How to Develop and Implement a Winning Trading Sytem

Beyond Technical Analysis

Beyond Technical Analysis: How to Develop and Implement a Winning Trading System

Tushar S. Chande, PhD

John Wiley 61 Sons, Inc. New York • Chichester • Brisbane • Toronto • Singapore • Weinheim

This text is printed on acid-free paper. Copyright © 1997 by Tushar S. Chande. Published by John Wiley & Sons, Inc. Data Scrambling is a trademark of Tushar S. Chande. TradeStadon, System Writer Plus, and Power Editor are trademarks of Omega Research, Inc. Excel is a registered trademark of Microsoft Corporation. Continuous Contractor is a trademark of TechTools, Inc. Portfolio Analyzer is a trademark of Tom Berry. All rights reserved. Printed simultaneously in Canada. Reproduction or translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright holder is unlawful. Requests for permission or further information should be addressed to the Permissions Department of John Wiley & Sons. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional services. If legal advice or other expert assistance is required, the services of a competent professional person should be sought. Library of Congress Cataloging in Publicaton Data: Chande, Tushar S., 1958Beyond technical analysis : how to develop & implement a winning trading system / Tushar S. Chande. Includes index. ISBN 0-471-16188-8 (cloth : alk. paper) 1. Investment analysis. I. Tide. II. Series. HG4529.C488 1997 332.6—dc20 96-34436 Printed in the United States of America 10 98765432

Contents

Preface xi Acknowledgments

xiii Trading Systems 1

1 Developing and Implementing Introduction 1 The Usual Disclaimer 3 What Is a Trading System? 3 Comparison: Discretionary versus Mechanical System Trader 4 Why Should You Use a Trading System? 5 Robust Trading Systems: TOPS COLA 6 How Do You Implement a Trading System? 7 Who Wins? Who Loses? 8 Beyond Technical Analysis 9 2 Principles of Trading System Design Introduction 11 What Are Your Trading Beliefs? 12 Six Cardinal Rules 14 Rule 1: Positive Expectation 15 Rule 2: A Small Number of Rules 17 11

viii Contents Rule 3: Robust Trading Rules 22 Rule 4: Trading Multiple Contracts 29 Rule 5: Risk Control, Money Management, and Portfolio Design 32 Rule 6: Fully Mechanical System 36 Summary 37 3 Foundations of System Design Introduction 39 Diagnosing Market Trends 40 To Follow the Trend or Not? 44 To Optimize or Not to Optimize? 48 Initial Stop: Solution or Problem? 52 Does Your Design Control Risks? 60 Data! Handle with Care! 64 Choosing Orders for Entries and Exits 66 Understanding Summary of Test Results 67 What the Performance Summary Does Not Show 70 A Reality Check 71 4 Developing New Trading Systems 73 Introduction 73 The Assumptions behind TrendFollowing Systems 74 The 65sma-3cc Trend-Following System 75 Effect of Initial Money Management Stop 88 Adding Filter to the 65sma-3cc System 93 Adding Exit Rules to the 65sma3cc System 99 Channel Breakout-Pull Back Pattern 101 An ADX Burst Trend-Seeking System 111 A Trend-Antitrend Trading System 116 Gold-Bond Intermarket System 123 A Pattern for Bottom-Fishing 132 39

Contents Identifying Extraordinary Opportunities 140 Summary 144 5 Developing Trading System Variations 147 Introduction 147 Channel Breakout on Close with Trailing Stops 149 Channel Breakout on Close with Volatility Exit 152 Channel Breakout with 20-Tick Barrier 155

ix

Channel Breakout System with Inside Volatility Barrier 159 Statistical Significance of Channel Breakout Variations 161 Two ADX Variations 165 The Pullback System 168 The Long Bomb — A Pattern-based System 173 Summary 177 6 Equity Curve Analysis 179 Introduction 179 Measuring the "Smoothness" of the Equity Curve 180 Effect of Exits and Portfolio Strategies on Equity Curves 186 Analysis of Monthly Equity Changes 194 Effect of Filtering on the Equity Curve 200 Summary 204 7 Ideas for Money Management Introduction 207 The Risk of Ruin 208 Interaction: System Design and Money Management 212 Projecting Drawdowns 218 Changing Bet Size after Winning or Losing 221 Summary 224 207

x Contents 8 Data Scrambling Introduction 227 What You Really Want to Know about Your System 227 Past Is Prolog: Sampling with Replacement 229 Data Scrambling: All the Synthetic Data You'll Ever Need 231 Testing a Volatility System on Synthetic Data 236 Summary 239 9 A System for Trading 241 Introduction 241 The Problem with Testing 242 Paper Trading: Pros and Cons 242 Do You Believe in Your System? 243 Time Is Your Ally 244 No Exceptions 245 Full Traceability 245 "Guaranteed" Entry into Major Trends 246 Starting Up 247 Risk Control 248 Do You Have a Plan? 248 How Will You Monitor Compliance? 249 Get It Off Your Chest! 249 Focus on Your Trading 250 Trading with Your Head and Heart 250 Summary 252 Selected Bibliography 255 About the Disk 261 253 Index 227

Preface

This is a book about designing, testing, and implementing trading systems for the futures and equities markets. The book begins by developing trading systems and ends by defining a system for trading. It focuses exclusively on trading systems. Hence, I have assumed that the reader has at least a working knowledge of technical analysis and is familiar with software for developing technical trading systems The book is broadly divided into two parts. The first half deals with development and testing—how the system worked on past data— and discusses basic rules, key issues, and many new systems. The second half explores how the system might do in the future, with a focus on equity curves, risk control, and money management. A key contribution is a new method called "data scrambling," which allows unlimited amounts of synthetic data to be generated for true out-ofsample testing. The last chapter brings all of the material together by offering solutions to practical problems encountered in implementing a trading system. This book goes beyond technical analysis—it bridges the gap between analysis and trading. It provides a comprehensive treatment of trading systems, and offers a stimulating mix of new ideas, timeless principles, and practical guidelines to help you develop trading systems that work.

Acknowledgments

I thank Nelson F. Freeburg for twice reading this manuscript. Nelson's meticulous attention to detail, outstanding grasp of the subject, sharp eye for inconsistencies, and love of the language have helped to improve this book immeasurably. Nelson edits a monthly newsletter, Formula Research, which is "must-reading" for serious students of the financial markets. A good editor is essential to guide a book to completion. I want to thank Pamela Van Giessen of John Wiley & Sons for being the accessible, cheerful, and resourceful editor every author loves.

Beyond Technical Analysis

Chapter

Developing and Implementing Trading Systems Nothing is easier than developing a trading system by the •usual process of trial and terror.

Introduction Хорошая система торговли удовлетворяет вашу индивидуальность. К счастью, самый быстрый способ находить каждый - через процесс испытания(суда) и ужаса(террора). Любое проверяющее система программное обеспечение на быстром компьютере поможет Вам произвести в большом количестве тысячу розовых сценариев. Рынки безошибочно покажут любые недостатки в вашем проекте. Они выдвинут(подтолкнут) Вас, чтобы определить то, чему Вы верно верите. В конечном счете, если Вы выживаете, Вы обнаружите ваши веры торговли. Рынки будут вести Вас к системе, которая лучше всего удовлетворяет Вас. Эта книга показывает Вам, как создавать, проверять, и осуществить системы, которые удовлетворяют вашу индивидуальность. Вы разовьете не только системы торговли, но и систему для торговли. Этот подход увеличит разницу(разногласия), что Вы выживете и будете процветать на рынках. Эти книжные центры исключительно на творческом проекте системы, полном испытании, заметном(разумном) управлении денег, благоразумном контроле(управлении) риска, и осторожном внимании к выполнению. Эти факторы отличают эту книгу от других РАЗВИТИЕ И ВНЕДРЕНИЕ ТОРГОВЫХ СИСТЕМ На предмете. Привлекательная особенность - то большинство материала, первоначальное или новое. Эта книга разделена на две половины по четыре главы каждая. Первая часть посвящена проектированию торговых систем. Вторая половина обсуждает, как внедрить системы торговли. Первая половина охватывает следующие темы: 1. Принципы проектирования торговой системы, которая охватывает шесть кардинальных правил

