- 2000: Volume 9, No. 5 The New Science of Parabolic Analysis

Editor's Note: The following was excerpted from the recently published book, New Concepts in Support & Resistance, Publishing Concepts, by Clif Droke.

Most traded equities and commodities are cyclical in nature. Simply put, their daily, weekly, monthly, and yearly price fluctuations are governed by various cycles, which, properly defined, are intervals of time during which a sequence of recurring price patterns are completed.

Most modern practitioners of cycle theory are unable to apply cycle theory to price trend forecasting with any consistent degree of accuracy, since they focus on time cycles to the exclusion of price cycles. All too often, they fail to realize that the charts are beholden to no one and can ignore precise time cycles seemingly at random. An adequate model used in forecasting prices based on cycles can only be useful insofar as one's timing is precise enough to catch the move and profit thereby. While it is exceedingly difficult to isolate price cycles based on time patterns, it is relatively easy to isolate cycles based on price patterns (once you know what to look for). To that end, we offer the following explanation of what we consider to be a revolutionary new form of technical analysis that combines classical chart patterns with price cycles—a method we will call "Parabolic Analysis." Moreover, we will demonstrate that no better form of technical or cyclical analysis is better suited for options strategies than this "new science" using parabolic cycles.

Parabolic Analysis Explained

Most forms of technical analysis are linear in nature in that they emphasize the construction of trend lines and other straight-edged geometric chart patterns within price charts. While there is some validity to this method, I believe it falls short of providing a comprehensive analysis of the price trend. That is because price, as we have already explained, are governed by cycles, and cycles are not linear in nature; rather, they are parabolic and evince a rounded-over appearance on the chart.

The most refined and superior technique for analyzing price cycles was introduced by cycle analyst P.Q. Wall, editor of the highly recommended newsletter, P.Q. Wall Forecast, who rates as one of the greatest market technicians of all time. Wall has devised a highly accurate method for analyzing the cycle and forecasting price trends that I will call "parabolic analysis." As the name implies, this form of cycle analysis consists of drawing parabolas on price charts to conform with the peaks and valleys of the price trend. A parabola, as you may remember from geometry courses, is essentially a bowl-shaped, or dome-shaped (depending on the direction of the curve), formation, the two sides of which are equidistant from the exact midpoint of the formation (see Figure 1).

Figure 1:

It is precisely this parabolic appearance of cycles that will form the basis for our examination of all prices of traded securities. Note, too, the more round-shaped dome and bowl-shapes that tend to transcend the smaller parabolas. This represents what we will call the "Grand Cycle," that is, the much larger cycle that encompasses the smaller parabolic cycles (See Figures 2 and 3).

Figure 2:

Figure 3:

Since we have established that the parabola is the basis of any price cycle, our next endeavor lies in identifying and constructing these formations on the chart. There are several ways of doing this, but in our experience, the easiest method is to concentrate on the extreme bottoms, or troughs, that prices make on the chart. These can be easily seen (in most cases) by their V-shaped appearance. Chart readers will recognize these patterns as being of the classical "head and shoulders" variety. Of course, bottoms in price do not always resemble a perfect "V." Sometimes a bottom takes more the appearance of a "W" or of a gently rounding bowl. The important thing to note, however, is that all these patterns represent important bottoms in price and are reflective of accumulation, or buying, interest by traders and almost always forecast a reversal of trend.

The mechanics of these patterns are unimportant—we are not concerned with how many times the price line touches the "support" (i.e., bottom) level on the chart. What matters is that a bottom has been posted based on the fact that prices are no longer falling and appear to be on the verge of reversing direction.

At tops, these same patterns will show up, only their appearance will be reversed. Instead of a "V-bottom" the chart produces an inverted V-top. Instead of a "W-bottom" the chart pattern becomes an M-top. And instead of a "bowl" (known variously as "saucer bottom," "rounding bottom," and "tea cup" patterns) the chart traces out a dome (the inverse of a bowl, also known as a "rounding top").

