Elliott Wave Principle : Chapter 4

Figure 4-10

Figure 4-11

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 4-12. In an expanding triangle, the multiple is 1.618.

Figure 4-12

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.

4.2 Applied Ratio Analysis

Elliott himself, a few years after Rhea’s book, was the first to realize the applicability of ratio analysis. He noted that the number of DJIA points between 1921 and 1926, encompassing the first through third waves, was 61.8% of the number of points in the fifth wave from 1926 to 1928 (1928 is the orthodox top of the bull market according to Elliott). Exactly the same relationship occurred again in the five waves up from 1932 to 1937 (for reference, see Figures 2-11 and 2-12).

A. Hamilton Bolton, in the 1957 Elliott Wave Supplement to the Bank Credit Analyst, gave this price forecast based on expectations of typical wave behavior:

The powerhouse that will be building up if the market consolidates for another year or so along orthodox lines, it seems to us, will offer the probability that Primary V could be quite sensational, taking the DJIA to 1000 or more in the early 1960s in a wave of great speculation.

Then, in The Elliott Wave Principle — A Critical Appraisal, reflecting on examples cited by Elliott, Bolton stated,

Should the 1949 market to date adhere to this formula, then the advance from 1949 to 1956 (361 points in the DJIA) should be completed when 583 points (161.8% of 361 points) have been added to the 1957 low of 416, or a total of 999 DJIA. Alternatively, 361 over 416 would call for 777 in the DJIA.

Later, when Bolton wrote the 1964 Elliott Wave Supplement, he concluded,

Since we are now well past the 777 level, it looks as if 1000 in the averages could be our next target.

The year 1966 proved those statements to be the most accurate prediction in stock market history, when the 3:00 p.m. hourly reading on February 9th registered a high at 995.82 (the "intraday" high was 1001.11). Six years prior to the event, then, Bolton was right to within 3.18 DJIA points, less than one third of one percent error.

Despite this remarkable portent, it was Bolton’s view, as it is ours, that wave form analysis must take precedence over the implications of proportionate relationships. Indeed, when undertaking a ratio analysis, it is essential that one understand and apply the Elliott counting and labeling method to determine from which points the measurements should be made in the first place. Ratios between lengths based on orthodox pattern termination levels are reliable; those based on nonorthodox price extremes generally are not.

The authors themselves have used ratio analysis, often with satisfying success. A.J. Frost became convinced of his ability to recognize turning points by catching the "Cuban crisis" low in October 1962 the hour it occurred and telegraphing his conclusion to Hamilton Bolton in Greece. Then, in 1970, in a supplement to The Bank Credit Analyst, he determined that the bear market low for the Cycle wave correction in progress would probably occur at a level .618 times the distance of the 1966 decline below the 1966 low, or 572. Four years later, the DJIA’s hourly reading in December 1974 at the exact low was 572.20, from which the explosive rise into 1975-76 occurred.

Ratio analysis has value at smaller degrees as well. In the summer of 1976, in a published report for Merrill Lynch, Robert Prechter identified the fourth wave then in progress as a rare expanding triangle, and in October used the 1.618 ratio to determine that the maximum expected low for the eight-month pattern should be 922 on the Dow. The low occurred five weeks later at 920.63 at 11:00 on November 11, launching the year-end fifth-wave rally.

In October 1977, five months in advance, Mr. Prechter computed a probable level for the 1978 major bottom as "744 or slightly lower." On March 1, 1978, at 11:00, the Dow registered its low at exactly 740.30. A follow-up report published two weeks after the bottom reaffirmed the importance of the 740 level, noting that:

...the 740 area marks the point at which the 1977-78 correction, in terms of Dow points, is exactly .618 times the length of the entire bull market rise from 1974 to 1976. Mathematically we can state that 1022 - (1022-572).618 = 744 (or using the orthodox high on December 31st, 1005 - (1005-572).618 = 737). Second, the 740 area marks the point at which the 1977-78 correction is exactly 2.618 times the length of the preceding correction in 1975 from July to October, so that 1005 - (885- 784)2.618 = 742. Third, in relating the target to the internal components of the decline, we find that the length of wave C = 2.618 times the length of wave A if wave C bottoms at 746. Even the wave factors as researched in the April 1977 report mark 740 as a likely level for a turn. At this juncture then, the wave count is compelling, the market appears to be stabilizing, and the last acceptable Fibonacci target level under the Cycle dimension bull market thesis has been reached at 740.30 on March 1st. It is at such times that the market, in Elliott terms, must "make it or break it."

