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Third EditionWILEY TRADING ADVANTAGE
Trading without Fear / Richard W. Arms, Jr.
Neural Network: Time Series Forecasting of Financial Markets / 6. Michael Azoff
Option Market Making / Alan J. Baird
Money Management Strategies for Futures Traders / Nauzer J. Balsara
Genetic Algorithms and Investment Strategies / Richard J. Bauer
Technical Market Indicators: Analysis and Performance / Richard J. Bauer and Julie R. Dahiquist
Seasonality: Systems, Strategies & Signals / Jacob Bernstein
The Hedge Fund Edge / Mark Boucher
Managed Futures: An Investor’s Guide / Beverly Chandler
Beyond Technical Analysis / Tushar Chande
The New Technical Trader / Tushar Chande and Stanley S. Kroll
Trading on the Edge / Guido J. Deboeck
Trading the Plan / Robert Deel
The New Science of Technical Analysis / Thomas R. DeMark
Point and Figure Charting / Thomas J. Dorsey
Trading for a Living / Dr. Alexander Elder
Study Guide for Trading for a Living / Dr. Alexander Elder
The Day Trader's Manual / William F. Eng
The Options Course: High Profit & Low Stress Trading Methods / George A. Fontanills
The Options Course Workbook / George A. Fontanills
Trading 101 / Sunny J. Harris
Trading 102 / Sunny J. Harris
Analyzing and Forecasting Futures Prices / Anthony F. Herbst _
Technical Analysis of the Options Markets / Richard Hexton
Pattern, Price & Time: Using Gann Theory in Trading Systems / James A. Hyerczyk
Profits from Natural Resources: How to Make Big Money Investingin Energy, Food & Metals / Roland A, Jansen
Trading Systems & Methods, Third Edition / Perry J. Kaufman
Trading to Win / Ari Kiev, M.D.
Understanding Options / Robert Kolb
The Intuitive Trader / Robert Koppel
McMillan on Options / Lawrence G. McMillan -
Trading on Expectations / Brendan Moynihan N
Intermarket Technical Analysis /John J. Murphy
Forecasting Financial Markets, 3rd Edition / Mark J. Powers and Mark G. Castelino
Neural Networks in the Capital Markets / Paul Refenes
Cybernetic Trading Strategies / Murray A. Ruggiero, Jr.
The Option Advisor: Wealth-Building Techniques Using Equity and Index Options / Bernie G. Schaeffer
Gaming the Market / Ronald B. Shelton
Option Strategies, 2nd Edition / Courtney Smith
Trader Vic If: Principles of Professional Speculation / Victor Sperandeo
Campaign Trading / John Sweeney
The Trader’s Tax Survival Guide, Revised / Ted Tesser
The Mathematics of Money Management / Ralph Vince
Portfolio Management Formulas / Ralph Vince
The New Money Management: A Framework for Asset Allocation / Ralph Vince
Trading Applications of Japanese Candlestick Charting / Gary Wagner and Brad Matheny
Trading Chaos: Applying Expert Techniques to Maximize Your Profits / Bill Williams
New Trading Dimensions: How to Profit from Chaos in Stocks, Bonds & Commodities / Bilt WilliamseeeTRADING SYSTEMSAND METHODS
Third Edition
PERRY J. KAUFMAN
John Wiley & Sons
NewYork « Chichester * Weinheim + Brisbane * Singapore + TorontoThis book is printed on acid-free paper.Copyright © 1998 by Perry J. Kaufman. All rights reserved.
Published by John Wiley & Sons, Inc.Published simultaneously in Canada.
No part of this publication may be reproduced; stored in a retrieval system or transmittedin any form or by any means, electronic, mechanical, photocopying, recording, scanningor otherwise, except as permitted under Sections 107 or 108 of the 1976 United StatesCopyright Act, without either the prior written permission of the Publisher, or authoriza-tion through payment of the appropriate per-copy fee to the Copyright Clearance Center,222 Rosewood Drive, Danvers, MA 01923, (508) 750-8400, fax (508) 750-4744. Requeststo the Publisher for permission should be addressed to the Permissions Department,John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011,fax (212) 850-6008, E-Mail: PERMREQ@WILEY.COM.
This publication is designed to provide accurate and authoritative information in regardto the subject matter covered. It is sold with the understanding that the publisher is notengaged in rendering professional services. If professional advice or other expert assis-tance is required, the services of a competent professional person should be sought.