While it is important to watch for topping formations such as the ones described above, the bottoming patterns are typically of greater import and carry a greater degree of accuracy and significance. An experienced "chartist" can attest to the unreliability of topping patterns such as the rounding top since it often leads a trader to believe the trend is changing from upward to downward. All too often, however, prices, after curving over in a dome-shape, will suddenly reverse and continue their ascendancy. This probably has to do with the fact that traders, being humans with over-riding hopes and fears, largely prefer higher prices to lower prices and have a relentless tendency to drive prices for most securities to higher levels.

Most cycle-based theories of price interpretation emphasize counting the cycle from trough-to-trough rather than from peak-to-peak. This is a further testimony to the accuracy of cycle bottoms over cycle tops and is why most cycle experts will focus more on bottoms than on tops. Besides all the reasons we have already enumerated, the basic reason for this is that identifying a cycle bottom will typically bring the trader more money over the long run than will identifying a cycle top—provided he has the discipline and fortitude to act upon it. Thus, our emphasis will be upon pinpointing cycle bottoms when trading cattle futures with the underlying assumption being that cycle bottoms tend to be more reliable for predicting price trends than cycle tops.

The chart will make the job of identifying a bottom easy for you when bottoms (and conversely, tops) register as "spikes." As the name implies, a spike bottom occurs when prices spike to an extreme low point in a selling climax. This produces an extremely long price bar for the day in question, indicating a wide range between the buyers and the sellers (which in itself is an indication of indecision). However, the closing tick on the price bar is considerably above the day's low point, which indicates that traders feel the declining trend has gone too far and are willing to become buyers again to support prices and attempt to drive them higher. The higher trading volume is on a "spike bottom" day, the more likely that a change of the trend has occurred, thus indicating the cycle has bottomed and will begin its ascending phase. At tops, this process is reversed, the result being a "spike top" (otherwise known as a "key reversal").

Locating spike tops and bottoms is very easy and is one of the best methods of determining changes in the cycle. Consequently, drawing parabolas on the chart becomes much easier using a spike top or bottom as a reference point, with the spike day serving as the exact midpoint of the parabola.

Another important aid to interpreting price cycles on the charts is to note the behavior of trading volume, especially on "spike" days. While cycle bottoms (i.e., "spike bottoms") are frequently attended by surges in trading volume, they may occasionally be accompanied by an abnormal contraction of volume. The former, however, will much more often prove to be the case.

At cycle tops, volume typically peaks out ahead of prices, then drops off sharply even as prices continue rising. This is an advanced warning that the trend is about to end since every upward move must be accompanied by strong volume in order to be sustainable. Sometimes, a peak in the cycle at tops is marked by a sharp surge in volume just prior to the downturn.

Drawing the Parameters of the Parabola

Now that we know how to go about identifying potential cycle bottoms (a cycle hasn't truly bottomed until it actually reverses in the opposite direction-we are merely trying to predict cycle bottoms before they reverse the price trend) we want to concentrate on how to determine the parameters of the cycle. As we mentioned earlier, the cycle can be expected to take the form of a parabola. However, parabolas differ in their size, degree, amplitude and width. So the question that confronts us is "how do we know we are drawing the parabola correctly?" Unfortunately, we can never be 100 percent certain we are drawing it correctly until we are proven correct by the price itself. Fortunately, however, we can almost always have a good idea as to the parameters of the parabola by following the contours of the price line itself. For an example of how this is done, see Figure 4.

Figure 4:

First and foremost, we would emphasize that the bottom of the parabola is the single most important element. Other aspects of the parabola will sometimes be unclear, but if you are able to isolate the bottom, you will be well on your way to correctly drawing the parabola. Notice how the right side of the parabola (that part which is unknown) is drawn based on the parameters of the left side of the parabola. The easiest way to draw the potential parabola is to start at the top left-hand side of the cycle you have identified and work your way downward to the cycle bottom. Use the extreme low points of the price bars as your guides. [Note: this is why it is important to use traditional high/low/close price bars instead of a line chart, since the intra-day extremes yield important clues as to the parameters of the cycle.] The overall effect is that by tracing the extreme lows of the price bars down to the cycle bottom, they should connect smoothly in a gradually rounding pattern.

