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For More Information Please Visit : T H E E N C Y C L O P E D I A O F T R A D I N G S T R A T E G I E S JEFFREY OWEN KATZ,Ph.D. DONNA1. MCCORMICK T R A D E M A R K S A N D S E R V I C E M A R K S Company and product names associated with listings in this book should be con- sidered as trademarks or service marks of the company indicated. The use of a reg- istered trademark is not permitted for commercial purposes without the permission of the company named. In some cases, products of one company are offered by other companies and are presented in a number of different listings in this book. It is virtually impossible to identify every trademark or service mark for every prod- uct and every use, but we would like to highlight the following: Visual Basic, Visual C++, and Excel are trademarks of Microsoft Corp. NAG function library is a service mark of Numerical Algorithms Group, Ltd. Numerical Recipes in C (book and software) is a service mark of Numerical Recipes Software. TradeStation, SuperCharts, and SystemWriter Plus are trademarks of Omega Research. Evolver is a trademark of Palisade Corporation. Master Chartist is a trademark of Robert Slade, Inc. TS-Evolve and TradeCycles (MESA) are trademarks of Ruggiero Associates. Divergengine is a service mark of Ruggiero Associates. C++ Builder, Delphi, and Borland Database Engine are trademarks of Borland. CQC for Windows is a trademark of CQG, Inc. Metastock is a trademark of Eqnis International. technical analysis function library is a service mark of FM Labs. Excalibur is a trademark of Futures Truth. MATLAB is a trademark of The MathWorks, Inc. MESA96 is a trademark of Mesa. ..~.NTENTS PREFACE xiii INTRODUCTION xv What Is a Complete Mechanical Trading System? - What Are Good Entries and Exits? *The Scientific Approach to System Development *Tools and Materials Needed for the Scientific Approach PART I Tools of the Trade Introduction 1 Chapter1 Data 3 Types of Data *Data Time Frames *Data Quality l Data Sources and Vendors Chapter 2 Simulators 13 Types of Simulators * Programming the Simulator *Simulator Output @erformance summnry reports; trade-by-trade rep*ris)ulator Perfomxmce (speed: capacity: power) l Reliability of Simulators - Choosing the Right Simulator * Simulators Used in This Book Chaoter 3 Optimizers and Optimization 29 What Optimizers Do *How Optimizers Are Used *?Lpes of Optimization (implicit optimizers; brute force optimizers; user-guided optimization; genetic optimizers; optimization by simulated annealing; analytic optim liiearp;mgrwnming) l How to Fail with Optimization (small samples: flxargetneter sets; noveri~cation) . How to Succeed with O&mization (h-ge, representative samples; reles andparameters; veriicatim @results) *Alternatives to Traditional Optimization *Optimizer Toolsand Information * Which Optimizer Is forYou? Chapter 4 Statistics 51 Why Use Statistics to Evaluate Trading Systems? l Sampling *Optimization and Curve-Fitting l Sample Size and Representativeness . Evaluating a System Statistically * Example 1: Evaluating the Out-of-Sample Tesitfth( ewhdattribution is not normal? what if there is serial dependence? what if tmarkets change?) lExample 2: Evaluating the In-Sample T* estIsnterpreting the Example Statistics (optimization i-esults;verification results)Other StatisticTechniques and Their Use (genetically evoJved systems; multiple regression; monte car10 simulations; out-of-sample testing; walk-forward testing) * Conclusion PART II The Study of Entries Introduction 71 What Constitutes a Good Entry? *Orders Used in Entries (stop orders; limit orders; market orders; selecting appropriate orders)* Entry Techniques Covered in This Book (breakouts and moving averages; oscillators; seasonality: lunar and solar phenomena: cycles and rhythms; neural networks; geneticaNy evolved entry rules) *Standardized Exits *Equalization of Dollar Volatility *Basic Test Portfolio and Platfcnm Chapt5 er Breakout Models 83 Kinds of Breakouts l Characteristics of Breakouts . Testing Breakout Models l Channel Breakout Entries (close only channel breakouts; highest higMowest low bnxzkouts) l Volatility Breakout Entriesl Volatility Breakout Variations(long positions only; currencies only; adx tremififilt. Summary Analyses (breakout types: entry orders; interactions; restrictions andjilters; analysis by marketConclusion l What Have WL eamed? Chapter 6 Moving Average Models 109 What is a Moving Avera -ge?rposeof a Moving Average *The Issue of Lag l Types of Moving Avera lgesypes of Moving Average Entry M odCesaracteristics of Moving Average Entries l Orders Used to Effect Entries *Test Methodology ’ Tests of Trend-Following Mo *Teests of Counter-Trend Models *Conclusion l What Have We Learned? ix Chapter 7 Oscillator-Based Entries 133 What Is an Oscillator?l Kinds of Oscillators * Generating Entries with Oscillators * Characteristics of Oscillator Entr. Test Methodology l Test Results (teas of overbought/oversold models; tests of signal line models; tests of divergence models; summary analyses) - Conclusion *What Have We Learned? ChapterS Seasonality 153 What Is Seasonality? l Generating Seasonal Entriel Characteristics of Seasonal Entries . Orders Used to Effect Seasonal Entries . Test Methodology . Test Results (tesof the basiccrossover model; seft the basmomentum model: testosf the crossover model with con$mtion; tests of the C~SSOV~~model with confirmation and inversions: summary analyses) * Conclusion *What Have We Learned? Chmter 9 Lunar and Solar Rhythm 1s79 Legitimacy or Lunacy? lLunar Cycles and Trading (generating lunar entries: lunar test methodology; lunar test resultsoftethe basic cmmo~er model; testsf the basic momentum model: te sfs the cnx~mer model with confirmattieosof.;the crmmver model with confirmation and inversions; summary analyses; conclusion) *Solar Activity and Trading (generazing solar entries: solar test results: conclusion) * What Have We Learned? Chapter 10 Cycle-Based Entries 2Q3 Cycle Detection Using MESA l Detecting Cycles Using Filter Banks (butterworth jilters; wavelet-basedjilter* Generating Cycle Entries Using Filter Banks * Characteristics of Cycle-Based Entries . Test Methodology . Test Results . Conclusion l What Have We Learned? Chapter 11 Neural Networks 227 What Are Neural Networks? (feed-forward neural networks) . Neural Networks in Trading l Forecasting with Neural Networksl Generating Entries with Neural Predictions . Reverse Slow %K Model (codefor the reverse slow %kmodel: test methodologfor the reverse slow%k model; training resuotr the reverse slow %k model) l Turning Point Models (codefor the turning point models; test methodology for the turning point models; training resulrs for the turning point models) *Trading Results for All Models (@adingresults for the reverse slow %k model: frading results for the bottom ruming point model; trading results for the top turning poinf model) * Summary Analyses l Conclusion *What Have We Learned? Chapter 12 Genetic Algorithms 257 What Are Genetic Algorithms? *Evolving Rule-Based Entry Models *Evolving an Entry Model @herule remplares) *Test Methodology (code for evolving an entry model) lTest Results (solutions evolved for long entries; solutions evolved for short enrries; fesf results for the standard portfolio; market-by-market tesf resulrs: equify curves; the rules for rhe solurions