TradeStation® is a registered trademark of Omega Research, Inc.
Library of Congress Cataloging-in-Publication Data:
Kaufman, Perry J.Trading systems and methods / Perry J. Kaufman.—3rd ed.Pp.  cm.—(Wiley trading advantage)Rev. ed. of: The new commodity trading systems and methods. 1987.Includes bibliographical references and index.ISBN 0-471-14879-2 (cloth : alk. paper) ~1. Commodity exchanges—Statistical methods. I. Kaufman, PerryJ. New commodity trading systems and methods. “II. Title.Ill. Series.HG6046.K34 1998332.64'4—dc21 98-24482
Printed in the United States of America. -
1098765432‘To Barbara, for providing dauntless supportFOIf you have a minute, I'll tell you how to make money in stocks.
Buy low and sell high—Now if you have five or ten years,
I'll tell you how to tell when stocks are low and high.
JRL June, 1966Contents
PREFACE: CLOSING THE GAP BETWEEN EXPECTATIONS AND REALITY
1 INTRODUCTIONTechnical versus FundamentalProfessional and AmateurRandom Walk.Background MaterialResearch SkillsObjectives of This BookProfile of a Trading SystemA Word on Notation Used in This Book
2 BASIC CONCEPTSAbout Data and AveragingOn the Average iDistributionDispersion and SkewnessStandardizing Returns and RiskThe IndexProbability -Supply and Demand
3 REGRESSION ANALYSISCharacteristics of the Price DataLinear RegressionMethod of Least SquaresLinear CorrelationNonlinear Approximations for Two VariablesSecond-Order Least SquaresEvaluation of 2-Variable TechniquesMultivariate Approximations
— ARIMALinear Regression Model
4 TREND CALCULATIONSForecasting and FollowingLeast-Squares ModelThe Moving Average‘Geometric Moving AveragesDrop-Off Effect
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Exponential Smoothing 75Relating Exponential Smoothing and Standard Moving Averages 81
5 TREND SYSTEMS 89Basic Buy and Sell Signals 89Bands and Channels 90Applications of Single Trends 95Comparison of Major Trend Systems 100Techniques Using Two Trendlines 116Comprebensive Studies 120Selecting the Right Moving Average 120Moving Average Sequences: Signal Progression 122Living with a Trend-Following Philosophy 123
6 MOMENTUM AND OSCILLATORS 126Momentum 126Oscillators . 133Double-Smoothed Momentum 144Adding Volume to Momentum 147Velocity and Acceleration : 149Other Rate-of-Change Indicators . 152Momentum Divergence 154Momentum Smoothing : : 157Some Final Comments on Momentum to 158
7 SEASONALITY . . 160A Consistent Factor 160The Seasonal Pattern . 161Popular Methods for Calculating Seasonality , 161Weather Sensitivity 174Seasonal Filters - 176Common Sense and Seasonality . x 188
8 CYCLE ANALYSIS 189Cycle Basics 189Uncovering the Cycle 193Maximum Entropy - 208Cycle Channel Index - . 209
- Phasing 2109 CHARTING ~ _ 213Finding Consistent Patterns 7 oF 214Interpreting the Bar Chart 215Chart Formations ~ 217Basic Trading Rules 218Tops and Bottoms 221Gaps 225Key Reversal Days - - 226Episodic Patterns 227
Price Objectives for Bar Charting 228CONTENTS 7
 
10
11
12
13
14
Candlestick ChartsUsing the Bar Chart
VOLUME, OPEN INTEREST, AND BREADTHContract Volume versus Total VolumeVariations from the Normal PatternsStandard Interpretation
Volume Indicators
Interpreting Volume SystematicallyAn Integrated Probability ModelIntraday Volume Patterns
Filtering Low Volume
Market Facilitation Index
Sources of Information
POINT-AND-FIGURE CHARTING
Plotting Prices Using the Point-and-Figure MethodChart Formations
Point-and-Figure Box Size
The Problem of Risk
Trading Techniques
Price Objectives
A Study in Point-and-Figure Optimization
CHARTING SYSTEMS
Swing Trading
William Dunnigan and the Thrust MethodNofri’s Congestion-Phase System
Outside Days with an Outside CloseAction and Reaction
Channel Breakout
Moving Channels -Combining Techniques
Complex Patterns
SPREADS AND ARBITRAGESpread and Arbitrage RelationshipsArbitrage
Changing Spread RelationshipsCarrying Charges
