also much larger. In fact, they can getso large that they can be as big in price and time movement as the othertwo primary waves (Figure 6.8).When an extension exists in one of the waves, the whole movementseems to be made up of five thrusting waves, not three. Extensions usu-
FIGURE 6.8 An Elliott wave variation called an extension, in which one of theprimary waves (wave 3 here) can be so large that the smaller movements thatmake it up become almost as large as the other two primary waves.53412
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FIGURE 6.9 In an Elliott wave variation called a flat, waves A and C end up atthe same level.B
A
C
ally occur in waves 3 or 5—especially wave 3, but they seldom occur inwave 1. They never occur in two similar waves of a movement. Extensionsoccur during powerful market periods, such as the big advance from 1994to 1998. Unfortunately, there is no known way to anticipate an extension.The FlatThe corrective waves 2 and 4 show the greatest amount of variation and, Ihave found, cause the most amount of trouble. The simple ABC structure,as drawn by Elliott in the idealized pattern, is seldom seen. What is seen isa slight variation on this pattern, called a flat. In the basic Elliott diagramthat is usually drawn, wave C goes lower than wave A. A flat occurs whenwaves A and C end up at the same level (Figure 6.9). You can see that thebasic ABC idea is still there, but the size and endpoint are different, as arethe internal movements that comprise each section.The Irregular CorrectionOne of the most interesting variations on a flat occurs when the B wavecontinues up and actually exceeds the top of wave 5 (Figure 6.10). Thisvariation is called an irregular correction, and because the market makesa new high on wave B, it gives the impression that the overall movementis composed of four sections rather than three. It also explains whatW.D. Gann meant by “three sections and possibly four”: he was observing what we now know is an irregular correction.The difference between an irregular correction taking the market tonew highs versus a normal thrusting wave is that the B wave is made upof three movements rather than the usual five. This is very important andhelps distinguish the B wave from a normal thrusting movement.
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FIGURE 6.10 An Elliott wave variation called an irregular correction, in whichthe B wave continues up and exceeds the top of the preceding wave 5.B
AC
Horizontal TriangleQuite often, the fourth-wave correction can have a much more complexpattern than normal, forming what is called a horizontal triangle orwedge (Figure 6.11). A horizontal triangle almost always happens whenthe corrective wave 2 is small and wave 3 turns into an extension. Whenthis happens, we have the picture of a huge, long advance with a smallwave 2 correction; a large and long correction is now overdue. It’s as ifthe whole correction for the move takes place in wave 4, therefore wave
FIGURE 6.11 A horizontal triangle usually occurs as a fourth-wave correctionafter a long runup. It’s as if all the correction for the whole move is being savedfor one long fourth wave. A horizontal correction is composed of five movements(1, 2, 3, 4, and 5) and is not a normal ABC correction.
2
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4 stretches out into a long sideways movement. It still has the 13 subwaves of the standard correction, but they are altered a little into a longersideways pattern. This type of correction is important because I believethe market has entered into one at this writing.
SEARCHING FOR AN UNDERLYING THEORYIf the real market exactly followed the perfectly drawn wave pattern, themarket would be completely predictable; we would know exactly whatwas coming next—and when. The real market doesn’t behave that way,and the Elliott wave theory acknowledges this. Elliott wave theorists believe that the basic pattern is always there; they think that if you add afew more ideas to the theory and study it hard enough, you can discoverthat pattern.Elliott wave theorists say that the real stock market is the idealizedcurve, just stretched and pulled out of shape a little. If Elliott wave practitioners are right, it means that the basic pattern is there and that themarket is generally predictable; if they are wrong and deluding themselves, the patterns are just a random jumble of zigzags and the marketis unpredictable.Elliott searched for an underlying theory that explained his waveprinciple. Because fractals were not known at the time, his ideas centered on the medieval mathematics of Fibonacci, whose number seriesmatches the ever-expanding counts of the wave pattern. The only applicable idea that came from Fibonacci is a ratio called the golden mean,which is 1.618. Over the years Elliott wave theorists have tried to makethe ratios of the size of price movements or the ratios of the time spanbehind these movements equal to the golden mean. I have never foundthat it worked.Elliott had the right idea in looking for an underlying theory thatwould explain his observation of waves within waves within waves, a theory that would support his octave pattern (12345ABC) repeating fromthe very small time scales up to the very large. He was too far ahead ofhis time, though; the underlying theory had not been developed yet.I was giving a seminar in 1982 about the Elliott wave theory whensomeone came up afterward and told me I had been describing fractals.I looked into it, learned what fractals are, and found out that the Elliottwave theory is exactly that—a fractal theory. Fractals are the correct underlying foundation for the whole wave principle.
