Utility Manual for the Precision Ratio Compass - Elliott Wave ...

Elliott Wave Educational Video Series

Utility Manual for the

Precision Ratio

Compass

Workbook 7

The Elliott Wave Educational Video Series — Workbook 7: Utility Manual for the Precision Ratio Compass

WORKBOOK for the

ELLIOTT WAVE EDUCATIONAL VIDEO SERIES

WORKBOOK 7

UTILITY MANUAL for the PRECISION RATIO COMPASS

Copyright © 1985, 1987 and 1995

by Robert R. Prechter, Jr.

Printed in the United States of America

First Edition: June 1985

Second Edition: September 1987

Third Edition: April 1995

For information, address the publishers:

Elliott Wave International

P.O. Box 1618

Gainesville, Georgia 30503

ISBN: 0-932750-25-7

Elliott Wave Educational Video Series

10 Volume videotape set including workbooks

ISBN: 0-932750-13-3

Elliott Wave Educational Video Series

Tape 7 and Workbook 7:

Introduction to the Elliott Wave Principle

NOTICE

All charts are copyright © Robert R. Prechter, Jr. 1990 or have been previously copyrighted by Elliott Wave International, Robert R. Prechter, Jr., or other entities. All rights are reserved. The material in this volume may not be reprinted or reproduced in any manner whatsoever without the written permission of the copyright holder. Violators will be prosecuted to the fullest extent of the law.

2


CONTENTS

Page

5 Introduction

16

17

17

19

21

7

9

13

15

16

26

31

35

22

25

35

35

35

PART 1: FIBONACCI AND THE COMPASS

What are Fibonacci Ratios?

Why Fibonacci Ratios?

Compass Terminology and Procedure

Compass Scales

What the Compass Does

Chart Scales

Price and Time

PART II: ELLIOTT WAVE APPLICATIONS

Typical Wave Structure

Using the Compass

Fibonacci Ratio Relationships

Contracting Fibonacci Ratios (for “Retracements”)

Expanding Fibonacci Ratios (for “Multiples” and extensions)

A Complete List of Known Reliable Relationships Within Patterns

Impulse Waves

Fifth Waves When Wave Three is Extended

Extensions in First or Fifth Waves

3


46

46

49

53

38

39

40

40

41

36

36

37

38

41

42

43

44

Corrective Waves

Zigzag Corrections

B Waves in Zigzags

C Waves in Zigzags

Flat and Irregular Corrections

B Waves in Flats

C Waves in Flats

B Waves in Irregular Corrections

C Waves in Irregular Corrections

Subwaves in Double and Triple Threes

Subwaves in Contracting, Ascending and Descending Triangles

Subwaves in Expanding Triangles

Advanced Ratio Application — A Comprehensive Forecasting Method

Real-Time Examples of Fibonacci Multiples and Retracements

The Bond Market

The Stock Market

The Gold Market

59

61

61

62

64

64

64

65

65

67

67

PART III: GANN ANALYSIS

Gann Analysis

The Gann-Blitz Approach

Squaring of Time and Price

1 x 1 lines

1 x 2 lines

2 x 1 lines

Unequal Chart Divisions

Gann Range Subdivisions

Erroneous Use of the Compass

Conclusion

4


INTRODUCTION

R.N. Elliott used a time-saving Fibonacci ratio calculation device, and his mention of it in “Nature’s

Law” has prompted many requests for a similar tool.

Elliott’s design necessitated a two-step recording procedure, since he did not have access to a compass specifically made for his purposes. Rather than create a copy of that more cumbersome tool, we decided to see if we could find a compass which would suit our specific needs. A long search finally turned up a company that produced a

Golden Ratio compass, but the construction was cheap and the tolerated error much too great. As any trader knows, a few cents’ difference on a stock or commodity chart can mean the difference between a perfect entry and a missed opportunity.

After much additional searching, we found a manufacturer which made compass tools for professional draftsmen. We felt that any less quality was unacceptable.

We’re extremely happy with the tool we’ve found and hope you will be, too.

Your Precision Ratio Compass is constructed of chromium plated solid brass, machine tooled to virtual precision. The PRC is a slim, handsome professional draftsman’s tool, built for a lifetime of use. The spread between points can be firmly locked so the compass won’t slip when being moved from one position on the chart to another. The compass points are sharp and true, so their position on the chart can be read with a minimum of effort. In sum, the Precision Ratio Compass has been thoughtfully designed to give you years of trouble-free service.

The uses of the Precision Ratio Compass are many and varied. Fibonacci retracements, Fibonacci price and time ratios, as well as all other ratios (from 1:10 to 10:1), can all be marked on a chart with a quick movement and a minimum of effort.

5


The following pages will show you in detail how to apply the

Compass. Undoubtedly there are uses for it which we have yet to discover. If you find any, please let us know. Perhaps your ideas will appear in the next edition of this manual.

Robert R. Prechter, Jr.

Elliott Wave International

ACKNOWLEDGEMENTS

This manual would not be here in its present form without the effort and talents of David A. Allman. His editing and illustrative skills, as well as his dedication to the project, were invaluable in attaining the quality we required for the final product.

Background charts for some of the illustrations were provided courtesy of the following sources:

Trendline (a division of Standard and Poor’s Corp.),

345 Hudson St., New York, NY 10014

Daily Graphs (a division of William O’Neil & Co., Inc.),

P.O. Box 24933, Los Angeles, CA 90024

Commodity Researach Bureau,

75 Montgomery Street, Jersey City, NJ 07302

6


PART I

FIBONACCI AND THE COMPASS

7


8


WHAT ARE FIBONACCI RATIOS?

Fibonacci Ratios are the ratios between numbers at a distance infinitely far along in any sequence which is derived by adding a number to the previous number to obtain the next. Like pi, these ratios are irrational numbers, i.e., they cannot be expressed precisely in either fractional or decimal form. The “Fibonacci Sequence” is the best known and the most basic additive sequence of this type. It is derived by adding each number, starting with the number 1, to the one just prior to it to obtain the next number. Thus, 1 added to nothing gives a second 1.

