The Wave Principle = Graphic of Mass Psychology
Motive Waves = 5 Wave Structures, Main Trend of One Larger Degree
Types of Motive Waves = Impulse, Diagonal Triangle
Impulse : Waves 1,3,5 = 5 Impulse Subwaves
Wave 4 ≠ Price Teritory of Wave 1
Diagonal Triangle : Waves 1,3,5 = 3 Subwave
Wave 4 = Price territory of Wave 1
Signal = Imminent Major Trend Reversal
Lesson 2 – Motive Waves
- Motive Waves
Motive waves subdivide into five waves and always move in the same direction as the trend of one larger degree. They are straightforward and relatively easy to recognize and interpret.
Within motive waves, wave 2 always retraces less than 100% of wave 1, and wave 4 always retraces less than 100% of wave 3. Wave 3, moreover, always travels beyond the end of wave 1. The goal of a motive wave is to make progress, and these rules of formation assure that it will.
Elliott further discovered that in price terms, wave 3 is often the longest and never the shortest among the three actionary waves (1, 3 and 5) of a motive wave. As long as wave 3 undergoes a greater percentage movement than either wave 1 or 5, this rule is satisfied. It almost always holds on an arithmetic basis as well.
There are two types of motive waves: impulse and diagonal.
The most common motive wave is an impulse, per Figure 1-1 (see Lesson 1). In an impulse, wave 4 does not enter the price territory of (i.e., “overlap”) wave 1. This rule holds for all non-leveraged “cash” markets. Futures markets, with their extreme leverage, can induce short term price extremes that would not occur in cash markets. Even so, overlapping is usually confined to daily and intraday price fluctuations and even then is rare. In addition, the actionary subwaves (1, 3 and 5) of an impulse are themselves motive, and subwave 3 is always an impulse. Figures 1-2, 1-3 and 1-4 all depict impulses in the 1, 3, 5, A and C wave positions.
As detailed in the preceding three paragraphs, there are only a few simple rules for interpreting impulses properly. A rule is so called because it governs all waves to which it applies. Typical, yet not inevitable, characteristics of waves are called guidelines. Guidelines of impulse formation, including extension, truncation, alternation, equality, channeling, personality and ratio relationships are discussed below. A rule should never be disregarded. In many years of practice with countless patterns, the authors have found but one or two instances above Subminuette degree when all other rules and guidelines combined to suggest that a rule was broken. Analysts who routinely break any of the rules detailed in this section are practicing some form of analysis other than that guided by the Wave Principle. These rules have great practical utility in correct counting, which we will explore further in discussing extensions.
Most impulses contain what Elliott called an extension. An extension is an elongated impulse with exaggerated subdivisions. The vast majority of impulses contain an extension in one and only one of their three actionary subwaves. The rest either contain no extension or an extension in both subwaves three and five. At times, the subdivisions of an extended wave are nearly the same amplitude and duration as the other four waves of the larger impulse, giving a total count of nine waves of similar size rather than the normal count of “five” for the sequence. In a nine-wave sequence, it is occasionally difficult to say which wave extended. However, it is usually irrelevant anyway, since under the Elliott system, a count of nine and a count of five have the same technical significance. The diagrams in Figure 2-1, illustrating extensions, will clarify this point.
The fact that an extension typically occurs in only one actionary subwave provides a useful guide to the expected lengths of upcoming waves. For instance, if the first and third waves are of about equal length, the fifth wave will likely be a protracted surge. Conversely, if wave three extends, the fifth should be simply constructed and resemble wave one.
In the stock market, the most commonly extended wave is wave 3. This fact is of particular importance to real-time wave interpretation when considered in conjunction with two of the rules of impulse waves: Wave 3 is never the shortest actionary wave, and wave 4 may not overlap wave 1. To clarify, let us assume two situations involving an improper middle wave, as illustrated in Figures 2-2 and 2-3.
In Figure 2-2, wave 4 overlaps the top of wave 1. In Figure 2-3, wave 3 is shorter than wave 1 and shorter than wave 5. According to the rules, neither is an acceptable labeling. Once the apparent wave 3 is proved unacceptable, it must be relabeled in some way that is acceptable. In fact, it is almost always to be labeled as shown in Figure 2-4, implying an extended wave (3) in the making. Do not hesitate to get into the habit of labeling the early stages of a third wave extension. The exercise will prove highly rewarding, as you will understand from the discussion under Wave Personality. Figure 2-4 is perhaps the single most useful guide to real time impulse wave counting.
Extensions may also occur within extensions. In the stock market, the third wave of an extended third wave is typically an extension as well, producing a profile such as shown in Figure 2-5. A real-life example is shown in Figure 2-7. Figure 2-6 illustrates a fifth wave extension of a fifth wave extension. Extended fifths are quite common in major bull markets in commodities.
Elliott used the word “failure” to describe a situation in which the fifth wave does not move beyond the end of the third. We prefer the less connotative term, “truncation,” or “truncated fifth.” A truncation can usually be verified by noting that the presumed fifth wave contains the necessary five subwaves, as illustrated in Figures 2-8 and 2-9. A truncation often occurs following a particularly strong third wave.
The U.S. stock market provides two examples of major degree truncated fifths since 1932. The first occurred in October 1962 at the time of the Cuban crisis (see Figure 2-10). It followed the crash that occurred as wave 3. The second occurred at yearend in 1976 (see Figure 2-11). It followed the soaring and broad wave (3) that took place from October 1975 to March 1976.
Elliott used the term “diagonal triangle” to describe this pattern. We now use the term “diagonal,” so as not to confuse this pattern with a corrective triangle.
A diagonal is a motive pattern yet not an impulse, as it has two corrective characteristics. As with an impulse, no reactionary subwave fully retraces the preceding actionary subwave, and the third subwave is never the shortest. However, a diagonal is the only five-wave structure in the direction of the main trend within which wave four almost always moves into the price territory of (i.e., overlaps) wave one and within which all the waves are “threes,” producing an overall count of 3-3-3-3-3. On rare occasions, a diagonal may end in a truncation, although in our experience such truncations occur only by the slimmest of margins. This pattern substitutes for an impulse at two specific locations in the wave structure.
- Ending Diagonal
An ending diagonal occurs primarily in the fifth wave position at times when the preceding move has gone “too far too fast,” as Elliott put it. A very small percentage of diagonals appear in the C-wave position of A-B-C formations. In double or triple threes (see Lesson 3: Corrective Waves), they appear only as the final C wave. In all cases, they are found at the termination points of larger patterns, indicating exhaustion of the larger movement.
A contracting diagonal takes a wedge shape within two converging lines. This most common form for an ending diagonal is illustrated in Figures 2-12 and 2-13 and shown in its typical position within a larger impulse wave.
We have found one case in which an ending diagonal’s boundary lines diverged, creating an expanding diagonal rather than a contracting one. However, it is unsatisfying analytically in that its third wave was the shortest actionary wave.
Ending diagonals have occurred recently in Minor degree as in early 1978, in Minute degree as in February-March 1976, and in Subminuette degree as in June 1976. Figures 2-14 and 2-15 show two of these periods, illustrating one upward and one downward “real life” formation. Figure 2-16 shows our real-life possible expanding diagonal. Notice that in each case, an important change of direction followed.
Although not so illustrated in Figures 2-12 and 2-13, the fifth wave of an ending diagonal often ends in a “throw-over,” i.e., a brief break of the trendline connecting the end points of waves one and three. The real-life examples in Figures 2-14 and 2-16 show throw-overs. While volume tends to diminish as a diagonal of small degree progresses, the pattern always ends with a spike of relatively high volume when a throw-over occurs. On rare occasions, the fifth subwave falls short of its resistance trendline.
A rising ending diagonal is usually followed by a sharp decline retracing at least back to the level where it began and typically much further. A falling ending diagonal by the same token usually gives rise to an upward thrust.
Fifth wave extensions, truncated fifths and ending diagonals all imply the same thing: dramatic reversal ahead. At some turning points, two of these phenomena have occurred together at different degrees, compounding the violence of the next move in the opposite direction.
- Leading Diagonal
It has recently come to light that a diagonal occasionally appears in the wave 1 position of impulses and in the wave A position of zigzags. In the few examples we have, the subdivisions appear to be the same: 3-3-3-3-3, although in two cases, they can be labeled 5-3-5-3-5, so the jury is out on a strict definition. Analysts must be aware of this pattern to avoid mistaking it for a far more common development, a series of first and second waves, as illustrated in Figure 2-4. A leading diagonal in the wave one position is typically followed by a deep retracement.
Figure 2-17 shows a real-life leading diagonal. We have recently observed that a leading diagonal can also take an expanding shape. This form appears to occur primarily at the start of declines in the stock market (see Figure 2-18). These patterns were not originally discovered by R.N. Elliott but have appeared enough times and over a long enough period that the authors are convinced of their validity.