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A Guiding PrincipleThe failure of trying to make the ratios of either the size or the duration of price movements equal to the golden mean (1.618) confirmed an earlier conclusion of mine. Any simple ratio is just that—it’stoo simple—and therefore it couldn’t possibly work. My reasoning isvery practical: If such a simple ratio worked, it would have been discovered years ago by one of the hundreds of thousands of intelligentpeople who have pored over investment numbers for the last twocenturies. I think the fact that no one has ever discovered a simpleratio shows that probably none exists.Based on this reasoning, I established a guiding principle for myself. A correct theory of the stock market must be complicatedenough to make the market unpredictable most of the time (so thatsimple ratios don’t work) and predictable only part of the time.Therefore, a correct theory cannot be too simple; it has to be somewhat complex. We hope, however, that it’s not too complicated todiscover.
FRACTALS: THE THEORY BEHINDTHE ELLIOTT WAVE PATTERNSWhat is a fractal? Benoit Mandelbrot, the mathematician who discovered fractals, defines a fractal as “a geometrical shape that can be separated into parts, where the shape of every part is a reduced-scale versionof the whole” (“A Fractal Walk Down Wall Street,” Scientific American,February 1999). Essentially, if you take any little part of the whole andmagnify it until it is the same size as the whole, that little part now lookslike and has all the characteristics of the whole.Stock price charts are this way. If you were to take a weekly chart ofthe stock market for 50 years, isolate any week and magnify up the pricefluctuations showing the minute-by-minute price changes, you wouldfind the same jiggles and patterns in the one-week period as in the 50year period. If you took away the time scale at the bottom and the priceson the side and laid the two periods side by side, you wouldn’t be able to
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A fractal, according to Benoit Mandelbrot, is “a geometrical shapethat can be separated into parts, where the shape of every part is areduced-scale version of the whole.”
tell which was the minute-by-minute chart and which was the 50-yearchart (there is a subtle way to tell between extreme time scales, but thathas no value to us here).The subject of fractals is an important new advancement in our understanding of the geometrical patterns formed in nature. Their study isconsidered a branch of chaos theory and has wide application in manyfields. Besides helping explain stock price movements, fractals also shedlight on the distribution of galaxies in the universe, the structure of bloodvessels in the body, the patterns of coastlines, and many previously confusing mathematical curves.
Stock Price Patterns Are Like FractalsStock prices follow the fractal definition. Let’s take a time view of theS&P 500—for example, 50 days. Then let’s take a little section out ofthis, such as what the market did minute by minute during one day.If you magnify the minute-by-minute chart to the same size as the 50day chart, they look the same (Figure 6.12). With stock prices, youcan’t tell whether you are looking at a 10-year sweep, with the backand-forth fluctuation taking place over months, or a one-day movement, with the fluctuations taking place over minutes.From the fractal definition in this example, you can understandwhy the Elliott wave theory is a perfect example of fractal theory. Itpostulates that the same pattern—12345ABC—is found in hourlymovements as well as movements that last years. Because stockprices are fractal in nature and the Elliott wave theory is the onlyknown fractal theory of stock prices, it should be clear that thistheory could be highly significant in helping us interpret market fluctuations. It might allow us to understand, using the modern discoveries of chaos theory, some of the price patterns we have beenexamining.
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FIGURE 6.12 The stock market follows the standard fractal definition in thateach small price movement is a part of and a reduced-scale version of the largerprice movement.
