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

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. UWM Student Investment Club

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 UWM Student Investment Club

UWM Student Investment Club 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 UWM Student Investment Club

UWM Student Investment Club 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 UWM Student Investment Club

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. UWM Student Investment Club

Corrective Wave Forms Zig-Zag: abc pattern composed of 5-3-5 sub-wave structure. Flat: abc pattern composed of 3-3-5 sub-wave structure, with b equals a. Irregular: abc pattern composed of 3-3-5 sub-wave structure, with b longer than a. Horizontal Triangle: 5-wave triangular pattern composed of 3-3-3- 3-3 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.

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

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?

UWM Student Investment Club 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. UWM Student Investment Club

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. UWM Student Investment Club

The Golden Mean Ratio of any two adjacent Fibonacci numbers is: 5/3, 8/5, 13/8, … tends to 1.618 (Golden Mean) The Golden Ratio is the inverse Golden Mean That is 1 / 1.618 = .618 Or 1 / 2.618 = .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.

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.

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 UWM Student Investment Club

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. UWM Student Investment Club

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. UWM Student Investment Club

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: www.prognosis.nl/principle/index.html UWM Student Investment Club