Though Fibonacci fan and arc lines are not as commonly used as the retracement or projection analysis, to many they are equally important. Their method of application does not change with the market environment, and to illustrate this, I will first look at a current long-term chart of the S&P 500 before reviewing some historical examples. These methods can be used on any time frame, and this analysis of the weekly S&P 500 will illustrate how the fan lines performed in the last few market cycles.
Fig. 1
The two periods of the weekly S&P chart that I would like to cover are the decline from the March 2000 highs (point 1) to the October 2002 lows (point 2) and the rally from these lows to the October 2007 highs (point 3). The first set of dashed fan lines are drawn using point 1 and 2 and intersecting a vertical line at the 38.2%, 50% and 61.8% retracement levels. The 38.2% fan line was broken the week of May 23, 2003, just a few weeks after the bottom formation was completed (point a). This made the 50% line the next target and it was surpassed in September 2003. The final 61.8% line at approximately 1100 was overcome in early 2004. As the S&P made further new highs, the uptrending fan lines were adjusted accordingly using the low at point 2. The final high was at 1576 in October 2007 (point 3). The 38.2% fan line was broken in both January and March of 2008 (point b), just before the bear market rally into the May highs. The 50% fan line was violated in July 2008, which also resulted in a brief bounce, but when the 61.8% line at 1150 was pierced in October 2008 (point c), there was no looking back. In the accompanying text below, I have provided more examples of the fan lines and how they can be used in conjunction with the Fibonacci arc lines.
In an earlier series of articles, I explained how Fibonacci ratios of 0.236, 0.382, 0.500, and 0.618 could be used to identify important levels of support and resistance. These levels can assist the trader or investor in three ways: 1) to close out existing positions, 2) to find favorable areas to buy or sell, and, 3) to determine stop placement. In this article, I would like to explain two other adaptations of Fibonacci relationships to the financial markets: Fibonacci fan and arc lines. They can be used independently, together, or accompanying the Fibonacci retracement analysis discussed in earlier articles.
Fig. 2
The weekly chart of Boeing (BA) shows the completion of a falling wedge formation, lines A and B, when BA moved above its downtrend (line A) on May 9th, 2003 (point 4). This supported the view that both the 2001 high at $69.85 and 2003 low at $24.73 (point 2) were indeed significant. The fan lines are constructed as follows: first, two extreme price points need to be selected, and then, a vertical line (not shown in most charting programs) is drawn. From the first point, lines are then drawn which intersect the vertical line (labeled 3 in Fig. 2) at the 38.2%, 50% and 61.8% levels. They are labeled as line a (38.2%), b (50%), and c (61.8%). After overcoming the downtrend on May 9th, 2003, BA's first target was the 38.2% fan line (line a), which it tested on June 20th, but did not overcome as BA's rally stalled. Nine weeks later, the 38.2% fan line was overcome and then acted as support (point 5). Once the 38.2% fan line was overcome, the 50% line was the next target. It also was exceeded, in November 2003. This left one remaining Fibonacci fan line to overcome, line c, which was exceeded first during early 2004, and then overcome in convincing fashion in April of 2004. The ability of BA to overcome the 61.8% fan line (line c) was quite positive, and suggested that BA would move higher. Over the next six months, BA gained another 20%, and by early 2006 had doubled in value since overcoming the 61.8% fan line.
I would now like to show you how fan lines can help you monitor a stock or market's uptrend, and possibly warn you when an uptrend might be ending. |pagebreak|Fig. 3
As I am sure you have been told before, sometimes the simplest approaches are the best ways to start. As you look at the above chart of Bausch & Lomb (BOL), you can see a long-term uptrend connecting both the 2003 lows and the late-2004 lows (line A). As long as BOL stayed above this uptrend, the long-term trend was considered positive. On October 11th, 2004 (point 3), this uptrend was broken, a signal I'm sure some traders and investors thought was unimportant at the time. In my experience, such a trend line break is usually a valid warning signal that one should not ignore. After it was broken, one way to identify additional levels of support is by using Fibonacci fan lines. For this example, I have chosen the major low of $27.16 in 2002 (point 1), and the 2005 high of $87.89 (point 2), to derive the fan lines. The 38.2% fan line was broken in late-December 2005 (point 4), making the next downside target the 50% line, which at the time stood at $62.50. You will note that BOL bounced up to the 38.2% fan line several times over the next few months before dropping to, and eventually through, the 50% line (point 5). It is common for both the Fibonacci fan and arc lines, once they are broken, to also act as support or resistance, and this behavior can give the trader an additional piece of information. The next area of likely support was at the 61.8% fan line, through which BOL gapped on heavy volume the week of April 10th, 2006, spurred on by a negative news report.