Daily Price Moves
Minute Price Moves
The Elliott wave theory and how the basic 12345ABC pattern buildsup and up is one of the best examples of a fractal and the way it is constructed. There are a number of ways to classify fractals, but the classification that is important to us is one that defines in some way thepredictability of the geometrical pattern of the fractal. In some fractals,
NOTEPlease do not be put off by the discussion of fractals. I have learnedover the years that important ideas are usually simple and easy tounderstand; they are made complex only by people who presentthem as such. Fractals are truly a simple concept, one that peopleseem to know instinctively. They are really quite easy to comprehend if approached correctly.
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the geometrical pattern is completely random. A random fractal still fitsthe definition of a fractal: when you take a little part of the whole andblow it up, it does look like the whole, except that with a random fractalthere is no way to predict the pattern you will see. Other fractals are notthis way. Some are 100% predictable, meaning that when you take apiece of the curve and magnify it, you know exactly what you are goingto see. For example, the idealistic Elliott pattern, as we drew it, is 100%predictable; at any point you can predict what you are going to see whenyou show greater detail.To help you understand these different kinds of fractals—and ultimately the stock market—I am going to show you two examples of fractals whose underlying patterns have varying degrees of predictability.These two examples are commonly used to illustrate what fractals are.The first example, the Koch curve, is probably the simplest fractalthere is, and the second example, the Mandelbrot curve, is probably themost famous. These examples will prepare us to ask and answer the mostimportant question of all: How predictable is the fractal pattern the stockmarket makes?
Fractal Example 1: The Koch CurveTo understand the Koch curve, take a straight line and put a little V shapein the middle (Figure 6.13). This V breaks the line into four smaller lines,each equal in length. Do the same with each of these four smaller lines—add a little V to the middle of them. Now there are 16 smaller lines. Adda V to each of these. Do this again and again and again—forever. This isthe mathematically infinite but very exact Koch curve. It is a fractal because each part, no matter how small, when magnified, is a scaled-downversion of the whole. The Koch curve is interesting because it is mathematically perfect, and it isn’t random; you know exactly what you will seeand what to expect at each magnification of the curve.The Elliott wave pattern, as we drew and explained it earlier, is created in a way similar to the Koch curve. The only real difference is thatthe repeating pattern is a little more complicated. However, the step ofrepeating a simple action over and over—taking any line and putting fivesmaller lines in its place—produces an exact pattern similar to the Kochcurve.
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FIGURE 6.13 The perfectly predictable fractal, the Koch curve, is made byperforming a simple procedure over and over. A straight line is broken into fourequal lines by putting a V kink in it. You put a V kink into each of these lines,making 16 smaller lines, ad infinitum.1. Start with a straight line.
AMFLY
2. Put a V kink into it.
TE
3. Then put this basic patterninto each straight line.
4. Again…and again… .
Fractal Example 2: The Mandelbrot CurveThe Mandelbrot curve has patterns that are not quite predictable butsimilar. Created by the man who discovered fractals, the Mandelbrotcurve is the fractal that has come to symbolize not only the entire subjectof fractals but also the theory of chaos (Figure 6.14).
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FIGURE 6.14 The famous Mandelbrot curve. This fractal pattern has appearedon innumerable book and magazine covers over the years, yet few people knowwhat it is. It comes from a very simple mathematical procedure. In this fractal, allthe points in the light area represent one possible answer to that procedurewhile the black area are those points that represent the other.
I’m going to show you how the Mandelbrot curve is created by giving you a ridiculously simple analogy. Let’s take a circle and paint all thepoints inside the circle white and all the points outside the circle black.The white points are all the points that satisfy one answer and the blackpoints satisfy the other answer. Answer to what? The answer to this question: How far from the center is each point? Every point painted whiteis at a location that is less than the radial distance from the center. Everypoint painted black (everything outside the circle) is at a location that isgreater than the radial distance from the center. The circle’s circumference is the boundary between these two areas.This obvious and trivial analogy shows the essence of the simple ideabehind the creation of the Mandelbrot curve. Basically, the Mandelbrotcurve is a boundary, like the boundary of the circle, that satisfies a similar type of condition. Here, however, the condition is a repeated mathematical calculation that can lead to only two possible results. In theMandelbrot curve, the white points represent numbers that lead to one
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result, and the black points represent numbers that lead to the other. Inthis example, however, the curve or boundary separating the white andblack points is not smooth, as the circle is . The curve (if you can call itthat) is ragged, with acorn-like shapes sticking out and a bunch of hairyfilaments all around it.To get a better look at the geometry of this boundary, let’s magnifyit and see what it looks like (Figure 6.15). As we systematically increasethe magnification and look deeper and deeper into this boundary, wealways find more and more detail. In fact, you never get to a simple,FIGURE 6.15 As we go deeper into the Mandelbrot curve, we find more andmore detail. This fractal never breaks down into a simple pattern or curve. Thepicture at top right is a magnification of the smaller box in the picture at top left.The middle-left picture is a magnification of the smaller box in the top-rightpicture, and so on. This magnification process can go on forever.