2. Основы проекта системы, который представляет десять главных проблем проекта 3. Развитие новых систем торговли, который подробно описывает семь новых систем 4. Development of trading system variations, which discusses eight variations of known ideas Once you have read the first half, you will be eager to explore questions about system implementation. The second half of the book is organized as follows: 5. Equity curve analysis, which explores what influences equity curve smoothness 6. Ideas for money management, which is the starting point for risk control 7. Data scrambling, which offers all the synthetic data you will ever need 8. A system for trading, which presents solutions to practical problems After reading this volume, you should be able to take your ideas and convert them into useful trading systems. This book develops deterministic trading systems, which means that all the rules can be explicitly evaluated. The book does not discuss trading systems based on expert systems, neural networks, or fuzzy logic for two simple but important reasons: (1) More users understand and easily implement deterministic systems than any other type of system. (2) The software for testing deterministic systems is widely available at an economical price. Put the two together, and this book becomes immediately accessible to a large audience.

What Is a Trading System? The Usual Disclaimer Throughout the book, a number of trading systems are explored as examples of the art of designing and testing trading systems. This is not a recommendation that you trade these systems. I do not claim that these systems will be profitable in the future, nor that profits or losses will be similar to those shown in the calculations. In fact, there is no guarantee that these calculations are defect free. I urge you to review the section in chapter 3 called a reality check. That section points out the inherent limitations of developing systems with the benefit of hindsight. You should use the examples in this book as an inspiration to develop your own trading systems. Do not forget that there is risk of loss in futures trading. What Is a Trading System? A trading system is a set of rules that defines conditions required to initiate and exit a trade. Usually, most trading systems have many parts, such as entry, exit, risk control, and money management rules. The rules of a trading system can be implicit or explicit, simple or complex. A system can be as simple as "buy sweaters in summer," or "buy when she sells." By definition, the system must be feasible. Ideally, the system accounts for "all" trading issues, from signal generation, to order placement, to risk control. A good way to visualize effective system design is to stipulate that someone who is not a trader must be able to implement the system. In practice, every trader uses a system. For most traders, a system could really be many systems. It could be discretionary, partly discretionary, or folly mechanical. The systems could use different types of data, such as 5-minute bars or weekly data. The systems may be neither consistent nor easy to test; the rules could have many exceptions. A system could have many variables and parameters. You can trade different combinations of parameters on the same market. You can trade different parameter sets on different markets. You can even trade the same parameter set on all markets. It should be clear by now that there is no single universal trading system. Every trader adapts a "system" to his or her style of trading. However, it is possible to draw a distinction between a discretionary trader and a 100% mechanical system trader, as compared in the next section.

4 Developing and Implementing Trading Systems Comparison: Discretionary versus Mechanical System Trader Table 1.1 compares two extremes in trading: a discretionary trader and a 100% mechanical system trader. Discretionary traders use all inputs that seem relevant to the trade: fundamental data, technical analysis, news, trade press, phases of the moon—their imagination is the limit. System traders, on the other hand, slavishly follow a mechanical system without any deviations. Their entire focus is on implementing the system "as is," with no variations, exceptions, modifications, or adaptations of any kind. Exceptional traders are discretionary traders, and they can probably outperform all mechanical system traders. Their biggest advantage is that they can change the key variable driving each trade, and therefore vary bet size more intelligently than in a mechanical system. Discretionary traders can change the relative importance of their trading variables so they can easily switch between trendfollowing and anti-trend modes. They can instantly switch between time frames of analysis, going from 5-minute bars to weekly bars as their assessment of the trading opportunity changes. Discretionary traders can make better use of market information other than price. For example, they can react to news or fundamental information to change bet size. Discretionary traders can adjust their perceived risk constantly, so they can increase or decrease positions more intelligently than mechanical traders. These infrequent "home runs" often make all the difference between good and great trading performance. However, for the average trader, being a mechanical system trader probably maximizes the chances of success. The goals of a mechanical system trader are to pick a time frame (for example, hourly, daily, weekly), identify the trend status, and anticipate the direction of the future trend. The system trader must then trade the anticipated trend, control losses, and take profits. The rules Table 1.1 Comparison of trading styles: Discretionary versus mechanical Discretionary Trader Trader 100% Mechanical System

Subjective Objective Many rules Few rules Emotional Unemotional Varies "key" indicator from trade to trade "Key" indicators are always the same Few markets Many markets

Why Should You Use a Trading System? 5 must be specific, and cover every aspect of trading. For example, the rules must specify how to calculate the number of contracts to trade and what type of entry order to use. The rules must indicate where to place the initial money management stop. The trader must execute the system "automatically," without any ambiguity about the implementation. Mechanical system traders are objective, use relatively few rules, and must remain unemotional as they take their losses or profits. The most prominent feature of a mechanical system is that its rules are constant. The system always calculates its key variables in the same way regardless of market action. Even though some indicators vary their effective length based on volatility, all the rules of the system are fixed, and known a priori. Thus, mechanical system traders have no opportunity to vary the rules based on background events, nor to adjust position size to match the markets more effectively. This is at once a strength and a weakness. A major benefit for system traders is that they can trade many more markets than can discretionary traders, and achieve a level of diversification that may not otherwise be possible. You can create different flavors of trading systems that use a small or limited amount of discretion. You. could, for example, have specific criteria to increase position size. This could include fundamental and technical information. You can be consistent only if you are specific. This discussion really begs the question of why to use trading systems, answered in the next section.

Why Should You Use a Trading System? The most important reason to use a trading system is to gain a "statistical edge." This often-used term simply means that you have tested the system, and the profit of the average trade—including all losing and winning trades—is a positive number. This average trade profit is large enough to make this system worth trading—it covers trading costs, slippage, and is, on average, likely to perform better than competing systems. Later in the book, I discuss all of these criteria in greater detail. The statistical edge is relevant to another statistical quantity called the probability of ruin. The smaller this number, the more likely you are, on paper, to survive and prosper. For example, if you have a probability of ruin less than, say, 1 percent, your risk control measures and other measures of system performance are typically sufficient to prevent instant destruction of your account equity.

6 Developing and Implementing Trading Systems My biggest source of concern about these statistical numbers is they assume you will trade the system exactly as you have tested it, with not one deviation. This is difficult to achieve in practice. Thus, your risk of ruin—and it is only a risk until it becomes a fact—could be higher than your calculations. Despite this concern, you should develop systems that meet sound statistical criteria, for that greatly enhances your odds of success. As usual, there are no guarantees, but at least the odds, if not the gods, will be on your side. Another reason to use a trading system is to gain objectivity. If you are steadfastly objective, you can resist the siren call of news events, hot tips, gossip, or boredom. Suppose you are a chart trader and you enjoy some flexibility in interpreting a given chart formation. It is very easy to identify a pattern after the fact, but it is rather difficult to do so as the pattern evolves in real time. Hence, analysis can paralyze you, and you may never make an executable trading decision. Being objective frees you to follow the dictates of your analysis. Consistency is another vital reason to use a trading system. Since the few rules in a trading system are applied in precisely the same way each time, you are assured of a rare consistency in your trading. In many ways, objectivity and consistency go together. Although consistency is known as the hobgoblin of little minds, it is certainly a useful trait when you are not quite a champion trader. A trading system gives another crucial advantage: diversification, particularly across trading models, markets, and time frames. No one can be certain when the markets will have their big move, and diversification is another way to increase your odds of being in the right place at the right time. In summary, you can use a trading system to gain a statistical edge, objectivity, consistency, and diversification across models and markets. A key assumption underlying this section is that the system you are using is well designed and robust. The next section discusses examples of a robust trading system. Robust Trading Systems: TOPS COLA A robust trading system is one that can withstand a variety of market conditions across many markets and time frames. A robust system is not overly sensitive to the actual values of the parameters it uses. It is not likely to be the worst or best performer, when traded over a "long" time (perhaps 2 years or more). Such a system is usually a trendfollowing