Technical Analysis of SpreadsVolatility and Spread RatiosLeverage in Spreads
BEHAVIORAL TECHNIQUESMeasuring the News
Event Trading
Commitment of Traders ReportOpinion and Contrary OpinionFibonacci and Human BebaviorElliott's Wave Principle
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272CONTENTS
 
15
16
17
Constructions Using the Fibonacci Ratio
Fischer’s Golden Section Compass System !WD. Gann—Time and Space
Financial Astrology
PATTERN RECOGNITION
Projecting Daily Highs and Lows
Time of Day
Opening Gaps and Intraday Patterns
Three Studies in Market Movement—Weekday, Weekend, and Reversal PatternsComputer-Based Pattern Recognition
Artificial Intelligence Methods
DAY TRADING
Impact of Transaction CostsApplicability of Trading TechniquesMarket Patterns
ADAPTIVE TECHNIQUESAdaptive Trend Calculations
* Adaptive Momentum Calculations
18
19
20
21
‘An Adaptive Process
‘ Considering Adaptive Methods
PRICE DISTRIBUTION SYSTEMS
Using the Standard Deviation
Use of Price Distributions and Patterns to Anticipate MovesDistribution of Prices
Steidlmayer’s Market Profile
MULTIPLE TIME FRAMES -Tuning Two Time Frames to Work TogetherElder's Triple-Screen Trading SystemRobert Krausz’s Multiple Time Frames
A Comment on Multiple Time Frames
ADVANCED TECHNIQUES
Measuring Volatility
Trade Selection
Price-Volume Distribution
Trends and Noise
Expert Systems
Fuzzy Logic ‘ os
Fractals and Chaos
Neural Networks
Genetic Algorithms
Considering Genetic Algorithms, Neural Networks, and FeedbackTESTING ° ootExpectations .Identifying the Parameters
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Selecting the Test Data
Searching for the Optimal ResultVisualizing and Interpreting the ResultsStep-Forward Testing and Out-of-Sample DataChanging Rules
Arriving at Valid Test ResultsPoint-and-Figure Testing
Comparing the Results of Two SystemsProfiting from the Worst ResultsRetesting Procedure
Comprehensive Studies
Price Shocks
Anatomy of an Optimization
Data Mining and OveroptimizationSummary
PRACTICAL CONSIDERATIONS
Use and Abuse of the Computer
Price Shocks
Gambling Technique—The Theory of RunsSelective Trading
System Trade-Offs
Trading Limits—A Dampening EffectGoing to Extremes
Similarity of Systems
RISK CONTROL
Risk Aversion
Liquidity
Capital
Measuring Risk
Leverage
Diversification
Individual Trade Risk
Ranking of Markets for SelectionProbability of Success and RuinCompounding a Position
Equity Cycles .
Investing and Reinvesting: Optimal £Comparing Expected and Actual Results
APPENDIX 1 STATISTICAL TABLES
Probability Distribution TablesTable of Uniform Random Numbers
APPENDIX 2 METHOD OF LEAST SQUARES
Operating Instructions
Computer Programs
Least-Squares Solution for Corn-SoybeansLeast-Squares Solution for Soybeans Only
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APPENDIX 3 MATRIX SOLUTIONS TO LINEAR EQUATIONS
AND MARKOV CHAINS 651Direct Solution and Convergence Method 651General Matrix Form 651Direct Solution 651Convergence Method 657
APPENDIX 4 TRIGONOMETRIC REGRESSION FOR FINDING CYCLES 659Single-Frequency Trigonometric Regression 659Two-Frequency Trigonometric Regression 663
APPENDIX 5 FOURIER TRANSFORMATION 669Fast Fourier Transform Program 669
APPENDIX 6 CONSTRUCTION OF A PENTAGON 673Construction of a Pentagon from One Fixed Diagonal 673Construction of a Pentagon from One Side 674
BIBLIOGRAPHY , 676
INDEX : : 687aesPreface to theThird Edition
CLOSING THE GAP BETWEENEXPECTATIONS AND REALITY
It has been a remarkable 11 years since I wrote the last edition of this book. The changesthat have occurred during that time are staggering, and they are reflected in new chapters,the expansion of many topics, and a thorough updating of most other areas. The ideas areno longer limited to futures markets, but are equally applicable to equities, index markets,interest rates, and foreign exchange.