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smooth pattern; the greater detail never ends. It is infinite in complexityand never resolves into something simple. The Mandelbrot curve is awonderful example of a fascinating concept: infinite variation and beautywithin a finite boundary.Can the complicated patterns we see as we magnify the Mandelbrotcurve be predicted the way the patterns of the Koch curve can? As far asI know, they cannot. We often see similar patterns as we go deeper intothe curve, but I do not believe anyone has developed a way to anticipateexactly what they will see next. There seems to be some symmetry; different forms of what is called the sea horse shape appear repeatedly, butthere is also randomness in how that symmetry is displayed. The fractaldefinition is there, however, since every small section contains all thecomplexity and variation of pattern that is contained in the whole.
HOW PREDICTABLE IS THE REALMARKET’S FRACTAL PATTERN?We saw that the Koch curve is a fractal in which the pattern is predictable. So is the pattern of the idealized Elliott wave pattern. With theMandelbrot fractal, we saw that the pattern is not identical, but it hassimilarities or similar repeating patterns that are predictable. There arealso fractals that have completely random patterns. All this leads to the$64,000 question: What type of fractal pattern does the stock market create—100% predictable, somewhat predictable, or random?The answer is central to any effort to predict stock prices and to theevaluation of the Elliott wave theory. Is the real stock market, as Elliottwave theorists believe, simply a stretched-out, pushed and pulled versionof the idealized Elliott wave pattern in which, if you study it hard enough,you can still see where you are in the pattern and therefore predict what’scoming next? Or is it really just a jumble of random zigzag lines?To understand the question better, let’s come back to the Kochcurve. We know that the Koch curve is a simple pattern that is 100% predictable; you know exactly what to expect as you magnify it. You cancompletely predict what you will see. Now let’s play a little game.Suppose, instead of drawing the curve on paper, we actually made itout of thin, malleable wire. We put all those little kinks into the wire,then we take the wire and pull on it a couple of times. What happens tothat perfect Koch curve? You should still be able to recognize the resulting curve as the original Koch curve, but pulled and stretched a little.
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FIGURE 6.16 If we stretched and pulled the perfect Koch curve, the fractalpattern would no longer be completely predictable. If you stretch it more andmore, the pattern eventually becomes completely random, having beentransformed from a predictable fractal into a random one. This example suggestsan interesting question: Is the real stock market pattern a stretched and pulledElliott wave pattern but not stretched so much as to be completely random?
Is the pattern now as predictable as it was originally? Not quite. Thebasic outline is still predictable, but some of the detail is not.If you continued to distort the wire more and more, yanking it hereand stretching it there, you would eventually lose any resemblance to theoriginal, perfect pattern (Figure 6.16). You would have transformedthe perfectly predictable Koch curve into a complex jumble of lines, allof different length and angles and now completely unpredictable.This is the idea behind the question that we are asking about the Elliott wave pattern. In the real stock market is the basic Elliott wave patternthere, just stretched and pulled a little but with the basic pattern still somewhat recognizable? Or is the stretching and pulling so great that, in practice, the real stock market loses any semblance of that basic ideal pattern?The Search for PredictabilityAfter 20 years of studying and applying the Elliott wave theory, my experience is that the Elliott wave pattern is sometimes clear and thereforeuseful for predicting or at least outlining what is coming up. At othertimes, the pattern of the market is so completely random that no Elliottwave pattern can be discerned. At these times, the market is completelyunpredictable using the Elliott wave theory. Therefore, sometimes theElliott wave fractal pattern is discernible, making the market somewhatpredictable, and at other times, it is random. This observation aligns withthe conclusion of the basic model introduced in Chapter 2.