tesred)clusion *What Have We Learned? PART III The Study of Exits Introduction 281 The Importance of the Exitl Goals of a Good Exit Strategy *Kinds of Exits Employed in an Exit Strategy (money management exits; trailing exits; projir tnrgef exiW rime-based exits; volarilify airs: barrier exits; signal exits) *Considerations When Exiting the Market (gunning; trade-offs with prorecrive stops: slippage; conC?nian rrading: conclusion) *Testing Exit Strategies *Standard Entries for Testing Exits (the random entry model) Chaot1 er The Standard Exit Strate2 g9y3 What is the Standard Exit Strategy?Characteristics of the Standard Exit *Purpose of Testing the SES lTests of the Original SES (test results) *Tests of the Modified SES (test resulrs) *Conclusion - What Have We Learned? Chapter 14 Improvements on the Standard E 3x0it Purpose of the Testsl Tests of the Fixed Stop and Profit Target *Tests of Dynamic Stops (rest of the highest higWlowest low stop; fesf of the dynamic arr-based stop: fat of the modified exponential moving average dynamic stop) *Tests of the Profit Taget * Test of the Extended Time Limit - Market-By-Market Results for the Best Exit * Conclusion l What Have We Learned? P R E F A C E In this book is the knowledge needed to becm omc~ersuccessful trader of com- modities. As a comprehensive reference and system developer’s guide, the book explains many popular techniques and puts them to the test, and explores innova- tive ways to take profits out of the market and to gain an extra edge. As well, the book provides better methods for controlling risk, and gives insight into which methods perform poorly and could devastate capital. Even the basics are covered: information on how to acquire and screen data, how to properly back-test systems using trading simulators, how to safely perform optimization, how to estimate and compensate for curve-fitting, and even how to assess the results using inferential statistics. This book demonstrates why the surest way to success in trading is through use of a good, mechanized trading system. For all but a few traders, system trading yields mm-e profitable results than discretionary trading. Discretionary trading involves subjective decisions that fre- quently become emotional and lead to losses. Affect, uncertainty, greed, and fear easily displace reason and knowledge as the driving forces behind the trades. Moreover, it is hard to test and verify a discretionary trading model. System- based trading, in contrast, is objective. Emotions are out of the picture. Through programmed logic and assumptions, mechanized systems express the trader’s reason and knowledge. Best of all, such systems are easily tested: Bad systems can be rejected or modified, and c gotescan be improved. This book contains solid information that can be of great help when designing, building, and testing a profitable mechanical trading system. While the emphasis is on an in-depth, critical analysis of the various factors purported to contribute to winning systems, the essential elements of a complete, mechanical trading system are also dissected and explained. To be complete, all mechanical trading systems must have an entry method and an exit method. The entry method must detect opportunities to enter the mar- ket at points that are likely to yield trades with a good risk-to-reward ratio. The exit method must protect against excessive loss of capital when a trade goes wrong or when the market turns, as well as effectively capture profits when the market moves favorably. A considerable amount of space is devoted to the systematic back-testing and evaluation of exit systems, methods, and strategies. Even the trader who already has a trading strategy or system that provides acceptable exits is likely to discover something that can be used to improve the system, increase profits, and reduce risk exposure. Also included in these pages are trading simulations on entire pqrtfolios of tradables.As is demonstrated, running analyses on portfolios is straightforward, if not easy to accomplish. The ease of computing equity growth curves, maximum drawdowns, risk-to-reward ratios, returns on accounts, numbers of trades, and all xiv PREFACE the other related kinds of information useful in assessing a trading system on a whole portfolio of commodities or stocks at once is made evident. The process of conducting portfolio-wide walk-forward and other forms of testing and optimiza- tion is also described. For example, instruction is provided on how to search for a set of parameters that, when plugged into a system used to trade each of a set of commodities, yields the best total net profit with thd eraodoestn(or perhaps the best SharpeRatio, or any other measure of portfolio performance desired) for that entire set of commodities. Small institutional traders (CTAs)wishing to run a system on multiple tradables, as a means of diversification, risk reduction, and liq- uidity enhancement, should find this discussion especially useful. Finally, to keep all aspects of the systems and components being tested objective and completely mechanical, we have drawn upon our academic and sci- entific research backgrounds to apply the scientific method to the study of entry and exit techniques. In addition, when appropriate, statistics are used to assess the significance of the results of the investigations. This approach should provide the most rigorous information possible about what constitutes a valid and useful com- ponent in a successful trading strategy. So that everyone will benefit from the investigations, the exact logic behind every entry or exit strategy is discussed in detail. For those wishing to replicate and expand the studies contained herein, extensive source code is also provided in the text, as well as on a CD-ROM (see offer at back of book). Since a basic trading system is always composed of two components, this book naturally includes the following two parts: “The Study of Entries” and “The Study of Exits.” Discussions of particular technologies that may be used in gener- ating entries or exits, e.g., neural networks, are handled within the context of devel- oping particular entry or exit strategies. The “Introduction” contains lessons on the fundamental issues surrounding the implementation of the scientific approach to trading system development.fT irhtepart of this book, “Tools of the Trade,” con- tains basic information, necessary for all system traders. The “Conclusion” pro- vides a summary of the research findings, with suggestions on how to best apply the knowledge and for future research. The ‘Appendix” contains references and suggested reading. Finally, we would like to point out that this book is a continuation and elab- oration of a series of articles we published as Contributing Writers to Technical Analysis of Stocks and Commod fites 1996, onward. Jeffrey Owen Katz, Ph.D., and Donna L. McCormick I N T R O D U C T I O N There is one thing that most traders have in common: They have taken on the challenge of forecasting and trading the financial markets, of searching for those small islands of lucrative inefficiency in a vast sea of efficient market behavior. For one of the authors, Jeffrey Katz, this challenge was initially a means to indulge an obsession with mathematics. Over a decade ago, he developed a model that pro- vided entry signals for the Standard & Poor’s 500 (S&P 500) and