Of course, there will often be alternative ways of constructing the parabola. When confronted with them, go ahead and try to trace out all the possibilities. Regardless of which one is actually correct, you will still have a very good idea as to the parameters of the cycle based on your drawings since they won't differ from each to any considerable degree. Once you have determined the likely path the parabola is going to take, we want to extend the parabola beyond the cycle bottom and upward toward the right side of the chart (the "unknown" price region that represents the future). One helpful guideline for doing this is to take a ruler and draw a perfectly straight, vertical line through the extreme bottom of the price cycle. Of course, you won't actually know what the exact bottom is until prices begin rising above the bottom, but until then we must use our best judgment. In fact, unless it is quite evident that a cycle bottom is in place (in the form of a single conspicuous spike bottom), it is good practice to draw several potential parabolas using various midpoints—remember, a parabola is distinguished by the fact that either side of it is equidistant from the extreme midpoint. When a bottom is irregular (i.e., there is no clear-cut spike bottom, but instead several possible bottoms), we must treat each one as a possible bottom until we have isolated the correct cycle. Only the passage of time will tell us which one is correct.

One prominent feature of the parabola is that any point on both sides of the parabola is equidistant from the center. We determined the center of the parabola by drawing a line throughout the bottom. From there we should take a ruler (a compass will serve as an even better instrument for this purpose) and measure the distance from the center line to the various points on the left side of the parabola. Then, after we have calculated these measurements, we want to mark these measurements on the corresponding points on the right side of the chart. Note how we do this in the diagram shown in Figure 5.

Figure 5:

After we have done this, simply use a compass or flexible curve to connect the dots from the bottom of the parabola all the way to the projected top. As we have mentioned, each side of this projected right-hand side of the parabola should correspond perfectly with the left-hand side of the parabola. Thus, we have isolated a complete cycle on the chart and have a very good idea where we can expect prices to travel in the near future.

Prepare To Make Adjustments

While this projected parabola is very useful in determining the overall tendency of the cycle and its likely course, it is by no means a determining measure. Prices won't always conform perfectly to the parabolas we draw, and the experienced cycle analyst knows he will likely have to redraw and adjust his parabolas many times within the course of a given cycle. But once the basic parabola has been established, we need not expect significant deviation from it. It is not precision we are concerned with (for indeed there is little precision when it comes to price forecasting); rather, we are mostly concerned with having a general idea—a broad overview—of where prices are likely headed within the context of the cycle.

Being able to identify parabolas at intermediate and minor degrees of the trend is important, but not nearly as important as being able to identify long-term "bowls," which provide underlying support for the major cycle and contain the smaller parabolic cycles within the bowl. An argument could be made that the bowl formation in chart analysis is the single most important pattern a trader or investor can find-they contain immense profit opportunities over the long run. Thus, we turn our attention to this important pattern.

In classical technical analysis a bowl is nothing more than any chart pattern that takes on a rounded appearance, preferably one that occurs after a prolonged declining phase in the price of a given security. Little attention is given to the actual construction of the bowl; the emphasis is on merely being able to roughly identify a bowl-shape on the chart. But with parabolic analysis, it becomes very important to determine the exact parameters of the bowl in order to achieve maximum profit as well as protect profits earned. This is not as daunting a task as it may sound. All it involves is locating the major lows on the high-low-close bar chart (whether it be a monthly, weekly, or daily chart) and connecting them with a continuous line that forms a perfect bowl-shape (the flexible curve is an indispensable tool for accomplishing this). The more points on the chart that can be connected with a continuous line to form a parabolic or bowl-shaped, pattern, the more likely it becomes that you have identified an important cycle in the security you are analyzing.

The Use of Bar Charts

The beauty of bar charts is that, in almost every case, they conform perfectly to the parabolic tendency of the cycles that govern all traded securities, making our task a fairly simple one. Of course, it is difficult to convey with words how to locate these bowls, so we are providing several real-life examples from charts, which display clearly the bowl pattern in their long-term timeframes. Note carefully how the curve of the bowl is drawn at every point along the way, from the left side of the chart to the right side. Note also how the extreme intra-day lows of the price bars are used to determine the parameters of the bowl, and notice how the bars lend themselves to drawing a perfect bowl. (See Figure 6.)

