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© 2008 Elliott Wave International 1
Elliott Wave International, Inc.P.O. Box 1618, Gainesville, GA 30503
(800) 336-1618 (770) 536-0309Fax (770) 536-2514
www.elliottwave.com
Wayne GormanMarch 17, 2008
How You Can Identify Turning Points Using Fibonacci
Part 1: Understanding Fibonacci Mathematics and its Connection to the Wave Principle
© 2008 Elliott Wave International 2
Understanding the Fibonacci Relationship in Financial Markets
� Golden Ratio, PHI, , Golden Spiral
� Examples in Nature, Human Biology and Human Decision Making
� Connection to the Wave Principle
� Fibonacci Ratios and Multiples, Golden Section
� Amplitude RelationshipsRetracements � Corrective WavesMultiples � Impulse and Corrective Waves
� Fibonacci Dividers
� Time Relationships
� Fibonacci Clusters
� Summary
© 2008 Elliott Wave International 3
Golden Ratio, PHI,
© 2008 Elliott Wave International 4
Golden Ratio, PHI,
© 2008 Elliott Wave International 5
The Golden Ratio
PHI
.618 or 1.618
© 2008 Elliott Wave International 6
The Golden Spiral
© 2008 Elliott Wave International 7
The Golden Spiral in Nature
© 2008 Elliott Wave International 8
The Golden Spiral in Nature
© 2008 Elliott Wave International 9
The Golden Spiral in Nature
© 2008 Elliott Wave International 10
The Golden Ratio in DNA
© 2008 Elliott Wave International 11
The Golden Ratio in the Human Body
© 2008 Elliott Wave International 12
The Golden Ratio in Human Decision Making
Binary-Choice Under Conditions of Uncertainty
Opinion is predisposed to 62/38 inclination.
62% is associated with positive responses.
38% is associated with negative responses.
© 2008 Elliott Wave International 13
Fibonacci-Based Behavior in Financial Markets
© 2008 Elliott Wave International 14
Fibonacci-Based Behavior in Financial Markets
© 2008 Elliott Wave International 15
Fibonacci-Based Behavior in Financial Markets
© 2008 Elliott Wave International 16
Golden Ratio, PHI,
© 2008 Elliott Wave International 17
© 2008 Elliott Wave International 18
Fibonacci Ratios and Multiples
Fibonacci Sequence Ratio Inverse
Adjacent .618 1.618 (1.618)1
Alternate .382 2.618 (1.618)2
2nd Alternate .236 4.236 (1.618)3
3rd Alternate .146 6.854 (1.618)4
4th Alternate .090 11.089 (1.618)5
N
© 2008 Elliott Wave International 19
© 2008 Elliott Wave International 20
Fibonacci Relationships are Seenin Time and Amplitude
� Retracements
� Multiples
Amplitude
© 2008 Elliott Wave International 21
Retracements
© 2008 Elliott Wave International 22
Retracements
© 2008 Elliott Wave International 23
Retracements
© 2008 Elliott Wave International 24
Retracements
© 2008 Elliott Wave International 25
Retracements
© 2008 Elliott Wave International 26
Retracements
© 2008 Elliott Wave International 27
Retracements
© 2008 Elliott Wave International 28
© 2008 Elliott Wave International 29
© 2008 Elliott Wave International 30
© 2008 Elliott Wave International 31
Multiples in Impulse Waves
© 2008 Elliott Wave International 32
Multiples in Impulse Waves
© 2008 Elliott Wave International 33
Multiples in Impulse Waves
Net of waves 1 through 3 times .382 = percent movement of wave 5
© 2008 Elliott Wave International 34
Multiples in Impulse Waves
© 2008 Elliott Wave International 35
Multiples in Impulse Waves
© 2008 Elliott Wave International 36
Multiples in Impulse Waves
© 2008 Elliott Wave International 37
© 2008 Elliott Wave International 38
© 2008 Elliott Wave International 39
© 2008 Elliott Wave International 40
Multiples in Impulse Waves with Extensions
© 2008 Elliott Wave International 41
Multiples in Impulse Waves with Extensions
© 2008 Elliott Wave International 42