Lesson 3 – Corrective Waves
Markets move against the trend of one greater degree only with a seeming struggle. Resistance from the larger trend appears to prevent a correction from developing a full motive structure. This struggle between the two oppositely-trending degrees generally makes corrective waves less clearly identifiable than motive waves, which always flow with comparative ease in the direction of the one larger trend. As another result of this conflict between trends, corrective waves are quite a bit more varied than motive waves. Further, they occasionally increase or decrease in complexity as they unfold so that what are technically subwaves of the same degree can by their complexity or time length appear to be of different degree (see Figures 5-4 and 5-5 in Lesson 5). For all these reasons, it can be difficult at times to fit corrective waves into recognizable patterns until they are completed and behind us. As the terminations of corrective waves are less predictable than those for motive waves, you must exercise more patience and flexibility in your analysis when the market is in a meandering corrective mood than when prices are in a persistent motive trend.
The single most important rule that can be gleaned from a study of the various corrective patterns is that corrections are never fives. Only motive waves are fives. For this reason, an initial five-wave movement against the larger trend is never the end of a correction, only part of it. The figures in this section should serve to illustrate this point.
Corrective processes come in two styles. Sharp corrections angle steeply against the larger trend. Sideways corrections, while always producing a net retracement of the preceding wave, typically contain a movement that carries back to or beyond its starting level, thus producing an overall sideways appearance. The discussion of the guideline of alternation explains the reason for noting these two styles.
Specific corrective patterns fall into three main categories: Zigzag (5-3-5; includes three types: single, double and triple);
Flat (3-3-5; includes three types: regular, expanded and running);
Triangle (3-3-3-3-3; three types: contracting, barrier and expanding; and one variation: running).
A combination of the above forms comes in two types: double three and triple three.
A single zigzag in a bull market is a simple three-wave declining pattern labeled A-B-C. The subwave sequence is 5-3-5, and the top of wave B is noticeably lower than the start of wave A, as illustrated in Figures 3-1 and 3-2.
In a bear market, a zigzag correction takes place in the opposite direction, as shown in Figures 3-3 and 3-4. For this reason, a zigzag in a bear market is often referred to as an inverted zigzag.
Occasionally zigzags will occur twice, or at most, three times in succession, particularly when the first zigzag falls short of a normal target. In these cases, each zigzag is separated by an intervening “three,” producing what is called a double zigzag (see Figure 3-5) or triple zigzag. These formations are analogous to the extension of an impulse wave but are less common. The correction in the Dow Jones Industrial Average from July to October 1975 (see Figure 3-6) can be labeled as a double zigzag, as can the correction in the Standard and Poor’s 500 stock index from January 1977 to March 1978 (see Figure 3-7). Within impulses, second waves frequently sport zigzags, while fourth waves rarely do.
R.N. Elliott’s original labeling of double and triple zigzags and double and triple threes (see later section) was a quick shorthand. He denoted the intervening movements as wave X, so that double corrections were labeled A-B-C-X-A-B-C. Unfortunately, this notation improperly indicated the degree of the actionary subwaves of each simple pattern. They were labeled as being only one degree less than the entire correction when in fact, they are two degrees smaller. We have eliminated this problem by introducing a useful notational device: labeling the successive actionary components of double and triple corrections as waves W, Y and Z, so that the entire pattern is counted “W-X-Y (-X-Z).” The letter W now denotes the first corrective pattern in a double or triple correction, Y the second, and Z the third of a triple. Each subwave thereof (A, B or C, as well as D or E of a triangle — see later section) is now properly seen as two degrees smaller than the entire correction. Each wave X is a reactionary wave and thus always a corrective wave, typically another zigzag.
A flat correction differs from a zigzag in that the subwave sequence is 3-3-5, as shown in Figures 3-8 and 3-9. Since the first actionary wave, wave A, lacks sufficient downward force to unfold into a full five waves as it does in a zigzag, the B wave reaction, not surprisingly, seems to inherit this lack of countertrend pressure and terminates near the start of wave A. Wave C, in turn, generally terminates just slightly beyond the end of wave A rather than significantly beyond as in zigzags.
In a bear market, the pattern is the same but inverted, as shown in Figures 3-10 and 3-11.
A flat correction usually retraces less of the preceding impulse wave than does a zigzag. It tends to occur when the larger trend is strong, so it virtually always precedes or follows an extension. The more powerful the underlying trend, the briefer the flat tends to be. Within an impulse, the fourth wave frequently sports a flat, while the second wave rarely does.
What might be called a “double flat” does occur. However, Elliott categorized such a formation as a “double three,” a term we discuss later in this lesson.
The word “flat” is used as a catch-all name for any A-B-C correction that subdivides 3-3-5. In Elliott literature, however, three types of 3-3-5 corrections have been named by differences in their overall shape. In a regular flat correction, wave B terminates about at the level of the beginning of wave A, and wave C terminates a slight bit past the end of wave A, as we have shown in Figures 3-8 through 3-11. Far more common, however, is the variety we call an expanded flat, which contains a price extreme beyond that of the preceding impulse wave. Elliott called this variation an “irregular” flat, although the word is inappropriate as they are actually far more common than “regular” flats.
In expanded flats, wave B of the 3-3-5 pattern terminates beyond the starting level of wave A, and wave C ends more substantially beyond the ending level of wave A, as shown for bull markets in Figures 3-12 and 3-13 and bear markets in Figures 3-14 and 3-15. The formation in the DJIA from August to November 1973 was an expanded flat correction in a bear market, or an “inverted expanded flat” (see Figure 3-16).
In a rare variation on the 3-3-5 pattern, which we call a running flat, wave B terminates well beyond the beginning of wave A as in an expanded flat, but wave C fails to travel its full distance, falling short of the level at which wave A ended, as in Figures 3-17 through 3-20. Apparently in this case, the forces in the direction of the larger trend are so powerful that the pattern is skewed in that direction. The result is akin to the truncation of an impulse.
It is always important, but particularly when concluding that a running flat has taken place, that the internal subdivisions adhere to Elliott’s rules. If the supposed B wave, for instance, breaks down into five waves rather than three, it is more likely the first wave up of the impulse of next higher degree. The power of adjacent impulse waves is important in recognizing running corrections, which tend to occur only in strong and fast markets.
We must issue a warning, however. There are hardly any examples of this type of correction in the price record. Never label a correction prematurely this way, or you’ll find yourself wrong nine times out of ten. A running triangle, in contrast, is much more common (see next section).
A triangle appears to reflect a balance of forces, causing a sideways movement that is usually associated with decreasing volume and volatility. The triangle pattern contains five overlapping waves that subdivide 3-3-3-3-3 and are labeled A-B-C-D-E. A triangle is delineated by connecting the termination points of waves A and C, and B and D. Wave E can undershoot or overshoot the A-C line, and in fact, our experience tells us that it happens more often than not.
There are three varieties of triangles: contracting, barrier and expanding, as illustrated in Figure 3-21. Elliott contended that the horizontal line of a barrier triangle could occur on either side of the triangle, but such is not the case; it always occurs on the side that the next wave will exceed. Elliott’s terms, “ascending” and “descending,” are nevertheless useful shorthand in communicating whether the barrier triangle occurs in a bull or bear market, respectively.
Figure 3-21 depicts contracting and barrier triangles as taking place entirely within the area of preceding price action, which may be termed a regular triangle. Yet, it is extremely common for wave B of a contracting triangle to exceed the start of wave A in what may be termed a running triangle, as shown in Figure 3-22. Despite their sideways appearance, all triangles, including running triangles, effect a net retracement of the preceding wave at wave E’s end.
Most of the subwaves in a triangle are zigzags, but sometimes one of the subwaves (usually wave C) is more complex than the others and can take the shape of a multiple zigzag. In rare cases, one of the sub-waves (usually wave E) is itself a triangle, so that the entire pattern protracts into nine waves. Thus, triangles, like zigzags, occasionally display a development that is analogous to an extension. One example occurred in silver from 1973 through 1977 (see Figure 3-23).
A triangle always occurs in a position prior to the final actionary wave in the pattern of one larger degree, i.e., as wave four in an impulse, wave B in an A-B-C, or the final wave X in a double or triple zigzag or combination. A triangle may also occur as the final actionary pattern in a corrective combination, although even then it usually precedes the final actionary wave in the pattern of one larger degree than the corrective combination. Although upon extremely rare occasions a second wave in an impulse appears to take the form of a triangle, it is usually due to the fact that a triangle is part of the correction, which is in fact a double three.
In the stock market, when a triangle occurs in the fourth wave position, wave five is sometimes swift and travels approximately the distance of the widest part of the triangle. Elliott used the word “thrust” in referring to this swift, short motive wave following a triangle. The thrust is usually an impulse but can be an ending diagonal. In powerful markets, there is no thrust, but instead a prolonged fifth wave. So if a fifth wave following a triangle pushes past a normal thrust movement, it is signaling a likely protracted wave. Post-triangle advancing impulses in commodities at degrees above Intermediate are usually the longest wave in the sequence.
Many analysts are fooled into labeling a completed triangle way too early. Triangles take time and go sideways. If you examine Figure 3-23 closely, you will see that one could have jumped the gun in the middle of wave b, pronouncing the end of five contracting waves. But the boundary lines of triangles almost never collapse so quickly. Subwave C is typically a complex wave, though wave B or D can fulfill that role. Give triangles time to develop.
On the basis of our experience with triangles, we propose that often the time at which the boundary lines of a contracting triangle reach an apex coincides with a turning point in the market. Perhaps the frequency of this occurrence would justify its inclusion among the guidelines associated with the Wave Principle.
