times, may have long horizon implications for a market. Look at price low B and the corresponding breakdown three bars to the right with a down arrow. This zone was calculated from different approaches and entirely different internals, but each time we had a sense something important was forming at this price level. In this time horizon, it is clear the price zone at $43.48 to $43.87 was the most significant pivot point.

  FIGURE 3.9 Centex 6-Month Chart—Short Time Horizons with Long-Term Market Implications

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

  You are ready to focus next on rally examples and walk through the steps needed to create price targets for markets making new market highs in Chapter 5. In Chapter 6, we will address some of the problems that develop in different price character, such as contracting triangles, which warns when a market is rescaling. We will also cover adding technical indicators and other methods so you know what action to take when a market reaches a target zone. But before we move forward with more charts, this is a very good place to digress and explain why these methods work the way they do. It also goes back to an unanswered question you still may have about how to transfer the Fibonac
ci spiral into two-dimensional charts. Learning how to see the mysterious thread that connects the spiral galaxy (see Figure 3.10), the nautilus shell, your DNA, and great masterpieces in art and music, including architecture such as the Colosseum in Rome, follows next.

  FIGURE 3.10 Galaxy Messier 101, Hubble Image: NASA and ESA, February 28, 2006

  Acknowledgment: K.D. Kuntz (GSFC), F. Bresolin (University of Hawaii), J. Trauger (JPL), J. Mould (NOAO), and Y.-H. Chu (University of Illinois, Urbana)

  CHAPTER 4

  Bridging the Gap Between the Nautilus Shell and a Market Chart

  AS DISCUSSED IN CHAPTER 1, Leonardo Fibonacci said in the introduction to his major book, Liber Abaci, that he accompanied his father Gulielmo on an extended commercial mission to Algeria with a group of Pisan merchants.1 The Pisan merchants would have traveled through the well-known Arab Mediterranean trade routes. Of greatest interest to us are his travels through the Fertile Crescent, or an area known in 6000 BC to 400 BC as Mesopotamia (Greek for “between the rivers”). Mesopotamia was a very fertile flood plain between the Euphrates and the Tigris rivers, now Iraq, northern Syria, and part of southeastern Turkey, and extending to the Persian Gulf.2 The area was frequently invaded, and texts were often written in many different languages. In ancient times, Babylon was a city of great fame. Although the biblical story of the Tower of Babylon is how most people in the West recall this city, few know that all mathematical texts we have from 2500 BC to 300 BC are Babylonian.3

  The ancient Babylonians knew how to create the golden rectangle. Excavated by Hormuzd Rassam from Sippar in southern Iraq, the Tablet of Shamash (Babylonian, early ninth century BC) now has a permanent home in Room 55 in the British Museum. The tablet has a length of just 29.210 cm and a width of 17.780 cm, but it is of great historical importance. (See Figure 4.2.)

  The Tablet of Shamash replicates the golden rectangle, and most people pass by this tablet in the museum without a glance. The depth of understanding that this tablet displays of the peoples of its time is staggering. The stone tablet shows Shamash the Sun God seated under an awning and holding a rod and a ring, symbols of divine authority. Just to the left and above his head (under the arched rod) are the symbols of the Sun, the Moon, and Venus. On the left is the Babylonian king Nabu-apla-iddina between two interceding deities. The Chaldeans, who lived in Babylonia, developed astrology as early as 3000 BC, and the Chinese were practicing astrology by 2000 BC.

  FIGURE 4.1 Map of Mesopotamia

  FIGURE 4.2 The Tablet of Shamash

  Source: © Trustees of the British Museum, The British Museum, Room 55: Mesopotamia

  The tablet is interesting because of its distinct golden rectangle design, but of even greater interest are the three symbols of the Sun, the Moon, and Venus above Shamash’s head. The mathematical relationship between the Sun, Venus, Earth, and its Moon form several phi relationships that one might not associate with the tablet if it did not clearly show the awareness of the golden sector.

  An example of the golden sector is the diagram of the Sun, Venus, and Earth in Figure 4.3. I’ve drawn a 1 by 1 square and divided it in half with a vertical line. Now imagine this square on the ground, and then place a peg at point A to stretch a rope out to point B. Then stretch the rope to draw an arc on the ground from B to point C. Now move the peg over to point D and measure a rope from D to C. Next, stretch the rope with length DC in an arc to create point E. Points D, F, and C are the near relationships between the Sun, Venus, and Earth. But why did you draw point E? Point E4 would produce what is known as the pyramid triangle, DEF, or the Great Pyramid of Khufu in Giza, Egypt. In ancient Egypt, rope stretching was a skill referenced and diagramed in several papyruses. You would have been known as a “rope stretcher” and highly respected.

