Gaps

Fibonacci Constants And Elliott Wave Theory

The Fibonacci theory named so after a prominent Italian mathematician of the late twelfth and

early thirteenth centuries gives ratios, which play important role in the forecasting of market

movements. Fibonacci introduced an additive numerical series that has come to be called the

Fibonacci sequence, which consists of following series of numbers:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144, 233, 377, 610, 987, 1597, 2584, 4181, (etc.).

These numbers exhibit several remarkable relationships, in particular the ratio of any term in the

series to the next higher term. This ratio tends asymptotically to 0.618. In addition, the ratio of

any term to the next lower term in the sequence tends asymptotically to 1.618, which is the

inverse of 0.618. Similarly constant ratios exist between numbers two terms apart, three terms

apart, and so on. The ratio 0.618, referred to as the Fibonacci ratio, or the “Gold Spiral” which is

observed in structures of many natural objects and events – from clam shell construction to the

form of whirlwinds and hurricanes. The financial markets exhibit Fibonacci proportions in a

number of ways; particularly they are powerful tools for calculating price targets and placing

stops. For example, if a corrective wave is expected to retrace 61.8 percent of the preceding

impulse wave, an investor might place a stop slightly below that level. This will ensure that if the

correction is of a larger degree of trend than expected, the investor will not be exposed to

excessive losses. On the other hand, if the correction ends near the target level, this outcome will

increase the probability that the investor's preferred wave interpretation is accurate (See also

section 4.1).

5.2 Elliott wave theory

The Elliott Waves Principle is a system of empirically derived rules about the amount of

ascending and descending waves during the history of a market movement. This theory postulates

that all the market movement consists of cycles containing 8 waves each including five waves in

the direction of the trend at one larger scale and three waves against that trend. In a rising market,

this five wave/three-wave pattern forms one complete bull market/bear market cycle of eight

waves. The five-wave upward movement as a whole is referred to as an impulse wave with sub

waves labeled with figures while the three-wave countertrend movement is described as a

corrective wave with sub waves labeled with letters (See Figure 5.1). Amplitudes of the

correction waves subordinate certain rules: a second wave may never retrace more than 100

percent of a first wave (for example, in a bull market, the low of the second wave may not go

below the beginning of the first wave); the third wave is never the shortest wave in an impulse

sequence, often, it is the longest; a fourth wave can never enter the price range of a first wave (see

Figure 5.2) As the illustration shows, waves of any degree in any series can be subdivided and resubdivided

into waves of smaller degree or expanded into waves of larger degree. Furthermore,

smaller-scale movements link up to create larger-scale movements possessing the same basic

form. Conversely, large-scale movements consist of smaller-scale subdivisions with which they

share a geometric similarity. Because these movements link up in increments of five waves and

three waves, they generate sequences of numbers that the analyst can use (along with the rules of

wave formation) to help identify the current state of pattern development, as shown in Figure 5.3.

Extentions In any given five-wave sequence, a tendency exists for one of the three impulse sub

waves (i.e., wave 1, wave 3, or wave 5) to be an extension—an elongated movement, usually with

internal subdivisions. At times, these subdivisions are of nearly the same amplitude and duration

as the larger degree waves of the main impulse sequence, giving a total count of nine waves of

similar size rather than the normal count of five for the main sequence (See Figure 5.4).

Extensions can provide a useful guide to the lengths of future waves. Most impulse sequences

contain extensions in only one of their three impulsive sub waves. Thus, if the first and third

waves are of about the same magnitude, the fifth wave probably will be extended, especially if

volume during the fifth wave is greater than during the third.

Diagonal Triangles There are certain patterns resembling known from the technical analysis

theory including two types of triangles, which are to be considered from the Elliott Wave theory

position. The diagonal triangle type 1 occurs only in fifth waves and in С waves, and it signals

that the preceding move has "gone too far, too fast," as Elliott put it. Essentially a rising wedge

formation defined by two converging trend lines, type 1 diagonal triangles indicates exhaustion of

the larger movement. Unlike other impulse waves, all of the patterns' sub-waves, including waves

1, 3, and 5, consist of three wave movements, and their fourth waves often enter the price range

of their first waves, as shown in Figures 5.5 and 5.6. A rising diagonal triangle type 1 is bearish,

because it is usually followed by a sharp decline, at least to the level where the formation began.

In contrast, a falling diagonal type 1 is bullish, because an upward thrust usually follows. The

diagonal triangle type 2 occurs even more rarely than type 1. This pattern, found in first wave or

A-wave positions in very rare cases, resembles a diagonal type 1 in that it is defined by

converging trend lines and its first wave and fourth wave overlap, as shown in Figure 5.7.

However, it differs significantly from type 1 in that its impulsive sub waves (waves 1, 3, and 5)

are normal, five-wave impulse waves, in contrast to the three-wave sub waves of type 1. This is

consistent with the message of the type 2 diagonal triangle, which signals continuation of the

underlying trend, in contrast to the type 1’s message of termination of the larger trend.

Failures (Truncated Fifths) Elliott used the word failure to describe an impulse pattern in

which the extreme of the fifth wave fails to exceed the extreme of the third wave. Figures 5.8

and 5.9 show examples of failures in bull and bear markets. As the illustrations show, the

truncated fifth wave contains the necessary impulsive (i.e., five-wave) substructure to

complete the larger movement. However, its failure to surpass the previous impulse wave's

extreme signals weakness in the underlying trend, and a sharp reversal usually follows.