Combination (Double and Triple Three)
Elliott called a sideways combination of two corrective patterns a “double three” and three patterns a “triple three.” While a single three is any zigzag or flat, a triangle is an allowable final component of such combinations and in this context is called a “three.” A combination is composed of simpler types of corrections, including zigzags, flats and triangles. Their occurrence appears to be the flat correction’s way of extending sideways action. As with double and triple zigzags, the simple corrective pattern components are labeled W, Y and Z. Each reactionary wave, labeled X, can take the shape of any corrective pattern but is most commonly a zigzag. As with multiple zigzags, three patterns appear to be the limit, and even those are rare compared to the more common double three.
Combinations of threes were labeled differently by Elliott at different times, although the illustrative pattern always took the shape of two or three juxtaposed flats, as shown in Figures 3-24 and 3-25. However, the component patterns more commonly alternate in form. For example, a flat followed by a triangle is a more typical type of double three (which we now know as of 1983), as illustrated in Figure 3-26.
A flat followed by a zigzag is another example, as shown in Figure 3-27. Naturally, since the figures in this section depict corrections in bull markets, they need only be inverted to observe them as upward corrections in bear markets.
For the most part, a combination is horizontal in character. Elliott indicated that the entire formation could slant against the larger trend, although we have never found this to be the case. One reason is that there never appears to be more than one zigzag in a combination. Neither is there more than one triangle. Recall that triangles occurring alone precede the final movement of a larger trend. Combinations appear to recognize this character and sport triangles only as the final wave in a double or triple three.
Although different in that their angle of trend is sharper than the sideways trend of combinations (see the guideline of alternation), double and triple zigzags (see Figure 3-5) can be characterized as non-horizontal combinations, as Elliott seemed to suggest in Nature’s Law. But double and triple threes are different from double and triple zigzags not only in their angle but in their goal. In a double or triple zigzag, the first zigzag is rarely large enough to constitute an adequate price correction of the preceding wave. The doubling or tripling of the initial form is usually necessary to create an adequately sized price retracement. In a combination, however, the first simple pattern often constitutes an adequate price correction. The doubling or tripling appears to occur mainly to extend the duration of the corrective process after price targets have been substantially met. Sometimes additional time is needed to reach a channel line or achieve a stronger kinship with the other correction in an impulse. As the consolidation continues, the attendant psychology and fundamentals extend their trends accordingly.
As this section makes clear, there is a qualitative difference between the series 3 + 4 + 4 + 4, etc., and the series 5 + 4 + 4 + 4, etc. Notice that while an impulse wave has a total count of 5, with extensions leading to 9 or 13 waves, and so on, a corrective wave has a count of 3, with combinations leading to 7 or 11 waves, and so on. The triangle appears to be an exception, although it can be counted as one would a triple three, totaling 11 waves. Thus, if an internal count is unclear, you can sometimes reach a reasonable conclusion merely by counting waves. A count of 9, 13 or 17 with few overlaps, for instance, is likely motive, while a count of 7, 11 or 15 with numerous overlaps is likely corrective. The main exceptions are diagonals of both types, which are hybrids of motive and corrective forces.
Orthodox Tops and Bottoms
Sometimes a pattern’s end differs from the associated price extreme. In such cases, the end of the pattern is called the “orthodox” top or bottom in order to differentiate it from the actual price high or low that occurs intra-pattern or after the end of the pattern. For example, in Figure 2-11 (see Lesson 2), the end of wave (5) is the orthodox top despite the fact that wave (3) registered a higher price. In Figure 2-10, the end of wave 5 is the orthodox bottom. In Figures 3-12 and 3-13, the starting point of wave A is the orthodox top of the preceding bull market despite the higher high of wave B. In Figures 3-14 and 3-15, the start of wave A is the orthodox bottom. In Figure 3-26, the end of wave Y is the orthodox bottom of the bear market even though the price low occurs at the end of wave W.
This concept is important primarily because a successful analysis always depends upon a proper labeling of the patterns. Assuming falsely that a particular price extreme is the correct starting point for wave labeling can throw analysis off for some time, while being aware of the requirements of wave form will keep you on track. Further, when applying forecasting concepts, the length and duration of a wave are typically determined by measuring from and projecting orthodox ending points.
Reconciling Function and Mode
Earlier in this course, we described the two functions waves may perform (action and reaction), as well as the two modes of structural development (motive and corrective) that they undergo. Now that we have reviewed all types of waves, we can summarize their labels as follows:
— The labels for actionary waves are 1, 3, 5, A, C, E, W, Y and Z.
— The labels for reactionary waves are 2, 4, B, D and X.
As stated earlier, all reactionary waves develop in corrective mode, and most actionary waves develop in motive mode. The preceding sections have described which actionary waves develop in corrective mode. They are:
— waves 1, 3 and 5 in an ending diagonal,
— wave A in a flat correction,
— waves A, C and E in a triangle,
— waves W and Y in a double zigzag and a double three,
— wave Z in a triple zigzag and a triple three.
Because the waves listed above are actionary in relative direction yet develop in corrective mode, we term them “actionary corrective” waves.
Lesson 4 – Rules Review
[We’ve reprinted some of the material from Lesson 2 here, as it serves as an important review of the rules at this juncture in the course]
Elliott noted three consistent aspects of the five-wave form. They are: Wave 2 never moves beyond the start of wave 1; wave 3 is never the shortest wave; wave 4 never enters the price territory of wave 1.
The most common motive wave is an impulse, per Figure 4-1 (reprinted from Lesson 1). In an impulse, wave 4 does not enter the price territory of (i.e., “overlap”) wave 1. This rule holds for all non-leveraged “cash” markets. Futures markets, with their extreme leverage, can induce short term price extremes that would not occur in cash markets. Even so, overlapping is usually confined to daily and intraday price fluctuations and even then is rare. In addition, the actionary subwaves (1, 3 and 5) of an impulse are themselves motive, and subwave 3 is always an impulse. Figures 1-2, 1-3 and 1-4 (see Lesson 1) all depict impulses in the 1, 3, 5, A and C wave positions.
[There] are only a few simple rules for interpreting impulses properly. A rule is so called because it governs all waves to which it applies. Typical, yet not inevitable, characteristics of waves are called guidelines. Guidelines of impulse formation, including extension, truncation, alternation, equality, channeling, personality and ratio relationships are discussed below and throughout the course material. A rule should never be disregarded. In many years of practice with countless patterns, the authors have found but one or two instances above Subminuette degree when all other rules and guidelines combined to suggest that a rule was broken. Analysts who routinely break any of the rules detailed in this section are practicing some form of analysis other than that guided by the Wave Principle. These rules have great practical utility in correct counting, which we explored further in discussing extensions. In the stock market, the most commonly extended wave is wave 3. This fact is of particular importance to real-time wave interpretation when considered in conjunction with two of the rules of impulse waves: Wave 3 is never the shortest actionary wave, and wave 4 may not overlap wave 1. To clarify, let us assume two situations involving an improper middle wave, as illustrated in Figures 4-2 and 4-3.
In Figure 4-2, wave 4 overlaps the top of wave 1. In Figure 4-3, wave 3 is shorter than wave 1 and shorter than wave 5. According to the rules, neither is an acceptable labeling. Once the apparent wave 3 is proved unacceptable, it must be relabeled in some way that is acceptable. In fact, it is almost always to be labeled as shown in Figure 4-4, implying an extended wave (3) in the making. Do not hesitate to get into the habit of labeling the early stages of a third wave extension. The exercise will prove highly rewarding, as you will understand from the discussion in Lesson 6 — Wave Personality. Figure 4-4 is perhaps the single most useful guide to real time impulse wave counting in this book.
The overall appearance of a wave must conform to the appropriate illustration. Although any five-wave sequence can be forced into a three-wave count by labeling the first three subdivisions as a single wave A, as shown in Figure 4-5, it is incorrect to do so. Elliott analysis would lose its anchor if such contortions were allowed. If wave four terminates well above the top of wave one, a five-wave sequence must be classified as an impulse. Since wave A in this hypothetical case is composed of three waves, wave B would be expected to drop to about the start of wave A, as in a flat correction, which it clearly does not. While the internal count of a wave is a guide to its classification, the right overall shape is, in turn, often a guide to its correct internal count.
GUIDELINES – VOLUME
Waves < Primary Degree
Normally, 3rd wave volume > 5th wave volume
5th wave volume ≥ 3rd wave volume = 5th wave extension
Waves ≥ Primary Degree
Higher Volume in 5th wave
All-time high volume at terminal points in bull markets
- Volume often spikes briefly at the throw-over point of a parallel trend channel line or a diagonal triangle resistance line
- Volume contracts in corrective waves
Guidelines of Wave Formation
The guidelines presented here are discussed and illustrated in the context of a bull market. Except where specifically excluded, they apply equally in bear markets, in which context the illustrations and implications would be inverted.
The guideline of alternation is very broad in its application and warns the analyst always to expect a difference in the next expression of a similar wave. Hamilton Bolton said,
The writer is not convinced that alternation is inevitable in types of waves in larger formations, but there are frequent enough cases to suggest that one should look for it rather than the contrary.