How Do You Implement a Trading System? 7 system, which cuts losses immediately and lets profits run. This philosophy, called TOPS COLA, merely says "take our profits slowly" and "cut off losses at once." Two examples of robust systems are a moving-average cross-over system and a price-range breakout system. Both systems are well known, and are widely traded in some form or another. The trades from these systems typically last more than 20 days. Hence I classify them as intermediate-term systems. They are trend-following in nature, in that they make money in trending markets and lose money in nontrending markets. The typical system has a winning record of 35 to 45 percent, with an average trade of more than $200. I will discuss these systems in detail later. The key feature to note is that, when systematically implemented over a "long" time and over many markets, robust systems tend to be, on the whole, profitable. If executed correctly, they guarantee entry in the direction of the intermediate trend, cut off losses quickly, and let profits run. Countless variations of these systems exist, and trendfollowing systems seem to account for a large percentage of professionally managed accounts. Robust systems do not make many assumptions about market behavior, have relatively few variables or parameters, and do not change their parameters in response to market action. There is no sharp drop in performance due to small changes in the values of system variables. Such systems are worthy of consideration in most portfolios, and are reasonably reliable. In addition, they are easy to implement.

How Do You Implement a Trading System? Begin with a trading system you trust. After sufficient testing, you can determine the risk control strategy necessary for that system. The risk control strategy specifies the number of contracts per signal and the initial dollar amount of the risk per contract. The risk control strategy may also specify how the initial stop changes after prices move favorably for many days. The system must clarify portfolio issues such as the number and type of markets suitable for this account. The trading system must also specify when and how to put on initial positions in markets in which it has signaled a trade before commencement of trading for a particular account.

8 Developing and Implementing Trading Systems A trade plan is at the heart of system implementation. The trade plan specifies entry, exit, and risk control rules along with the statistical edge. You should record a diary of your feelings and the quality of your implementation, plus any deviations from the plan and the reasons for those deviations. You should monitor position risk and the status of all exit rules. Last, take the long view: Imagine you are going to implement 100 trades with this plan, not just one. Thus, you can ignore the performance of any one trade, whether profitable or not, and focus on executing the trade plan. These and other implementation issues are discussed in detail in chapter 9. Who Wins? Who Loses? Tewles, Harlow, and Stone (1974) report a study by Blair Stewart of the complete trading accounts of 8,922 customers in the 1930s. That may seem like a long time ago, but the human psychology of fear, hope, and greed has changed little in the last 60 or so years. The results of the study are worth considering seriously. Stewart reported three mistakes made by these customers. (1) Speculators showed a clear tendency to cut profits short, while letting their losses run. (2) Speculators were more likely to be long than short, even though prices generally declined during the nine years of the study. (3) Longs bought on weakness and shorts sold on strength, indicating they were price-level rather than price-movement traders. I should contrast this experience with the TOPS COLA philosophy discussed earlier. By taking profits slowly and cutting off losers at once, you will avoid the first mistake reported by Stewart. Second, by being a trend follower, you will avoid the next two mistakes. If you follow trends, you will be long or short per the intermediate trend, and avoid any tendency to be generally long. Third, if you follow trends, you will follow price movement, rather than being a price-level trader. You will win in the trading business if you have a specific trade plan that contains all the necessary details. You should focus much of your effort and energy on implementing the trade plan as accurately and consistently as possible. Thus, you must go beyond technical analysis, deep into trade management and organized trading, to win.

Beyond Technical Analysis 9 Beyond Technical Analysis The usual advice for technical traders is a collection of rules with many exceptions and exceptions to the exceptions. The trading rules are difficult to test and the observations are hard to quantify. I want you to go beyond technical analysis by converting an art form into a concrete trading system, and then focusing on implementing the system to the best of your ability. Trading is analysis in action. Thus, this book is an attempt to bridge the gap between the development and the implementation of a trading system.

Chapter

Principles of Trading System Design If not the gods, put the odds on your side. Introduction This chapter presents some basic principles of system design. "You should try to understand these issues and adapt them to your preferences. First, assess your trading beliefs—these beliefs are fundamental to your success and should be at the core of your trading system. You may have several strong beliefs, and they can all be used to formulate one or more trading systems. After you have a list of your core beliefs, you can build a trading system around them. Remember, it will not be easy to stick with a system that does not reflect your beliefs. The six major rules of system design are covered in this chapter in considerable detail. The specific issues to be examined are why your system should have a positive expectation and why you should have a small number of robust rules. The focus in the later sections of this chapter is on money-management aspects such as trading multiple contracts, using risk control, and trading a portfolio of markets. The real difficulties lie in implementing a system, and hence, the chapter ends by explaining why a system should be mechanical.

12 Principles of Trading System Design By the end of this chapter, you should be able to tern design. write down your trading beliefs, as well as explain and apply the six basic principles of system design. What Are Your Trading Beliefs? You can trade only what you believe; therefore, your beliefs about price action must be at the core of your trading system. This will allow the trading system to reflect your personality, and you are more likely to succeed with such a system over the long run. If you hold many beliefs about price action, you can develop many systems, each reflecting one particular belief. As we will see later, trading multiple systems is one form of diversification that can reduce fluctuations in account equity. The simplest way to understand your trading beliefs is to list them. Table 2.1 presents a brief checklist to help you get started. You can expand the items in Table 2.1 to include many other items. For example, you can include beliefs about breakout systems, moving-average methods, or volatility systems. Your trading beliefs are also influenced by what you do. For example, you may be a market marker, with a very short term trading horizon. Or, you may be a proprietary trader for a big bank, trading currencies. You may wish to keep an eye on economic data as one ingredient in your decision process. As a former floor trader, you may like to read the commitment of traders report. Perhaps you were once a buyer of coffee beans for a major manufacturer, and you like to look at crop yield data as you trade coffee. The range of possible beliefs is as varied as individual traders. You must ensure that your beliefs are consistent. For example, if you like fast action, you probably will not use weekly data, nor hold positions as long as necessary. Nor are you likely to use fundamental data in your analysis. Hence, a need for fast action is more consistent with day trading, and using cycles, patterns, and oscillators with intraday data. Similarly, if you like a trend-following approach, you are more likely to use daily and weekly data, hold positions for more than five days, trade a variable number of contracts, and trade a diversified portfolio. If you hold multiple beliefs, ensure that they are a consistent set and develop models that fit those beliefs. A set of consistent beliefs that can be used to build trading systems is listed below as an example. 1. I like to trade with the trend (5 to 50 days). 2. I like to trade with a system.

What Are Your Trading Beliefs? 13 3. 4. 5. I like to hold positions as long as necessary (1 to 100 days). I like to trade a variable number of shares or contracts. I like to use stop orders to control my risk.

Pare down your list to just your top five beliefs. You can review and update this list periodically. When you design trading systems, check that they reflect your five most strongly held beliefs. The next section presents other rules your system must also follow.

