🔸4.1 Ration Analysis And Fibonacci Time Sequences
Last updated
Last updated
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.
The study of wave amplitude relationships in the stock market can often lead to such startling discoveries that some Elliott wave practitioners have become almost obsessive about its importance. Although Fibonacci time ratios are far less common, years of plotting the averages have convinced the authors that the amplitude (measured either arithmetically or in percentage terms) of virtually every wave is related to the amplitude of an adjacent, alternate and/or component wave by one of the ratios between Fibonacci numbers. However, we shall endeavor to present some evidence and let it stand or fall on its own merit.
The first data reflecting time and amplitude ratios in the stock market come from, of all suitable sources, the works of the great Dow Theorist, Robert Rhea. In 1934, Rhea, in his book The Story of the Averages, compiled a consolidated summary of market data covering nine Dow Theory bull markets and nine bear markets spanning a thirty-six-year time period from 1896 to 1932. He had this to say about why he felt it was necessary to present the data despite the fact that no use for it was immediately apparent:
Whether or not [this review of the averages] has contributed anything to the sum total of financial history, I feel certain that the statistical data presented will save other students many months of work.... Consequently, it seemed best to record all the statistical data we had collected rather than merely that portion which appeared to be useful.... The figures presented under this heading probably have little value as a factor in estimating the probable extent of future movements; nevertheless, as a part of a general study of the averages, the treatment is worthy of consideration.
One of the observations was this one:
The footings of the tabulation shown above (considering only the industrial average) show that the nine bull and bear markets covered in this review extended over 13,115 calendar days. Bull markets were in progress for 8,143 days, while the remaining 4,972 days were in bear markets. The relationship between these figures tends to show that bear markets run 61.1 percent of the time required for bull periods.
And finally,
Column 1 shows the sum of all primary movements in each bull (or bear) market. It is obvious that such a figure is considerably greater than the net difference between the highest and lowest figures of any bull market. For example, the bull market discussed in Chapter II started (for Industrials) at 29.64 and ended at 76.04, and the difference, or net advance, was 46.40 points. Now this advance was staged in four primary swings of 14.44, 17.33, 18.97, and 24.48 points respectively. The sum of these advances is 75.22, which is the figure shown in Column 1. If the net advance, 46.40, is divided into the sum of advances, 75.22, the result is 1.621, which gives the percent shown in Column 1. Assume that two traders were infallible in their market operations and that one bought stocks at the low point of the bull market and retained them until the high day of that market before selling. Call his gain 100 percent. Now assume that the other trader bought at the bottom, sold out at the top of each primary swing, and repurchased the same stocks at the bottom of each secondary reaction — his profit would be 162.1, compared with 100 realized by the first trader. Thus the total of secondary reactions retraced 62.1 percent of the net advance. [Emphasis added.]
So in 1934 Robert Rhea discovered, without knowing it, the Fibonacci ratio and its function relating bull phases to bear in both time and amplitude. Fortunately, he felt that there was value in presenting data that had no immediate practical utility, but that might be useful at some future date. Similarly, we feel that there is much to learn on the ratio front, and our introduction, which merely scratches the surface, could be valuable in leading some future analyst to answer questions we have not even thought to ask.
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 4-1, 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√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 4-2.
Retracements come in all sizes. The ratios shown in Figures 4-1 and 4-2 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.
Chapter 2 mentioned that when wave 3 is extended, waves 1 and 5 tend towards equality or a .618 relationship, as illustrated in Figure 4-3. 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. A 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.
Figure 4-3 | Figure 4-4 | Figure 4-5 |
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 4-4, 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 4-5.
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 4-6, and .618 when it is, as shown in Figure 4-7. Real life examples are shown in Figures 6-8 and 6-9. 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.
In a zigzag, the length of wave C is usually equal to that of wave A, as shown in Figure 4-8, 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 4-9.
In a regular flat correction, waves A, B and C are, of course, approximately equal, as shown in Figure 4-10. 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 4-11. 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.
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.