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Elliott wave theorists often say that this is wrong and that the complete pattern is almost always clearly there. In general, they are right; thestudy of past markets almost always shows the market making a completed pattern. However, they always do this analysis after the fact.When you have to make real-time, day-to-day decisions, there are justtoo many points along the way where you could have said a movementwas complete when it really wasn’t. The rules and exceptions are sobroad and so many variations are allowed that we often don’t know whatto project. So yes, after the fact one can look back and say, “See, here itis”; but in practice, it isn’t this way.The record of people using the Elliott wave theory over the yearsgenerally demonstrates partial predictability. Although there have beenmany startling successes, there have also been many failures. In practice,there always seems to be an alternate wave count, which indicates thatthe Elliott wave theory, by itself, is somewhat incomplete.It is interesting that neither the Elliott wave theorists nor those critical of the theory address this important question in any depth. Both believers in and critics of the theory see it as being either 100% right or100% wrong. This is unfortunate because the Elliott wave theory doesnot, by its nature, lie at either of these two extremes. Efforts to make ita perfect theory actually destroy its value, and efforts to deny it ignorethe new discoveries made in chaos theory.The idea that the Elliott wave theory is not complete on its own doesnot invalidate the theory or make it wrong. It just reflects what I believeis the actual situation—that the market is sometimes predictable andsometimes random.Nevertheless, even with this limitation, there is no better way to tryto map the market. If you have to forecast how prices will probably unfold, there is no better starting point than the basic Elliott wave fractalpattern. This is especially true when you add to the Elliott wave theorythe information presented in the first five chapters of this book. Withthese other tools, it often becomes possible to overcome many of the uncertainties in the Elliott wave pattern.Applying the Elliott Wave TheoryHow do you actually make the Elliott wave theory work? As I have said,the Elliott wave theory presents the pattern or map against which youevaluate the actual pattern of the real market. It is a constant, ongoing activity and one that needs to remain flexible so you can change your mind
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freely if warranted. I use the tools described in the previous chapters tohelp me estimate where in the wave count the stock market is, but wideallowances are made for the Elliott wave variations I mentioned earlier.I usually start at a major market bottom or other relative point of certainty. Then, I make every effort to determine where that point is in theElliott wave count. I study both daily and weekly charts of the major indexes to help me find the count. I use the S&P 500, the Dow Jones industrials, the Russell 2000, the NASDAQ Composite Index, and a high-techindex, because sometimes the count is clearer on one index than it is on another. I have found that the Elliott wave count is clearest during volatilemarkets—when feedback loops are functioning—and that dull marketswith low volatility usually produce random and confusing patterns.NOTEDon’t force the count. If you don’t know, you don’t know. Remember that there will be times when the pattern is incomprehensibleand prediction impossible. Learn to live with that; you must becomeused to not knowing. Because of this, be suspicious of anyone whoalways has an opinion. People who always have an opinion are either fooling themselves or selling something.
No matter how impatient you get while waiting to identify exactlywhere the wave count is, you must fight the tendency of always having toknow. This is very important. I have learned that the market will alwaysshow what it is doing if you have patience. You have to be willing to say,“I don’t know,” and then wait until you see something that you canclearly identify. Remember, there are many times when the market israndom and unpredictable—in fact, it’s like that most of the time.Accurate Prediction Takes VigilanceYou might think that after 30 years I would have become more certain inthe art of stock prediction, but this is not what has happened; I have become more humble. I originally thought that the fundamentals of themarket stayed the same, that behind the ever-changing economic picture, a few things remained constant. After all, there are always buyersand sellers and the market either goes up or down. I still believe that, butmuch less so.
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Be Wary of DoomsayersThe Elliott wave theory should never be used to predict majorcrashes or calamities in the future, and prognosticators who do thisonly contribute to the invalidation of a very useful theory. When youare pretty certain the stock market has completed a major 12345movement, all you know is that the market is probably headed foran ABC correction. It could be a crash, but it is just as likely to be anirregular correction in which, after a very mild wave A, the wave Bwill carry prices to new highs for a number of years. The Elliott wavetheory alone cannot predict what form the ABC correction will take.You must include other factors to help you decide what type of topit is going to be.
