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 Chapter 1.
As we first showed in Figure 1-4, 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 3-10, 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.
Figure 3-10
Now compare the formations shown in Figures 3-11 and 3-12. Each illustrates the natural law of the inwardly directed Golden Spiral and is governed by the Fibonacci ratio. Each wave relates to the previous wave by .618. In fact, the distances in terms of the Dow points themselves reflect Fibonacci mathematics. In Figure 3-11, showing the 1930-1942 sequence, the market swings cover approximately 260, 160, 100, 60, and 38 points respectively, closely resembling the declining list of Fibonacci ratios: 2.618, 1.618, 1.00, .618 and .382.
Starting with wave X in the 1977 upward correction shown in Figure 3-12, the swings are almost exactly 55 points (wave X), 34 points (waves a through c), 21 points (wave d), 13 points
Figure 3-12
(wave an of e) and 8 points (wave b of e), the Fibonacci sequence itself. The total net gain from beginning to end is 13 points, and the apex of the triangle lies on the level of the correction’s beginning at 930, which is also the level of the peak of the subsequent reflex rally in June. Whether one takes the actual number of points in the waves as a coincidence or part of the design, one can be certain that the precision manifested in the constant .618 ratio between each successive wave is not a coincidence. Chapters 4 and 7 will elaborate substantially on the appearance of the Fibonacci ratio in market patterns.
Does the Fibonacci-based behaviour of the stock market reflect spiral growth? Once again, the answer is yes. The idealized Elliott concept of the progression of the stock market, as presented in Figure 1-3, is an excellent base from which to construct a logarithmic spiral, as Figure 3-13 illustrates with a rough approximation. In this construction, the top of each successive wave of a higher degree is the touch point of the exponential expansion.
In these two crucial ways (Fibonacci and spiralling), the sociological valuation of man’s productive enterprise reflects other growth forms found throughout nature. We conclude, therefore, they all follow the same law.
Figure 3-13
Figure 3-14