1 + 1 gives 2, 2 + 1 gives 3, 3 + 2 gives 5, 5 + 3 gives 8, and so on. The first sixteen terms in the sequence are 1,

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 and

987. A full mathematical description of the Fibonacci sequence can be found in FIBONACCI NUMBERS by

N. Vorobev, and a description of its relevance to the financial markets can be found in Chapters 3 and 4 of

ELLIOTT WAVE PRINCIPLE (New Classics Library,

$29).

Figure 1

9


10


As infinity is approached, the ratio between adjacent Fibonacci numbers, smaller over larger, is

.6180339... (phi), commonly abbreviated as .618; the inverse (larger over smaller), gives 1.618.

As infinity is approached, the ratio between alternate Fibonacci numbers, smaller over larger, is

.382; the inverse (larger over samller), gives 2.618.

The ratios for second alternate Fibonacci numbers are .236 and 4.236.

The ratios for third alternate Fibonacci numbers are .146 and 6.854.

This progression can be continued forever, as demonstrated in the bottom row and far right column of Figure 2 (from “Historical and Mathematical Background” chapter of Elliott Wave Principle ). Note that each of the decreasing ratios is the result of multiplying the preceding ratio by .618 and each of the increasing ratios is the result of multiplying the preceding ratio by 1.618. It is for this reason that any

Fibonacci ratio can be calculated with only one or two quick and simple steps with the PRC.

The spiral-like form of market action is repeatedly shown to be governed by the Golden Ratio, and, as has often been observed, even the Fibonacci numbers themselves appear in market statistics more often than mere chance would allow. However, it is crucial to understand that the numbers themselves have no theoretic weight in the grand concept of the Wave Principle. It is the ratio which is the key to growth patterns of this type because, although it is rarely pointed out in the literature, the Fibonacci ratio results from this type of additive sequence no matter what two numbers start the sequence. Take, for instance, two randomly selected numbers and add them to produce a third, continuing in that manner to produce additional numbers.

11


You will find that as this sequence approaches infinity, the ratio between adjacent terms in the sequence will approach .618... This relationship becomes obvious generally before the tenth term is produced (see Figure 3, using the starting numbers 17 and 352). Thus, while specific numbers making up the Fibonacci sequence are not necessarily important in markets, the Fibonacci ratio is a basic law of geometric progression, and does govern many relationships in data series relating to natural phenomena of growth and decay.

Figure 3

12


WHY FIBONACCI RATIOS?

The occurrence of Fibonacci ratios in markets is not coincidence, and it is not a mystical numerological theory developed in an ivory tower and forced into real life situations. When Elliott began to research the markets, he had no idea that the Fibonacci sequence would be representative of his eventual discovery. What he found initially was that the basic Dow Theory idea that primary bull markets traveled in three upward phases applied to all degrees of market trend, from hourly waves to those lasting centuries. From this discovery, he developed a system of naming and labeling the different sizes of waves, and soon realized that the total number of waves in each degree turned out to be a different Fibonacci number. In fact, these totals not only produced the Fibonacci sequence, but did so exactly, with no omissions and no repetitions.

The discussion below is a reprint from the “Historical and Mathematical Background” chapter of Elliott

Wave Principle , and illustrates this concept.

We can generate the complete Fibonacci sequence by using Elliott’s explanation of the natural progression of markets. If we start with the simplest expression of the concept of a bear swing, we get one straight line decline. A bull swing, in its simplest form, is one 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, this sequence can be taken to infinity.

Elliott came to the conclusion, and rightly so, that the stock market, as a measure of the value of man’s productive capacity, is a direct recording of changes in mankind’s progress and regress through history. The fact that this process is governed by the Fibonacci sequence, furthermore, led to

13


Figure 4

Elliott’s ultimate theory that man’s progress through history was following a natural law of growth often found in nature’s growth/decay and expansion/contraction phenomena.

The Fibonacci ratio enters the picture when we realize that the number of waves in a correction approximates 61.8% of the number of waves in the preceding impulse wave of the same degree. The ideal irrational number phi (.618...) is approached by

14

The Elliott Wave Educational Video Series — Workbook 7: Utility Manual for the Precision Ratio Compass this method the further on breaks down the wave, that is, the greater the number of subwaves one counts. Empirical evidence reveals, moreover, that Fibonacci ratio relationships occur throughout the price structure in markets. The following pages will give specific examples of the most common occurrences.

COMPASS TERMINOLOGY AND PROCEDURE

For the purpose of this manual, we will refer to the compass as having points AB (top, narrow end) and points CD (bottom, wide end), as shown in Figure 5. The procedure for setting the center guide is as follows: Close the compass, loosen the center guide nut, set the scale as desired, and tighten the nut. The ratio you have chosen will remain fixed for whatever distance you now open the compass. For the balance of this manual, all distances will be designated by a bar underneath the points in question. For example, the distance between points A and B will be referred to as AB.

15


COMPASS SCALES

Generally, proportional dividers are used for dividing lines into equal parts, for enlarging or reducing length by different ratios, or for dividing the circumference of a circle into equal parts. The left hand scale of this compass is used for length multiples while the right hand scale is used for circle division.

To relate the two scales, notice that the sequence of Fibonacci ratios, 1.618, 2.618, 4.236, 6.854, 11.090,

17.944, 29.034, 46.978, 76.012..., when multiplied by pi, 3.1416..., yields the series 5 + .1, 8 + .2, 13 + .3, 21 +

.5, 34 + .8, 55 + 1.3, 89 + 2.1 +.1, 144 + 3.4 + .2, 233 +

5.5 + .3... Notice that the numbers of the first sequence on the left-hand (lines) scale of the PRC correspond to the numbers of the second sequence on the right-hand

(circles) scale fo the PRC. One formula illustrating the eternal relationship between pi and phi is as follows:

Fn ≈ 100 x

π

2

x

φ

(15-n)

, where

φ

= .618..., n represents the numerical position of the term in the sequence and Fn represents the term itself. The number ‘1’ is represented only once. This F1 ≈ 1,

F2 ≈ 2, F3 ≈ 3, F4 ≈ 5, etc.