OEX. While these signals were, at that time, about 80% accurate, Katz found himself second- guessing them. Moreover, he had to rely on his own subjective determinations of such critical factors as what kind of order to use for entry, when to exit, and where to place stops. These determinations, the essence of discretionary trading, were often driven more by the emotions of fear and avarice than by reason and knowl- edge. As a result, he churned and vacillated, made bad decisions, and lost more often than won. For Katz, like for most traders, discretionary trading did not work. If discretionary trading did not work, then what did? Perhaps system trading was the answer. Katz decided to develop a completely automated trading system in the form of a computer program that could generate buy, sell, stop, and other necessary orders without human judgment or intervention. A good mechanical system, logic suggested, would avoid the problems associated with discretionary trading, if the discipline to follow it could be mustered. Such a system would pro- vide explicit and well-defined entries, “normal” or profitable exits, and “abnor- mal” or money management exits designed to control losses on bad trades, A fully automated system would also make it possible to conduct historical tests, unbiased by hindsight, and to do such tests on large quantities of data. Thorough testing was the only way to determine whether a system really worked and would be profitable to trade, Katz reasoned. Due to familiarity with the data series, valid tests could not be performed by eye. If Katz looked at a chart and “believed” a given formation signaled a good place to enter the market, he could not trust that belief because he had already seen what happened after the forma- tion occurred. Moreover, if charts of previous years were examined to find other examples of the formation, attempts to identify the pattern by “eyeballing” would be biased. On the other hand, if the pattern to be tested could be formally defined and explicitly coded, the computer could then objectively do all the work: It would run the code on many years of historical data, look for the specified for- mation, and evaluate (without hindsight) the behavior of the market after each instance. In this way, the computer could indicate whether he was indeed correct in his hypothesis that a given formation was a profitable one. Exit rules could also be evaluated objectively. Finally, a well-defined mechanical trading system would allow such things as commissions, slippage, impossible tills, and markets that moved before he xvi could to be factored in. This would help avoid unpleasant shocks when moving from computer simulations to real-world trading. One of the problems Katz had in his earlier trading attempt was failing to consider the high transaction costs involved in trading OEX options. Through complete mechanization, he could ensure that the system tests would include all such factors. In this way, potential surprises could be eliminated, and a very realistic assessment could be obtained of how any system or system element would perform. System trading might, he thought, be the key to greater success in the markets. WHAT IS A COMPLETE, MECHANICAL TRADING SYSTEM? One of the problems witb Katz’s early trading was that his “system” only provided entry signals, leaving the determination of exits to subjective judgment; it was not, therefore, a complete, mechanical trading system. A complete, mechanical trading system, one that can be tested and deployed in a totally objective fashion, without requiring human judgment, must provide both entries and exits. To be truly com- plete, a mechanical system must explicitly provide the following information: 1. When and how, and possibly at what price, to enter the market 2. When and how, and possibly at what price, to exit the market with a loss 3. When and how, and possibly at what price, to exit th weimarket a profit The entry signals of a mechanical trading system can be as simple as explic- it orders to buy or sell at the next day’s open. The orders might be slightly more elaborate, e.g., to enter tomorrow (or on the next bar) using either a limit or stop. Then again, very complex contingent orders, which are executed during certain periods only if specified conditions are met, may be required-for example, orders to buy or sell the market on a stop if the market gaps up or down more than so many points at the open. A trading system’s exits may also be implemented using any of a range of orders, from the simple to the complex. Exiting a bad trade at a loss is frequently achieved using a money management stop, which tertninates the trade that has gone wrong before the loss becomes seriously damaging. A money management stop, which is simply a stop order employed to prevent runaway losses, performs one of the functions that must be achies vedeinanner by a system’exit strat- egy; the function is that of risk control. Exiting on a profbe maccomplished in any of several different ways, including by the use pm@ targets, which are simply limit orders placed in such a way that they end the trade once the market moves a certain amount in the trader’s favortrailing stowhich are stop orders used to exit with a profit when the market begins to reverse direction; and a wide variety of other orders or combinations of orders. In Katz’s early trading attempts, the only signals available were of probable direction or turning points. These signals were responded to by placing buy-at- market or sell-at-market orders, orders that are often associated with poor fills and lots of slippage. Although the signals were often accurate, not every turning point was caught. Therefore, Katz could not simply reverse his position at each signal. Separate exits were necessary. The software Katz was using only served as a par- tially mechanical entry model; i.e., it did not provide exit signals. As such, it was not a complete mechanical trading system that provided both entries and exits. Since there were no mechanically generated exit signals, all exits had to be deter- mined subjectively, which was one of the factors responsible for his trading prob- lems at that time. Another factor that contributed to his lack of success was the inability to properly assess, in a rigorous and objective manner, the behavior of the trading regime over a sufficiently long period of historical data. He had been fly- ing blind! Without having a complete system, that is, exits as well as entries, not to mention good system-testing software, how could such things as net profitabil- ity, maximum drawdown, or the Sharpe Ratio be estimated, the historical equity curve be studied, and other important characteristics of the system (such as the likelihood of its being profitable in the future) be investigated? To do these things, it became clear-a system was needed that completed the full circle, providing complete “round-turns,” each consisting of an entry followed by an exit. WHAT ARE GOOD ENTRIES AND EXITS? Given a mechanical trading system that contains an entry model to generate entry orders and an exit model to generate exit orders (including those required for money management), how are the entries and exits evaluated to determine whether they are good? In other words, what constitutes a good entry or exit? Notice we used the terms entry orders and exitorders, not