Table 2.1 A checklist of your trading beliefs Beliefs That Can Influence Your Trading Decisions 1 like to trade using fundamentals only. 1 like to trade with technical analysis only. 1 like to trade with the trend (you define time 1 like to trade against the trend (you define time 1 like to buy dips (you define time frame). 1 like to sell rallies (you define time frame). 1 like to hold positions as long as necessary (1 I like to hold positions for a short time (1 to 5 I like to trade intraday only, closing out all I like to trade a fixed number of shares or I like to trade a variable number of shares or I like to trade a small number of markets or 1 like to trade a diversified portfolio (more markets). 1 like to trade using cycles because 1 can 1 like to trade price patterns because 1 can 1 like to trade with price oscillators. 1 like to read the opinions of others on the 1 like to use only my own analysis of price 1 like to use daily data in my analysis. 1 like to use intraday data in my analysis. 1 like to use weekly data in my analysis. 1 like to trade with a system. 1 like to use discretion, matching wits with the 1 like lots of fast action in my trading. 1 like to use stop orders to control my risk. 1 like to trade with variable-length movingt

Yes,l Agree a a a a D a a a a a a a a a a a a a a a a a a a a a

No,l Disagree a a a a a a a a a a a a a a a a a a a a a D a a a a

14 Principles of Trading System Design Six Cardinal Rules Once you identify your strongly held trading beliefs, you can switch to the task of building a trading system around those beliefs. The six rules listed below are important considerations in trading system design. You should consider this list a starting point for your own trading system design. You may add other rules based on your experiences and preferences. 1. The trading system must have a positive expectation, so that it is "likely to be profitable." 2. The trading system must use a small number of rules, perhaps ten rules or less. 3. The trading system must have robust parameter values, usable ^ over many different time periods and markets. 4. The trading system must permit trading multiple contracts, if possible. 5. The trading system must use risk control, money management, and portfolio design. 6. The trading system must be fully mechanical. There is a seventh, unwritten rule: you must believe in the trading principles governing the trading system. Even as the system reflects your trading beliefs, it must satisfy other rules to be workable. For example, if you want to day-trade, then your short-term, day-trading system must also follow the six rules. You can easily modify this list. For example, rule 3 suggests that the system must be valid on many markets. You may modify this rule to say the system must work on related markets. For example, you may have a system that trades the currency markets. This system should "work" on all currency markets, such as the Japanese yen, deutsche mark, British pound, and Swiss franc. However, you will not mandate that the system must also work on the grain markets, such as wheat and soybeans. In general, such market-specific systems are more vulnerable to design failures. Hence, you should be careful when you relax the scope of any of the six cardinal rules.

Rule 1: Positive Expectation 15 Another way to modify the rules is to look at rule 6, which says that the system must be fully mechanical. For example, you may wish to put in a volatility-based rule that allows you to override the signals. Be as specific as possible in defining the conditions that will permit you to deviate from the system. You can likely test these exceptional situations on past market data, and then directly include the exception rules in your mechanical system design. In summary, these rules should help you develop sound trading systems. You can add more rules, or modify the existing ones, to build a consistent framework for system design. The following sections discuss these rules in greater detail. Rule 1: Positive Expectation A trading system that has a positive expectation is likely to be profitable in the future. The expectation here refers to the dollar profit of the average trade, including all available winning and losing trades. The data may be derived from actual trading or system testing. Some analysts call this your mathematical edge, or simply your "edge" in the markets. The terms "average trade" and "expectation" represent the same object, so they are freely interchanged in the following discussion. Expectation can be written in many different ways. The following formulations are identical: Expectation($) = Average Trade($), Expectation($) = Net profit($)/(Tbtal number of trades), Expectation($) = [(Pwin) x (Average win($))] - (1 - Pwin) x (Average loss($))]. The expectation, measured in dollars, is the profit of the average trade. The net profit, measured in dollars, is the gross profit minus the gross loss over the entire test period. Pwin is the fraction of winning trades, or the probability of winning. The probability of losing trades is given by (1-Pwin). The average win is the average dollar profit of all winning trades. Similarly, the average loss is the average dollar loss of all losing trades.

16 Principles of Trading System Design The expectation must be positive because, on balance, we want the trading system to be profitable. If the expectation is negative, this is a losing system, and money management or risk control cannot overcome its inherent limitations. Assume that you are using system test results to estimate your average trade. Note that your estimate of the expectation is limited by the available data. If you test your system on another data set, you will get a different estimate of the average trade. If you test your system on different subsets of the same data set, you will find that each subset gives a different result for the average trade. Thus, the expectation of a trading system is not a "hard and fixed" constant. Rather, the expectation changes over time, markets, and data sets. Hence, you should use as long a time period as possible to calculate your expectation. Since the expectation is not constant, you should stipulate a minimum acceptable value for the average trade. For example, the minimum value should cover your trading costs and provide a "risk premium" to make it attractive. Hence, a value such as $250 for the expectation could be used as a threshold for accepting a system. In general, the larger the value of the average trade, the easier it is to tolerate its fluctuations. Note that the expectation does not provide any measure of the variability of returns. The standard deviation of the profits of all trades is a good measure of system variability, system volatility, or system risk. Thus, the expectation does not fully quantify the amount of risk (read volatility) that must be absorbed to benefit from its profitability. The expectation is also related to your risk of ruin. You can use statistical theory to calculate the probability that your starting capital will diminish to some small value. These calculations require assumptions about the probability of winning, the payoff ratio, and the bet size. The payoff ratio can be defined as the ratio of the average winning trades to the average losing trades. As your payoff ratio increases, and your Pwin increases, your risk of ruin decreases. The risk of ruin is also governed by bet size, that is, percentage of capital risked on every trade. The smaller your bet size, the lower the risk of ruin. Detailed calculations of risk of ruin are presented in chapter 7. In summary, it is essential that your system have a positive expectation, that is, a profitable average trade. The value of the average trade is not fixed, but changes over time. Hence, you can specify a threshold value, such as $250, before you will accept a trading system. The expectation is also important because it affects your risk of ruin. Avoid trading systems that have a negative expectation when tested over a long time.

Rule 2: A Small Number of Rules 17 The expectation of your system is determined by its trading rules. The next section examines how the number of trading rules affects your system design. Rule 2: A Small Number of Rules This book deals with deterministic trading systems using a small number of rules or variables. These trading systems are similar to systems people have developed for tasks such as controlling a chemical process. Their experience suggests that robust, reliable control systems have as few variables as possible. Consider two well-known trend-following systems. The common dual moving-average system has just two rules. One says to buy the upside crossover, and the other says to sell the downside crossover. Similarly, the popular 20-bar breakout system has at least four rules, two each for entries and exits. You can show with testing software that these systems are profitable over many markets across multiyear time frames. You can contrast this approach with an expert system-based trading system that may have hundreds of rules. For example, one commercially available system apparently has more than 400 rules. However, it turns out that only one rule is the actual trigger for the trades. The deterministic systems differ from neural-net-based systems that may have an unknown number of rules. The statistical theory of design of experiments says that even complex processes are controllable using five to seven "main" variables. It is rare for a process to depend on more than ten main variables, and it is quite difficult to reliably control a process that depends on 20 or more variables. It is also rare to find processes that depend on the interactions of four or more variables. Thus, the effect of higher-order interactions is usually insignificant. The goal is to keep the overall number of rules and variables as small as possible. There are many hazards in designing trading systems with a large number of rules. First, the relative importance of rules decreases as the number of rules increases. Second, the degrees of freedom decrease as the number of rules or variables increases. This means larger amounts of test data are needed to get valid results as the number of rules or variables increases. A third problem is the danger of curve-fitting the data in the test sample. For example, given a data set, a simple linear regression with just

Principles of Trading System Design two variables may fit the data adequately. As the number of variables in the regression increases to, say, seven, the line fits the data more closely. Therefore, we can pick up nuances in the data when we curvefit our trading system, only to pick up patterns that may never repeat in the future. The total degrees of freedom decrease by two for the simple linear regression, but will decrease by seven for the polynomial regression. These ideas can be illustrated by using regression fits of daily closing data for the December 1995 Standard and Poors 500 (S&P500) futures contract. The data set covers 95 days from August 1, 1995, through December 13, 1995. Two regression lines are fitted to the same data: Figure 2.1 presents a simple linear regression; Figure 2.2 fits higher-order polynomial terms, going out to the fifth power. As higher-order terms are added, the regression line becomes a curve, and we pick up more nuances in the data. For simplicity, the daily closes are numbered 1 through 95 and denoted by D. All numbers represented by C (such as Ci) are constants. Est Close is the closing price estimated from the regression.