Technology has had an immense impact on every phase of the financial markets, fromthe broadest scope of economic globalization to the most specific tools that we use whenwe make a trading decision. We see electronic exchangés in many countries, electronicheadphones on the trading floors, Internet, and handheld quote machines. It’s a tremen-dous leap forward since I wrote the second edition of this book; at that time, no one wassure what role the computer or technical analysis would play in the future. Now it seemscertain that, to be competitive, you need to be automated in every aspect of trading. ~
You can’t underestimate the effect of the computer on our lives. Investors, traders,analysts, and the markets themselves are in the process of change; and although thesechanges have come quickly, they seem natural. Many of us have adjusted to a new way ofoperating without actually being conscious of it happening. We now expect to receiveinstant price quotes from around the world; we don’t expect our data feeds or our com-puters to fail; we find it very normal to view the price charts of the long-term interest ratesin the United States, Europe, and Asia on the same screen. We can watch how a Bundes-bank announcement of lower interest rates impacts the German stock market and almostinstantly affects the S&P 500 and Eurodollars. These changes create ideas and opinions onhow these markets interact and how we might profit from those relationships. It is mucheasier to see a chart of the impact of one market on another than to intellectualize thecause-and-effect situations or study the economic theory.
The greatest change of all has been in the expectations of traders and market analysts.When you look at an historic price chart it is impossible to ignore seeing how profits couldhave been made. Once you have seen the long trend in bond prices in the early 1990s, it iseasy to believe that those profits could have been yours. If you add the new trading tools,especially the variety of testing software and intelligent quote machines, you have the abil-ity to combine and manipulate price data, find intermarket relationships, test and monitortrading strategies, create buy and sell orders, and even execute them electronically. With allthese tools and hindsight we form expectations that surpass reality.
High expectations put pressure on us to perform better. We may have missed the goldmove that began in 1977 and lasted until January 1980 (which would have returned$60,000 on a $2,000 investment), but we don’t expect to miss the next one. History is fullof sustained trends, price shocks, and languishing periods of meandering sideways pricexiv PREFACE TO THE THIRD EDITION
 
patterns. Had we purchased crude oil during the Gulf War, the investment would havereturned 1,200% during a few months. The dilemma is that these situations are only clearin retrospect; we would never have made those decisions correctly at the right time. As aconsequence, investors torture themselves because they are certain that those profits werereally within their reach.
Because the investor can see past opportunities and believe them to be attainable, bro-kerage firms and investment managers, along with the investors themselves, try to createstrategies that will profit from similar situations in the future. But the big profits of thepast, just as ones that will come in the future, are spectacular and unusual, they are excep-tions to norma! market activity. To focus on those events would be to ignore the day-to-daytrading needed to yield steady returns. In the long run, if you can’t trade profitably eachday, or each week, you would never survive the period in between these events. You can-not compete against a perfect, imaginary adversary.
The key idea in a successful trading program is robustness, not a few large profits. Aninvestment, program must work on a broad sampling of markets, under many differentconditions. This requires extensive testing using many years of historic data. There will beperiods when the strategy is not successful, but a part of the problems can be correctedwith diversification and asset allocation. If you concentrate on fixing a bad performanceperiod in one market, you will have worse results in another market or at another time.Fiddling with individual profits and losses undermines the effort.
Technology, in the form of faster computers and strategy development software, givesus the ability to look at the big picture, to compare one method with another, one marketwith another, all test results and many years at one time. Robustness is found in the bigpicture, not under the microscope. The robust solution is not perfect, but it will bringsuccess.
Just a few last words about what I have included and not included in this edition. Thechoices were not always easy because a lot has been written in the past 11 years. Mostly, Ihave expanded on the different trading systems and techniques, as you would expect. Ihave included many computer programs and spreadsheet code to make it easier for you totransfer these to any computer and begin your own work.