entry or exit sig- nals. Why? Because “signals” are too ambiguous. Does a buy “signal” mean that one should buy at the open of the next bar, or buy using a stop or limit order? And if so, at what price? In response to a “signal” toexit a long position, does the exit occur at the close, on a profit target, or perhaps on a money management stop? Each of these orders will have different consequences in terms of the results achieved. To determine whether an entry or exit method works, it must produce more than mere signals; it must, at smnepoint, issue highly specific entry and exit orders.A fully specified entry or exit order may easily be tested to determine its quality or effectiveness. In a broad sense, good entry orderis one that causes the trader to enter the market at a point where there is relatively low risk and a fairly high degree of potential reward. A trader’s Nirvana would be a system that generated entry orders to buy or sell on a limit at the most extreme price of every turning point. Even if xviii lNTR”D”Cn”N the exits were only merely acceptable, none of the trades would have more than one or two ticks of adverse excursion (the largest unrealized loss to occur within a trade), and in every case, the market would be entered at the best obtainable price. In an imperfect world, however, entries will never be that good, but they can be such that, when accompanied by reasonable effective exits, adverse excursion is kept to acceptable levels and satisfying risk-reward ratios are obtained. What constitutes an elective exit? An effective exit must quickly extricate the trader from the market when a trade has gone wrong. It is essential to preserve cap- ital from excessive erosion by losing trades; an exit must achieve this, however, without cutting too many potentially profitable trades short by converting them into small losses. A superior exit should be able to hold a trade for as long as it takes to capture a significant chunk of any large move; i.e., it should be capable of riding a sizable move to its conclusion. However, riding a sizable move to conclusion is not a critical issue if the exit strategy is combined with an entry formula that allows for reentry into sustained trends and other substantial market movements. In reality, it is almost impossible, and certainly unwise, to discuss entries and exits independently. To back-test a trading system, both entries and exits must be present so that complete round-turns will occur. If the market is entered, but never exited, how can any completed trades to evaluate be obtained? An entry method and an exit method are required before a testable system can exist. However, it would be very useful to study a variety of entry strategies and make some assessment regarding how each performs independent of the exits. Likewise, it would be advantageous to examine exits, testing different tech- niques, without having to deal with entries as well. In general, it is best to manip- ulate a minimum number of entities at a time, and measure the effects of those manipulations, while either ignoring or holding everything else constant. Is this not the very essence of the scientific, experimental method that has achieved so much in other fields? But how can such isolation and control be achieved, allow- ing entries and exits to be separately, and scientifically, studied? THE SCIENTIFIC APPROACH TO SYSTEM DEVELOPMENT This book is intended to accomplish a systematic and detailed analysis of the individual components that make up a complete trading system. We are propos- ing nothing less than a scientific study of entries, exits, and other trading system elements. The basic substance of the scientific approach as applied herein is as f0110ws: 1. The object of study, in this case a trading system (or one or more of its elements), must be either directly or indirectly observable, preferably without dependence on subjective judgment, something easily achieved with proper testing and simulation software when working with com- plete mechanical trading systems. 2. An orderly means for assessing the behavior of the object of study must be available, which, in the case of trading systems, is back-testing over long periods of historical data, together with, if appropriate, the applica- tion of various models of statistical inference, the aim of the latter being to provide a fix or reckoning of how likely a system is to hold up in the future and on different samples of data. 3. A method for making the investigative task tractable by holding most parameters and system components fixed while focusing upon the effects of manipulating only one or two critical elements at a time. The structure of this book reflects the scientific approach in many ways. Trading systems are dissected into entry and exit models. Standardized methods for exploring these components independently are discussed and implemented, leading to separate sections on entries and exits. Objective tests and simulations are run, and statistical analyses are performed. Results are presented in a consistent manner that permits direct comparison. This is “old hat” to any practicing scientist. Many traders might be surprised to discover that they, like practicing scien- tists, have a working knowledge of the scientific method, albeit in different guise! Books for traders often discuss “paper trading” or historical back-testing, or pre- sent results based on these techniques. However, this book is going to be more consistent and rigorous in its application of the scientific approach to the prob- lem of how to successfully trade the markets. For instance, few books in which historical tests of trading systems appear offer statistical analyses to assess valid- ity and to estimate the likelihood of future profits. In contrast, this book includes a detailed tutorial on the application of inferential statistics to the evaluation of trading system performance. Similarly, few pundits test their entries and exits independently of one another. There are some neat tricks that allow specific system components to be tested in isolation. One such trick is to have a set of standard entry and exit strate- gies that remain fixed as the particular entry, exit, or other element under study is varied. For example, when studying entry models, a standardized exit strategy will be repeatedly employed, without change, as a variety of entry models are tested and tweaked. Likewise, for the study of exits, a standardized entry technique will be employed. The rather shocking entry technique involves the use of a random number generator to generate random long and short entries into various markets! Most traders would panic at the idea of trading a system with entries based on the fall of the die; nevertheless, such entries are excellent in making a harsh test for an exit strategy. An exit strategy that can pull profits out of randomly entered trades is worth knowing about and can, amazingly, be readily achieved, at least for the S&P 500 (Katz and McCormick, March 1998, April 1998). The tests will be done in a way that allows meaningful comparisons to be made between different entry and exit methods. To summarize, the core elements of the scientific approach are: 1. The isolation of system elements 2. The use of standardized tests that allow valid comparisons 3. The statistical assessment of results TOOLS AND MATERIALS NEEDED FOR THE