When approaching the discovery of mathematical relationships in the markets, the Wave Principle offers a mental foothold for the practical thinker. If studied carefully, it can satisfy even the most cynical researcher. A side element of the Wave Principle is the recognition that the Fibonacci ratio is one of the primary governors of price movement in the stock market averages. The reason that a study of the Fibonacci ratio is so compelling is that the 1.618:1 ratio is the only price relationship whereby the length of the shorter wave under consideration is to the length of the longer wave as the length of the longer wave is to the length of the entire distance traveled by both waves, thus creating an interlocking wholeness to the price structure. It was this property that led early mathematicians to dub 1.618 the "Golden Ratio."

The Wave Principle is based on empirical evidence, which led to a working model, which subsequently led to a tentatively developed theory. In a nutshell, the portion of the theory that applies to anticipating the occurrence of Fibonacci ratios in the market can be stated this way:

a) The Wave Principle describes the movement of markets.

b) The numbers of waves in each degree of trend correspond to the Fibonacci sequence.

c) The Fibonacci ratio is the governor of the Fibonacci sequence.

d) The Fibonacci ratio has reason to be evident in the market.

As for satisfying oneself that the Wave Principle describes the movement of markets, some effort must be spent attacking the charts. The purpose of this Lesson is merely to present evidence that the Fibonacci ratio expresses itself often enough in the averages to make it clear that it is indeed a governing force (not necessarily the governing force) on aggregate market prices.

As the years have passed since the "Economic Analysis" section of Lesson 31 was written, the Wave Principle has dramatically proved its utility in forecasting bond prices. Interest rates, after all, are simply the price of an important commodity: money. As a specific example of the Fibonacci ratio's value, we offer the following excerpts from The Elliott Wave Theorist during a seven month period in 1983-84.

The Elliott Wave Theorist

November 1983

Now it's time to attempt a more precise forecast for bond prices. Wave (a) in December futures dropped 11¾ points, so a wave (c) equivalent subtracted from the wave (b) peak at 73½ last month projects a downside target of 61¾. It is also the case that alternate waves within symmetrical triangles are usually related by .618. .As it happens, wave [B] fell 32 points. 32 x .618 = 19¾ points, which should be a good estimate for the length of wave [D]. 19¾ points from the peak of wave [C] at 80 projects a downside target of 60¼. Therefore, the 60¼ - 61¾ area is the best point to be watching for the bottom of the current decline. [See Figure B-14.]

Figure B-14