For example, let n = 7. Then

F7 ≈ 100 x 3.1416

2

x .6180339

(15-7)

≈ 986.97 x .6180339

8

≈ 986.97 x .02129 ≈ 21.01 ≈ 21

WHAT THE COMPASS DOES

Very simply, the distance between points C and

D will be the multiple of the distance between points

A and B which is indicated on the left-hand scale of the compass. For example, if the compass is set on

“5”, CD will be 5 times as long as AB. AB, in turn, will be 1/5 as long as CD . Because of space

16

The Elliott Wave Educational Video Series — Workbook 7: Utility Manual for the Precision Ratio Compass restrictions, the Golden section marking for length has been placed on the right-hand scale.

When the left hand scale of the compass is set at

Fibonacci multiples, CD will be a Fibonacci multiple of

AB, while AB will equal the inverse Fibonacci multiple of CD. For example, when the center guide reference is placed at “GS”, Golden Section (on the right-hand scale of the compass), the distance at the narrow end AB will always equal .618 of the distance of the wide end CD.

Conversely, CD = 1.618 x AB. We frequently refer to the right-hand scale under “USING THE COMPASS” because there is often a convenient equivalent marking correspoinding to the Fibonacci ratio we wish to locate on the left-hand scale.

CHART SCALES

All the charts in this manual use arithmetic scale.

The difference between arithmetic and semi-logarithmic chart scale is that equal vertical distances on arithmetic charts reflect an equal number of points traveled whereas equal vertical distances on semi-log charts reflect equal percentage changes. Empirical research confirms that

Fibonacci relationships in markets, in almost all cases, are based upon the number of actual points traveled, an observation which is consistent with the theoretical basis for the Wave Principle. To obtain true multiples, the PRC must always be used on charts with arithmetic scale. Fortunately, this requirement fits the industry standard since

9 out of 10 chart services use arithmetic scale.

PRICE AND TIME

All examples under “USING THE COMPASS” refer to Fibonacci price relationships. These relationships are always determined by the vertical

17


Figure 6 distance covered on a chart by a wave. In these examples, do not measure from the actual beginning of a wave to the actual end, a process which would include time in the calculation, but rather vertically to the price level of the end of the wave.

You will see that in each of the calculations, the

PRC is placed with one point at the origin of the wave to be measured and the other point vertically equivalent to the terminus of that same wave. (See Figure 6.)

Although experience reveals that Fibonacci time realtionships are less commonly found in markets than

Fibonacci price relationships, the PRC can be used to discover where in the past or future the Fibonacci time multiples lie. Just apply the Compass in exactly the same manner as described under “USING THE COMPASS,” but do it along the horizontal axis instead of the vertical.

When reading the instructions, replace the word “vertical” with the word “horizontal” and the word “wave” with the words “time segment.”

18


PART II

ELLIOTT WAVE APPLICATIONS

19


20


TYPICAL WAVE STRUCTURE

This graph of one rendition of an ideal Elliott wave has been created as a reference for this manual. It contains all of the multiples and retracements discussed on the following pages. The index numbers starting at 1000 are for an imaginary market. Actual real-time examples begin on page 46.

Figure 7

The exercises under “USING THE COMPASS” on the following pages involve ratio relationships which are commonly found in real-life markets. They will show you how to apply the PRC quickly and efficiently to project targets based upon many of these measurements.

Once you’ve mastered the PRC, you should memorize the complete list of known reliable wave relationships, which begins on page 35.

21


USING THE COMPASS

1.00 (equality)

After closing the PRC, the center guide may be set at any point on the scale and either end may be used depending upon the length of the wave in question. Place point A

(or C) at one end and point B (or D) at a vertical equivalent to the other end of a recently completed move to determine its length. Then, transfer this distance to the extreme point of the most recent move to project an equivalent length.

Sample Objective: You wish to mark the level of a 1.00

multiple of wave (A) as an estimate for the low of wave

(C). Refer to Figure 8.

Example: wave (A) = wave (C)

.50

Procedure: Close the PRC. Set the center guide at 2 on the left hand scale. Place point C at one end and point D at a vertical equivalent to the other end of a recently completed move. Flip the compass. AB = .50 x CD.

Sample Objective: You wish to mark a standard 50% through 5 as an estimate for the next correction. A 50% correction is likely since it is quite near the typical retracement point marked by the previous fourth wave low at 4 . Refer to Figure 9.

Example: Next major correction = .50 x entire wave

22


Figure 8

Figure 9

23


As you may have already deduced, all desired ratios from 1:10 to 10:1 may be obtained by simply adjusting the setting on the left-hand scale (or the right-hand scale equivalent) of the PRC. For orientation, if you were to set the center guide at 1 on the left-hand scale (lowest hash mark), the distance between points A and B, AB, and points C and D, CD, would be identical (AB = CD).

The compass settings for AB/CD relationships most useful for market analysis are listed below.

.50/2.00.

Set PRC at 2.00 on the left-hand scale.

AB = .50 x CD, and CD = 2.00 x AB.

.618/1.618.

Set PRC at GS on the right-hand scale.

AB = .618 x CD, and CD = 1.618 x AB.

.382/2.618.

Set PRC at 8.2 on the right-hand scale.

AB = .382 x CD, and CD = 2.618 x AB.

.236/4.236.

Set PRC at 13.3 on the right-hand scale.

AB = .236 x CD, and CD = 4.236 x AB.

.146/6.854.

Set PRC at 6.854 on the left-hand scale.

AB = .146 x CD, and CD = 6.854 x AB.

For the most precise application of all Fibonacci ratios using the Precision Ratio Compass, however, keep the setting on GS. To understand why, take a few minutes to study the unique properties of the Fibonacci ratio, phi, as presented in the following tables.

24


FIBONACCI RATIO RELATIONSHIPS

Multiplicative

.618

.382

.236

.146

x x x x

.618

=

.618

=

.618

=

.618

=

Additive

.382

.236

.146

.090, etc.

1.000 -

.618

-

.382

-

.236

-

1.618 x

2.618 x

4.236 x

.618

=

.382

=

.236

=

.146

=

1.618 =

1.618 =

1.618 =

Additive

.382

.236

.146

.090, etc.