Although alternation does not say precisely what is going to happen, it gives valuable notice of what not to expect and is therefore useful to keep in mind when analyzing wave formations and assessing future probabilities. It primarily instructs the analyst not to assume, as most people tend to do, that because the last market cycle behaved in a certain manner, this one is sure to be the same. As “contrarians” never cease to point out, the day that most investors “catch on” to an apparent habit of the market is the day it will change to one completely different. However, Elliott went further in stating that, in fact, alternation was virtually a law of markets.
Alternation Within An Impulse
If wave two of an impulse is a sharp correction, expect wave four to be a sideways correction, and vice versa. Figure 5-1 shows the most characteristic breakdowns of an impulse wave, either up or down, as suggested by the guideline of alternation.
Sharp corrections never include a new price extreme, i.e., one that lies beyond the orthodox end of the preceding impulse wave. They are almost always zigzags (single, double or triple); occasionally they are double threes that begin with a zigzag.
Sideways corrections include flats, triangles, and double and triple corrections. They usually include a new price extreme, i.e., one that lies beyond the orthodox end of the preceding impulse wave. In rare cases, a regular triangle (one that does not include a new price extreme) in the fourth wave position will take the place of a sharp correction and alternate with another type of sideways pattern in the second wave position.
The idea of alternation within an impulse can be summarized by saying that one of the two corrective processes will contain a move back to or beyond the end of the preceding impulse, and the other will not.
A diagonal does not display alternation between subwaves 2 and 4. Typically both corrections are zigzags.
An extension is an expression of alternation, as the motive waves alternate their lengths. Typically the first is short, the third is extended, and the fifth is short again. An extension, which normally occurs as wave 3, sometimes occurs as wave 1 or 5, another manifestation of alternation.
Alternation Within Corrective Waves
If a correction begins with a flat a-b-c construction for wave A, expect a zigzag a-b-c formation for wave B, and vice versa (see Figures 5-2 and 5-3). With a moment’s thought, it is obvious that this occurrence is sensible, since the first illustration reflects an upward bias in both subwaves while the second reflects a downward bias.
Quite often, when a large correction begins with a simple a-b-c zigzag for wave A, wave B will stretch out into a more intricately subdivided a-b-c zigzag to achieve a type of alternation, as in Figure 5-4. Sometimes wave C will be yet more complex, as in Figure 5-5. The reverse order of complexity is somewhat less common.
Depth of Corrective Waves
No market approach other than the Wave Principle gives a satisfactory answer to the question, “How far down can a bear market be expected to go?” The primary guideline is that corrections, especially when they themselves are fourth waves, tend to register their maximum retracement within the span of travel of the previous fourth wave of one lesser degree, most commonly near the level of its terminus.
Example #1: The 1929-1932 Bear Market
Our analysis of the period from 1789 to 1932 uses the chart of stock prices adjusted to constant dollars developed by Gertrude Shirk and presented in the January 1977 issue of Cycles magazine. Here we find that the 1932 Supercycle low bottomed within the area of the previous fourth wave of Cycle degree, an expanding triangle spanning the period between 1890 and 1921. (See Figure 5-6.)
Example #2: The 1942 Bear Market Low
In this case, the Cycle degree bear market from 1937 to 1942 was a zigzag that terminated within the area of the fourth Primary wave of the bull market from 1932 to 1937. (See Figure 5-7.)
Example #3: The 1962 Bear Market Low
The wave ④ plunge in 1962 brought the averages down to just above the 1956 high of the five-wave Primary sequence from 1949 to 1959. Ordinarily, the bear would have reached into the zone of wave (4), the fourth wave correction within wave ③. This narrow miss nevertheless illustrates why this guideline is not a rule. The preceding strong third wave extension and the shallow A wave and strong B wave within (4) indicated strength in the wave structure, which carried over into the moderate net depth of the correction.(See Figure 5-7.)
Example #4: The 1974 Bear Market Low
The final decline into 1974, ending the 1966-1974 Cycle degree wave IV correction of the entire wave III rise from 1942, brought the averages down to the area of the previous fourth wave of lesser degree (Primary wave ④). Again, Figure 5-7 shows what happened.
Example #5: London Gold Bear Market, 1974-1976
Here we have an illustration from another market of the tendency for a correction to terminate in the area of travel of the preceding fourth wave of one lesser degree.(See Figure 5-8.)
Our analysis of small degree wave sequences over the last twenty years further validates the proposition that the usual limitation of any bear market is the travel area of the preceding fourth wave of one lesser degree, particularly when the bear market in question is itself a fourth wave. However, in a clearly reasonable modification of the guideline, it is often the case that if the first wave in a sequence extends, the correction following the fifth wave will have as a typical limit the bottom of the second wave of lesser degree. For example, the decline into March 1978 in the DJIA bottomed exactly at the low of the second wave in March 1975, which followed an extended first wave off the December 1974 low.
On occasion, a flat correction or triangle, particularly if it follows an extension, will fail, usually by a slim margin, to reach into the fourth wave area. A zigzag, on occasion, will cut deeply and move down into the area of the second wave of lesser degree, although this almost exclusively occurs when the zigzag is itself a second wave. “Double bottoms” are sometimes formed in this manner.
Behavior Following Fifth Wave Extensions
Having cumulatively observed the hourly changes in the DJIA for over twenty years, the authors are convinced that Elliott imprecisely stated some of his findings with respect to both the occurrence of extensions and the market action following an extension. The most important empirically derived rule that can be distilled from our observations of market behavior is that when the fifth wave of an advance is an extension, the ensuing correction will be sharp and find support at the level of the low of wave two of the extension. Sometimes the correction ends there, as illustrated in Figure 5-9, and sometimes only wave A ends there. Although a limited number of real life examples exist, the precision with which A waves have reversed at this level is remarkable. Figure 5-10 is an illustration showing both a zigzag and an expanded flat correction. An example involving a zigzag can be found in Figure 5-7 at the low of wave Ⓐ of II and an example involving an expanded flat can be found in Figure 5-11 at the low of wave a of A of 4. As you may be able to discern in Figure 5-7, wave a of (IV) bottoms near wave (2) of ⑤, which is an extension within the wave V from 1921 to 1929.
Since the low of the second wave of an extension is commonly in or near the price territory of the immediately preceding fourth wave of one larger degree, this guideline implies behavior similar to that of the preceding guideline. It is notable for its precision, however. Additional value is provided by the fact that fifth wave extensions are typically followed by swift retracements. Their occurrence, then, is an advance warning of a dramatic reversal to a specific level, a powerful combination of knowledge. This guideline need not apply when the market is ending a fifth wave at more than one degree, yet the action in Figure 5-7 (see above reference) suggests that we should still view this level as at least potential or temporary support.
One of the guidelines of the Wave Principle is that two of the motive waves in a five-wave sequence will tend toward equality in time and magnitude. This is generally true of the two non-extended waves when one wave is an extension, and it is especially true if the third wave is the extension. If perfect equality is lacking, a .618 multiple is the next likely relationship (see Lesson 7: Fibonacci).
When waves are larger than Intermediate degree, the price relationships usually must be stated in percentage terms. When waves are of Intermediate degree or below, the price equality can usually be stated in arithmetic terms, since the percentage lengths will also be nearly equivalent. The guideline of equality is often extremely accurate.
Charting the Waves
The foremost aim of wave classification is to determine where prices are in the stock market’s progression. This exercise is easy as long as the wave counts are clear, as in fast-moving, emotional markets, particularly in impulse waves, when minor movements generally unfold in an uncomplicated manner. In these cases, short term charting is necessary to view all subdivisions. However, in lethargic or choppy markets, particularly in corrections, wave structures are more likely to be complex and slow to develop. In these cases, a longer term chart often effectively condenses the action into a form that clarifies the pattern in progress. With a proper reading of the Wave Principle, there are times when a sideways trend can be forecasted (for instance, for a fourth wave when wave two is a zigzag). Even when anticipated, though, complexity and lethargy are two of the most frustrating occurrences for the analyst. Nevertheless, they are part of the reality of the market and must be taken into account. The authors highly recommend that during such periods you take some time off from the market to enjoy the profits made during the rapidly unfolding impulse waves. You can’t “wish” the market into action; it isn’t listening. When the market rests, do the same.
The correct method for tracking the stock market is to use semilogarithmic chart paper, since the market’s history is sensibly related only on a percentage basis. The investor is concerned with percentage gain or loss, not the number of points traveled in a market average. For instance, ten points in the DJIA in 1980 meant a one percent move. In the early 1920s, ten points meant a ten percent move, quite a bit more important. For ease of charting, however, we suggest using semilog scale only for long term plots, where the difference is especially noticeable. Arithmetic scale is quite acceptable for tracking hourly waves since a 40 point rally with the DJIA at 800 is not much different in percentage terms from a 40 point rally with the DJIA at 900. Thus, channeling techniques work acceptably well on arithmetic scale with shorter term moves.
…[T]he question of whether to expect a parallel channel on arithmetic or semilog scale is still unresolved as far as developing a tenet on the subject. If the price development at any point does not fall neatly within two parallel lines on the scale you are using, switch to the other scale in order to observe the channel in correct perspective. To stay on top of all developments, you should always use both.