The activity of stock market speculation takes intense and persistentstudy, and you must be open to the study of something that is evolvingand changing. People do learn. Investors know a lot more about stocksthan their forbears. The professors have pushed forward our understanding of investment markets, and we now have a firmer theoreticalfoundation. Investors therefore react differently than they used to.I have methodically covered all the information that I believe is necessary to understand most stock markets and to condition the reader toexpect a new market environment. It is now time to show how I applysuch knowledge in the real world—to the stock market at the end of2001. The theories I used to do this are the same ones I used to predictthe end of the 1982–2000 bull market in my first book, A Strategic Guideto the Coming Roller-Coaster Market. This time, however, I’ll applythem to help determine the structure and form of the expected tradingrange market, how long it will last, and how low and high it will range.The Elliott wave theory is used to forecast the basic form for this tradingrange. Finally, in Chapter 8, strategies are offered that might do wellduring this forecasted period.
7TradingRange Markets
THE CORRECTION: WHAT WILL IT LOOK LIKE?As we saw in the last chapter, the most complicated part of Elliott wavetheory is the corrective waves. More variations of pattern are allowed forcorrective waves than for any other wave types. Basically, a correction is ahalt in the primary trend of the market. It can manifest either by prices declining or by prices marking time by moving up and down in a sidewayspattern. It is our business now to investigate and consider the most likelyform and type of correction and how to possibly profit from it.Past Trading Range MarketsThere is a long history of the stock market entering into extended trading ranges, periods where prices moved up and down in large bull andbear markets but made little forward progress. In fact, since 1900, stockprices were in essentially long-term trading ranges more than 50% of thetime. I calculate that we have had three such periods since 1900.The first period occurred right after the turn of the century (a hundred years ago) and lasted about 15 years. It started with the Dow Jonesindustrials making an all-time high of 75.57 on January 19, 1906. Fromthat lofty peak it declined 48% over almost two years, hitting bottom onNovember 15, 1907, at 38.88. Within two years it had recovered almost148
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the entire previous decline, reaching a second peak at 73.76 on November 19, 1909. The cheer was short-lived, however, as the market then slidslowly toward bottom almost two years later, at 53.51, on September 1,1911.For the next three years, prices were completely lifeless. From thatSeptember low, prices worked their way up to a local high of 69.08 onSeptember 30, 1912, then eroded back down to a second bottom on July30, 1914, at 52.40. Prices then came back to life. They rallied strongly toa new all-time high of 110.15, a gain of 110% over two and a half years,hitting the peak price on November 21, 1916. The cheer was again shortlived as prices declined in one year to 65.95, hitting bottom on December 19, 1917. Another two-year bull market followed, with prices risingslightly above the previous peak, getting to 119.62 on November 3, 1919.This was again followed by a bear market, which hit a low of 63.90 on August 21, 1921. From the 1906 high of 75.57 to the low in 1921 of 63.90,prices had effectively gone nowhere.The second trading range period started in 1937 after a five-yearrally recovered some of the collapsed prices of the Great Crash. From ahigh of 195.59 on March 10, 1937, the market declined to a low of 97.46almost exactly one year later, on March 31, 1938. From that low itquickly recovered to 158.90 by November 10, 1938, only to again go intoa long, slow decline over four years back to 92.69, hitting bottom onApril 28, 1942. A four-year bull market ensued, hitting a high of 213.36on May 29, 1946. For the next three years, prices went into a dead period, first hitting a low of 160.49 on October 30, 1946, followed by a highof 194.49 on June 14, 1948, and then another low of 160.62 on June 14,1949. Over the 12 years between 1937 to 1949, prices effectively wentnowhere.The third trading range period was the 16 years between 1966 and1982. The Dow industrials hit 1,000 in 1966 and didn’t effectively breakabove it until 1982. The next chapter goes into the details of this period.“Normalized” ThinkingI remember as a child sitting with my parents and their friends oneevening when my father posed a question that everyone, including me,failed to answer correctly. He asked: “If a car goes a half a mile at 30miles an hour, how fast does it have to go the second half-mile to average 60 miles an hour for the whole mile?” After a lot of arguing, we allagreed that it had to be 9