Figure 6:

The best way for you to learn this concept is to simply train your eye to find bowls and parabolas whenever you look at a chart. Don't concentrate the erratic wiggles and fluctuations, don't focus on drawing trendlines, and don't worry about geometric price patterns such as "triangles," "rectangles," "flags," etc. Just look for the semi-circular bowls that exist in almost every chart. When you have mastered this concept (and with practice you will) you are well on your way to becoming a successful trader, and nothing will be able to separate you from the profits that await you in the markets.

In any given long-term chart there will usually be more than one "correct" way to draw the bowl. Sometimes there will be as many as three or four ways of drawing the "sides" of the bowl, particularly on the right-hand side (since the left-hand side, which represents the past, is already drawn for you—the right-hand side, of course, is the unknown future). Do not let this throw you off. Simply follow out the bowl pattern, conforming your bowl to the parameters that the price bars are providing you. If at some point, the right side of your bowl is penetrated by the price line, you should always treat this as a sell signal and immediately unload your "line." Often, this sell signal turns out to be a false move and the upward trend will resume shortly thereafter. That's okay—we're not afraid to get "whipsawed" from time-to-time in our pursuit of profits. The important thing for us to practice is the diligent application of our trading rules. Safety should always come first when you are trading in the markets. If this has occurred, once prices start moving higher again (albeit, at a different slope of ascent) simply redraw your bowl to conform to the parameters of the new bowl.

This leads us to the formal statement of an important trading rule of parabolic analysis: whenever the bowl is penetrated by the price line, you must view this as a signal that the trend has changed and therefore you must move to protect your profits by exiting your position. This leads us to a further rule: whenever two parabolas, or bowls, that are opposite one another (i.e., one in the upward phase and another in the downward phase) intersect, you can almost always expect a significant—nay, an explosive—movement in one direction or the other. If this explosive price movement does not occur soon after the intersection of the two parabolas, then you haven't drawn the parabolas correctly.

Options Strategies to Use With Parabolic Analysis

The reason for this can be attributed to the fact that the energies behind the two opposing cycles are clashing—much as opposing air currents such as warm and cool produce thunder when they clash. It only follows, then, that one of the forces must prevail, and while it is difficult to always predict which one it is, you can still profit from this principle by being prepared to act quickly once the price line has broken out of the parabolas and has made clear which direction it is heading. It is precisely this convergence of two conflicting cycles (as represented by the bowl and dome) which almost guarantees a profitable use of the "butterfly spread," or the straddle option strategy (i.e., the simultaneous purchase of and equal number of puts and a calls). This will enable him to profit regardless of which direction the price may take upon breaking out.

For trading dome patterns (i.e., topping patterns), simply reverse everything we have written in this chapter about bowls since a dome is nothing more than the reverse of a bowl. The same rules apply to a dome pattern as they do to a bowl, only in reverse. Being able to identify domes is important, but as we intimated earlier in this chapter, not nearly as important as finding bowls. That's because domes are less reliable than bowls for reasons we have already outlined. When you begin to notice the formation of a clear-cut bowl pattern in any given price chart—especially if that equity or commodity has just posted an important low—that is the best time for initiating trading strategies involving call options. The wider the base and the longer it takes for the bowl to form, the further out the option's expiration can be.

The most important thing for you as a trader to remember is that every chart contains several cycles (smaller cycles within larger ones), and these cycles always take the form of the parabola, either in the bowl phase or the dome phase. Learn to see these parabolas in the charts and you will fast become a proficient and profitable trader.

Clif Droke is the author of several books on technical analysis, including Technical Analysis Simplified and Elliott Wave Simplified (Marketplace Books), Tape Reading for the 21st Century (Traders Press), How to Trade Cattle Futures (Publishing Concepts), and most recently, New Concepts in Support & Resistance (Traders Press). He is also the editor of the weekly Leading Indicators and bi-weekly Gold Strategies Review newsletters.

He will be a featured speaker at Futures & Options Expo 2000 which will take place at the Hyatt Regency Chicago on Tuesday, Wednesday and Thursday, November 7, 8 and 9. For information on attending Expo, visit the FIA Web site at www.fiafii.org, phone FIA at 202-466-5460 or e-mail: ann-marie@fiafii.org.