Multiples in Impulse Waves with Extensions
© 2008 Elliott Wave International 43
Multiples in Impulse Waves with Extensions
© 2008 Elliott Wave International 44
Fibonacci Dividers in Impulse Waves
© 2008 Elliott Wave International 45
Fibonacci Dividers in Impulse Waves
© 2008 Elliott Wave International 46
Fibonacci Dividers in Impulse Waves
© 2008 Elliott Wave International 47
Fibonacci Dividers in Impulse Waves
© 2008 Elliott Wave International 48
Fibonacci Dividers in Impulse Waves
© 2008 Elliott Wave International 49
Fibonacci Dividers in Impulse Waves
© 2008 Elliott Wave International 50
© 2008 Elliott Wave International 51
© 2008 Elliott Wave International 52
© 2008 Elliott Wave International 53
Multiples within Corrective Waves � Zigzags
© 2008 Elliott Wave International 54
Fibonacci Relationships
Single Zigzag
� Wave C = Wave A
� Wave C = .618 Wave A
� Wave C = 1.618 Wave A
� Wave C = .618 Wave A past Wave A
Double Zigzag
� Wave Y = Wave W
� Wave Y = .618 Wave W
� Wave Y = 1.618 Wave W
� Wave Y = .618 Wave W past Wave W
Triple Zigzag
� Equality for W, Y and Z
� Ratio of .618, i.e. Wave Z = .618 Wave Y
© 2008 Elliott Wave International 55
Multiples within Zigzags
© 2008 Elliott Wave International 56
Multiples within Zigzags
© 2008 Elliott Wave International 57
Guidelines for Typical Retracementsof Wave A by Wave B in Zigzags
Wave B Net Retracement (%)
Zigzag 50-79
Triangle 38-50
Running Triangle 10-40
Flat 38-79
Combination 38-50
© 2008 Elliott Wave International 58
Multiples for Flats
© 2008 Elliott Wave International 59
Fibonacci Multiples for Expanded Flats
© 2008 Elliott Wave International 60
Multiples within Flats
© 2008 Elliott Wave International 61
© 2008 Elliott Wave International 62
Multiples for Triangles
© 2008 Elliott Wave International 63
Multiples for Triangles
© 2008 Elliott Wave International 64
Multiples for Triangles
© 2008 Elliott Wave International 65
Multiples for Triangles
© 2008 Elliott Wave International 66
Fibonacci Time Relationships
The progression of years from the 1928 (possible orthodox) and 1929 (nominal) high of the last Supercycle produces a Fibonacci sequence:
1929 + 3 = 1932 bear market bottom
1929 + 5 = 1934 correction bottom
1929 + 8 = 1937 bull market top
1929 + 13 = 1942 bear market bottom
1928 + 21 = 1949 bear market bottom
1928 + 34 = 1962 crash bottom
1928 + 55 = 1983 probable Supercycle peak
© 2008 Elliott Wave International 67
Fibonacci Time Relationships
© 2008 Elliott Wave International 68
Fibonacci Time Relationships
© 2008 Elliott Wave International 69
Fibonacci Time Dividers in Impulse Waves
© 2008 Elliott Wave International 70
© 2008 Elliott Wave International 71
© 2008 Elliott Wave International 72
Fibonacci Time Relationships
© 2008 Elliott Wave International 73
Multiple Fibonacci Relationships
Fibonacci Clusters
© 2008 Elliott Wave International 74
Summary
� The Fibonacci Ratio ( ), an irrational number approximating .618, known as the Golden Ratio, is found in nature, human biology, human thought, and aggregate human behavior such as the stock market.
� The Wave Principle is a robust fractal governed by Fibonacci mathematics.
� Sharp wave corrections tend to retrace 61.8% or 50% of the previous wave.
� Sideways corrections tend to retrace 38.2% of the previous wave.
� Subdivisions of impulse waves tend to be related by Fibonacci numbers .618, 1.0, 1.618 and 2.618.
� Subdivisions of corrective waves tend to be related by Fibonaccinumbers .382, .618, 1.0 and 1.618.
© 2008 Elliott Wave International 75
© 2008 Elliott Wave International 76
Elliott Wave International
770-536-0309 or 800-336-1618
www.elliottwave.com