These properties of the Fibonacci ratio are also true with regard to the inverse of phi, 1.618:

Multiplicative

2.618

4.236

6.854, etc.

1.000 +

1.618 +

2.618 +

1.618 =

2.618 =

4.236 =

2.618

4.236

6.854, etc.

Once you understand these tables, you will quickly see why all Fibonacci multiples and retracements can be obtained with the PRC without ever changing the setting. As a matter of fact, the most common multiples and retracements which are found in everyday markets can be marked on your charts in a matter of seconds after a bit of practice with the PRC. Simply set the center guide at GS on the right-hand scale and use the compass as described in the section beginning on page 26.

25


Contracting Fibonacci Ratios

(for “Retracements”)

Use the wide end of the PRC (points C and D) to measure the vertical distance of the move for which you desire Fibonacci retracements points. See Figure 10a

Figure 10a

Step #1) For .618 retracements: Keeping CD fixed, flip the compass. Now, AB is a .618 retracement of your original distance. Measure from the top down and mark this point W. See Figure 10b.

Figure 10b

26


Step #2) For .382 retracements: Keeping the PRC fixed, measure from the bottom up and mark a second point, X.

The remaining length is a .382 retracement of your original distance. See Figure 10c.

Figure 10c

Set #3) For .236 retracements: Contract the PRC, placing compass points A and B on points W and X. This length is a .236 retracement of your original distance.

Keeping the PRC fixed, measure from the top down and mark point Y. See Figure 10d.

Figure 10d

27


Step #4) For .146 retracements: Contract the PRC, placing compass points A and B on points X and Y.

This length is a .146 retracement of your original distance. Keeping the PRC fixed, measure from the top down and mark point Z.

Thus, in four quick steps, you have marked all the important retracements of your original distance, CD. See

Figure 10e.

Figure 10e

The above directions are applicable to retracements of a rally. For retracements of a decline, of course, you must measure from the bottom up in Steps

#1, 3 and 4, and from the top down in Step #2.

Once you become adept at using the PRC, there are even more shortcuts possible. For example, if you want only a .382 retracement, Step #2 works independently. If you want only a .236 retracement, follow Step

#2, flip the compass, and contract it so that its points fit the .382 span. Flip the compass again. Now, AB is a .236

retracement of your original distance.

28


Let’s apply this method to our textbook graph:

.618

Sample Objective: You wish to mark the level of a .618

retracement of wave 1 as an estimate for the low of wave

2 . Refer to Step #1 and Figure 11.

Example: wave 2 = .618 x wave 1

Figure 11

.382


retracement of wave 3 as an estimate for the low of wave

4 . Refer to Step #2 and Figure 12.

Example: wave 4 = .382 x wave 3

Figure 12

29


.236


retracement of wave (1) as an estimate for the low of wave (2). Refer to Steps #2-3 and Figure 13.

Example: wave (2) = .236 x wave (1)

Figure 13

.146


retracement of wave (3) as an estimate for the low of wave (4). Refer to steps #2-4 and Figure 14.

Example: wave (4) = .146 x wave (3)

Figure 14

30


Expanding Fibonacci Ratios

(for “Multiples” and extensions)

Use the narrow end of the PRC (points A and B) to measure the vertical distance of the move for which you desire Fibonacci multiples.

Step 1) For 1.618 multiples: Flip the compass, keeping the spread fixed. CD now measures 1.618 times the original distance. Place point C on the chart at the point from which you wish to project a longer wave. Place point D vertically above or below it. Make a small mark where point D touches the paper. See Figure 15.

Figure 15

31


Step 2) For 2.618 multiples: After following the above steps, flip and expand the PRC so that the narrow end fits the 1.618 multiple distance. Now, CD = 2.618 times your original distance. Flip the compass again and mark the 2.618 multiple. See Figure 16.

Step 3) For 4.236 multiples: The sum of the 1.618 and

2.618 multiples yields 4.236 times the original distance.

Just flip the compass and add AB (which is now the 1.618

multiple length) to the 2.618 multiple distance. See

Figure 16.

Figure 16

Let’s again apply this method to our textbook graph:

32


1.618


multiple of wave (1) as an estimate for the length of wave

(3). Refer to Step #1 and Figure 17.

Example: wave (3) = 1.618 x wave (1)

Figure 17

2.618


multiple of wave 1 as an estimate for the length of wave

3 . Refer to Steps #1-2 and Figure 18.

Example: wave 3 = 2.618 x wave 1

Figure 18

33


4.236

Sample Objective: You wish to corroborate your preferred count by finding additional internal

Fibonacci relationships between waves. Refer to Steps

#1-3 and Figure 19.

Example: wave 3 = 4.236 x wave 2

Figure 19

Smaller or larger multiples can be obtained with the PRC by adding or subtracting multiples of first generation ratios. For example, .236 - .146 = .090, while 2.618 + 4.236 = 6.854. Note: While these methods can be followed infinitely, we have found little evidence that the extremely large or extremely small Fibonacci ratios are of any practical value.

34


A COMPLETE LIST OF KNOWN RELIABLE

RELATIONSHIPS WITHIN PATTERNS developed by

R.N. ELLIOTT and R.R. PRECHTER, JR.

The following pages list the most common and useful Fibonacci ratio relationships in markets.

IMPULSE WAVES

Fifth Waves When Wave Three is Extended

(see Figure 20)

The most common multiple is 1.00 times the length of wave 1. Transfer the fixed length of wave 1 to the end of wave 4 to project the end of wave 5.

The next most common multiple is .618 times the length of wave 1. Follow Step #1 under “Retracements” on page 2 6 to project this target.

The next most common multiple is 1.618 times the length of wave 1. Follow Step #1 under “Multiples” on page 31 to project this target.

Extensions in First or Fifth Waves

(see Figure 20)

By far the most common multiple for the extended wave is 1.618 times the net price advance of the other two impulse waves. Thus, when wave 5 is extended, the most common multiple for its length is

1.618 times the length of wave 1 through wave 3.

Similarly, when wave 1 is extended, the most common multiple for its length is 1.618 times the length of waves 3 through 5. Follow Step #1 under “Multiples” to project this target.

