<s> SmarterTradingImproving Performance inChanging Markets
Perry J. Kaufman
McGraw-Hill, Inc.New York San Francisco Washington, D.C. Auckland BogotaCaracas Lisbon London Madrid Mexico City MilanMontreal New Delhi San Juan SingaporeSydney Tokyo Toronto
Library of Congress Cataloging-in-Publication DataKaufman, Perry J.Smarter trading : improving performance in changing markets /Perry J. Kaufman.p.cm.Includes index.ISBN 0-07-034002-1 (alk. paper)1. Program trading (Securities) I. Title.HG4515.5.K381995332.64'5—dc2094-23636CIP
Copyright © 1995 by Perry Kaufman. All rights reserved. Printed in theUnited States of America. Except as permitted under the United StatesCopyright Act of 1976, no part of this publication may be reproduced ordistributed in any form or by any means, or stored in a data base orretrieval system, without the prior written permission of the publisher.2 3 4 5 6 7 8 9 0 DOC/DOC 9 0 9 8 7 6 5ISBN 0-07-034002-1
The sponsoring editor for this book was David Conti, the editing supervisorwas Nancy Land, and the production supervisor was Donald Schmidt. Thisbook was set in Palatino by McGraw-Hill's Professional Book Group composition unit.Printed and bound by R. R. Donnelley & Sons Company.
This book is printed on recycled, acid-free paper containing aminimum of 50% recycled de-inked fiber.
This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It issold with the understanding that the publisher is not engagedin rendering legal, accounting, or other professional service. Iflegal advice or other expert assistance is required, the servicesof a competent professional person should be sought.—From the declaration of principles jointly adopted by a committee ofthe American Bar Association and a committee of publishers.
ContentsPreface
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Part 1. How Changing Markets and TechnologyAffect Results1. The Impact of Change on Markets and TradingChanging Factors Affecting Markets and PricesTechnical Analysis7Evolution and Obsolescence12Structural Change: Seasonality15The Evolution of Markets17
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2. Assessing Market Reality
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The Screen Is History19Execution Problems and Performance22Globalization: Simultaneous Absorption26Factors That Always Exist27Change and Evolution28
3. Reasonable Expectations Give Achievable ResultsTrade-Offs31Giving the Computer Free ReignThrowing Microchips at It35The Use of Systems38Expectations40
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Contents
4. Risk and Return
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Risk Preference41Standardizing Risk and Return42Choosing between the Currency and Bond PortfoliosTime Periods Tell Different Stories48Specifying Acceptable Risk50Graphing Risk and Reward51Diversification and Risk Reduction53Adding Common Sense to Statistics61Risk of Ruin66Profit Goals66Summary68
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Part 2. Using Old and New Trading Tools toAchieve Reasonable Objectives5 . Profit-Taking
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A Test for Profit-Taking74The Results77Profit Objectives versus Time81Benefits of Using More Than One Profit ObjectiveSummary88
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6 . T h e Mixed Role o f S t o p s for Controlling R i s k
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Need for Risk Control90Risk Protection or False Hope?90Testing a System with a Stop-Loss94A Stop-Loss May Conflict with the Strategy103Managing Risk with and without Stops104Summary1057. Understanding Price ShocksTrading Risk Is Higher Than ExpectationsT y p e s of Price S h o c k s
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Impact of a Price Shock on an InvestmentHandling Price Shocks118Managing a Price Shock120Summary1278 . Smarter Trend-FollowingForecasting and FollowingTrend Trading131Adaptive Approach133
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129129
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ContentsThe Adaptive Moving Average138Trading Rules143Testing the AMA146Programming the Adaptive Moving Average
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9. Computer Learning, Neural Networks, andNew T e c h n o l o g yThe Teaching Process: First the Trainer156Artificial Intelligence and Pattern RecognitionApplications of Expert Systems160Neural Networks164Fuzzy Logic171
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Part 3. Making a Trading Strategy Robust1 0 . T e s t i n g for R o b u s t n e s s
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Overfitting177Separating Robustness from Parameter Selection178Testing Process181Part 1: Deciding What to Test182Part 2: Deciding How to Test186Part 3: Evaluating the Results204Part 4: Choosing the Specific Parameters to Trade209Part 5: Trading and Monitoring Performance212Other Important Practical Guidelines213Summary2171 1 . Improving the Performance of Existing Systems
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Measuring and Monitoring Predictability219Anticipation223Filtering System Signals227Reversing the Optimization Concept235Overnight Risk236Leverage, Costs, and Trend Speed238
Appendix: Notation and TerminologyIndex
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PrefaceYou can't dig a new hole by making the old one deeper
Trading is a difficult business. Finding a way to build steady profitstakes long, hard work or very good luck. Sometimes the effort fails; nomatter how much energy is applied, there is no answer to be found.Other times, a successful program has only a short lifespan before themarket changes. Smarter Trading tries to be realistic about how to findbroad-based trading strategies that can survive change. It uses a lateralsolution rather than a vertical one.