SPZ5 Dally Close with OLS Line

CLO SE LR1

40

60

80

Days since 08/01/95 Figure 2.1 SScP-500 closing data with simple linear regression straight line.

Rule 2: A Small Number of Rules 19 SPZ5 dally close with 5th order regression

40

60

Days since 08/01/95 Figure 2.2 SScP-500 closing data with regression using terms raised to the fifth power. Est Close = Co + (Ci x D) Est Close = Co + (Ci x D) + (C^ x D ) + (Cj x D3) + (C4 x D4) + C; x D5)
2

(2.1) (2.2)

Table 2.2 illustrates several interesting features about curvefitting a data set. First, observe that the value of the constant Co is approximately the same for each equation. This implies that the simplest model, the constant Co, captures a substantial amount of information in the data set. Then, notice that the absolute value of the constants decreases as the order of the term increases. In other words, in absolute value, Co is greater than Ci, which is greater than C2 and on down the line. Therefore, the relative contribution of the higher-order polynomial terms becomes smaller and smaller. However, as you add the higher-order polynomial terms, the line takes on greater curvature and fits the data more closely, as seen in Figures 2.1 and 2.2.

20 Principles of Trading System Design Table 2.2 Comparison of linear regression coefficients Co C4 Ci Cs C2 C3

Equation 560.0865 0.537870 2.1 Equation 570.2379 0.0000006 2.2 -1.94509 0.131279 -0.00154 -0.00003

This exercise illustrates many important ideas. First, any model you build for the data should be as simple as possible. In this case, the simple linear regression, with a slope and intercept, captured essentially all the information in the data. Second, adding complexity by adding higher-order terms (read rules) does improve the fit with the data. Thus, we pick up nuances in the data as we build more complex models. The probability that these nuances will repeat exactly is very small. Third, the purpose of our models is to describe how prices have changed over the test period. We used our data to directly calculate the linear regression coefficients. Thus, our model is hostage to the data set. There is no reason why these coefficients should accurately describe any future data. This means that over-fitted trading systems are unlikely to perform as well in the future. Another example, a variant of the moving-average crossover system, illustrates why it makes sense to limit the number of rules. In the usual case, the dual moving average system has just two rules. For example, for the long entry the 3-day average should cross over the 65day average and vice versa. Now, consider a variant that uses more than two averages. For example, buy on the close if both the 3-day and the 4-day moving averages are above the 65-day average. Since there are two "short" averages, this gives us four rules, two each for long and short trades. Using more and more "short" averages rapidly increases the number of rules. For example, if the 3-, 4-, 5-, 6-, and 7-day moving averages should all be above the 65-day average for the long entry, ten rules would apply. Consider 10 years of Swiss franc continuous contract data, from January 1, 1985, through December 31, 1994, without any initial stop, but allowing $100 for slippage and commissions. The number of rules is varied from 2 to 128 to explore the effects of increasing the number of rules. As the number of rules increases, the number of trades decreases, as shown in Figure 2.3. This illustrates the fact that as you

increase the number of rules, you need more data to perform reliable tests.

Rule 2: A Small Number of Rules 21 More rules need more data

2

4

8

12

16

24

32

48

64

96

128

Number of rules Figure 2.3 Adding rules reduced the number of trades generated over 10 years of Swiss franc data. Note that the horizontal scale is not linear. Figure 2.4 shows that the profit initially increased as we added more rules. This means that the extra rules first act as filters and eliminate bad trades. As we add even more rules, however, they choke off profits and moreover increase equity curve roughness. Thus, you should be careful to not add dozens of rules. As stated, this example did not include an initial stop. Hence, as we increase the number of rules, the maximum intraday drawdown should increase because both entries and exits are delayed. You can verify this by using Figure 2.5, page 23. Calculations for the U.S. bond market from January 1, 1975, through June 30, 1995, illustrate that the general pattern still holds. Figure 2.6, page 24, shows that as the number of rules increases, the profits decrease. The exact patterns will depend on the test data. Data from other markets confirm that increasing rules decreases profits. Thus, adding rules does not produce endless benefits. Not only do you need more data, but the rising complexity may lead to worsening system performance. A complex system with many rules merely captures

22 Principles of Trading System Design Increasing rules first filter, then choke profits 95000 85000 75000 S 8) 65000 55000 45000 35000

25000 2

4 128

8

12

16

24

32

48

64

96

Number of rules Figure 2.4 Adding rules increased profits moderately on 10-years of Swiss franc continuous contracts from January 1, 1985, through December 31, 1994. Note that the horizontal scale is not linear. nuances within the test data, but these patterns may never repeat. Hence, relatively simple systems are likely to perform better in the future.

Rule 3: Robust Trading Rules

Robust trading rules can handle a variety of market conditions. The performance of such systems is not sensitive to small changes in parameter values. Usually, these rules are profitable over multiperiod testing, as well as over many different markets. Robust rules avoid curve-fitting, and are likely to work in the future. An example of a system with delayed long entries illustrates the use of nonrobust parameters. The entry rule is as follows: if the crossover between 3- and 12-day simple moving averages (SMAs) occurred x days ago, and the low is greater than the parabolic, then buy tomorrow at the

Rule 3: Robust Trading Rules 23 MIDD follows same pattern as profits

-5000 S S I -10000 -15000 -20000 -25000 -30000 Number of rules Figure 2.5 Adding more rules delayed entries and exits, increasing maximum intraday drawdown. Note that the horizontal scale is not linear. today's high + 1 point on a buy stop. A $1,500 initial stop was used and $100 was charged for slippage and commissions. The results above are for an IMM (International Monetary Market) Japanese yen futures continuous contract, from August 2, 1976 through June 30, 1995. The dollar profits are sensitive to the number of days of delay, and can vary widely due to small changes in parameter values. It also does not seem reasonable to wait 12 days after a crossover for such short-term moving averages. Hence, the flattening out of the curve after a 9-day delay is of little practical relevance. The delay parameter is not robust because a small change in the value of this parameter can make system performance vary widely with markets and time frames. Next consider the effect of nonrobust, curve-fitted rules, illustrated by the August 1995 N.Y. light crude oil futures contract (Figure 2.8, page 26). The market was in a narrow trading range during February and March, and then broke out above the $18.00 per barrel price level. The market moved up quickly, reaching the $20 level by May. A volatile consolidation period ensued through June, before prices broke down toward the $17 per barrel level by July.

24 Principles of Trading System Design More rules, less profit in US Bonds 50000 40000 30000 S 20000 10000

-10000 Number of rules Figure 2.6 Increasing the number of rules decreased profits in the U.S. bond market from January 1, 1975 through June 30, 1995. Note that the horizontal scale is not linear. The following trading rules were derived simply by visual inspection of the price chart in an attempt to develop a curve-fitted system that picked up specific patterns in this contract. Rule 1: Buy tomorrow at highest 50-day high + 5 points on a buy stop (breakout rule). Rule 2: Sell tomorrow at low -2 x (h-1) - 5 points on a sell stop (downside range-expansion rule). Rule 3: If this is the twenty-first day in the trade, then exit short trades on the close (time-based exit rule). Rule 4: If Rule 3 is triggered, then buy two contracts on the close (countertrend entry rule). Rule 5: If short, then sell tomorrow at the highest high of last 3 days +1 point limit (sell rallies rule).