35


Figure 20

CORRECTIVE WAVES

Zigzag Corrections

The most common retracement is 61.8% of the previous impulse wave and is most likely when the correction itself is in the “wave 2” position. Follow

Step #1 under “Retracements” to project this target.

See Figure 21.

Figure 21

36


The next most common retracement is 50%. See page 22 to project this target.

The least common retracement is 38.2%. Follow

Step #2 under “Retracements” to project this target.

Figure 22

B Waves in Zigzags

(See Figure 22)

The most common retracement of wave A is

38.2%. Follow Step #2 under “Retracements” to project this target.

The next most common retracement is 61.8% of wave A. Follow Step #1 under “Retracements” to project this target.

The next most common retracement is 50%. See page 22 to project this target.

These same relationships also apply in regard to

X waves as retracements of first or second zigzags in a double or triple zigzag formation. (See Figure 23).

37


Figure 23

C Waves in Zigzags

(See Figure 23)

By far the most common multiple is 1.00 times the length of wave A. Transfer the fixed length for wave

A to the end of wave B to project the end of wave C.

The next most common multiple is 1.618 times the length of A. Follow step #1 under “multiples” to project this target.

The least common multiple is .618 times the length of A. Follow Step #1 under “Retracements” to project this target.

These same relationships apply to second zigzags relative to first zigzags in a double zigzag pattern.

Flat and Irregular Corrections

By far the most common retracement is 38.2% of the previous impulse wave. Follow Step #2 under

“Retracements” to project this target. See Figure 24.

38


Figure 24

Figure 25

The next most common retracement is 23.6%.

Follow Steps #2-3 under “Retracements” to project this target.

The least common retracements are 50% and

61.8%, which occur only when the correction itself is in the wave B or wave 2 position. See page 22 or follow

Step #1 under “Retracements” respectively to project these targets.

B Waves in Flats

The only retracement is 100% of the preceding A wave. Expect wave B to end at the same level from which wave A began. See Figure 25.

39


C Waves in Flats

By far the most common multiple is just over 1.00

times the length of A. Transfer the fixed length for wave

A to the end of wave B to project the end of wave C.

Then look for the market to turn slightly beyond that point.

See Figure 25.

Figure 26

B Waves in Irregular Corrections

The most reliable multiple with respect to irregular corrections is the relationship between the lengths of waves A and C (see Figure 26). However, often B waves will fit one of these two cases:

The most common Fibonacci multiple for the length of wave B is 1.236 times the preceding A wave.

Follow Steps #2-3 under “Retracements” and add this length to the beginning of wave A to project a 1.236

multiple.

40


The next most common Fibonacci multiple is

1.382 times the preceding A wave. Follow Step #2 under

“Retracements” and add this length to the beginning of wave A to project a 1.382 multiple.

C Waves in Irregular Corrections

By far the most common multiple is 1.618 times the length of wave A. Follow Step #1 under “Multiples” to project this target. See Figure 26.

The next most common multiple is 2.618 times the length of A. Follow Steps #1-2 under “Multiples” to project this target.

Figure 27

Figure 28

Subwaves in Double and Triple Threes

(See Figures 27, 28)

The most common relationship is that each “three” is 1.00 times the length of the adjacent “threes.” Expect the second and third three each to end just beyond the level at which the first “three” ended.

41


The next most common relationship is that alternate “threes” are related by 1.618. Follow Step

#1 under “Multiples” to project this target.

The least common relationship is that adjacent

“threes” are related by 1.618. Follow Step #1 under

“Multiples” to project this target.

Figure 29

Subwaves in Contracting, Ascending and Descending Triangles

(See Figure 29)

The most common relationship is that each subwave is .618 times the length of the previous alternate subwave, i.e., wave e = .618 x wave c =

.382 x wave a; wave d = .618 x wave b. Follow Step #1 under “Retracements” to project these targets.

The next most common relationship is that each subwave is .618 times the length of the previous adjacent subwave, i.e., wave e = .618 x wave d = .382

x wave c = .236 x wave b = .146 x wave a. Follow

Step #1 under “Retracements” to project these targets.

42


Figure 30

Subwaves in Expanding Triangles

(See Figure 30)

The most common relationship is that each subwave is 1.618 times the length of the previous alternate subwave, i.e., wave e = 1.618 x wave c =

2.618 x wave a; wave d = 1.618 x wave b. Follow

Step #1 under “Multiples” to project these targets.

The next most common relationship is that each subwave is 1.618 times the length of the previous adjacent subwave, i.e., wave e = 1.618 x wave d =

2.618 x wave c = 4.236 x wave b = 6.854 x wave a.

Follow Step #1 under “Multiples” to project these targets.

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ADVANCED RATIO APPLICATION —

A COMPREHENSIVE FORECASTING METHOD

Keep in mind that all degrees of trend are always operating on 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 points which are found to be in Fibonacci relationship to several market lengths have a greater likelihood of marking a turning point in the future than a point which is in

Fibonacci relationship to only one length.

The group-ratio approach works best when the guidelines of the Elliott Wave Principle are kept in mind.

For instance, if a .618 retracement of a Primary wave 1 by a 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 most powerful argument for expecting a turn at that calculated price level. Figure 31 illustrates this example.

Figure 31

At the target market by the arrow,

2 = .618 1 , (C) = 1.618 (A), and 5=1

44


If one of the above calculations were to yield one level, but two of them were to yield another level, the level supported by two calculations is more likely the valid one.

Years of experience have proved this to be the most valid, reliable and useful approach to price forecasting in markets. The graph on page 21 is full of such confirming ratios, and serves as a good illustration of how markets often build an interlocking grid of Fibonacci relationships.