SCIENTIFIC APPROACH Before applying the scientific approach to the study of the markets, a number of things must be considered. First, a universe of reliable market data on which to perform back-testing and statistical analyses must be available. Since this book is focused on commodities trading, the market data used as the basis for our universe on an end-of-day time frame will be a subset of the diverse set of markets supplied by Pinnacle Data Corporation: these include the agriculturals, metals, energy resources, bonds, currencies, and market indices. Intradaytime-frame trading is not addressed in this book, although it is one of our primary areasof interest that may be pursued in a subsequent volume. In addition to standard pricing data, explorations into the effects of various exogenous factors on the markets some- times require unusual data. For example, data on sunspot activity (solar radiation may influence a number of markets, especially agricultural ones) was obtained from the Royal Observatory of Belgium. Not only is a universe of data needed, but it is necessary to simulate one or more trading accounts to perform back-testing. Such a task requires the use of a trading simulator, a software package that allows simulated trading accounts to be created and manipulated on a computer. The C+ + Trading Simulator from Scientific Consultant Services is the one used most extensively in this book because it was designed to handle portfolio simulations and is familiar to the authors. Other programs, like Omega Research’s TradeStationor SystemWriter Plus, also offer basic trading simulation and system testing, as well as assorted charting capabilities. To satisfy the broadest range of readership, we occasionally employ these products, and even Microsoft’s Excel spreadsheet, in our analyses. Another important consideration is thoptimization of model parameters. When running tests, it is often necessary to adjust the parameters of some compo- nent (e.g., an entry model, an exit model, or some piece thereof) to discover the best set of parameters and/or to see how the behavior of the model changes as its parameters change. Several kinds of model parameter optimizations may be con- livmOD”CTlON xxi ducted. In manual optimization, the user of the simulator specifies a parameter that is to be manipulated and the range through which that parameter is to be stepped; the user may wish to simultaneously manipulate two or more parameters in this manner, generating output in the form of a table that shows how the para meters interact to affect the outcome. Another method is brute force optimization, which comes in several varieties: The most common form is stepping every param eter through every possible value. If there are many parameters, each having many pos- sible values, running this kind of optimization may take years. Brute fo rce opti- mization can, however, be a workable approach if the number of parameter s, and values through which they must be stepped, is small. Other forms of brute forc e optimization are not as complete, or as likely to find the global optimum, but can be run much more quickly. Finally, for heavy-duty optimization (and, if naive ly applied, truly impressive curve-fitting) there are genetic algorithms. An appropri- ate genetic algorithm (GA) can quickly tind a good solution, if not a global opti- mum, even when large numbers of parameters are involved, each having lar ge numbers of values through which it must be stepped. A genetic optimizer is an important tool in the arsenal of any trading system developer, but it mu st be used cautiously, with an ever-present eye to the danger of curve-fitting. In the inves- tigations presented in this book, the statistical assessment techniques, out-of- sample tests, and such other aspects of the analyses as the focus on ent ire portfolios provide protection against the curve-fitting demon, regardless of the op timization method employed. Jeffrey Owen Katz, Ph.D., and Donna F. McCormick P A R T I Tools of the Trade Introduction T oobJectlve1ystudythe behavior of mechanical trading systems, various exper- imental materials and certain tools are needed. To study the behavior of a given entry or exit method, a simulation should be done using that method on a portion of a given market’s past performance; that requiresdata. Clean, historical data for the market on which a method is being tested is the starting point. Once the data is available, software is needed to simulate a trading account. Such software should allow various kinds of trading orders to be posted and should emulate the behavior of trading a real account over the historical period of interest. Software of this kind is caltrading simulator. The model (whether an entry model, an exit model, or a complete system) may have a number of parameters that have to be adjusted to obtain the best results from the system and its elements, or a number of features to be tamed on or off. Here is where an optimizeplays its part, and a choice must be made among the several types of optimizers available. The simulations an optimizations will produce a plethora of results. The sys- tem may have taken hundreds or thousands of trades, each wp itofislows,n maximum adverse excursion, and maximum favorable excursion. Also generated will be simulated equity curves, risk-to-reward ratios, profit factors, and other infor- mation provided by the trading simulatortha ebosit ulated trading account(s). A way to assess the significance of these results is needed. Is the apparent profitabili- ty of the trades a result of excessive optimization? Could the system have been prof- itable due to chance alone, or might it really be a valid trading ttratyst?mIf is valid, is it likely to hold up as well in the future, when actually being traded, as in 2 the past? Questions such as tr heqseire the basic machinery provided by inferen- tial statistics. In the next several chapters, we will cover data, simulators, optimizers, and statistics. These items will be used throughout this book when examining entry and exit methods and when attempting to integrate entries and exits into complete trading systems. C H A P T E R 1 D a t a A determination of what works, and what does not, cannot be made in the realm of commodities trading without quality data for use in tests and simulations. Several types of data may be needed by the trader interested in developing a prof- itable commodities trading system. At the very least, the trader will require his- torical pricing data for the commodities of interest. TYPES OF DATA Commodities pricing data is available for individual or continuous contracts. Individual contract datconsists of quotations for individual commodities con- tracts. At any given time, there may be several contracts actively trading. Most speculators tradteefront-month contracts, those that are most liquid and closest to expiration, but are not yet past first notice date. contreanears expira- tion, or passes first notice date, the trader “rolls over” any open position into the next contract. Working with individual contracts, therefore, can add a great deal of complexity to simulations and tests. Not only must trades directly generated by the trading system be dealt with, but the system developer must also correctly handle rollovers and the selection of appropriate contracts. To make system testing easier and more