The three charts from that report are reproduced here as Figures 4-13 (with a few extra markings to condense comments from the text), 4-14 and 4-15. They illustrate the wave structure into the recent low from Primary down to Minuette degree. Even at this early date, 740.30 seems to be firmly established as the low of Primary wave ② in Cycle Wave V.

Figure 4-13

Figure 4-14

Figure 4-15

The 740 level has proved important other times in the past as well, quite possibly because while the 1974 low at 572.20 lies exactly 423.60 points under the 1966 peak at 995.82, 740.30 lies approximately 261.80 points under the 1004.65 level, the orthodox top in 1976. Both of these distances are expressions of Fibonacci ratios. Mr. Prechter further discussed the 740 level as follows:

It is certainly not coincidence that the 740 level has proved of some importance in the past. In 1961, the intraday Dow peak at 741.30 accompanied the highest market P/E ratio in history; in 1966, the intraday low of 735.74 marked the end of the first slide to the measuring low in the Cycle wave IV bear market (the point which was 61.8% of the entire decline of Cycle wave IV); in 1963, 1970, 1974 and 1975, breaks through 740 in each direction accompanied extreme violence; in 1978, the 740 level corresponds with long term trendline support. Furthermore, the Wave Principle holds that the limit of any market correction is the bottom of the previous fourth wave of lesser degree. When the first wave in a five-wave sequence extends, however, the limit of the ensuing correction is often the bottom of the second wave of that five-wave sequence. Given this guideline, the recent low on March first at 740.30 was a remarkable level at which to stop. A check with the hourly back figures as printed in the Wall Street Journal reveals that on March 25, 1975 the DJIA bottomed at 740.30 to complete the pullback of the second wave. [See note on Figure 4-13.]

In addition to the more traditional Elliott forecasting methods, Mr. Prechter has begun to research mathematical wave factors in terms of both time and price, of which motive waves have been found to be whole number multiples and corrective waves Fibonacci ratio multiples. The approach was discussed recently in several reports for Merrill Lynch.

Undoubtedly to some it will seem that we are patting ourselves on the back, which we most certainly are! Truthfully, though, we are hoping that an account of the successes which we have personally experienced with Elliott will inspire others to strive for similar achievements using this approach. To our knowledge, only the Wave Principle can be used to forecast with such accuracy. Of course, we have experienced failures as well, but nevertheless we feel that any drawbacks in the Elliott wave approach have been grossly overstated in the past, and that when expectations with regard to the market are not fulfilled, the Wave Principle warns the analyst in plenty of time to chart the next most likely course and to avoid losses by letting the market itself dictate his course of action.

We have found that predetermined price objectives are useful in that if a reversal occurs at that level and the wave count is acceptable, a doubly significant point has been reached. When the market ignores such a level or gaps through it, you are put on alert to expect the next calculated level to be achieved. As the next level is often a good distance away, this can be extremely valuable information. Moreover, targets are based upon the most satisfying wave count. Thus, if they are not met or are exceeded by a significant margin, in many instances you will be forced in a timely manner to reconsider your preferred count and investigate what may be rapidly developing as a more attractive interpretation. This approach helps keep you one step ahead of nasty surprises. It is a good idea to keep all reasonable wave interpretations in mind so you can use ratio analysis to obtain additional clues as to which one is operative.

4.3 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 4-16 illustrates this example.

Figure 4-16

Figure 4-17 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;

Figure 4-17

② = .618 x ④;

in ②, (A) = (B) = (C);

in ④, (A) = (C);

in ④, (B) = .382 x (A).