45


REAL-TIME EXAMPLES OF

FIBONACCI MULTIPLES AND RETRACEMENTS

Rather than give the reader ‘doctored-up’ examples and charts of what might transpire with regard to

Fibonacci multiples and retracements, we have chosen real-time examples of how Fibonacci relationships were actually applied in forecasting future market turning points. The following paragraphs are excerpted from past issues of The Elliott Wave Theorist :

THE BOND MARKET

November 1983

“Now it’s time to attempt a more precise forecast for bond futures prices. Wave (a) in

December futures dropped 11 3/4 points, so a wave (c) equivalent subtracted from the wave (b) peak at 73 1/2 last month projects a downside target of 61 3/4. 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

= 19 3/4 points, which should be a good estimate for the length of wave D . 19 3/4 points from the peak of wave C at 80 projects a downside target of 60 1/4. Therefore, the 60 1/4 - 61 3/4 area is the best point to be watching for the bottom of the current decline. This target zone fits the fact that futures contracts lose premium, and if the 10 3/8 bond projects an equivalent of 63 on a “cash” basis, an additional point or two would probably be lost in the price of the futures contract over the time period of the decline.” [See Figure 32.]

46


Figure 32

April 3, 1984 [adjusting and confirming the target after (b) ended in a triangle itself]

“...the ultimate downside target will probably occur nearer the point at which wave D is

.618 times as long as wave B , which took place from June 1980 to September 1981 and traveled 32 points basis the weekly continuation chart. Thus, if wave D travels 19 3/4 points, the nearby contract should bottom at

60 1/4. In support of this target is the five wave (A), which indicates that a zigzag decline is in force from the May 1983 highs.

Within zigzags, waves (A) and (C) are typically of equal length. Basis the June contract,

47

The Elliott Wave Educational Video Series — Workbook 7: Utility Manual for the Precision Ratio Compass wave (A) fell 11 points. 11 points from the triangle peak at 70 3/4 projects 59 3/4, making the 60 zone (+ or - 1/4) a point of strong support and a potential target. As a final calculation, thrusts following triangles usually fall approximately the distance of the widest part of the triangle. Based on the accompanying chart, that distance is 10 1/2 points, which subtracted from the triangle peak gives 60 1/4 as a target.”

June 4, 1984

“The bond market ended a one-year decline on May 30, hitting the long-standing Elliott target of ‘59 3/4-60 1/4’ basis the nearby futures with a dramatic reversal off [an intraday] spike low at 59 1/2 on the June contract [closing that day at 59 31/32]. In the

2 1/2 days following that low, bonds have rebounded two full points.” [See Figure 33].

Figure 33

48


THE STOCK MARKET

November 7, 1983 [See Figure 34.]

“A break of Dow 1206 will virtually confirm that Primary 1 has peaked and assure a continuation of the decline. If 1158 is broken, the next point of support is 1090, which marks a

.382 retracement of Primary 1 ”.

Figure 34

March 5, 1984

Downside Targets

“As the correction progresses, we should be able to get closer and closer to estimating where the final bottom will actually occur.

Here are the calculations:

1) Primary wave 2 will retrace .382 of

Primary wave 1 at 1094.20.

2) Within the ABC decline, wave C will be

.618 times as long as wave A at 1089.19.

June 4, 1984 [See Figures 35, 36.]

“In terms of price, the downside target of 1090 was first computed seven months ago in the

November 7, 1983 issue. That basic target was reiterated in the March and April issues,

49

The Elliott Wave Educational Video Series — Workbook 7: Utility Manual for the Precision Ratio Compass with ‘buy’ strategy outlined (with minor variations) for the 1087-1099 area. The hourly low on May 30 was 1087.93.

Figure 35

The list of Fibonacci wave relationships now in place is so perfect as to be a compelling argument all by itself that a low is in the making.

1) Wave (C) at 90.99 points, is .22 of a

Dow point from being exactly .618 times as long as wae (A) at 146.88 points, a typical relationship in zigzags.

2) Wave (B) at 35.27 points, is 1/2 point from being exactly .382 times as long as wave

(C).

3) Not only is wave (A) 1.618 times as long as wave (C), which is 2.618 times as long as wave (B), but the actual lengths are remarkably close to Fibonacci numbers: 146.88

points (Fibonacci 144), 90.99 points (Fibonacci 89), and 35.27(Fibonacci 34).

4) Wave (A) lasted 5 weeks, wave (B) lasted 13 weeks, and wave (C) lasted 3 weeks, just as forecast in the May issue. The two impulse waves totaled 8 weeks. The entire

50

The Elliott Wave Educational Video Series — Workbook 7: Utility Manual for the Precision Ratio Compass correction lasted 21 weeks. Thus, the time lengths create the Fibonacci sequence, 3, 5, 8,

13, 21, revealing that each time period, as precisely defined by their Elliott Wave structures, is related to each of the others by a Fibonacci ratio.

5) Even the Minor moves are related precisely by Fibonacci ratios (see March and

April issues).

6) The Dow Jones Transports have retraced exactly 50% of their 1982-1984 advance as of the low on May 30.”

Figure 36

June 24, 1984

“Today’s slight new closing low in the Dow at

1086.57 generated ‘sell signals’ all over Wall

Street. However, it appears to me that, just like the May 30 low and the June 15 low, this minor decline is actually providing another excellent opportunity to buy.

Based on typical Fibonacci relationships, I doubt that our ‘stop’ at Dow 1070 hourly reading will be taken out.”

51


August 6, 1984

“The leap out of that bottom (as if you hadn’t heard) has been one for the record books, and is powerful enough virtually to confirm that

Primary wave 3 has begun. The first important level of resistance is Dow

1290-1340.” [See Figure 37.]

Figure 37

52


THE GOLD MARKET

The quotes presented below detail 5 consecutive forecasts, which were made in The Elliott Wave Theorist between November 1979 and January 1982, as follows:

1) Gold should drop to $477.

Outcome: Dropped to $474.

2) Gold should rise to $710.

Outcome: Rose to $710.

3) Gold should drop to $388.

Outcome: Dropped to $388.

4) Gold should undergo a rise to new highs.

Outcome: Short 3-month rise followed by

renewed decline. But because of stop

placement, the loss on the erroneous

forecast was only $10.

5) Gold going lower. Move back to the short side.

Outcome: Gold dropped another $90 to $296.75.