A large number of new topics have been added and all of the traditional ones havebeen expanded. You'll find a chapter on adaptive techniques and another on volume; sea-sonal methods and cycles have their own chapters; there is a short chapter on multipletime frames, and much more on advanced techniques, testing, and behavior. All the chap-ters have been rewritten because there have been so many changes in technology. Whereapplicable, system studies have been retested using current data and the computer pro-grams used for testing have been included so that you may continue on your own. For bet-ter or-worse, many of the studies and all of the opinions and conclusions in this book areentirely my own. These methods have been applied to the broader group of cash, deriva-tives, and equity markets.
There are some new tools, such as neural networks, that have become a an entire studyof their own, and there are many books devoted to that subject. Instead, you will find ageneral discussion and examples of how neural networks, fuzzy logic, and genetic algo-rithms work, and how they might help the development of a trading strategy. In some casesyou can adapt your current tools to produce the same results, perhaps without the ele-gance of these new techniques.
Lastly, I have left some of the references to older technical works, along with theircharts and examples. Not only do these valuable writings hold important information invery simple form, but they are a part of our Industry’s history. Many successful techniqueshave strong roots in the past.PREFACE TO THE THIRD EDITION xv
 
We are very fortunate that today’s world markets make this an exciting time to be aninvestment decision maker. I hope this new edition provides a lasting resource to help youachieve greater success.
Perry J. Kaufman
Chicago1998 
Introduction
uantitative methods for evaluating price movement and making trading decisionshave become a dominant part of market analysis. At one time, the only acceptablemanner of trading was by understanding the factors that make prices move, and‘determining the extent or potential of future movement. The market now supportsdozens of major funds and managed programs, which account for a sizable part of futuresmarket open interest and operate primarily by decisions based on “technical analysis.”Stock selection, which can require sorting through thousands of individual world equitieseach day, has become a problem in data reduction—finding specific patterns that offer thebest expectations of profit. Many commercial participants in the markets, who oncerestricted research to supply and demand, or institutions once only interested in earningsand debt, now include various technical methods for the purpose of “timing” or confirm-ing price direction. :
In many ways, there is no conflict between fundamental and technical analysis. Thedecisions that result from economic or policy changes are far-reaching; these actions maycause a long-term change in the direction of prices and may not be reflected immediately.Actions based on long-term forecasts may involve considerable risk and often can be anineffective way to manage a position. Integrated with-a technical method of known risk,which determines price trends over shorter intervals, investors at all levels have gainedpractical solutions to their trading problems.
Leverage in the futures markets has a strong influence on the methods of trading. Withmargin deposits ranging from 5 to 10% of the contract value (the balance does not have tobe borrowed as in stocks), a small movement in the underlying price can result in largeprofits and losses based on the invested margin. Because high leverage is available, it isnearly always used. Methods of analysis will therefore concentrate on short-term price fluc-tuations and trends, in which the profit potential is reduced, so that the risk is oftensmaller than the required margin. Futures market systems can be characterized as empha-sizing price moves of less than 20% of the contract value. Trading requires conservation ofcapital, and the management of investment risk becomes essential.
Even with the distinction forced by high leverage, many of the basic systems covered inthis book were first used in the stock market. Compared with securities, the relatively smallnumber of futures markets offer great diversification and liquidity. The relative lack of liq-uidity in a single stock lends itself to index analysis, whereas the “commodity” index, nowtradeable as the CRB index, has never become very popular.
TECHNICAL VERSUS FUNDAMENTAL
Two basic approaches to trading futures are the same as in trading equities: fundamentaland technical analysis. In futures, a fundamental study may be a composite of supply-and-demand elements: statistical reports on production, expected use, political ramifications,labor influences, price support programs, industrial development—everything that makesprices what they are. The result of a fundamental analysis is a price forecast, a predictionof where prices will be at some time in the future.2 INTRODUCTION
 
Technical analysis is a study of patterns and movement. Its elements are normally limitedto price, volume, and open interest. It is considered to be the study of the market itself Theresults of technical analysis may be a short- or long-term forecast based on recurring pat-terns; however, technical methods often limit their goals to the statement that today’s pricesare moving up or down. Some systems will go as far as saying the direction is indeterminate.
Due to the rapid growth of computers, technical systems now use tools previouslyreserved for fundamental analysis. Regression and cycle (Seasonal) analysis are built intomost spreadsheet programs and allow these more complex studies, which were oncereserved for serious fundamental analysts, to be performed by everyone. Because they arecomputerized, many technicians now consider them in their own domain. There willalways be purists on either side, rigid fundamentalists and technicians, but a great numberof professionals combine the two techniques. This book draws on some of the more pop-ular, automated fundamental trading approaches.