Rule 3: Robust Trading Rules 25 Effect of delayed entry on profits: 3/12 SMAXO

Delay (» of days) after crossover Figure 2.7 The effect on profits of changing the number of days of delay in accepting a crossover signal of a 3-day SMA by 12-day SMA system is highly dependent on the delay. The first rule is a typical breakout system entry rule, albeit for a breakout over prior 50-bar trading range. The second rule is a volatility-inspired sell rule. The idea was to sell at a point five ticks below twice the previous day's trading range subtracted from the previous low. This will typically be triggered after a narrow-range day, if the daily range expands on die downside due to selling near an intermediate high. The third rule is a time-dependent exit rule, optimized by visual inspection over the August contract. The idea behind time-based exits is that one expects a reaction opposite the intermediate trend after x days of trending prices. Rule 4 merely reinforces rule 3 by not only exiting the short position but putting on a two-contract long position at the close. Rule 5 is a conscious attempt to sell rallies during downtrends. In this case, limit orders were used to sell, to avoid slippage. These rules assumed diat as many as nine contracts could be traded at one time, using a $1,000 initial moneymanagement stop. The results of the testing are summarized in Table 2.3, page 27. The first clue that this may be a curve-fitted system is the number of

26 Principles of Trading System Design ."''ll1-) h, ^ M19 All ^2 3 -® -TaJnf'l1}!? ^A,^ ;1 ('

-te -^ A1 tl^t . -5 1 46 ' 1/1 , I11,!

•20 .00 •I 9.5 •,• 18. 50 18. Iflllll 17 l2 1 16

Mar

Apr

May

Jun

Jul

Figure 2.8 The August 1995 crude oil contract with curve-fitted system profitable trades. As many as 87 percent of all trades (20 out of 23) were profitable. A second clue was in the 14 consecutive profitable trades. A third clue was in a suspiciously large profit factor (= gross profit/gross loss) of 13.49. These results are what you might see in curve-fitted systems tested over a relatively short time period. The computer-generated buy and sell signals are shown in Figure 2.8. This curve-fitted system was tested by using a continuous contract of crude oil futures data from January 3, 1989, through June 30, 1995. Not surprisingly, this system would have lost $107,870 on paper, as shown in Table 2.4. Note how only 32 percent of the trades would have been profitable. There would have been as many as 48 consecutive losing trades, requiring quite an act of faith to continue trading this system. Also, the profit factor was a less impressive 0.61, a sharp drop from the 13.49 value in Table 2.3. These calculations show that curve-fitted systems may not work over long periods of time. Interestingly, this system has its merits. When tested over 12 other markets to check if these rules were robust enough to use across many

Rule 3: Robust Trading Rules 27 Table 2.3 Results of testing August 1995 crude oil curvefitted system N.Y. Light Crude Oil 08/95-Daily 12/01 /94 - 07/20/95

Total

net profit 12,990.00 Gross profit 14,030.00 Total number of trades Number of winning trades Largest winning trade 1,370.00 Average winning trade 701.50

($) ($) 23 20 ($) ($)

Maximum consecutive 14 winners Average number of bars 20 in winners Maximum intraday -1,670.00 drawdown ($) Profit factor 13.49

Open position profit/loss ($) 520.00 Gross loss ($) 1,040.00 Percent profitable 87 Number of losing trades 3 Largest losing trade ($) 860.00 Average losing trade ($) 346.67 Average trade ($) 564.78 Maximum consecutive losers 2 Average number of bars in 1 losers Maximum number of contracts held

markets (Table 2.5), the results were better than expected; on some markets the system tested very well. This result was surprising because (1) this particular combination of rules had never been tested on these markets and were derived by inspection of just one chart; and (2) the Table 2.4 Results of testing crude oil curve-fitted system over a long time period Performance Summary: All Trades 01/03/89 - 06/30/95 Total net profit ($) Total number of Number of winning Largest winning trade Average winning Maximum winners Average number of winners Maximum intraday 538 173 7,160 983 9 12 Percent profitable Number of losing trades Largest losing trade ($) Average losing trade ($) Average trade ($) Maximum consecutive losers Average number of bars losers 32 365 -3,670 -761 -200 48 6

drawdown ($) Profit factor

0 61

Maximum number of contracts held

9

28 Principles of Trading System Design Table 2.5 A check for robustness: crude oil curve-fitted system over 12 markets (test period: 1 /3/89-6/30/95, using continuous contracts, $100 slippage, and commission charge) Market Paper Profit (S) Average Trade ($) Coffee 132,908 445 S&P-500 145,545 547 Cotton 84,925 284 U.S. bond 84,319 324 Japanese yen 67,975 176 Swiss franc 1 7,975 51 1 3,538 48 10-year T-note Gold, Comex -1 3,270 -33 Copper, high-grade -22,167 -49 Soybeans ^1,656 -117 Heating oil -45,868 -80 Sugar #11 -56,394 -136

long entries and short entries are asymmetric. A symmetrical trading system uses identical rules for entries and exits, except that the signs of the required changes are reversed. For example, a moving average system would require an upside crossover or a downside crossunder for signals. A closer look at the rules shows that they do follow some sound principles. For example, during an uptrend, each successive 50-bar breakout adds a contract until nine contracts are acquired. Thus, market exposure is increased during strong uptrends. The sell rule tends to lock in profits close to intermediate highs. As we sell rallies in downtrends, we are increasing exposure in the direction of the intermediate term trend. Also, a relatively tight $1,000 initial money management stop was used. Thus, even though these rules were derived by inspection, they followed sound principles of following the trend, adding to with-the-trend positions, letting profits run, and cutting losses quickly. In summary, it is easy to develop a curve-fitted system over a short test sample. If these rules are not robust, they will not be profitable over many different market conditions. Hence, they will not be profitable over long time periods and many markets. Such rules are unlikely to be consistently profitable in the future. Hence, you should try to develop robust trading systems.

Rule 4: Trading Multiple Contracts Contracts

29 Rule 4: Trading Multiple

Multiple contracts allow you to make larger profits when you are right. However, the drawdowns are larger if you are wrong. You are betting that with good risk control, the overall profits will be greater than the drawdowns. An essential requirement is that your account equity must be sufficiently large to permit trading multiple contracts. Your risk control guidelines must permit multiple contracts to benefit from this approach. If your account permits you to trade just one contract at a time, then this approach must be deferred until your equity has increased. Multiple contracts also allow you to add a nonlinear element to your system design. This means the results of trading, say, five contracts using this nonlinear logic are better than trading five contracts using the usual linear logic. The linear logic trades one contract per signal. The nonlinear logic uses a price-based criterion such as volatility. The volatility rule buys more contracts when volatility is low. Markets often have low volatility after they have consolidated for many weeks. If a strong trend develops as the market emerges from the consolidation, then the nonlinear effect is to boost profits significantly. A simple example illustrates these ideas. Assume that your account is so large that trading up to 15 contracts in the 10-year T-note market is well within your risk control guidelines. For example, with a 1 percent risk per position and a $1,000 initial money management stop, you would need $1,500,000 in equity to trade 15 T-note contracts. This assumes that the 15-lot margin is also within your moneymanagement guidelines. Consider a simple moving average crossover system using 5-day and 50-day simple moving averages. The trade day is one day after the crossover day. You will buy or sell on the next day's open if you get a 5/50 crossover tonight after the close. Use a $1,000 initial stop on each contract and allow $100 for slippage and commissions. Let us compare system performance with one contract versus variable contracts, rising to a maximum of 15 contracts. The test period is from January 3, 1989, through June 30, 1995, using a continuous contract. Table 2.6 compares four variations of the 5/50 crossover system. The column labeled "fixed 1 contract" shows the results over the test period for always trading one contract per trade. The next column, "fixed 15 contracts" shows the calculated results for always trading 15 contracts per trade. The column, "variable #1" trades a maximum of