Here are the exact comments which appeared:

November 18, 1979

“London gold appears to be in its final blowoff rally on a long term basis. One all-important question, in Elliott terms, is whether the

1967-68 rise in gold stocks was actually wave I of the long term gold bull market. If the true first wave was masked by the artifical price controls on gold at $34 per ounce, then we are witnessing the peak of the final fifth wave advance in gold from a true low in 1967! [For the time being, I will proceed under the assumption that only wave III is peaking.]”

53


Figure 38

March 9, 1980

“Fibonacci support levels for gold are $565,

$477 and $388. An ideal Elliott scenario for gold over the next year or two would be an A wave down to $477, forming the first retracement of the extended fifth wave within wave III. Then a strong rally would ensue forming wave B, followed by a declining wave C down to the final target of $388. The

$388 level would correspond with a .618

retracement of wave III and with the area of the previous fourth wave of lesser degree, a normal Elliott support level. The $388 level is the most reasonable target for the eventual end to the large wave IV correction.” [See

Figure 38.]

54


Figure 39

April 6, 1980

“Gold has since declined to a low of $474 on

March 18.” [See Figure 39.]

May 12, 1980

“There is nothing to add to my expectations for gold. ...a .618 retracement of the decline to just over $700 should be the maximum potential of any intermediate rally.”

July 6, 1980

“I still feel that the $710 level is a very likely target for this rally.”

55


Figure 40

September 23, 1980 (the day of the high)

“Gold has now hit its minimum target of $710 per ounce London fixing. From here on out,

I’d rather let the other guy have the profits.

The ‘guaranteed’ part of the rise is behind us.”

[See Figure 40.]

56


Figure 41

August 5, 1981

“Yesterday the Fibonacci ratio target of $388 per ounce computed a year and a half ago was satisfied quite closely, and the time zone of

‘mid-1981,’ refined last May to ‘August

1981,’ is upon us.” [See Figures 41, 42.]

Figure 42

57


September 8, 1981

“The exact low on the COMEX nearby futures contract was $388.00 and the lowest price for a cash bullion sale was $388.00 by the Bank of Nova Scotia, both on the same date.”

January 11, 1982

“[The a-b-c rally into the September 1981 high] in gold is indicating that a break of the

$388 level is now extremely likely. If gold fixes below $380, I suggest reinstating your short position. The net result will be as if we had never exited the short side at all.”

While most commodities’ wave structures clearly indicated that wave I began in 1967, some uncertainty had existed in bullion’s pattern due to government-imposed price controls. The subsequent break of the $388 level conclusively resolved this matter, confirming the wave count shown below.

Figure 43

58


PART III

GANN ANALYSIS

59


60


GANN ANALYSIS

The PRC is ideally suited for many of the methods pracaticed by the late W.D. Gann. We do not attempt to evaluate Gann theory in this manual, rather to illustrate the usefulness of the PRC to those already convinced of the benefits of Gann analysis.

THE GANN-BLITZ APPROACH

Those researchers with either computers or a good deal of spare time may wish to explore a method similar to that used by Gann. Of course, the basis of

Gann’s choice of “important numbers” is strictly numerological, and the long list of numbers he considered important leaves almost no number untouched. However, his idea of finding groups of such numbers to reveal highreliability future turning points can be applied successfully to Fibonacci ratios. This method is essentially a

“shotgun” approach, in which the analyst takes every applicable Fibonacci ratio (2.618, 1.618, 1.00, .618, .382,

... etc.), applies it to each discernible market swing on the chart, and plots every one of these points in order to find “clusters” which might reveal “magnets” for price turning points.

This approach is not as useful as that which takes into account the guidelines of the Elliott Wave Principle

(see ADVANCED RATIO APPLICATION). However, for those who have no desire to learn or apply the tenets of the Wave Principle, this exercise will certainly reveal price levels which are worth watching for changes in trend. Any single price level or time zone which were to come up repeatedly during a long series of Fibonacci calculations is one that an analyst should not fail to watch closely.

61


Procedure:

1) Choose the most recent swing in the market of the largest degree in which you are interested and apply all the functions under “USING THE COMPASS” to that swing. Add (and subtract) each of the results to (and from) both the beginning and end of that swing and of the preceding swing of the same degree. Lightly mark all resulting price levels on the chart.

2) Choose the most recent swing of the next smaller size and repeat the process.

3) Continue this process until the computations have been performed on the smallest applicable swing from the available data.

4) Mark with heavy lines the boundaries around those price levels which cluster, or which appear a greater than average number of times in your calculations. Look for these areas to coincide with turning points. Experience shows that Fibonacci relationships are generally quite precise, so “clusters” should be tight where market turns are indeed likely.

This method is best accomplished using a computer.

SQUARING OF TIME AND PRICE

By far the most widely used Gann approach is that of squaring time and price. This approach is based upon the concept that lines determined by certain points of intersection of time and price will provide support and resistance for future activity. Once a top or bottom has been identified, measure forward ‘x’ time units

(i.e., hours, days, weeks, months, years) and up or down

‘x’ price units (i.e., cents, dollars, points), tracing out the top (or bottom) and right side of a “square”. The diagonal of the “square”, moving forward in time is, in theory, significant in determining turning points in the

62


Figure 44 market. This line is referred to as a 1x1 line (1 time unit by 1 price unit).

Other frequently drawn lines regarded by

Gannophiles as having significance are 2x1 lines (2 time units by 1 price unit) and 1x2 lines (1 time unit by 2 price units).

An alternate method of ‘squaring’ is accomplished by measuring forward in time a number of time units equal to the number of price units represented by the levels of prior significant turning points. For example, a ‘square’ for a stock with a peak at

$100 per share would occur at 100 hours, days, weeks, month, years, etc. from that peak, and allegedly indicate a turning point in price at that point in time.

(Note: The method described on page 64 requires the use of chart paper where equal units are used for time and price. An alternate method is described on page 65 for paper with unequal units.)

63


1x1 lines

Procedure: Place point C at the beginning or end of the move from which the line will be drawn. Place point D forward in time at a price equivalent to point C. Keeping point D fixed, pivot the PRC so that point C is at a time equivalent to point D (above D for bottoms, below D for tops). Make a small mark. Connect the extreme point of the move to the mark, and extend the line into the future.

You have just drawn a 1x1 (45 degree) line to your initial point.