Elliott noted that a parallel trend channel typically marks the upper and lower boundaries of an impulse wave, often with dramatic precision. You should draw one as early as possible to assist in determining wave targets and provide clues to the future development of trends.
The initial channeling technique for an impulse requires at least three reference points. When wave three ends, connect the points labeled 1 and 3, then draw a parallel line touching the point labeled 2. This construction provides an estimated boundary for wave four. (In most cases, third waves travel far enough that the starting point is excluded from the final channel’s touch points.)
If the fourth wave ends at a point not touching the parallel, you must reconstruct the channel in order to estimate the boundary for wave five. First connect the ends of waves two and four. If waves one and three are normal, the upper parallel most accurately forecasts the end of wave five when drawn touching the peak of wave three, as in Figure 5-12. If wave three is abnormally strong, almost vertical, then a parallel drawn from its top may be too high. Experience has shown that a parallel to the baseline that touches the top of wave one is then more useful, as in our depiction of gold bullion from August 1976 to March 1977. In some cases, it may be useful to draw both potential upper boundary lines to alert you to be especially attentive to the wave count and volume characteristics at those levels and then take appropriate action as the wave count warrants.
Always remember that all degrees of trend are operating at the same time. Sometimes, for instance, a fifth wave of Intermediate degree within a fifth wave of Primary degree will end when it reaches the upper channel lines at both degrees simultaneously. Or sometimes a throw-over at Supercycle degree will terminate precisely when prices reach the upper line of the channel at Cycle degree.
Zigzag corrections often form channels with four touch points. One line connects the starting point of wave A and then end of wave B; the other line touches the end of wave A and end of wave C. Once the former line is established, a parallel line drawn from the end of wave A is an excellent tool for recognizing the exact end of the entire correction.
Within a parallel channel or the converging lines of a diagonal, if a fifth wave approaches its upper trendline on declining volume, it is an indication that the end of the wave will meet or fall short of it. If volume is heavy as the fifth wave approaches its upper trendline, it indicates a possible penetration of the upper line, which Elliott called a “throw-over.” Near the point of throw-over, a fourth wave of small degree may trend sideways immediately below the parallel, allowing the fifth then to break it in a final burst of volume.
A throw-over is occasionally telegraphed by a preceding “throw-under,” either by wave 4 or by wave two of 5, as suggested by Figure 5-13. A throw-over is confirmed by an immediate reversal back below the line. A throw-over can also occur, with the same characteristics, in a declining market. Elliott correctly warned that a throw-over at large degree causes difficulty in identifying the waves of smaller degree during the throw-over, as smaller degree channels are sometimes penetrated on the upside during the final fifth wave. Figures 2-14, 2-16 (see Lesson 2) and Figure 5-14 show real-life examples of throw-overs.
Elliott used volume as a tool for verifying wave counts and in projecting extensions. He recognized that in a bull market, volume has a natural tendency to expand and contract with the speed of price change. Late in a corrective phase, a decline in volume often indicates a decline in selling pressure. A low point in volume often coincides with a turning point in the market. In a normal fifth wave below Primary degree : , volume tends to be less than in the third wave. If volume in an advancing fifth wave of less than Primary degree is equal to or greater than that in the third wave, an extension of the fifth is in force. While this outcome is often to be expected anyway if the first and third waves are about equal in length, it is an excellent warning of those rare times when both a third and a fifth wave are extended.
(Extension in 5th wave : volume w5=< volume w3 , and length w1=w3)
At Primary degree and greater, volume tends to be higher in an advancing fifth wave merely because of the natural long term growth in the number of participants in bull markets. Elliott noted, in fact, that volume at the terminal point of a bull market above Primary degree tends to run at an all-time high. Finally, as discussed earlier, volume often spikes briefly at the throw-over point of a parallel trend channel line or the resistance line of a diagonal. (Upon occasion, such a point can occur simultaneously, as when a diagonal fifth wave terminates right at the upper parallel of the channel containing the price action of one larger degree.)
To the extent that volume guides wave counting or expectations, it is most significant. Elliott once said that volume independently follows the patterns of the Wave Principle, a claim for which the authors find no convincing evidence.
The “Right Look”
The overall appearance of a wave must conform to the appropriate illustration. Although any five-wave sequence can be forced into a three-wave count by labeling the first three subdivisions as a single wave A, as shown in Figure 5-15, it is incorrect to do so. Elliott analysis would lose its anchor if such contortions were allowed. If wave four terminates well above the top of wave one, a five-wave sequence must be classified as an impulse. Since wave A in this hypothetical case is composed of three waves, wave B would be expected to drop to about the start of wave A, as in a flat correction, which it clearly does not. While the internal count of a wave is a guide to its classification, the right overall shape is, in turn, often a guide to its correct internal count.
The “right look” of a wave is dictated by all the considerations we have outlined so far. In our experience, we have found it extremely dangerous to allow our emotional involvement with the market to let us accept a wave count that reflects disproportionate wave relationships or a misshapen pattern merely on the basis that the Wave Principle’s patterns are somewhat elastic.
Elliott cautioned that “the right look” may not be evident at all degrees of trend simultaneously. The solution is to focus on the degrees that are clearest. If the hourly chart is confusing, step back and look at the daily or weekly chart. Conversely, if the weekly chart offers too many possibilities, concentrate on the shorter term movements until the bigger picture clarifies. Generally speaking, you need short term charts to analyze subdivisions in fast moving markets and long term charts for slowly moving markets.
There are exceptions to guidelines, but without those, market analysis would be a science of exactitude, not one of probability. Nevertheless, with a thorough knowledge of the guidelines of wave structure, you can be quite confident of your wave count. In effect, you can use the market action to confirm the wave count as well as use the wave count to predict market action.
Notice also that Elliott wave guidelines cover most aspects of traditional technical analysis, such as market momentum and investor sentiment. The result is that traditional technical analysis now has a greatly increased value in that it serves to aid the identification of the market’s position in the Elliott wave structure. To that end, using such tools is by all means encouraged.
LESSON 6 WAVE Personality
The idea of wave personality is a substantial expansion of the Wave Principle. It has the advantage of bringing human behavior more personally into the equation.
The personality of each wave in the Elliott sequence
- is an integral part of the reflection of the mass psychology it embodies.
- The progression of mass emotions from pessimism to optimism and back again tends to follow a similar path each time around, producing similar circumstances at corresponding points in the wave structure.
As the Wave Principle indicates, market history repeats but not exactly.
Every wave has :
siblings (same-directional waves of the same degree within a larger wave) and
cousins (same-degree and same-numbered waves within different larger waves) but
no wave has a twin.
Related waves — particularly cousins — have similar market and social characteristics. The personality of each wave type is manifest whether the wave is of Grand Supercycle degree or Subminuette. Waves’ properties not only forewarn what to expect in the next sequence but at times can help determine the market’s present location in the progression of waves, when for other reasons the count is unclear or open to differing interpretations. As waves are in the process of unfolding, there are times when several different wave counts are perfectly admissible under all known Elliott rules. It is at these junctures that a knowledge of wave personality can be invaluable. Recognizing the character of a single wave can often allow you to interpret correctly the complexities of the larger pattern. The following discussions relate to an underlying bull market picture, as illustrated in Figures 6-1 and 6-2. These observations apply in reverse when the actionary waves are downward and the reactionary waves are upward.
1) First waves — As a rough estimate, about half of first waves are part of the “basing” process and thus tend to be heavily corrected by wave two. In contrast to the bear market rallies within the previous decline, however, this first wave rise is technically more constructive, often displaying a subtle increase in volume and breadth. Plenty of short selling is in evidence as the majority has finally become convinced that the overall trend is down. Investors have finally gotten “one more rally to sell on,” and they take advantage of it. The other fifty percent of first waves rise from either large bases formed by the previous correction, as in 1949, from downside failures, as in 1962, or from extreme compression, as in both 1962 and 1974. From such beginnings, first waves are dynamic and only moderately retraced.
2) Second waves — Second waves often retrace so much of wave one that most of the profits gained up to that time are eroded away by the time it ends. This is especially true of call option purchases, as premiums sink drastically in the environment of fear during second waves. At this point, investors are thoroughly convinced that the bear market is back to stay. Second waves often end on very low volume and volatility, indicating a drying up of selling pressure.
3) Third waves — Third waves are wonders to behold. They are strong and broad, and the trend at this point is unmistakable. Increasingly favorable fundamentals enter the picture as confidence returns. Third waves usually generate the greatest volume and price movement and are most often the extended wave in a series. It follows, of course, that the third wave of a third wave, and so on, will be the most volatile point of strength in any wave sequence. Such points invariably produce breakouts, “continuation” gaps, volume expansions, exceptional breadth, major Dow Theory trend confirmations and runaway price movement, creating large hourly, daily, weekly, monthly or yearly gains in the market, depending on the degree of the wave. Virtually all stocks participate in third waves. Besides the personality of B waves, that of third waves produces the most valuable clues to the wave count as it unfolds.
4) Fourth waves — Fourth waves are predictable in both depth and form, because by alternation they should differ from the previous second wave of the same degree. More often than not they trend sideways, building the base for the final fifth wave move. Lagging stocks build their tops and begin declining during this wave, since only the strength of a third wave was able to generate any motion in them in the first place. This initial deterioration in the market sets the stage for non-confirmations and subtle signs of weakness during the fifth wave.