30 Principles of Trading System Design Table 2.6 Performance comparison using variable number of contracts Variable #1 Variable #2 Fixed Fixed Maximum Maximum Item 1 Contract 15 15 15 Net profit ($) 24,018.75 360,281 339,774 294,869 Maximum intra-6,918.75 -103,781 -66,650 -62,763 day drawdown (MIDD) ($) Net profit /MIDD 3.47 3.47 5.10 4.70 -16,500 -1,350 -13,200 Largest losing trade -1,100 Total number of 48 48 594 48 Number of 15 15 215 15 Number of 500.39 2,448 7,50 572 6,14 winning trades 0.09 340 6 5,83 3 Average trade 36,72 6 25,50 ($) Standard 1 6 0.10 deviation 0.20 0.24 of trades ($) 15 contracts 364 Average trade/ with the 5,09 3,362 standard contracts deviation added at the Standard open on 2 deviation: successive losing trades days. The ($) "variable #2" trades a maximum of 15 contracts with all the contracts bought on the same day. The volatility in dollars here is four times the average 20-day true range. The volatility divided into $15,000 gives the number of contracts. Thus, variable #2 uses a volatility-based criterion for calculating the number of contracts, always trading 15 or less. Let us compare the net profit produced by the four strategies. It should come as no surprise that the absolute amount of profit increases as we trade more contracts. However, as the next row of Table 2.6 shows, the maximum intraday drawdown also increases as we trade more contracts. The ratio of net profits to maximum intraday drawdown shows whether we gain anything by trading multiple contracts. This ratio is 3.47 for fixed contract trading strategy. The ratio increases to 4.7 or 5.1 for the variable contracts strategies. This is a 39 to 47 percent improvement, a strong reason to consider multiple contracts. Hence, profits can increase without proportionately increasing drawdowns. Observe from Table 2.6 that the largest losing trade for variable #1 is considerably less than simply trading a fixed number of 15 contracts.

Rule 4: Trading Multiple Contracts 31 Similarly, the largest losing trade in variable #2 is less than always trading 15 contracts. This too confirms the benefits of going to the multiple-contract strategy. The total number of trades remains the same for the fixed-1, fixed-15 and variable #2 strategies, since all the contracts are bought on the same day. The number of trades increases for variable #1 since not all the contracts are bought on the same day. The average trade for each strategy is relatively high, suggesting that this simple model seems to catch significant trends. The average trade is higher when all the contracts are bought at the same time. This is merely an artifact of system design. As pointed out before, the average trade does not provide a measure of variability in system results. The standard deviation per trade is naturally smaller when we trade one contract at a time rather than all at once. The standard deviation in trade returns increases as the number of contracts increases. As Table 2.6 shows, there is a higher volatility in trade returns ($36,721) for fixed 15-contract trading than either of the variable contract strategies. This means volatility can be reduced by trading a variable number of multiple contracts, rather than a fixed number of multiple contracts. This is another desirable design goal. Dividing the average trade profit by the standard deviation in trade profitability yields a composite picture of model performance. The higher this number, the more desirable the system. For the fixed 1contract strategy, this reward to risk ratio is only 0.09, and it increases to 0.24 for the variable #2 strategy. Remember, however, that the volatility in trading profits increases significantly with multiple contracts. The last line of Table 2.6, the downside volatility, explains that the increased volatility occurs due to rising profits of winning trades. Note that the fixed 15-contract downside volatility is the highest, followed by the variable #2 and variable #1 strategies. There is not a large difference in downside volatility between the fixed 1-contract strategy and variable #1 strategy, which buys one contract at a time but on multiple days. Note also that the standard deviation of all trades (including winning trades) is much greater than the downside volatility. Thus, rather than all volatility being undesirable, note that adding multiple contracts increases upside volatility more than downside volatility. Increasing upside volatility is easier to cope with than sharply rising downside volatility. In summary, if your account equity and mental makeup permit, consider the benefits of a multiple contract strategy.

32 Principles of Trading System Design Rule 5: Risk Control, Money Management, and Portfolio Design All traders have accounts of finite size as well as written or unwritten guidelines for expected performance over the immediate future. These performance guidelines have a great influence over the existence and longevity of an account. For example, consider a trading system that produces a 30 percent loss over five months. The same trading system then goes on to perform extremely well. One person may close the account after the 30 percent drawdown. Another may go on to reap excellent returns. Your money management rules could cause you to close out an account too soon, or keep it open too long. Thus, money management guidelines are crucial to trading success. Given performance expectations and finite size of the trading account, it is essential to maintain good risk control, sensible money management, and good portfolio design. Risk control is the process of managing open trades with predefined exit orders. Money management rules determine how many contracts to trade in a given market and the amount of money to risk on particular positions. Portfolio-level issues must be considered to obtain a smoother equity curve. Table 2.7 illustrates the effects of not using an initial money management stop versus adding an initial money management stop of $2,000. The trading system, a "canned" system using four consecutive up or down closes to initiate a trade, comes with the Omega Research's System Writer Plus™. As expected, the largest losing trade can be horrifying, and most real-world accounts would probably close before swallowing such huge losses. Of course, recent headlines of billion-dollar plus losses in sophisticated trading firms illustrate that trading without adequate risk control is not uncommon. Adding a money management stop constrains the worst initial loss to predictable levels. Even with slippage, the largest loss is usually lower than trading without any stop at all. Thus, your profitability is likely to improve with improved risk control. Observe that average net profits improved from a loss of -$5,085 with no stop to a loss of -$424 using risk control. The maximum drawdown also improved with the added risk control. The lesson from this comparison is clear. There is much to gain if you use proper risk control. You can reduce swings in equity and improve account longevity if you combine risk control with sound money management ideas. Your money management guidelines will specify how much of your equity to

Rule 5: Risk Control, Money Management, and Portfolio Design 33 Table 2.7 Effect of adding an initial money management stop, May 1989-June 1995 (dollars) Market No Stop $2000 S Net Largest Maximum Net Largest Profit Loss Drawdow Profit Loss Coffee -4,206 -50,868 -24,149 33,776 -2,594 Copper 5,082 -3,542 -14,810 -5,455 -2,302 Cotton 4,370 -4,620 -14,585 7,580 -3,025 Crude -14,350 -12,350 -20,760 -8,690 -2,870 Gold, 7,180 -2,250 -6,560 3,750 -2,340 Comex Heating 16,758 -4,174 -16,350 -378 -3,989 Japane -36,800 -6,550 -65,673 -23,675 -3,388 yen Sugar -9,770 -3,594 -14,428 -7,799 -2,194 Swiss 8,225 -7,613 -16,438 15,688 -2,663 10-year -15,913 -4,413 -29,444 -8,788 -2,100 T note U.S. -16,506 -6,194 -28,969 -10,625 -2,100 b d Worst -36,800 -50,868 -65,673 -23,675 -3,989 Best 16,758 Averag -5,085 -2,250 -9,652 -6,560 -22,924 33,776 -424 -2,100 -2,688

Maximu m -13,970 -20,430 -13,800 -15,100 -6,650 -16,334 -50,300 -12,456 -15,263 -21,881 -22,856 -50,300 -6,650 -19,004

risk on any trade. These guidelines convert the initial stop into a specific percentage of your equity. One common rule of thumb is to risk or "bet" just 2 percent of your account equity per trade. The 2-percent rule converts into a $1,000 initial stop for a $50,000 account. This $1,000 initial stop is often called a "hard dollar stop," applied to the entire position. A position could have one or more contracts. Thus, if you had two contracts, you would protect the position with a stop loss order placed $500 away from the entry price. Chapter 7 discusses the bet size issue in detail. Overtrading an account is a common problem cited by analysts for many account closures. For example, if you consistently bet more than 2 percent per trade, you are overtrading an account. If you do not use any initial money management stop, then the risk could be much greater than 2 percent of equity. In the worst case, you risk your entire account equity. Some extra risk, say up to 5 percent of equity, may be justified if the market presents an extraordinary market opportunity (see chapter 4). However, consistently exceeding the 2 percent limit can cause large and unforeseen swings in account equity.