1x2 lines

Procedure: Set the center guide at 2 on the left-hand scale. Place point A at the beginning or end of the move from which the line will be drawn. Place point B forward in time at a price equivalent to point A. Make a small mark. Flip the compass. Place point C at the mark you have just made. Keeping point C fixed, pivot the PRC so that point D is at a time equivalent to point C (above C for bottoms, below C for tops). Make another small mark.

Connect the extreme point of the move to the second mark, and extend the line into the future. You have just drawn a 1x2

2x1 lines

Procedure: Set the center guide at 2 on the left-hand scale. Place point C at the beginning or end of the move from which the line will be drawn. Place point D forward in time at a price equivalent to point C. Make a small mark. Flip the compass. Place point A at the mark you have just made. Keeping point A fixed, pivot the PRC so that point B is at a time equivalent to point A (above A for bottoms, below A for tops). Make another small mark.

Connect the extreme point of the move to the second mark, and extend the line into the future. You have just drawn a 2x1 line to your initial point.

64


UNEQUAL CHART DIVISIONS

For chart paper where the price units and the time units are not equal, Gann lines are still easily drawn with the PRC by adjusting the center guide on the PRC to correspond with the ratio of time to price on your chart paper. As an example, suppose your time units are twice the size of your price units (i.e., the height of paper used for 2 points is equal to the length of paper used for 1 day). Your objective is to draw a

1x1 line. Set the center guide at 2 on the left-hand scale.

Place point C at the beginning or end of the move from which the line will be drawn. Place point D forward in time at a price equivalent to point C. Make a small mark. Flip the compass. Place point A at the mark you have just made. Keeping point A fixed, pivot the PRC so that point B is at a time equivalent to point A (above

A for bottoms, below A for tops). Make another small mark. Connect the extreme point of the move to the second mark, and extend the line into the future. You have just drawn a 1x1 line to your initial point, squaring time and price. For 2x1 lines, you can then multiply the setting chosen by 2. for 1x2 lines, multiply the setting chosen by 1/2. This technique can be applied to various scales of chart paper by setting the center guide on the left hand scale at the ratio of the number of price units in a certain height of chart paper to the number of time units in the same length of chart paper.

GANN RANGE SUBDIVISIONS

Another Gann assertion is that certain equal subdivisions of any important move will provide levels of support and resistance for subsequent market action. According to Gann, many fractions were found to be important in this regard, with 1/4,

1/3, 1/8, and 1/16 respectively having the most significance. For example, if the previous range was

100 units, then a 1/4 subdivision would result in the

65

The Elliott Wave Educational Video Series — Workbook 7: Utility Manual for the Precision Ratio Compass conclusion that every 25 unit demarcation would represent a potential area of support or resistance.

The most widely used range subdivision by Gann practicioners is that of eighths. The usefulness of the PRC to believers in this method is illustrated in Figure 45.

Step 1) Set the center guide at 2. AB = .50 x CD.

Step 2) Measure the wave length with the wide end of the PRC. Flip the compass. Place point A at one end and point B at an equivalent point in time to point A.

Mark this point.

Step 3) Flip and contract the PRC so that points C and D fit on the smaller length you have marked. Flip the compass again. Now AB = .25 x the original length.

Step 4) Flip and contract the PRC so that points C and D fit on the smallest length you have marked. Flip the compass again. Now AB = .125 x the original length.

The subdivisions can be projected into new high or low price territory for levels of resistance or support as illustrated.

Figure 45

66


ERRONEOUS USE OF THE COMPASS

Some people have attempted to find value in measuring the physical length of waves on chart paper, taking into account both price and time. The problem with this approach lies in the fact that a physical length as defined above is subject to the time and price scales of the chart paper which is used, and thus a retracement or multiple will not transfer from one type of chart paper to another. If a method is to have significance, it should certainly not be dependent on chart scale.

CONCLUSION

The Precision Ratio Compass is the perfect tool for projecting ratio-based price and time targets in the financial markets. The foremost advantage is a tremendous saving of time, since you will not have to calculate price or time distances, write down figures, and then transfer the result to your chart. In fact, you won’t even have to check your records to make sure of exactly what the price levels at the turning points are. The Compass knows that when you place it on the chart. The second important advantage is that you will now have time to investigate all the relevant ratio relationships, not just one or two. You can even experiment with your own special ratio theories (pi multiples have been suggested). And last but not least, you will eliminate any possibility of miscalculation in hitting a wrong button on a calculator or reading and transferring the wrong number from a chart to the keys. The final result is a quicker and more accurate analysis, leaving you more time to make trades, with greater confidence that they’ll be based on complete and accurate information.

67


ADDITIONAL CHARTS PRESENTED DURING

CALCULATING FIBONACCI RELATIONSHIPS

Using the PRECISION RATIO COMPASS

68


69


70


71


72


1-770-536-0309 (outside the U.S.) or 1-800-336-1618 (inside the U.S.)

73

Utility Manual for the Precision Ratio Compass - Elliott Wave ...

Elliott Wave Educational Video Series

Utility Manual for the

Precision Ratio

Compass

Workbook 7

PART I

FIBONACCI AND THE COMPASS

φ

φ

PART II

ELLIOTT WAVE APPLICATIONS

PART III

GANN ANALYSIS

ADDITIONAL CHARTS PRESENTED DURING

CALCULATING FIBONACCI RELATIONSHIPS

Using the PRECISION RATIO COMPASS

1-770-536-0309 (outside the U.S.) or 1-800-336-1618 (inside the U.S.)

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Utility Manual for the Precision Ratio Compass - Elliott Wave ...

Elliott Wave Educational Video Series

Utility Manual for the

Precision Ratio

Compass

Workbook 7

PART I

FIBONACCI AND THE COMPASS

φ

φ

PART II

ELLIOTT WAVE APPLICATIONS

PART III

GANN ANALYSIS

ADDITIONAL CHARTS PRESENTED DURING

CALCULATING FIBONACCI RELATIONSHIPS

Using the PRECISION RATIO COMPASS

1-770-536-0309 (outside the U.S.) or 1-800-336-1618 (inside the U.S.)

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