Vertical and LateralSolutionsA vertical solution is where each new part reinforces the previous work.A lateral solution is where the parts fit side by side, resting on theirown foundation. Think of searching for buried treasure. You know it'sin the back yard. You can dig one hole deeper and deeper or dig aseries of holes in different places.An 50-floor skyscraper is a vertical solution to living space. Buildingon the same foundation makes the final result dependent on all theprevious work. But markets change causing some assumptions to fail.The top of the building becomes very fragile when you start removingbricks from the middle.
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Preface
The lateral solution builds a wide base by taking the pieces, each oneof which can stand on its own and combining them side-by-side into asingle structure. None of the parts are complicated and none of themduplicate another piece. If one part fails, the others continue to work.
A Lesson fromSupercomputersAt one time, the biggest "supercomputers," used only for high-powered research, were the creation of a few brilliant engineers. Theybecame so sophisticated that each wire and connection between partsneeded to be as short as possible to enable the electric current to travelat maximum speed. The main processing units were designed as asphere so that each wire was an equal distance from the center.Faster computers are now built with a lot of slower, off-the-shelfparts. In this design, called "parallel processing," the slower components operate on different parts of the problem at the same time. Thecomputer companies that had invested tremendous resources in building complex systems were put out of business by someone who simplydivided the problem into many little pieces and solved them usinginexpensive, ready-made parts.Not all problems can be divided into many small parts, but most canbe divided. This book will teach the most important lessons about different aspects of trading, including profit-taking, trends, stops, riskand return, and testing methods. Using any one will improve results;using all of them will improve performance even more.
Looking for WhatIs Not ThereOmissions cause the biggest problems, and they are the hardest to findbecause they are not there. The mind's eye often fills the empty spaceswith what it expects to be there. In the same way that we fill theseomissions, we often overlook repeated, small events. We do not hearthe ticking of a clock that once seemed too loud.We will try to understand what to expect, then question the resultsthat are either much better or worse than expected. We are always fastto look for ways to fix losses, but slow to question profits.Learning is the result of experience. You do the best you can to analyze the problem, find a solution, and see if it works. Most often it
Preface
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does not work the first time because you failed to see the complete picture, underrated the importance of some factors, or missed an important part altogether. That is the normal way things work. Do notassume that anyone comes up with the perfect answer without trialand error. The process is not glamorous, but it is necessary. Being successful means being tenacious.
Wandering from the PathLateral thinking benefits from not following one path. It may take thebest from each area, applying those parts in which we have great confidence, rather than developing the "ultimate" indicator. As we getmore complicated, the benefits derived from the effort become questionable, and the solution may not be as lasting. Making very smallimprovements takes much more time and effort once you haveextracted the essence of an idea. It is often a good time to switch toanother approach when you feel that your efforts are becomingunproductive.One approach to lateral thinking is to reverse an idea. For example,baby Jane—by playing with the ball of wool—is annoying Grandma,who is trying to knit. A likely solution would be to put baby Jane intoher playpen where she cannot reach the wool. Another solution wouldbe to put Grandma and the wool into the playpen to protect them frombaby Jane. Either solution could work although most people wouldnot consider asking Grandma to get in the playpen. Later in the book,we look at using the worst test results rather than the best.Lateral thinking is results oriented. The goal is to get the bestanswer. A lateral solution often develops from a stumbling block, apoint where you can no longer go forward. You shift to another areawhere there is a possible solution. In doing this, you may discover thatparts of each direction can work together to create a better result.
GeneralistsWe will try to keep our perspective about the value of the techniquesused to build a robust trading strategy. We will be generalists, ratherthan specialists. We want to know, "Should we take profits or shouldwe wait for a trend reversal?" We could always find one case wheretaking profits is better than staying with the trend. Our objective is tofind out if it is a good rule in most cases.