5) Fifth waves — Fifth waves in stocks are always less dynamic than third waves in terms of breadth. They usually display a slower maximum speed of price change as well, although if a fifth wave is an extension, speed of price change in the third of the fifth can exceed that of the third wave. Similarly, while it is common for volume to increase through successive impulse waves at Cycle degree or larger, it usually happens in a fifth wave below Primary degree only if the fifth wave extends. Otherwise, look for lesser volume as a rule in a fifth wave as opposed to the third. Market dabblers sometimes call for “blowoffs” at the end of long trends, but the stock market has no history of reaching maximum acceleration at a peak. Even if a fifth wave extends, the fifth of the fifth will lack the dynamism that preceded it. During advancing fifth waves, optimism runs extremely high despite a narrowing of breadth. Nevertheless, market action does improve relative to prior corrective wave rallies. For example, the year-end rally in 1976 was unexciting in the Dow, but it was nevertheless a motive wave as opposed to the preceding corrective wave advances in April, July and September, which, by contrast, had even less influence on the secondary indexes and the cumulative advance-decline line. As a monument to the optimism that fifth waves can produce, the advisory services polled two weeks after the conclusion of that rally turned in the lowest percentage of “bears,” 4.5%, in the history of the recorded figures despite that fifth wave’s failure to make a new high!
6) A waves — During the A wave of a bear market, the investment world is generally convinced that this reaction is just a pullback pursuant to the next leg of advance. The public surges to the buy side despite the first really technically damaging cracks in individual stock patterns. The A wave sets the tone for the B wave to follow. A five-wave A indicates a zigzag for wave B, while a three-wave A indicates a flat or triangle.
7) B waves — B waves are phonies. They are sucker plays, bull traps, speculators’ paradise, orgies of odd-lotter mentality or expressions of dumb institutional complacency (or both). They often involve a focus on a narrow list of stocks, are often “unconfirmed” by other averages, are rarely technically strong, and are virtually always doomed to complete retracement by wave C. If the analyst can easily say to himself, “There is something wrong with this market,” chances are it’s a B wave. X waves and D waves in expanding triangles, both of which are corrective wave advances, have the same characteristics. Several examples will suffice to illustrate the point.
— The upward correction of 1930 was wave B within the 1929-1932 A-B-C zigzag decline. Robert Rhea describes the emotional climate well in his opus, The Story of the Averages (1934):
…many observers took it to be a bull market signal. I can remember having shorted stocks early in December, 1929, after having completed a satisfactory short position in October. When the slow but steady advance of January and February carried above [the previous high], I became panicky and covered at considerable loss. …I forgot that the rally might normally be expected to retrace possibly 66 percent or more of the 1929 downswing. Nearly everyone was proclaiming a new bull market. Services were extremely bullish, and the upside volume was running higher than at the peak in 1929.
— The 1961-1962 rise was wave (b) in an (a)-(b)-(c) expanded flat correction. At the top in early 1962, stocks were selling at unheard of price/earnings multiples that had not been seen up to that time and have not been seen since. Cumulative breadth had already peaked along with the top of the third wave in 1959.
— The rise from 1966 to 1968 was wave Ⓑ in a corrective pattern of Cycle degree. Emotionalism had gripped the public and “cheapies” were skyrocketing in the speculative fever, unlike the orderly and usually fundamentally justifiable participation of the secondaries within first and third waves. The Dow Industrials struggled unconvincingly upward throughout the advance and finally refused to confirm the phenomenal new highs in the secondary indexes.
— In 1977, the Dow Jones Transportation Average climbed to new highs in a B wave, miserably unconfirmed by the Industrials. Airlines and truckers were sluggish. Only the coal-carrying rails were participating as part of the energy play. Thus, breadth within the index was conspicuously lacking, confirming again that good breadth is generally a property of impulse waves, not corrections.
As a general observation, B waves of Intermediate degree and lower usually show a diminution of volume, while B waves of Primary degree and greater can display volume heavier than that which accompanied the preceding bull market, usually indicating wide public participation.
8) C waves — Declining C waves are usually devastating in their destruction. They are third waves and have most of the properties of third waves. It is during these declines that there is virtually no place to hide except cash. The illusions held throughout waves A and B tend to evaporate and fear takes over. C waves are persistent and broad. 1930-1932 was a C wave. 1962 was a C wave. 1969-1970 and 1973-1974 can be classified as C waves. Advancing C waves within upward corrections in larger bear markets are just as dynamic and can be mistaken for the start of a new upswing, especially since they unfold in five waves. The October 1973 rally in the DJIA, for instance, was a C wave in an inverted expanded flat correction.
9) D waves — D waves in all but expanding triangles are often accompanied by increased volume. This is true probably because D waves in non-expanding triangles are hybrids, part corrective, yet having some characteristics of first waves since they follow C waves and are not fully retraced. D waves, being advances within corrective waves, are as phony as B waves. The rise from 1970 to 1973 was wave Ⓓ within the large wave IV of Cycle degree. The “one-decision” complacency that characterized the attitude of the average institutional fund manager at the time is well documented. The area of participation again was narrow, this time the “nifty fifty” growth and glamour issues. Breadth, as well as the Transportation Average, topped early, in 1972, and refused to confirm the extremely high multiples bestowed upon the favorite fifty. Washington was inflating at full steam to sustain the illusory prosperity during the entire advance in preparation for the presidential election. As with the preceding wave Ⓑ, “phony” was an apt description.
10) E waves — E waves in triangles appear to most market observers to be the dramatic kickoff of a new downtrend after a top has been built. They almost always are accompanied by strongly supportive news. That, in conjunction with the tendency of E waves to stage a false breakdown through the triangle boundary line, intensifies the bearish conviction of market participants at precisely the time that they should be preparing for a substantial move in the opposite direction. Thus, E waves, being ending waves, are attended by a psychology as emotional as that of fifth waves.
Lesson 7 – Fibonacci
Historical and Mathematical Background of the Wave Principle
The Fibonacci (pronounced fib-eh-nah´-chee) sequence of numbers was discovered (actually rediscovered) by Leonardo Fibonacci da Pisa, a thirteenth century mathematician.
The Fibonacci Sequence
The sum of any two adjacent numbers in the sequence forms the next higher number in the sequence, viz., 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, and so on to infinity.
The Golden Ratio
After the first several numbers in the sequence, the ratio of any number to the next higher is approximately .618 to 1 and to the next lower number approximately 1.618 to 1. The further along the sequence, the closer the ratio approaches phi (denoted ϕ) which is an irrational number, .618034…. Between alternate numbers in the sequence, the ratio is approximately .382, whose inverse is 2.618. Refer to Figure 7-1 for a ratio table interlocking all Fibonacci numbers from 1 to 144.
Phi is the only number that when added to 1 yields its inverse: 1 + .618 = 1 ÷ .618.
1.618 (or .618) is known as the Golden Ratio or Golden Mean. Its proportions are pleasing to the eye and ear. It appears throughout biology, music, art and architecture. William Hoffer, writing for the December 1975 Smithsonian Magazine, said:
…the proportion of .618034 to 1 is the mathematical basis for the shape of playing cards and the Parthenon, sunflowers and snail shells, Greek vases and the spiral galaxies of outer space. The Greeks based much of their art and architecture upon this proportion. They called it “the golden mean.”
The continual occurrence of Fibonacci numbers and the golden spiral in nature explains precisely why the proportion of .618034 to 1 is so pleasing in art. Man can see the image of life in art that is based on the golden mean.
Nature uses the Golden Ratio in its most intimate building blocks and in its most advanced patterns, in forms as minuscule as microtubules in the brain and the DNA molecule to those as large as planetary distances and periods. It is involved in such diverse phenomena as quasi crystal arrangements, reflections of light beams on glass, the brain and nervous system, musical arrangement, and the structures of plants and animals. Science is rapidly demonstrating that there is indeed a basic proportional principle of nature. By the way, you are holding this book with two of your five appendages, which have three jointed parts, five digits at the end, and three jointed sections to each digit, a 5-3-5-3 progression that mightily suggests the Wave Principle.
Fibonacci in the Spiraling Stock Market
Can we both theorize and observe that the stock market operates on the same mathematical basis as so many natural phenomena? The answer is yes. As Elliott explained in his final unifying conclusion, the progress of waves has the same mathematical base. The Fibonacci sequence governs the numbers of waves that form in the movement of aggregate stock prices, in an expansion upon the underlying 5:3 relationship described at the beginning of the course material.
As we first showed in Figure 1-4 (see Lesson 1), the essential structure of the market generates the complete Fibonacci sequence. The simplest expression of a correction is a straight-line decline. The simplest expression of an impulse is a straight-line advance. A complete cycle is two lines. In the next degree of complexity, the corresponding numbers are 3, 5 and 8. As illustrated in Figure 7-2, this sequence can be taken to infinity. The fact that waves produce the Fibonacci sequence of numbers reveals that man’s collectively expressed emotions are keyed to this mathematical law of nature.