pract ioa,ntoes contractas invented. A continuous contract consists of appropriate individual contracts strung together, end to end, to form a single, continuous data series. Some data massaging usually takes place when putting together a continuous contract; the purpose is to close the gaps that occur at rollover, when one contract ends and another begins, Simple back-aajustmentappears to be the most reasonable and popular gap-closing 3 method (Schwager, 1992). Back-adjustment involves nothing more than the sub- traction of constants, chosen to close the gaps, from all contracts in a series other than the most recent. Since the only operation performed on a contract’s prices is the subtraction of a constant, all linear price relationships (e.g., price changes over time, volatility levels, and ranges) are preserved. Account simulations performed using back-adjusted continuous contracts yield results that need correction only for rollover costs. Once corrected for rollover, simulated trades will produce profits and losses identical to those derived from simulations performed using individual con- tracts. However, if trading decisions depend upon information involving absolute levels, percentages, or ratios of prices, then additional data series (beyond back- adjusted continuous contracts) will be required before tests can be conducted. End-of-day pricing data, whether in the form of individual or continuous contracts, consists of a series of daily quotations. Each quotation, “bar,” or data point typically contains seven fields of information: date, open, high, low, close, volume, and open interest. Volume and open interest are normally unavailable until after the close of the following day; when testing trading methods, use only past values of these two variables or the outcome may be a fabulous, but essentially untradable, system! The open, high, low, and close (sometimes referred to as the settlement price) are available each day shortly after the market closes. Intraday pricing data consists either of a series of fixed-interval bars or of individual ticks. The data fields for fixed-interval bars are date, time, open, high, low, close, and tick volume. Tick volume differs from the volume reported for end- of-day data series: For intraday data, it is the number of ticks that occur in the peri- od making up the bar, regardless of the number of contracts involved in the transactions reflected in those ticks. Only date, time, and price information are reported for individual ticks: volume is not. Intraday tick data is easily converted into data with fixed-interval bars using readily available software. Conversion soft- ware is frequently provided by the data vendor at no extra cost to the consumer. In addition to commodities pricing data, other kinds of data may be of value. For instance, long-term historical data on sunspot activity, obtained from the Royal Observatory of Belgium, is used in the chapter on lunar and solar influ- ences. Temperature and rainfall data have a bearing on agricultural markets. Various economic time series that cover every aspect of the economy, from infla- tion to housing starts, may improve the odds of trading commodities successfully. Do not forget to examine reports and measures that reflect sentiment, such as the Commitment of Traders (COT) releases, bullish and bearish consensus surveys, and put-call ratios. Nonquantitative forms of sentiment data, such as news head- lines, may also be acquired and quantified for use in systematic tests. Nothing should be ignored. Mining unusual data often uncovers interesting and profitable discoveries. It is often the case that the more esoteric or arcane the data, and the more difficult it is to obtain, the greater its value! CMR I Data 5 DATA TIME FRAMES Data may be used in its natural time frame or may need to be processed into a dif- ferent time frame. Depending on the time frame being traded and on the nature of the trading system, individual ticks, 5.minute bars, 20-minute bars, or daily, week- ly, fortnightly (bimonthly), monthly, quarterly, or even yearly data may be neces- sary. A data source usually has a natural time frame. For example, when collecting intraday data, the natural time frame is the tick. The tick is an elastic time frame: Sometimes ticks come fast and furious, other times sporadically with long inter- vals between them. The day is the natural time frame for end-of-day pricing data. For other kinds of data, the natural time frame may be bimonthly, as is the case for the Commitment of Traders releases; or it may be quarterly, typical of company earnings reports. Although going from longer to shorter time frames is impossible (resolution that is not there cannot be created), conversions from shorter to longer can be read- ily achieved with appropriate processing. For example, it is quite easy to create a series consisting of l-minute bars from a series of ticks. The conversion is usual- ly handled automatically by the simulation, testing, or charting software: by sim- ple utility programs; or by special software provided by the data vendor. lf the data was pulled from the Internet by way of ftp (tile transfer protocol), or using a stan- dard web browser, it may be necessary to write a small program or script to con- vert the downloaded data to the desired time frame, and then to save it in a format acceptable to other software packages. What time frame is the best? It all depends on the trader. For those attracted to rapid feedback, plenty of action, tight stops, overnight security, and many small profits, a short, intraday time frame is an ideal choice. On an intraday time frame, many small trades can be taken during a typical day. The nttmerooustrades hasten the learning process. It will not take the day trader long to discover what works, and what does not, when trading on a short, intraday time frame. In addition, by closing out all positions at the end of the trading day, a day trader can completely sidestep overnight risk. Another desirable characteristic of a short time frame is that it often permits the use of tight stops, which can keep the losses small on losing trades. Finally, the statistically inclined will be enamored by the fact that representative data samples containing hundreds of thousands of data points, and thousands of trades, are readily obtained when working with a short time frame. Large data samples lessen the dangers of curve-fitting, lead to more stable statistics, and increase the likelihood that predictive models will perform in the future as they have in the past. On the downside, the day trader working with a short time frame needs a real- time data feed, historical tick data, fast hardware containing abundant memory, spe- cialized software, and a substantial amount of time to commit to actually trading. The need for fast hardware with plenty of memory arises for two reasons: (1) System tests will involve incredibly large numbers of data points and trades; and (2) the real-time software that collects the data, runs the system, and draws the 6 charts must keep up with a heavy flow of ticks without missing a beat. Both a data- base of historical tick data and software able to handle sizable data sets are neces- sary for system development and testing. A real-time feed is required for actual trading. Although fast hardware and mammoth memory can now be purchased at discount