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It is unproductive to try to prove that an exponentially weightedtrend is better than a simple moving average. Does the accuracy of oneapproach really make a difference to the direction of prices? If a system worked using an exponential calculation but did not work with asimple moving average, one would be forced to question the validityof the "trend." As a realistic analyst, I can say that all techniques areimperfect but many have value. When you are estimating answers,you should not calculate them to the 10th decimal place.
RealistsIn dealing with a market problem, we must ask if we are looking at thereal cause of the price move. Patterns may be coincidental. Even if weknow the cause, can we predict the result? Throughout this book, wewill return to the need for a logical solution, rather than one that iscomputer-generated.Trading programs cannot be perfect, but we need to know what toexpect. Is a stop-loss a good way to control risk, or does it only give usunfounded confidence? It is not important whether a stop-loss is goodor bad, only that we know the right answer.This book will also present some new ideas, such as an adaptive, orself-adjusting, moving average and a detailed plan for creating arobust trading program. In the spirit of a lateral solution, it will take anew look at simple ways to improve most trading models, extractingthe essential aspects from each idea. Examples will use forex, futures,stock, and stock index markets to show how readily these techniquesapply to all markets, and trading in general.PERRY J. KAUFMAN
Wells River, Vermont
AcknowledgmentsWriting a book is a long process that takes time from those closest toyou. Without the encouragement and support of Barbara, this volumewould have been long delayed. Credit must be given to our dog Terra,who always knew when it was time to take a break.P.J.K.
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PART 1How Changing Marketsand TechnologyAffect Results
1The Impact ofChange on Marketsand TradingThis book is about how to improve your trading in the stock, foreignexchange and futures markets. Although many technical solutions andspreadsheet applications appear in these pages, Smarter Trading is really about making decisions and solving problems. It will identify whymany trading strategies and forecasts fail and will show how toimprove results and create more lasting solutions.The approach taken here tries to be realistic; trading systems havelimitations, as do the tools and the traders. The techniques for improving profits and assessing risk focus on those areas that offer the greatestimprovement, rather than the subtleties of fine tuning. Most of the moredifficult topics are concerned with risk. Experienced traders usuallyknow what to do with profits; even for novice traders, profits often takecare of themselves. It is an unreasonably optimistic attitude toward riskthat gets many traders into trouble; therefore, sections of this book keepreturning to risk evaluation and control. We're in this for the long term.
Changing Factors AffectingMarkets and PricesRecent years have seen political and economic changes of large proportion. The emergence of China, the instability of the European MonetarySystem, and the faltering of Russia are all poised to produce massivechanges in trade. At the same time, technology has made immense3
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How Changing Markets and Technology Affect Results
advances. More powerful computers come in smaller packages. Prices canbe displayed for any time period in an array of multicolored windows.Methods that once worked do not work anymore. IBM stumbles, patterns change, markets are more volatile than ever, and even seasonalsare not the same. Program trading has been declared "disruptive" allover the world. Traders sit behind screens in massive bank tradingrooms, surrounded by high-powered displays, looking for arbitrageopportunities between any two markets in any two countries. All thiscontinues 24 hours each day.This evolution of markets is a structural change that moves in onlyone direction. The introduction of the automated exchanges in theUnited States and United Kingdom aren't anomalies, but a trend.Eventually, the floor traders will disappear—not all at one time, butedged out by automated exchanges that will surround them and slowlyinfringe on the sanctity of even the largest trading floors. Adapting maytake more effort than simply retesting a program, adjusting for inflation, or changing the value of a stop-loss, but it cannot be ignored.Along with increasing complexity is additional competition. Floortraders once had the advantage of being aware of every price tick. Nowwe can recall prices and volume instantly, and catch up on marketaction even when we have been away from the picture for hours ordays. It requires more to compete successfully. This book will helpidentify the problems. It will provide solutions and an understandingof new tools and how to use them.Changing Technology forMarket AnalysisAdvances in technology have caused great changes in the tradingindustry. New tools and techniques are absorbed quickly. The goal ofimproving returns by a fraction of a point has tremendous rewards,
Figure 1-1. Technology evolves, markets evolve
The Impact of Change on Markets and Trading