Phi and the Additive Growth
Market action is governed by the Golden Ratio. Even Fibonacci numbers appear in market statistics more often than mere chance would allow. However, it is crucial to understand that while the numbers themselves do have theoretic weight in the grand concept of the Wave Principle, it is the ratio that is the fundamental key to growth patterns of this type.
In its broadest sense, the Wave Principle suggests the idea that the same law that shapes living creatures and galaxies is inherent in the spirit and activities of men en masse.
- Because the stock market is the most meticulously tabulated reflector of mass psychology in the world, its data produce an excellent recording of man’s social psychological states and trends.
- This record of the fluctuating self-evaluation of social man’s own productive enterprise makes manifest specific patterns of progress and regress.
What the Wave Principle says is that mankind’s progress (of which the stock market is a popularly determined valuation) does not occur in a straight line, does not occur randomly, and does not occur cyclically. Rather, progress takes place in a “three steps forward, two steps back” fashion, a form that nature prefers. More grandly, as the activity of social man is linked to the Fibonacci sequence and the spiral pattern of progression, it is apparently no exception to the general law of ordered growth in the universe. In our opinion, the parallels between the Wave Principle and other natural phenomena are too great to be dismissed as just so much nonsense. On the balance of probabilities, we have come to the conclusion that there is a principle, everywhere present, giving shape to social affairs, and that Einstein knew what he was talking about when he said, “God does not play dice with the universe.” The stock market is no exception, as mass behavior is undeniably linked to a law that can be studied and defined. The briefest way to express this principle is a simple mathematical statement: the 1.618 ratio.
The Desiderata, by poet Max Ehrmann, reads, “You are a child of the Universe, no less than the trees and the stars; you have a right to be here. And whether or not it is clear to you, no doubt the Universe is unfolding as it should.” Order in life? Yes. Order in the stock market? Apparently.
Ratio Analysis and Fibonacci Time Sequences
Ratio analysis is the assessment of the proportionate relationship, in time and amplitude, of one wave to another. In discerning the working of the Golden Ratio in the five up and three down movement of the stock market cycle, one might anticipate that on completion of any bull phase, the ensuing correction would be three-fifths of the previous rise in both time and amplitude. Such simplicity is seldom seen. However, the underlying tendency of the market to conform to relationships suggested by the Golden Ratio is always present and helps generate the right look for each wave.
Ratio analysis has revealed a number of precise price relationships that occur often among waves. There are two categories of relationships: retracements and multiples.
Occasionally, a correction retraces a Fibonacci percentage of the preceding wave. As illustrated in Figure 7-4, sharp corrections tend more often to retrace 61.8% or 50% of the previous wave, particularly when they occur as wave 2 of an impulse, wave B of a larger zigzag, or wave X in a multiple zigzag. A leading diagonal in the wave one position is typically followed by a zigzag retracement of 78.6% (√ϕ). Sideways corrections tend more often to retrace 38.2% of the previous impulse wave, particularly when they occur as wave 4, as shown in Figure 7-5.
Retracements come in all sizes. The ratios shown in Figures 7-4 and 7-5 are merely tendencies. Unfortunately, that is where most analysts place an inordinate focus because measuring retracements is easy. Far more precise and reliable, however, are relationships between alternate waves, or lengths unfolding in the same direction, as explained in the next section.
Motive Wave Multiples
When wave 3 is extended, waves 1 and 5 tend towards equality or a .618 relationship, as illustrated in Figure 7-6. Actually, all three motive waves tend to be related by Fibonacci mathematics, whether by equality, 1.618 or 2.618 (whose inverses are .618 and .382). These impulse wave relationships usually occur in percentage terms. For instance, wave I from 1932 to 1937 gained 371.6%, while wave III from 1942 to 1966 gained 971.7%, or 2.618 times as much. Semilog scale is required to reveal these relationships. Of course, at small degrees, arithmetic and percentage scales produce essentially the same result, so that the number of points in each impulse wave reveals the same multiples.
Another typical development is that wave 5’s length is sometimes related by the Fibonacci ratio to the length of wave 1 through wave 3, as illustrated in Figure 7-7, showing an extended fifth wave. .382 and .618 relationships occur when wave five is not extended. In those rare cases when wave 1 is extended, it is wave 2, quite reasonably, that often subdivides the entire impulse wave into the Golden Section, as shown in Figure 7-8.
Here is a generalization that subsumes some of the observations we have already made: Unless wave 1 is extended, wave 4 often divides the price range of an impulse wave into the Golden Section. In such cases, the latter portion is .382 of the total distance when wave 5 is not extended, as shown in Figure 7-9, and .618 when it is, as shown in Figure 7-10. This guideline is somewhat loose in that the exact point within wave 4 that affects the subdivision varies. It can be its start, end or extreme countertrend point. Thus, it provides, depending on the circumstances, two or three closely clustered targets for the end of wave 5. This guideline explains why the target for a retracement following a fifth wave often is doubly indicated both by the end of the preceding fourth wave and the .382 retracement point.
Corrective Wave Multiples
In a zigzag, the length of wave C is usually equal to that of wave A, as shown in Figure 7-11, although it is not uncommonly 1.618 or .618 times the length of wave A. This same relationship applies to a second zigzag relative to the first in a double zigzag pattern, as shown in Figure 7-12.
In a regular flat correction, waves A, B and C are, of course, approximately equal, as shown in Figure 7-13.
In an expanded flat correction, wave C is often 1.618 times the length of wave A. Sometimes wave C will terminate beyond the end of wave A by .618 times the length of wave A. Each of these tendencies is illustrated in Figure 7-14.
In rare cases, wave C is 2.618 times the length of wave A. Wave B in an expanded flat is sometimes 1.236 or 1.382 times the length of wave A.
In a triangle, we have found that at least two of the alternate waves are typically related to each other by .618. I.e.,
in a contracting or barrier triangle, wave e = .618c, wave c = .618a, or wave d = .618b, as illustrated in Figure 7-15.
In an expanding triangle, the multiple is 1.618.
In double and triple corrections, the net travel of one simple pattern is sometimes related to another by equality or, particularly if one of the threes is a triangle, by .618.
Finally, wave 4 quite commonly spans a gross and/or net price range that has an equality or Fibonacci relationship to its corresponding wave 2. As with impulse waves, these relationships usually occur in percentage terms.
Multiple Wave Relationships
Keep in mind that all degrees of trend are always operating in the market at the same time. Therefore, at any given moment, the market will be full of Fibonacci ratio relationships, all occurring with respect to the various wave degrees unfolding. It follows that future levels that will create several Fibonacci relationships have a greater likelihood of marking a turn than a level that will create only one.
For instance, if a .618 retracement of Primary wave ① by Primary wave ② gives a particular target, and within it, a 1.618 multiple of Intermediate wave (A) in an irregular correction gives the same target for Intermediate wave (C), and within that, a 1.00 multiple of Minor wave 1 gives the same target yet again for Minor wave 5, then you have a powerful argument for expecting a turn at that calculated price level. Figure 7-16 illustrates this example.
Figure 7-17 is an imaginary rendition of a reasonably ideal Elliott wave, complete with parallel trend channel. It has been created as an example of how ratios are often present throughout the market. In it, the following eight relationships hold:
② = .618 x ① ;
④ = .382 x ③ ;
⑤ = 1.618 x ① ;
⑤ = .618 x Ⓞ → ③ ;
② = .618 x ④;
in ②, (A) = (B) = (C);
in ④, (A) = (C);
in ④, (B) = .382 x (A).
Fibonacci Time Sequences
There is no sure way of using the time factor by itself in forecasting. Elliott said that the time factor often “conforms to the pattern,” for instance with regard to trend channels, and therein lies its primary significance. Frequently, however, durations and time relationships themselves reflect Fibonacci measurements. Exploring Fibonacci numbers of time units appears to go beyond an exercise in numerology, fitting wave spans with remarkable accuracy. They serve to give the analyst added perspective by indicating possible times for a turn, especially if they coincide with price targets and wave counts.
Lesson 8 – Summary
Summary of Additional Technical Aspects
Most motive waves take the form of an impulse, i.e., a five-wave pattern like those shown in Figures 1-1 through 1-4 (see Lesson 1), in which subwave 4 does not overlap subwave 1, and subwave 3 is not the shortest subwave. Impulses are typically bound by parallel lines. One motive wave in an impulse, i.e., 1, 3 or 5, is typically extended, i.e., much longer than the other two. There is a rare motive variation called a diagonal, which is a wedge-shaped pattern that appears at the start (wave 1 or A) or the end (wave 5 or C) of a larger wave.
Corrective waves have numerous variations. The main ones are named zigzag (which is the one shown in Figures 1-2, 1-3 and 1-4), flat and triangle (whose labels include D and E). These three simple corrective patterns can string together to form more complex corrections (the components of which are labeled W, X, Y and Z). In impulses, waves 2 and 4 nearly always alternate in form, where one correction is typically of the zigzag family and the other is not. Each wave exhibits characteristic volume behavior and a “personality” in terms of attendant momentum and investor sentiment.