prices, adequate software does not come cheap. Historical tick data is like- ly to be costly, and a real-time data feed entails a substantial and recurring expense. In contrast, data costs and the commitment of time to trading are minimal for those operating on an end-of-day (or longer) time frame. Free data is available on the Internet to anyone willing to perform cleanup and formatting. Software costs are also likely to be lower than for the day trader. The end-of-day trader needs less time to actually trade: The system can be run after the markets close and trading orders are communicated to the broker before the markets open in the morning: perhaps a total of 15minutes is spent on the whole process, leaving more time for system development and leisure activities. Another benefit of a longer time frame is the ability to easily diversify by simul- taneously trading several markets. Because few markets offer the high levels of volatility and liquidity required for day trading, and because there is a limit on how many things a single individual can attend to at once, the day trader may only be able to diversify across systems. The end-of-day trader, on the other hand, has a much wider choice of markets to trade and can trade at a more relaxed pace, making diver- sification across markets more practical than for intraday counterparts. Diversification is a great way to reduce risk relative to reward. Longer time frame trading has another desirable feature: the ability to capture large profits from strong, sustained trends: these are the profits that can take a $50,000 account to over a mil- lion in less than a year. Finally, the system developer working with longer time frames will find more exogenous variables with potential predictive utility to explore. A longer time frame, however, is not all bliss. The trader must accept delayed feedback, tolerate wider stops, and be able to cope with overnight risk. Holding overnight positions may even result in high levels of anxiety, perhaps full-blown insomnia. Statistical issues can become significant for the system developer due to the smaller sample sizes involved when working with daily, weekly, or monthly data. One work-around for small sample size is to develop and test systems on complete portfolios, rather than on individual commodities. Which time frame is best? It all depends on you, the trader! Profitable trad- ing can be done on many time frames. The hope is that this discussion has clar- fied some of the issues and trade-offs involved in choosing correctly. DATA QUALITY Data quality varies from excellent to awful. Since bad data can wreak havoc with all forms of analysis, lead to misleading results, and waste precious time, only use the best data that can be found when running tests and trading simulations. Some forecasting models, including those based on neural networks, can be exceeding- ly sensitive to a few errant data points; in such cases, the need for clean, error-free data is extremely important. Time spent finding good data, and then giving it a final scrubbing, is time well spent. Data errors take many forms, some more innocuous than others. In real-time trading, for example, ticks are occasionally received that have extremely deviant, if not obviously impossible, prices. The S&P 500 may appear to be trading at 952.00 one moment and at 250.50 the next! Is this the ultimate market crash? No-a few seconds later, another tick will come along, indicating the S&P 500 is again trading at 952.00 or thereabouts. What happened? A bad tick, a “noise spike,” occurred in the data. This kind of data error, if not detected and eliminat- ed, can skew the results produced by almost any mechanical trading model. Although anything but innocuous, such errors are obvious, are easy to detect (even automatically), and are readily corrected or otherwise handled. More innocuous, albeit less obvious and harder to find, are the common, small errors in the settling price, and other numbers reported by the exchanges, that are frequently passed on to the consumer by the data vendor. Better data vendors repeatedly check their data and post corrections as such errors are detected. For example, on an almost daily basis, Pinnacle Data posts error corrections that are handled automatically by its software. Many of these common, small errors are not seriously damaging to software-based trading simulations, but one never knows for sure. Depending on the sensitivity of the trading or forecasting model being ana- lyzed, and on such other factors as the availability of data-checking software, it may be worthwhile to run miscellaneous statistical scans to highlight suspicious data points. There are many ways to flag these data points, or ourlieru, as they are sometimes referred to by statisticians. Missing, extra, and logically inconsistent data points are also occasionally seen; they should be noted and corrected. As an example of data checking, two data sets were run through a utility program that scans for missing data points, outliers, and logical inconsistencies. The results appear in Tables I-1 and 1-2, respectively. Table I1 shows the output produced by the data-checking program when it was used on Pinnacle Data Corporation’s (800-724-4903) end-of-day, continuous-con- tract data for the S&P 500 futures. The utility found no illogical prices or volumes in this data set; there were no observed instances of a high that wan less than the close, a low that was greater than the open, a volume that was less than zero, or of any cog- nate data faux pas. Rvo data points (bars) with suspiciously high ranges, however, were noted by the software: One bar with unusual range occurred on 1 O/l 9/87 (or 871019 in the report). The other was dated 10/13/89.The abnormal range observed on 10/19/87does not reflect an error, just tbe normal volatility associated with a major crash like that of Black Monday; nor is a data error responsible for the aberrant range seen on 10/13/89,which appeared due to the so-called anniversary effect. Since these statistically aberrant data points were not errors, corrections were unnecessary. 8 Nonetheless, the presence of such data points should emphasize the fact that market events involving exceptional ranges do occur and must be managed adequately by a trading system. All ranges shown in Table l-l are standardized ranges, computed by dividing a bar’s range by the average range over the last 20 bars. As is common with market data, the distribution of the standardized range had a longer tail than would be TABLE I-1 O u t p u t f r o m D a t a - C h e c k i n g U t i l i t y f o r E n d - o f - D a y S & P 5 0 0 C o n t i n u o u s - C o n t rF u t u r e sD a t a f r o m P i n n a c l e CHAPTER1 oata 9 expected given a normally distributed underlying process. Nevertheless, the events of 10/19/87 and 10/13/89 appear to be statistically exceptional: The distribution of all other range data declined, in an orderly fashion, to zero at a standardized value of 7, well below the range of 10 seen for the critical bars. The data-checking utility also flagged 5 bars as having exceptionally deviant closing prices. As with range, deviance has been defined in terms of a distribution, using a standardized close-to-close price measure. In this instance, the standard- ized measure was computed by dividing the absolute value of the difference between each closing