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enough to motivate and finance major research projects. And asmachines increase in their ability to process more of everything, pushing those limits becomes a compulsion.There is also a fascination with the new tools and the ability to display graphics and analyze prices. Real-time data from all over theworld is being processed at speeds measured in nanoseconds. We cando more faster and cheaper, even when we're not always sure what weare doing.Fundamentals at the Root"Fundamentals" will always be the reason for price change.Fundamental analysis is the study of information that can influence corporate earnings, dividends, and interest rates, resulting in a pricechange. In both stock and commodity markets, forecasts are the resultof comparing current and past economic data, and determining theeffects of government policy on interest rates and growth. Unexpectedevents introduce volatility and uncertainty.In general, the direction of stock prices is related to the health of business, which might include data on the Gross National Product (GNP),Consumer Price Index (CPI), retail sales, employment, and interestrates. If the economy is expanding, you can expect equity markets torise. It is still a challenge to look further for the industries and sectorsthat will perform independently, or without correlation, to the marketas a whole.Supply and demand determine the price of goods and materials: howmuch there is versus how much is wanted. The more material, the lowerthe price; the more that is wanted, the higher the price. The fundamentals of price change are clear. It is the changes in those factors or theanticipation of change that causes prices to move.One of the first computer applications for price forecasting used atechnique called multiple regression (Box 1-1). Data on imports, exports,production, consumption, interest rates, inflation, technology, andother essentials could be analyzed in conjunction with the price.Fundamental analysis explains what has happened in the past by assigning "weighting factors" to the information put into the computer. If youdon't put in the right data, you don't get a good answer. Putting in toomuch data isn't as bad, but it takes a longer time to process. Sometimes,too much data allows the computer to find answers that are only coincidental, which we call "overfit."The answer to a regression analysis is assigned a confidence level,which indicates its accuracy. It is stated as "plus or minus" an error factor (e.g., interest rates will drop to 5½ percent ± 1 percent by May).
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How Changing Markets and Technology Affect Results
Box 1-1. DETERMINING A COMMODITY PRICEWITH FUNDAMENTALSA simple regression model calculates a commodity price from the history of fundamental factors. In this example, the price of soybeans issimply the weighting of supply and demand:Est_Price = constant + (weights x supply) + (weightD x demand)± error
where Est_Price is the current estimated valuesupply is the total productiondemand is the total distributionerror is the error reflecting the accuracy of the resultsand constant, weights, and weightD are calculated using aregression program.Data from 1964 to 1975 gives constant = -1.64, weights = 3.97 andweightD = 0.81, indicating that changes in the supply of soybeans, represented by the much larger value of weights, are much more important than demand. The error factor would be large because only a fewyears were used in the calculation.
A regression analysis of fundamental data tells where prices shouldbe, in the same sense as an option fair value calculation. It is very structured and provides only a single price range, which is considered "normal." It may not include data that cause the market to anticipatechanges.In general, this classic approach is not helpful to a trader because itsays nothing about risk. If the current price level is below the calculated one, but prices start to fall instead of rise, when do you say thatsomething is wrong? The forecast only shows where the price shouldbe; it does not tell anything about how it will get there.Fundamental analysis still makes sense, but it remains the domain ofinstitutions and long-term traders. It requires a well-capitalizedinvestor to absorb fairly large equity swings during periods when lessimportant factors cause market volatility. For others, the risk is toohigh, the analysis takes too much time and effort, and the profits are toofar off.This method of econometric analysis can be applied to the stock index,but not to individual shares; however, results are still very general.
The Impact of Change on Markets and Trading
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Newer methods, such as neural networks and expert systems, which arediscussed in later chapters, have replaced econometric analysis, offeringsome additional accuracy when used in the traditional way, and muchmore flexibility.
Technical AnalysisTechnical analysis is a broad area that uses price and related data todecide when to buy and sell. It tries to bridge the problems that fundamental analysis has about the specifics of timing and risk. The methodsused can be as interpretive as chart patterns and astrology, or as specific as mathematical formulas and spectral analysis.From the time chart interpretation first appeared to the early use ofthe home computer, technicians have been separated from fundamentalists. More recently, the line between them has become gray.Fundamentals provide the reason and direction of price movement, andtechnicals give the timing and risk control.The two methods can be kept separate by making a decision and commitment based on fundamentals, then creating and implementing theplan using technicals. Or, the process can be integrated with an expertsystem approach, a sophisticated neural network, or simply a combination of individual programs. It is only necessary that each make senseand satisfy the preset objectives.Automating the TrendComputerized technical analysis is associated most with the movingaverage (Box 1-2). It came into greatest popularity in the early 1980s andhas remained the basis for many technical programs. All factors thatinfluence the market are assumed to be netted out as the current price.A simple moving average applied to those prices gives a trend. Thelonger term 200-day average is a benchmark indicator of price directionfor most stock issues. Short-term 5-, 10-, and 20-day trends, related toweekly and monthly periods, are often used for timing entries and exitsand for leveraged futures and options markets.A moving average, or similar technical indicator, is frequently usedto confirm a decision to enter the market. Although there may be reasonto believe prices will move higher, fundamental analysis can be complex, and occasionally unexpected external factors overwhelm the normal situation. By waiting for a moving average to turn up, the programmay sacrifice some initial profit for a greater chance of being correctand of using capital effectively.
