1. Technical Analysis of Stocks by Richard D. Marcus
Repeated patterns, fractal geometry, and tessellations appear in biology, art, stock prices and foreign exchange rates.
These have been useful to some who do technical analysis.
Liberation by M.C. Escher
February 24, 2004

2. Fractal Geometry and security prices
A fractal is a shape which can be divided into parts that are smaller or larger versions of the whole
Irregularly shaped objects & fine-particle aggregates.
Used in repetition for fast computer screens
Stock market movements can be sub-divided into sections and returns calculated for each section
When each section relates to other sections in patterns, we find the fractal nature of security prices
Fractals imply ‘memory’ in prices, not random walks.
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3. Basics of Elliott Waves
Market cycles are composed of two major types of waves
Impulse Waves
and Corrective Waves
Every impulse wave can be sub-divided into a five wave structure
Corrective waves can be sub-divided into three.
Total waves = 8
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Waves Within Waves
Elliott Waves are fractal in nature.
'Fractal' means that they are built from similar patterns on both larger or smaller scales.
The waves appears in long-term yearly market charts as well as short-term hourly charts.
Total number of waves = 34
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Types of Impulse Waves
Extended first impulse, #1
Extended second impulse
Extended third impulse
Extension means the wave is elongated in nature
Only one wave is an extension
Sometimes impulse waves collapse
But they follow rules
, #2 (never the shortest)
, #3
#1 #2 #3
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6. Rules for Reading Impulse Elliott Waves
1. Wave 2 should not break below the beginning of Wave 1;
2. Wave 3 should not be the shortest wave among Wave 1, 3 and 5;
3. Wave 4 should not overlap with Wave 1, except for wave 1, 5, a or c of a higher degree.
4. Rule of Alternation: Wave 2 and 4 should unfold in two different wave forms.
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7. Corrective Wave Forms
Zig-Zag: abc pattern composed of sub-wave structure.
Flat: abc pattern composed of sub-wave structure, with b equals a.
Irregular: abc pattern composed of sub-wave structure, with b longer than a.
Horizontal Triangle: 5-wave triangular pattern composed of sub-wave structure.
Double Three: abcxabc pattern composed of any two from above, linked by x wave.
Triple Three: abcxabcxabc pattern composed of any three from above, linked by two x waves.

8. Top 100 FTSE Firms: Eurotop 100
How far
will it
fall?

9. The Elliott waves above are applied to short term
Where is the
the top of
Wave 3?
Wave 1 3?
Horizontal
Triangle
Wave 2
The Elliott waves above are applied to short term
pound-denominated debt.
As the impulse wave 3 tends to be long, wave 3 has
five sub-waves. We are in the fifth sub-wave. Are we
near the top of the 3rd wave?

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Fibonacci Series
The Fibonacci numbers are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 …
Add the last two to get the next.
In 1202 Fibonacci investigated how fast rabbits could breed in ideal circumstances in one year:
At the end of the first month, they mate, but there is still one only 1 pair.
At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.
At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.
At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs. Etc.
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12. Fibonacci Rectangles and Shell Spirals
We add squares around the picture. Each new square having a side which is as long as the sum of the latest two square's sides. These are Fibonacci Rectangles.
We draw a spiral by putting together quarter circles, one in each new square. This is a spiral (the Fibonacci Spiral).
The shape of a snail shell or some sea shells.
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13. The Golden Mean
Ratio of any two adjacent Fibonacci numbers is: 5/3, 8/5, 13/8, … tends to (Golden Mean)
The Golden Ratio is the inverse Golden Mean
That is 1 / = .618
Or 1 / = .382
When trying to figure how far a wave might go, the Golden Mean and Golden Ratio are guides.
Wave lengths tend to relate to each other by 2.618, 1.618, 1, .618, .382, and .236.

14. Golden Ratios and Elliott Waves
Target for wave 1
Often 38.2% or 61.8% of the previous correction
Target for wave 2
Retraces at least 38.2% but mostly 61.8% of wave 1.
Target for wave 3
Longest, tends to be 161% of wave 1 or even 262%
Target for wave 4
Retraces 23%, often 38.2% of wave 3 A B C
Target for wave 5
- Travels the same length as wave 1, or 61.8% of wave 1, or 161.8% of wave 1.

15. A Slice through a Nautilus Shell
Distances in the Nautilus shell expand by the Square Root of the Fibonacci series
Sometimes known as the ‘silver ratio’, the square root of the Golden Ratio or .786
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16. Evaluation of Elliott Waves
Reading chart patterns is more an art than science
Two analysts make different predictions
To test it, we tend to follow an expert or guru on waves.
Test results vary widely.
Experts post test on in-sample work
“If you had followed my advice, you’d have made millions!”
Compare several experts’ newsletters
Elliott wave theorists fair poorly to modestly in such contests.
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17. Commodity Traders Consumer Report
Notice that the numbers on the dice are 3, 8, and 5
Commodity Traders Consumer Report
Damaging to Elliott wave theorists, Futures, (March, 1984) magazine compared returns following the advice of ten newsletters (including the Elliott Wave Theorist).
Listed in order of profits per trade and consistency: Elliott Wave was not in the top half.
Third best in terms of return on initial margin, however.
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18. Readings on Technical Analysis
The Encyclopedia of Technical Market Indicators, Colby and Meyers.
Cornelius Luca, Trading in the Global Currency Markets, 2nd Edition, Prentice-Hall, 2000, especially Chapter 28.
Robert R. Prechter and A.J. Frost, Elliott Wave Principle: Key to Market Behavior, New Classics Library, June 1998.
Great Internet site on Elliott Wave Principle:
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