Figure 4
The Fibonacci arc lines, like the fan lines, also add a time component to one's analysis. They are derived by first drawing a trend line between two extreme points on a bar chart, and drawing three arcs, using the second point as the center, so that they intersect the trend line at 38.2%, 50%, and 61.8%. This is shown in Fig 4, which is a weekly chart of the Nasdaq Composite from mid-1998 through 2002. For the first extreme point, I chose the October 1998 low of 1357 (point 1), and for the second, I used the early 2000 high of 5132 (point 2). The decline from the March 2000 highs was very sharp, and quickly reached the long-term uptrend, line B, which connected the 1998 and 1999 lows. The Nasdaq tested the uptrend at point 3, yet did not close below it until five weeks later, when it also violated the 38.2% arc (line a). The Nasdaq then rebounded for the next five months before closing back below the 38.2% arc line (point 4). Just as is the case with the other methods of Fibonacci analysis, once the Nasdaq closed below the 38.2% arc line, the next target was the 50% arc line that was also soon broken. This made the 61.8% arc line the next level to watch. It was broken in December of 2001 (point 5), which had negative, long-term implications.
Fig 5
The Tokyo stock market, as represented by the weekly chart of NK225, had been in an uptrend from the April 2005 lows at 10,770 (point 1). After reaching a high of 17,563 in April 2006 (point 2), it had a very sharp correction. The arc lines are derived from these two extremes. In June 2006, the NK225 declined to the 38.2% arc line (line a) during the week, but closed above it. During one week in July, the NK225 once again tested this arc line (point 4), but moved higher afterwards. As of late-August 2006, the NK225 had not closed below its 38.2% arc line. It was rising rather sharply at this point, and a close below it suggests that the NK225 is going to decline to the 50% arc line.
Fig 6
Of course, it is also valid to combine fan and arc lines on the same chart. In this weekly chart of the NK225, I have added the Fibonacci fan lines (in red) to the arc lines using the same high and low points to generate both the fan and arc lines. This adds another interesting layer to our analysis. The NK225 closed below the 38.2% fan line (line a) on May 26th (point 3), and three weeks later, it also closed below the 50% fan line (point 4). Note that at the June lows of 14,045 (point 5), the 61.8% fan line and the 38.2% arc lines coincide, and this convergence suggests that this should be a particularly important level of support. So far, the NK225 is holding above both lines. This convergence of the fan and arc lines could have been noticed in May, when the 38.2% fan line was broken. Even more interesting is that one would have been able to see that the two lines were intersecting in mid-June, which gave a time frame as well as a price level.
Fig. 7
Sometimes, though not always, combining all three types of Fibonacci analysis that have been discussed gets very interesting. Once again, we look at the weekly chart of the Nasdaq covering the rally up to the 2000 highs. I don't want you to be overwhelmed by all of the lines on this chart, but would just like to concentrate on three specific periods. As I discussed earlier, it is often important when the various Fibonacci zones converge. This occurred during April-June of 2000, as indicated by the green circle labeled A. Specifically, during the week of April 20th, the Nasdaq dropped below the 50% fan line, and reached the 50% retracement level and the 38.2% arc line during the week, reaching a low of 3227. It rallied by the end of the week to close at 3643. Four months later, in October 2000 (circle B), the Nasdaq closed below its 61.8% fan line, but held above its 50% retracement level and 50% arc line. After three weeks of sideways trading, the Nasdaq closed below both of these levels. The decline over the next six weeks was sharp as the Nasdaq closed below both the 61.8% retracement and arc lines. The rebound from the early 2001 lows took the Nasdaq right back to the 61.8% arc and retracement resistance before the decline resumed, as the index declined another 30% over the next ten weeks.
One should realize that the Fibonacci analysis does not always work as well as it did in the examples I have chosen. Of the three different types of Fibonacci analysis, I use the retracement and projection analysis the most, and have found them to consistently provide the most interesting information.