  Other relationships to Phi develop between Earth, Venus, the Moon, Mars, and Mercury. Only in modern times with the help of NASA could we determine that an average distance of all planets, with the largest asteroid Ceres, relative to Mercury in astrological units, equals 1.618.5 There is no question from whom or where Leonardo Fibonacci gained his interest in Phi and phi. But even well before Leonardo’s time, the ancient Babylonians did not use the Fibonacci numbers; they used geometry to produce the ratios phi and Phi. That is how we are going to use them as well.

  FIGURE 4.3 Phi Relationships

  Source: Connie Brown, www.aeroinvest.com

  So we know Phi (1.618) and phi (0.618) have been known and utilized for a long time. In order to show how to map the golden spiral, we need to learn new skills that will help bridge the gap between the mathematical model and the reality of having to work with price data that expands and contracts.

  Proportional Analysis

  The best place to begin is in the “pit.” No, not the S&P pit, but the ancient pit of Rome: the Roman Colosseum. The Colosseum, with its “gladi-trader” connotation of do-or-die, offers an interesting way to introduce the new tools you need to bridge the gap between the proportions found in a nautilus shell and their reappearance in your financial data. More important, it will help explain why you want to identify the proportions within your charts from internal pivots and other key features such as gaps, truncated spikes, directional signals, and segments that start the larger meltdowns and melt-ups.

  Fibonacci may have displaced Roman numerals with the Hindu-Arabic number system for conducting business and currency exchanges throughout Europe in the thirteenth century, but the Romans were clearly infatuated by Phi and phi long before. The photograph of the Roman Colosseum has been graphically delineated in Figure 4.4 in order to analyze the basic proportions and elevations using a proportional divider.6 There are so many Phi and phi proportions within the Colosseum relative to key architectural lines; we will use this image to learn how a proportional divider is used.

  Using a Proportional Divider

  The proportional divider allows us to make easy proportional measurements on our computer screens or paper without making any notations on the chart. It also allows us to consider how to study any image or printed chart in a book to define Phi and phi within the image. The proportional divider is a drafting tool with two arms held by an adjustable wheel in the center (see Appendix A). The first thing to do is set up the proportional divider by loosening the center wheel. We want the two arms to be in registration, which makes the points at the ends align precisely to one another. The two arms have a registration pin on the inside of the arm to ensure this task is done correctly. When the pin inside the arm fits a small notch, the points will be together. Next, hold the two arms and points together and slide the center wheel so that a registration line aligns with the number 10 marked on the “circles” arm. The illustration in Figure 4.5 is a detailed image of a correctly set proportional divider. Some dividers will just be marked GS for golden section.

  The key here is to ensure the center wheel is tightened enough to separate the arms, but not so loose that the arms slide from their registration setting at 10 or GS, as seen in Figure 4.5. Don’t loosen the center dial so much that the parts all come apart. It takes very little movement of the wheel to accomplish this task. When the proportional divider is set in this manner, the spread between the arms will be different when the arms are opened. This is correct because anything measured with the longer side will produce a 0.618 relationship to this measurement on the short side. If you measure a length with the shorter side first, you will have a proportion of 1.618 to this measurement when you turn the tool over to use the longer side.

  FIGURE 4.4 The Colosseum in Rome

  Source: www.aeroinvest.com/Connie Brown

  FIGURE 4.5 Example of a Correctly Set Proportional Divider

  Source: www.aeroinvest.com/Connie Brown

  Figure 4.6 illustrates the correct measurement of a data swing. Be sure your proportional divider has the registration line set at 10 (or GS). Separate the arms and use the ends that open farthest. Place the points in the circles marked A and B. This is how you would use the tool on the char
t. You have to measure the y-axis difference and not the diagonal. Don’t direct the points on the swing low on the far left and on the price high. Now that the long arms measure line AB, flip the arms around and never change the set arm spread from your first measurement. The shorter arms will fit exactly on the 38.2 percent line if you place one point on point B. If you start from point A, the second arm will fit on the 61.8 percent line. You have discovered why 38.2 and 61.8 are the same length.

  FIGURE 4.6 Right-Angle Measurement for Proportional Dividers

  Source: Connie Brown, www.aeroinvest.com

  In the analysis diagram of the Roman Colosseum (Figure 4.4), you will find two lines at the top of the drawn image. These lines are marked 1 and 0.618. You have to imagine points A and B now, but they are the start and end points of these lines. Check the registration of the arms again. Using your proportional divider, spread the points of the two arms apart and use the longest side of the drafting tool to measure line 1. Being careful not to move the arms, turn the tool over so you can see how the short side fits between the arrows on line 0.618 just under the line you first measured. You have just found your first proportional ratio of phi or 0.618 within the Roman Colosseum.

  Like anything, a tool can be hard to handle at first. Setting the center wheel has a certain feel to it that you will soon have without thought. The first few times, it is essential you check the center registration line often. It is easy to make errors because the registration line shifts when you begin, because many do not set the center tension of the wheel tight enough. This is easy enough to fix if you just glance down on occasion.