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How Changing Markets and Technology Affect Results
Box 1-2. EASIER NEW WAYS OF CALCULATINGMOVING AVERAGESA moving average is now a "function" in a strategy testing program ora spreadsheet. A 3-day moving average may appear as:@Average(close,3) = (close + close[1] + close[2])/3or the spreadsheet form:@AVG(B3..B5)/3
An exponential trend is simply another function, @Exp_MA(close,10),all of which makes price analysis very easy to perform. The trendlineformed by the daily averages produces a buy signal when it turns upand a sell when it turns down.
Trend trading was very successful during the 1970s and into the1980s. Even now, it is just as important to know the direction of prices,but it has become more difficult to trade a simple trend system. Whatwas once a strong commitment to "the trend is your friend," we nowhear that there are too many systematic trend-followers who are "pushing the market" and "triggering stops."Trend following proved to many investors that technical analysis isviable. Some analysts, equipped with real-time intraday data, were ableto continue trading the trend by applying the same logic to hourly or15-minute prices. Others looked for additional indicators or moresophisticated tools, often adapted from another industry.IndicatorsTiming indicators, such as relative strength and stochastics have becomevery popular. Most quote equipment provides a broad selection of techniques that users can modify. The Relative Strength Index (RSI), developed by Welles Wilder, is a ratio of the total daily upmoves to totaldaily downmoves over the past 14 days, expressed from 0 to 100:@RSI(close,14) = 100 x (RS/(1 + RS)whereRS = @SUM(TotaLUp_Moves,14)/@SUM(Total_Down_Moves,14)
The Impact of Change on Markets and Trading
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Because of the flexibility of computers, any trader can substitute another time period for the standard 14-day interval.The stochastic, developed by George Lane, is equally popular. It givesthe relative position of the closing price within the previous high-lowrange, determined by the length of the period used for the calculation.The raw stochastic, called FastK, which ranges from a value of 0 to 100,is not normally used for trading because it is too sensitive to pricechange. Instead, the SlowK (also called %D) and SlowD, a 3-day smoothing of SlowK,- have become the popular values for trading. The 5-periodstochastic is given as@FastK(series,5) = 100 x (close - @Lowest(5)/(@Highest(5)- @Lowest(5))@SlowK(series,5) = @Moving_Average(@FastK(series,5),3)@SlowD(series,5) = @Moving_Average(@SlowK(series,5),3)
As with the RSI, traders vary the period of the stochastic to make itmore or less sensitive to price movement.Stock Market Advance/DeclineIndicatorsIn addition to indicators that use price, a wide selection of calculationsare based on volume, or the number of advancing and declining stocks.It is interesting to see how the same numbers are used with slightly different emphasis:Bolton-Tremblay:Schultz A/T:McClellan Oscillator:
BT = (Advancing - Declining)/UnchangedSAT = Advancing/(Advancing + Declining+ Unchanged)McC = Advancing - Declining
For each of the indicators, an index is created by adding the currentvalue to the accumulated index value for the previous day, as in theBolton-Tremblay Index:BTX = BTX[1] + BTWhile there is virtue in simplicity, it is not clear that an index such asthe one based on advancing and declining issues improves a moving
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How Changing Markets and Technology Affect Results
average signal. The indexes themselves require interpretation andselection because they do nothing to filter noise, nor is it apparent howto use those days with significantly greater advancing or decliningissues. Instead of just one difficult price series to work with, you nowhave the original price data plus an equally difficult index.Status of Technical AnalysisSimple moving averages and indicators do not give the complete pictureof technical analysis. There are sophisticated graphics programsthat allow the user to draw trendlines and channels. They can performspectral analysis to find cycles; give Gann lines and angles, Fibonaccispirals, and Elliott waves; and create ARIMA (Autoregressive IntegratedMoving Average) models, which constantly recalculate the best movingaverage for every new piece of data.Testing software has also pushed the industry forward. Anyone withan untried trading strategy or theory can enter simple instructions andtest the rules on a wide selection of data. The most popular examples ofthis software are Dow Jones' TeleTrac, Omega's System Writer, andEquis' MetaStock. These programs eliminate the need for a computerspecialist, by providing standard "functions" (as described earlier inthis chapter) for calculating a moving average, true range, highest andlowest price, and many other convenient values, in an easy-to-use form.For example,@Average(Price,Length)@Bollinger_Band(Price,Length,StdDev)@Bullish_Divergence(Price,0sc,Strength,l_ength)@Linear_Regression(Price,Length)
are the functions for a simple moving average, a Bollinger band, bullishdivergence, and the angle from the horizontal of a linear regression line.They are all easy to understand even without a manual. Length is thenumber of periods used in the calculation, and price is any data series,whether daily, hourly, or user defined.Strategy-testing software takes two forms: (1) a spreadsheet style system, such as TeleTrac, in which each calculation becomes a new row, andeach day appears as a column; (2) the System Writer design, which allowsall the power of computer programming, similar to the BASIC language(Box 1-3). In Omega's software, the individual calculation can be displayed by day on request.