A Summary of Rules and Guidelines for Waves
From a theoretical standpoint, we must be careful not to confuse Elliott waves with their measures, which are as a thermometer is to heat. A thermometer is not designed to gauge rapid short-term fluctuations in air temperature and neither is an index of 30 stocks constructed so as to be able to record every short-term fluctuation in social mood. While we fully believe that the listed rules govern Elliott waves as a collective mental phenomenon, recordings of actions that Elliott waves induce — such as buying and selling certain lists of stocks — may not perfectly reflect those waves. Therefore recordings of such actions could deviate from a perfect expression of the rules simply because of the imperfection of the chosen gauge. That being said, we have found that the Dow Jones Industrial Average has followed Elliott’s rules impeccably at Minor degree and above and almost always at lesser degrees as well. Below is a summary of the rules and known guidelines (excepting Fibonacci relationships) for the five main wave patterns, variations and combinations.
- An impulse always subdivides into five waves
- Wave 1 always subdivides into an impulse or (rarely) a leading diagonal.
- Wave 3 always subdivides into an impulse
- Wave 5 always subdivides into an impulse or an ending diagonal.
- Wave 2 always subdivides into a zigzag, flat or combination.
- Wave 4 always subdivides into a zigzag, flat, triangle or combination.
- Wave 2 never moves beyond the start of wave 1.
- Wave 3 always moves beyond the end of wave 1.
- Wave 3 is never the shortest wave.
- Wave 4 never moves beyond the end of wave 1.
- Never are waves 1, 3 and 5 all extended.
- Wave 4 will almost always be a different corrective pattern than wave 2.
- Wave 2 is usually a zigzag or zigzag combination.
- Wave 4 is usually a flat, triangle or flat combination.
- Sometimes wave 5 does not move beyond the end of wave 3 (in which case it is called a truncation).
- Wave 5 often ends when meeting or slightly exceeding a line drawn from the end of wave 3 that is parallel to the line connecting the ends of waves 2 and 4, on either arithmetic or semilog scale.
- The center of wave 3 almost always has the steepest slope of any equal period within the parent impulse except that sometimes an early portion of wave 1 (the “kickoff”) will be steeper.
- Wave 1, 3 or 5 is usually extended. (An extension appears “stretched” because its corrective waves are small compared to its impulse waves. It is substantially longer, and contains larger subdivisions, than the non-extended waves).
- Often, the extended subwave is the same number (1, 3 or 5) as the parent wave.
- Rarely do two subwaves extend, although it is typical for waves 3 and 5 both to extend when they are of Cycle or Supercycle degree and within a fifth wave of one degree higher.
- Wave 1 is the least commonly extended wave.
- When wave 3 is extended, waves 1 and 5 tend to have gains related by equality or the Fibonacci ratio.
- When wave 5 is extended, it is often in Fibonacci proportion to the net travel of waves 1 through 3.
- When wave 1 is extended, it is often in Fibonacci proportion to the net travel of waves 3 through 5.
- Wave 4 typically ends when it is within the price range of subwave iv of 3.
- Wave 4 often subdivides the entire impulse into Fibonacci proportion in time and/or price.
- A diagonal always subdivides into five waves.
- An ending diagonal always appears as wave 5 of an impulse or wave C of a zigzag or flat.
- A leading diagonal always appears as wave 1 of an impulse or wave A of a zigzag.
- Waves 1, 2, 3, 4 and 5 of an ending diagonal, and waves 2 and 4 of a leading diagonal, always subdivide into zigzags.
- Wave 2 never goes beyond the start of wave 1.
- Wave 3 always goes beyond the end of wave 1.
- Wave 4 never moves beyond the end of wave 2.
- Wave 4 always ends within the price territory of wave 1.*
- Going forward in time, a line connecting the ends of waves 2 and 4 converges towards (in the contracting variety) or diverges from (in the expanding variety) a line connecting the ends of waves 1 and 3.
- In a leading diagonal, wave 5 always ends beyond the end of wave 3.
- In the contracting variety, wave 3 is always shorter than wave 1, wave 4 is always shorter than wave 2, and wave 5 is always shorter than wave 3.
- In the expanding variety, wave 3 is always longer than wave 1, wave 4 is always longer than wave 2, and wave 5 is always longer than wave 3.
- In the expanding variety, wave 5 always ends beyond the end of wave 3.
- Waves 2 and 4 each usually retrace .66 to .81 of the preceding wave.
- Waves 1, 3 and 5 of a leading diagonal usually subdivide into zigzags but sometimes appear to be impulses.
- Within an impulse, if wave 1 is a diagonal, wave 3 is likely to be extended.
- Within an impulse, wave 5 is unlikely to be a diagonal if wave 3 is not extended.
- In the contracting variety, wave 5 usually ends beyond the end of wave 3. (Failure to do so is called a truncation.)
- In the contracting variety, wave 5 usually ends at or slightly beyond a line that connects the ends of waves 1 and 3. (Ending beyond that line is called a throw-over.)
- In the expanding variety, wave 5 usually ends slightly before reaching a line that connects the ends of waves 1 and 3.
* We have found one diagonal in the Dow in which wave four did not reach the price territory of wave one. See Figure 2-15 in Lesson 2.
- A zigzag always subdivides into three waves.
- Wave A always subdivides into an impulse or leading diagonal.
- Wave C always subdivides into an impulse or ending diagonal.
- Wave B always subdivides into a zigzag, flat, triangle or combination thereof.
- Wave B never moves beyond the start of wave A.
- Wave A almost always subdivides into an impulse.
- Wave C almost always subdivides into an impulse.
- Wave C is often about the same length as wave A.
- Wave C almost always ends beyond the end of wave A.
- Wave B typically retraces 38 to 79 percent of wave A.
- If wave B is a running triangle, it will typically retrace between 10 and 40 percent of wave A.
- If wave B is a zigzag, it will typically retrace 50 to 79 percent of wave A.
- If wave B is a triangle, it will typically retrace 38 to 50 percent of wave A.
- A line connecting the ends of waves A and C is often parallel to a line connecting the end of wave B and the start of wave A. (Forecasting guideline: Wave C often ends upon reaching a line drawn from the end of wave A that is parallel to a line connecting the start of wave A and the end of wave B.)
- A flat always subdivides into three waves.
- Wave A is never a triangle.
- Wave C is always an impulse or an ending diagonal.
- Wave B always retraces at least 90 percent of wave A.
- Wave B usually retraces between 100 and 138 percent of wave A.
- Wave C is usually between 100 and 165 percent as long as wave A.
- Wave C usually ends beyond the end of wave A.
- When wave B is more than 105 percent as long as wave A and wave C ends beyond the end of wave A, the entire formation is called an expanded flat.
- When wave B is more than 100 percent as long as wave A and wave C does not end beyond the end of wave A, the entire formation is called a running flat.
- A triangle always subdivides into five waves.
- At least four waves among waves A, B, C, D and E each subdivide into a zigzag or zigzag combination.
- Wave C never moves beyond the end of wave A, wave D never moves beyond the end of wave B, and wave E never moves beyond the end of wave C. The result is that going forward in time, a line connecting the ends of waves B and D converges with a line connecting the ends of waves A and C.
- A triangle never has more than one complex subwave, in which case it is always a zigzag combination or a triangle.
- Usually, wave C subdivides into a zigzag combination that is longer lasting and contains deeper percentage retracements than each of the other subwaves.
- Sometimes, wave D subdivides into a zigzag combination that is longer lasting and contains deeper percentage retracements than each of the other subwaves.
- Sometimes one of the waves, usually wave C, D or E, subdivides into a contracting or barrier triangle. Often the effect is as if the entire triangle consisted of nine zigzags.
- About 60 percent of the time, wave B does not end beyond the start of wave A. When it does, the triangle is called a running triangle.
- A barrier triangle has the same characteristics as a contracting triangle except that waves B and D end at essentially the same level. We have yet to observe a 9-wave barrier triangle, implying that this form may not extend.
- When wave 5 follows a triangle, it is typically either a brief, rapid movement or an exceptionally long extension.
Most rules are the same as for contracting triangles, with these differences:
- Wave C, D and E each moves beyond the end of the preceding same-directional subwave. (The result is that going forward in time, a line connecting the ends of waves B and D diverges from a line connecting the ends of waves A and C.)
- Subwaves B, C and D each retrace at least 100 percent but no more than 150 percent of the preceding subwave.
Most guidelines are the same, with these differences:
- Subwaves B, C and D usually retrace 105 to 125 percent of the preceding subwave.
- No subwave has yet been observed to subdivide into a triangle.
- Combinations comprise two (or three) corrective patterns separated by one (or two) corrective pattern(s) in the opposite direction, labeled X. (The first corrective pattern is labeled W, the second Y, and the third, if there is one, Z.)
- A zigzag combination comprises two or three zigzags (in which case it is called a double or triple zigzag).
- A “double three” flat combination comprises (in order) a zigzag and a flat, a flat and a zigzag, a flat and a flat, a zigzag and a triangle or a flat and a triangle.
- A rare “triple three” flat combination comprises three flats.
- Double and triple zigzags take the place of zigzags, and double and triple threes take the place of flats and triangles.
- An expanding triangle has yet to be observed as a component of a combination.
- When a zigzag or flat appears too small to be the entire wave with respect to the preceding wave (or, if it is to be wave 4, the preceding wave 2), a combination is likely.