How You Can Identify Turning Points Using Fibonacci Part 1: Understanding Fibonacci Mathematics and its Connection to the Wave Principle
Wayne Gorman March 17, 2008 Elliott Wave International, Inc. P.O. Box 1618, Gainesville, GA 30503 (800) 336-1618 (770) 536-0309 Fax (770) 536-2514 www.elliottwave.com
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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 Relationships Retr Retrac acem emen ents ts — Corr Correc ecti tive ve Wave Waves s Multiples Multiples — Impulse Impulse and and Correcti Corrective ve Waves Waves Fibonacci Dividers Time Relationships Fibonacci Clusters Summary 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 Relationships Retr Retrac acem emen ents ts — Corr Correc ecti tive ve Wave Waves s Multiples Multiples — Impulse Impulse and and Correcti Corrective ve Waves Waves Fibonacci Dividers Time Relationships Fibonacci Clusters Summary 2
Golden Ratio, PHI,
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Golden Ratio, PHI,
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The Golden Ratio
PHI
.618 or 1.618
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The Golden Spiral
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The Golden Spiral in Nature
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The Golden Spiral in Nature
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The Golden Spiral in Nature
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The Golden Ratio in DNA
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The Golden Ratio in the Human Body
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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.
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Fibonacci-Based Behavior in Financial Markets
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Fibonacci-Based Behavior in Financial Markets
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Fibonacci-Based Behavior in Financial Markets
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Golden Ratio, PHI,
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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
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Fibonacci Relationships are Seen in Time and Amplitude
Amplitude
•
Retracements
•
Multiples
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Retracements
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Retracements
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Retracements
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Retracements
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Retracements
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Retracements
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Retracements
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28
29
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Multiples in Impulse Waves
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Multiples in Impulse Waves
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Multiples in Impulse Waves
Net of waves 1 through 3 times .382 = percent movement of wave 5
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Multiples in Impulse Waves
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Multiples in Impulse Waves
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Multiples in Impulse Waves
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Multiples in Impulse Waves with Extensions
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Multiples in Impulse Waves with Extensions
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Multiples in Impulse Waves with Extensions
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Multiples in Impulse Waves with Extensions
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Fibonacci Dividers in Impulse Waves
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Fibonacci Dividers in Impulse Waves
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Fibonacci Dividers in Impulse Waves
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Fibonacci Dividers in Impulse Waves
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Fibonacci Dividers in Impulse Waves
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Fibonacci Dividers in Impulse Waves
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50
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Multiples within Corrective Waves — Zigzags
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Fibonacci Relationships
Single Zigzag
Double Zigzag
• • • •
• • • •
Wave C = Wave A Wave C = .618 Wave A Wave C = 1.618 Wave A Wave C = .618 Wave A past Wave A
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
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Multiples within Zigzags
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Multiples within Zigzags
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Guidelines for Typical Retracements of 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
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Multiples for Flats
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Fibonacci Multiples for Expanded Flats
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Multiples within Flats
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Multiples for Triangles
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Multiples for Triangles
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Multiples for Triangles
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Multiples for Triangles
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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
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Fibonacci Time Relationships
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Fibonacci Time Relationships
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Fibonacci Time Dividers in Impulse Waves
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Fibonacci Time Relationships
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Multiple Fibonacci Relationships Fibonacci Clusters
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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 Fibonacci numbers .382, .618, 1.0 and 1.618. 74
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