If a complete method of ratio analysis could be successfully resolved into basic tenets, forecasting with the Elliott Wave Principle would become more scientific. It will always remain an exercise to determine probability, however, not certainty. Nature’s laws governing life and growth, though immutable, nevertheless allow for an immense diversity of specific outcome, and the market is no exception. All that can be said at this point is that comparing the price lengths of waves frequently confirms, often with pinpoint accuracy, that Fibonacci ratios are a key determinant of where waves will stop. It was awe-inspiring, but no surprise to us, for instance, that the advance from December 1974 to July 1975 traced just over 61.8% of the preceding 1973- 74 bear slide, and that the 1976-78 market decline traced exactly 61.8% of the preceding rise from December 1974 to September 1976. Despite the continual evidence of the importance of the .618 ratio, however, our basic reliance must be on form, with ratio analysis as evidence to support or challenge what we see in the patterns of movement. Bolton’s advice with respect to ratio analysis was, "Keep it simple." Research may still achieve further progress, as ratio analysis is still in its infancy. We are hopeful that those who labor with the problem of ratio analysis will add worthwhile material to the Elliott approach. 

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.

In Nature’s Law, Elliott gave the following examples of Fibonacci time spans between important turning points in the market:

In Dow Theory Letters on November 21, 1973, Richard Russell gave some additional examples of Fibonacci time periods:

Walter E. White, in his 1968 monograph on the Elliott Wave Principle, concluded that "the next important low point may be in 1970." As substantiation, he pointed out the following Fibonacci sequence: 1949 + 21 = 1970; 1957 + 13 = 1970; 1962 + 8 = 1970; 1965 + 5 = 1970. May 1970, of course, marked the low point of the most vicious slide in thirty years. Taken in toto, these distances appear to be a bit more than coincidence.

The progression of years from the 1928 (possible orthodox) and 1929 (nominal) high of the last Super cycle produces a remarkable Fibonacci sequence as well:

A similar series has begun at the 1965 (possible orthodox) and 1966 (nominal) highs of the third Cycle wave of the current Super cycle:

Thus, we foresee some interesting possibilities with respect to DJIA turning points in the near future. These possibilities are further explored in Chapter 8.

Besides their significant frequency, there is reason to believe that Fibonacci numbers and ratios of time units in the stock market are something other than numerology. For one thing, natural time units are related to the Fibonacci sequence. There are 365.24 days in a year, just shy of 377. There are 12.37 lunar cycles in a year, just shy of 13. The ratios between these actual numbers and Fibonacci numbers are .9688 and .9515. When the Earth’s orbit and rotation were faster, these numbers would have been concurrently quite close to actual Fibonacci numbers. (Might the solar system have begun its periodicities at those frequencies?) Music of the spheres, indeed.

There are also 52.18 weeks in a year, just shy of 55. Weeks may not be natural time units, but the fact that there are four weeks in a month forces weeks into a near-Fibonacci relationship with months because Fibonacci numbers x 4.236 yield other Fibonacci numbers. Any duration of a Fibonacci number of months will be close to a Fibonacci number of weeks as well. For example, 13 months = 56 (55 + 1) weeks. There is no reason to believe that man-made time constructs such as minutes and centuries should follow Fibonacci time sequences, but we have not investigated such durations.

We have noted that the longer the duration of a wave sequence, the further it tends to deviate from a Fibonacci number of time units. The range of deviation itself appears to create a Fibonacci progression as the durations increase. Here are the typical time durations of wave sequences in natural units of time (days, weeks, months, years), along with their ranges of deviation:

In applying Fibonacci time periods to the pattern of the market, Bolton noted that time "permutations tend to become infinite" and that time "periods will produce tops to bottoms, tops to tops, bottoms to bottoms or bottoms to tops." Despite

this reservation, he successfully indicated within the same book, which was published in 1960, that 1962 or 1963, based on the Fibonacci sequence, could produce an important turning point. 1962, as we now know, saw a vicious bear market and the low of Primary wave ④, which preceded a virtually uninterrupted advance lasting nearly four years.