One advantage of technical analysis is that it is completely self-contained. The accuracyof the data is certain. One of the first great advocates of price analysis, Charles Dow, said:
The market reflects all the jobber knows about the condition of the textile trade;all the banker knows about the money market; all that the best-informed presidentknows of his own business, together with his knowledge of all other businesses; itsees the general condition of transportation in a way that the president of no sin-gle railroad can ever see; it is better informed on crops than the farmer or even theDepartment of Agriculture..In fact, the market reduces to a bloodless verdict allknowledge bearing on finance, both domestic and foreign.
Much of the price movement reflected in commodity cash and futures markets is anticipa-tory; the expectations of the effects of economic developments. It is subject to changewithout notice. For example, a hurricane bound for the Philippines will send sugar priceshigher, but if the storm turns off course, prices will drop back to prior levels. Major sched-uled crop reports cause a multitude of professional guessing, which may correctly or incor-rectly move prices just before the actual report is released. By the time the public is readyto act, the news is alreatly reflected in the price.
PROFESSIONAL AND AMATEUR
- \Beginning traders often find a system or technique that seems extremely simple and con-venient to follow, one that they think has been overlooked by the professionals. Sometimesthey are right, but most often that method doesn’t work. Reasons for not using a techniquecould be the inability to get a good execution, the risk/reward ratio, or the number of con-secutive losses that occur. Speculation is a difficult business, not one to be taken casually.As Wyckoff said, “Most men make money-in their own business and lose it in some otherfellow's.” :
To compete with a professional speculator, you must be more accurate in anticipatingthe.next move or in predicting prices from current news—not the article printed in today’snewspaper (“Government Buys Beef for School Lunch Program”), which was discountedweeks ago, and not the one on the wire service (“15% Fewer Soybeans and 10% MoreFishmeal”), which went into the market two days ago. You must act on news that has notyet been printed. To anticipate changes, you must draw a single conclusion for the manycontingencies possible from fundamental data, or
1. Recognize recurring patterns in price movement and determine the most likely re-sults of such patterns. - -
2. Determine the trend of the market by isolating the basic direction of prices over aselected time interval.RANDOMWALK - 3
 
The bar chart, discussed in Chapter 9 (“Charting”), is the simplest representation ofthe market. These patterns are the same as those recognized by Livermore on the tickertape. Because they are interpretive, more precise methods such as point-and-figure chart-ing are also used, which add a level of exactness to charting. Point-and-figure charts arepopular because they offer specific trading rules and show formations similar to both barcharting and ticker-tape trading.
Mathematical modeling, using traditional regression or discrete analysis, has become apopular technique for anticipating price direction. Most modeling methods are modifica-tions of developments in econometrics, basic probability, and statistical theory. They areprecise because they are based entirely on numerical data.
The proper assessment of the price trend is critical to most commodity trading sys-tems. Countertrend trading is just as dependent on knowing the trend as a trend-followingtechnique. Large sections of this book are devoted to the various ways to isolate the trend,although it would be an injustice to leave the reader with the idea that a price trend is auniversally accepted concept. There have been many studies published claiming thattrends, with respect to price movement, do not exist. The most authoritative papers on thistopic are collected in Cootner, The Random Character of Stock Market Prices (MIT Press);more recent and readable discussions can often be found in The Financial Analysts Jour-nal, an excellent resource. . :
Personal financial management has gained an enormous number of tools during thisperiod of computerized expansion. The major spreadsheet providers include linear regres-sion and correlation analysis; there is inexpensive software to perform spectral analysisand apply advanced statistical techniques; and development software, such as Trade-Station and MetaStock, have provided trading platforms and greatly reduced the effortneeded to program your ideas. The professional maintains the advantage of having all oftheir time to concentrate on the investment problems; however, the nonprofessional is nolonger at a disadvantage because of the tools. ,
RANDOM WALK
It has been the position of many fundamental and economic analysis advocates that thereis no sequential correlation between the direction of price movement from one day to thenext. Their position is that prices will seek a level that will balance the supply-demand fac-tors, but that this level will be reached in an unpredictable manner as prices move in anirrégular response to the latest available information or news release.
If the random walk theory is correct, many well-defined trading methods based onmathematics and pattern recognition will