The Impact of Change on Markets and Trading
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Box 1-3. PROGRAMMING SYSTEMS USING NEWCOMPUTER SOFTWAREAn "efficiency ratio" is calculated as 10-day price changes divided bythe sum of 10 daily closing price differences. The EfRatio gives the efficiency, or relative noise, of price movement over the 10-day period,and is used for the Adaptive Moving Average in Chapter 8.TeleTrac allows the calculations to be entered in their own spreadsheet format. The first column is the name of the value being createdand the second gives the formula. Results are shown for each timeinterval selected, from ticks to monthly. This example has daily data:18 Feb 93 23 Feb 93 24 Feb 93 25 Feb 93diffAbs_val(close-close[1])noise Sum(diff,10)signal close-close[10]EfRatio Abs_val(signal)/noise
0.643.9691.290.325
0.974.5212.680.593
0.454.8392.090.433
0.575.1241.810.353
System Writer uses Omega's fully programmable Easy Language to findthe same ratio:noise = @Summation(@AbsValue(close[0] - close[1], length)signal = close[0] - close[10]if noise <> 0, then Efficiency_Ratio = signal/noise
The last line of the System Writer code tests that the noise is not equal to("<>") zero before dividing. In the first line, it "nests" the first two linesof the TeleTrac code.
Buy and sell signals, as well as moving average lines, oscillators, anduser-defined values can be displayed on split-screen graphics. Everycalculation and detailed statistics of the test results can be easilyretrieved and printed.New TechnologyAs computers have become more powerful and scientists try to synthesize the human brain, some new techniques have become more practicalfor market analysis. The area called artificial intelligence includes themost promising neural networks, as well as simple pattern recognition,expert systems, and fuzzy logic. These will be covered later in this book.
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How Changing Markets and Technology Affect Results
Neural networks are already replacing regression analysis as the bestmethod for finding how fundamental factors change price. But thepower of neural nets is still untouched. It is primarily used to find thesame continuous relationships between dividends, economic conditions, and price—or supply, demand, and price—that was the technique of the older tools. It has the ability to identify how today's set offactors compares with specific cases in history, an equally sophisticatedand practical approach.
Evolution and ObsolescenceIt is easy to argue that communications and computers have changedworld and local economies, trading tools, and market participants. Theextent of these changes requires us to look at the process as an evolution. It should not be a surprise that simple systems that worked wellduring the 1970s and 1980s are no longer profitable.Economic changes have altered price relationships. Countries havefloated their currencies and interest rates, as gold was allowed to betraded in the United States in 1975. Other countries have tried to controlthe fluctuation by forming pacts, such as the European MonetarySystem or OPEC (Organization of Petroleum Exporting Countries). Foreach of these events, there is a change in price patterns, sometimes morevolatile; other times less volatile; and still other cases go unnoticed. Asimple way of looking at this evolution is by comparing the performance of a trend-following system in different types of markets.
Maturing Markets andPrice TrendsAs markets become familiar and accepted, participation increases, andwith more participation comes a higher level of "noise." The U.S. stockmarket has been a main investment for pension funds, individuals, andother countries for many years. Broad interest takes on the characteristic of a constant level of