In addition to this type of time sequence analysis, the time relationship between bull and bear as discovered by Robert Rhea has proved useful in forecasting. Robert Prechter, in writing for Merrill Lynch, noted in March 1978 that "April 17 marks the day on which the A-B-C decline would consume 1931 market hours, or .618 times the 3124 market hours in the advance of waves (1), (2) and (3)." Friday, April 14 marked the upside breakout from the lethargic inverse head and shoulders pattern on the Dow, and Monday, April 17 was the explosive day of record volume, 63.5 million shares (see Figure 1-18). While this time projection did not coincide with the low, it did mark the exact day when the psychological pressure of the preceding bear was lifted from the market.

4.4 Benner's Theory

Samuel T. Benner was an ironworks manufacturer until the post-Civil War panic of 1873 ruined him financially. He turned to wheat farming in Ohio and took up the statistical study of price movements as a hobby to find, if possible, the answer to the recurring ups and downs in business. In 1875, Benner wrote a book entitled Business Prophecies of the Future Ups and Downs in Prices. The forecasts contained in his book are based mainly on cycles in pig iron prices and the recurrence of financial panics. Benner’s forecasts proved remarkably accurate for many years, and he established an enviable record for himself as a statistician and forecaster. Even today, Benner’s charts are of interest to students of cycles and are occasionally seen in print, sometimes without due credit to the originator.

Benner noted that the highs of business tend to follow a repeating 8-9-10 yearly pattern. If we apply this pattern to high points in the Dow Jones Industrial Average over the past seventy-five years starting with 1902, we get the following results. These dates are not projections based on Benner’s forecasts from earlier years, but are only an application of the 8-9-10 repeating pattern applied in retrospect.

With respect to economic low points, Benner noted two series of time sequences indicating that recessions (bad times) and depressions (panics) tend to alternate (not surprising, given Elliott’s rule of alternation). In commenting on panics, Benner observed that 1819, 1837, 1857 and 1873 were panic years and showed them in his original "panic" chart to reflect a repeating 16-18-20 pattern, resulting in an irregular periodicity of these recurring events. Although he applied a 20-18-16 series to recessions, or "bad times," less serious stock market lows seem rather to follow the same 16-18-20 pattern as do major panic lows. By applying the 16-18-20 series to the alternating stock market lows, we get an accurate fit, as the Benner-Fibonacci Cycle Chart (Figure 4-18), first published in the 1967 supplement to the Bank Credit Analyst, graphically illustrates.

Figure 4-18

Note that the last time the cycle configuration was the same as the present was the period of the 1920s, paralleling both the Kondratieff picture, which we discuss in Chapter 7, and the last occurrence of a fifth Elliott wave of Cycle degree.

This formula, based upon Benner’s idea of repeating time series for tops and bottoms, has fit most of this century’s stock market turning points. Whether the pattern will always reflect future highs is another question. These are fixed cycles, after all, not Elliott. Nevertheless, in our search for the reason for its fit with reality, we find that Benner’s theory conforms reasonably closely to the Fibonacci sequence in that the repeating series of 8-9-10 produces Fibonacci numbers up to the number 377, allowing for a marginal difference of one point, as shown below.

Our conclusion is that Benner’s theory, which is based on different rotating time periods for bottoms and tops rather than constant repetitive periodicities, falls within the framework of the Fibonacci sequence. Had we no experience with the approach, we might not have mentioned it, but it has proved useful in the past when applied in conjunction with a knowledge of Elliott wave progression. A.J. Frost applied Benner’s concept in late 1964 to make the inconceivable (at the time) prediction that stock prices were doomed to move essentially sideways for the next ten years, reaching a high in 1973 at about 1000 DJIA and a low in the 500 to 600 zone in late 1974 or early 1975. A letter sent by Frost to Hamilton Bolton at the time is reproduced on the following page. Figure 4-19 is a reproduction of the accompanying chart, complete with notes. As the letter was dated December 10, 1964, it represents yet another long term Elliott prediction that turned out to be more fact than fancy.

Figure 4-19