price and its predecessor by the average of the preceding 20 such absolute values. When the 5 flagged (and most deviant) bars were omitted, the same distributional behavior that characterized the range was observed: a long- tailed distribution of close-to-close price change that fell off, in an orderly fasb- ion, to zero at 7 standardized units. Standardized close-to-close deviance scores (DEV) of 8 were noted for 3 of the aberrant bars, and scores of 10 were observed for the remaining 2 bars. Examination of the flagged data points again suggests that unusual market activity, rather than data error, was responsible for their sta- tistical deviance. It is not surprising that the 2 most deviant data points were the same ones noted earlier for their abnormally high range. Finally, the data-check- ing software did not find any missing bars, bars falling on weekends, or bars with duplicate or out-of-order dates. The only outliers detected appear to be the result of bizarre market conditions, not cormpted data. Overall, the S&P 500 data series appears to be squeaky-clean. This was expected: In our experience, Pinnacle Data Corporation (the source of the data) supplies data of very high quality. As an example of how bad data quality can get, and the kinds of errors that can be expected when dealing with low-quality data, another data set was ana- lyzed with the same data-checking utility. This data, obtained from an acquain- tance, was for Apple Computer (AAPL). The data-checking results appear in Table l-2. In this data set, unlike in the previous one, 2 bars were flagged for having outright logical inconsistencies. One logically invalid data point had an opening price of zero, which was also lower than the low, while the other bar had a high price that was lower than the closing price. Another data point was detected as having an excessive range, which may or may not be a data error, In addition, sev- eral bars evidenced extreme closing price deviance, perhaps reflecting uncorrect- ed stock splits. There were no duplicate or out-of-order dates, but quite a few data points were missing. In this instance, the missing data points were holidays and, therefore, only reflect differences in data handling: for a variety of reasons, we usually fill holidays with data from previous bars. Considering that the data series extended only from l/2/97 through 1 l/6/98 (in contrast to the S&P 500, which ran from l/3/83 to 5/21/98), it is distressing that several serious errors, including log- ical violations, were detected by a rather simple scan. The implication of this exercise is that data should be purchased only from a T A B L E 1 - 2 Output from Data-Checking Utility for Apple Computer, Symbol AAPL reputable vendor who takes data quality seriously; this will save time and ensure reliable, error-free data for system development, testing, and trading, In addition, all data should be scanned for errors to avoid disturbing surprises. For an in-depth discussion of data quality, which includes coverage of how data is produced, trans- mitted, received, and stored, see Jurik (1999). DATA SOURCES AND VENDORS Today there are a greatmany sowces from which datamay be acquired. Data may be purchased from value-added vendors, downloaded from any of several exchanges, and extracted from a wide variety of databases accessible over the Internet and on compact discs. Value-added vendors, such as Tick Data and Pinnacle, whose data have been used extensively in this work, can supply the trader with relatively clean data in easy-to-use form. They also provide convenient update services and, at least in the case of Pinnacle, error corrections that are handled automatically by the down- loading software, which makes the task of maintaining a reliable, up-to-date data- base very straightforward. Popular suppliers of end-of-day commodities data include Pinnacle Data Corporation (800-724-4903), Prophet Financial Systems (650-322-4183). Commodities Systems Incorporated (CSI, 800.274.4727), and Technical Tools (800-231-8005). Intraday historical data, which are needed for testing short time frame systems, may be purchased from Tick Data (SOO-822- 8425) and Genesis Financial Data Services (800-62 l-2628). Day traders should also look into Data Transmission Network (DTN, SOO-485-4000), Data Broadcasting Corporation (DBC, 800.367.4670), Bonneville Market Information (BMI, 800-532-3400), and FutureSource-Bridge (X00-621 -2628); these data dis- tributors can provide the fast, real-time data feeds necessary for successful day trading. For additional information on data sources, consult Marder (1999). For a comparative review of end-of-day data, see Knight (1999). Data need not always be acquired from a commercial vendor. Sometimes it can be obtained directly from the originator. For instance, various exchanges occa- sionally furnish data directly to the public. Options data can currently be down- loaded over the Internet from the Chicago Board of Trade (CBOT). When a new contract is introduced and the exchange wants to encourage traders, it will often release a kit containing data and other information of interest. Sometimes this is the only way to acquire certain kinds of data cheaply and easily. FiiaIly, a vast, mind-boggling array of databases may be accessed using an Internet web browser or ftp client. These days almost everything is on-line. For exam- ple, the Federal Reserve maintains files containing all kinds of economic time series and business cycle indicators. NASA is a great source for solar and astronomical data. Climate and geophysical data may be downloaded from the National Climatic Data Center (NCDC) and the National Geophysical Data Center (NGDC), respectively. For the ardent net-surfer, there oiveawh&lming abundance of data in a staggering variety of formats. Therein, however, lies another problem: A certain level of skill is required in the art of the search, as is perhaps some basic programming or scripting experience, as well as the time and effort to find, tidy up, and reformat the data. Since “time is money,” it is generally best to rely on a reputable, value-added data vendor for basic pricing data, and to employ the Internet and other sources for data that is more specialized or difficult to acquire. Additional sources of data also include databases available through libraries and on compact discs. ProQuestand other periodical databases offer full text retrieval capabilities and can frequently be found at the public library. Bring a floppy disk along and copy any data of interest. Finally, do not forget newspapers such as Investor’s Business Daily, Barron’and theWall StreetJournal; these can be excellent sources for certain kinds of information and are available on micro- film from many libraries. In general, it is best to maintain data in a standard text-based (ASCII) for- mat. Such a format has the virtue of being simple, portable across most operating systems and hardware platforms, and easily read by all types of software, from text editors to charting packages. C H A P T E R 2 Simulators N o savvy trader would trade a system with a real account and risk real money without first observing its behavior on paper. A trading simulator is a software application or component that allows the user to simulate, using historical data, a trading account that is trad
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