Principles of Trading System Design As another rule of thumb, you are overtrading an account if the monthly equity swings are often greater than 20 percent. Again, there may be an occasional exception due to extraordinary market conditions. You mast also consider the benefits and problems of diversification, that is, trading many different markets in a single account. The main advantage of trading many markets is that it increases the odds of participating in major moves. The main problem is that many of the markets respond to the same or similar fundamental forces, so their price moves are highly correlated in time. Therefore, trading many correlated markets is similar to trading multiple contracts in one market. For example, the Swiss franc (SF) and deutsche mark (DM) often move together, and trading both these markets is equivalent to trading multiple contracts in either the franc or the mark. Let us look specifically at SF and DM continuous contracts from May 26, 1989, through June 30, 1995, with a dual moving average system using a $1,500 stop and $100 for slippage and commissions. The two moving averages were 7 and 65 days. As Figure 2.9 shows, the equity curves have a correlation of 83 percent. For example, you would have made $60,619 trading one Comparison of equity curves: DM and SF

5 15000 ^ g 10000

D M SF

Date Figure 2.9 Swiss franc and deutsche mark equity curves are highly correlated at 83 percent.

Rule 5: Risk Control, Money Management, and Portfolio Design 35 contract each of SF and DM, but your profits would have been $63,850 trading two contracts of DM and $57,388 trading two contracts of SF. Note one important difference between the two cases. Since the two markets may have negative correlation from time to time, the drawdown for both SF and DM together may be in between trading two contracts of just DM or SF. For example, the drawdown for SF and DM in this case was -$10,186 versus -$22,375 for two DM contracts and $9,950 for two SF contracts. Hence, the benefits of trading correlated markets are relatively small. Thus, it may be better to trade uncorrelated or weakly correlated markets in the same portfolio. The benefits of adding usually unrelated markets to a portfolio can be illustrated by an example of trading the Swiss franc (SF), cotton (CT) and 10-year Treasury note (TY) in a single account, using the same dual moving average system as above. The paper profits from trading three SF contracts add up to $86,801 versus $85,683 for SF plus TY and CT. The equity curve for the two combinations is shown in Figure 2.10. The smoothness of the two curves can be compared by using linear regression analysis to calculate the standard error (SE) of the daily equity Equity Curve: 3SF vs SF+TY+CT

S 50000 r S 40000

-3SF SU M

Days (5/89-6/95) Figure 2.10 Adding 10-year T-note (TY) and cotton to the portfolio trading just Swiss francs provides a smoother equity curve versus trading three SF contracts.

36 Principles of Trading System Design Simulated "Jagged" equity curve

4

5

6

7

8

9 Time

(months) Figure 2.11 This contrived jagged equity curve has a standard error of 2.25. The perfectly smooth equity curve has an SE of zero. The standard deviation of monthly returns is 33 percent. curve. The SE for trading three SF contracts in $6238, and the SE for SF and TY plus CT is just $4,902, a reduction of 21 percent. Thus, adding TY and CT to a portfolio of SF produced a smoother equity curve with essentially the same nominal profits. The relevance of the standard error is illustrated in Figure 2.11, which shows a contrived equity curve. The SE for that curve was 2.25, since it was quite "jagged." A perfectly smooth equity would have an SE reading of zero. Diversification can be more than just adding markets. You can also trade multiple trading systems and multiple time frames within a single account. You should try to use uncorrelated or weakly correlated systems. In summary, risk control, money management, and portfolio design are important issues in designing trading systems. Rule 6: Fully Mechanical System The simplest answer to why a system must be mechanical is that you cannot test a discretionary system over historical data. It is impossible to

Summary 37 forecast what market conditions you will face in future and how you will react to those conditions. Therefore, in this book, we will restrict ourselves to fully mechanical systems. If you can define how you make discretionary decisions, then these rules could be formalized and tested. The process of formalization could itself provide many interesting ideas for further testing. Hence you are encouraged to move toward mechanical systems. You are more likely to make consistent trading decisions if you use mechanical systems. The manner in which a mechanical system will process price data is predictable, and hence assures that you will make consistent trading decisions. However, there is no assurance that these logically consistent decisions will also be consistently profitable. Nor is there any assurance that these trading decisions will be implemented without modification by the trader. Summary This chapter developed a checklist for narrowing your trading beliefs. You should narrow your beliefs down to five or less to build effective trading systems around them. This chapter also reviewed six major rules of the system design. A trading system with a positive expectation is likely to be profitable in the future. The number of rules in a system should be limited because increasing complexity often hurts performance. Relatively simple systems are likely to fare better in the future. The rules should be robust, so they will be profitable over long periods and over many markets. You should trade multiple contracts if possible because they allow you to make more profits when you are right. Risk control, money management, and portfolio design give you a smoother equity curve and are the keys to profitability. Lastly, a system should be mechanical to provide consistent, objective decision making. You should follow the six major rules to build superior systems that are consistent with your trading beliefs.

Chapter

Foundations of System Design The best system provides instant gratification and constant satisfaction. Introduction This chapter examines many key system design issues. Now that you understand some basic principles of system design, you can consider more complex issues. And as you understand these issues, you can design more powerful systems. We will begin by asking the question: Do markets trend? The answer to the next big question, whether you should trade with the trend or against the trend, is that you should trade with the trend. This chapter presents some test results to support this answer. You can then ask whether you should or should not optimize your trading system. We explore here how well you can predict future performance based on optimization of historical data. The chapter begins the discussion on risk control issues by addressing whether the initial stop is a problem or a solution and discussing the different types of risk you may face in your trading. You should consider these issues early in your design process. We then look at the different types of data you can use for your testing and what difference, if any,

40 Foundations of System Design they make. Finally, the chapter explains what is found as well as what is lacking in the system performance summary. At the end of this chapter, you will be able to: 1. Explain how you can diagnose trending markets. 2. Know whether to use a trend-following or countertrend strat^ 3. Explain the benefits and pitfalls of optimization. 4. Understand the type of risks you may encounter. 5. Know how to select data for tests. 6. Effectively use the performance summary of system testing results. 7. Understand and explore what is not covered in the performance summary. 8. Explain why system design has its limits. Diagnosing Market Trends You can design a profitable trading strategy if you can correctly and consistently diagnose whether a market is trending. In simple terms, the market exists in two states: trending and ranging. A market is trending if it moves steadily in one direction. If the market is going back and forth within a relatively narrow price range, then it is ranging. Longer-term strategies are likely to succeed in trending markets, and shorter-term strategies in ranging markets. As always, the market may not make a crisp transition from trending to ranging and back again. Sometimes the market begins to range only to break out into a trend, or vice versa. There are many different ways to determine if a market is trending. Clearly, you must make a number of trade-offs, and these trade-offs largely define your answer. For example, one well-known measure is the average directional index (ADX) developed by Welles Wilder Jr. (see bibliography for references). This is usually a built-in function in most technical analysis software programs. The ADX describes double-smoothed, absolute market momentum. A rising ADX line usually indicates trend. You have to choose the number of days to calculate the ADX; the sensitivity of the indicator decreases as the time increases. A

Diagnosing Market Trends 41 value of 14 days is common, although 18 days works well. You must also define two reference levels to screen out false signals. An ADX value of 20 is useful as a reference level—that is to say a market is not trending unless the rising 18-day ADX is above 20. A second useful barrier level is 40, which says that when the ADX rises above 40 and then turns down, a consolidation is likely. You will find that in particularly strong trends, the "hook" from above 40 often signals just a brief consolidation phase. The trend then has a strong second "leg" toward higher highs or lower lows. Sometimes you will find that the ADX will rise above 20 in markets that are in a broad trading range. Another quirk is that the ADX can head lower even though prices march steadily and smoothly in either direction. In short, this is not a perfect indicator. The main difficulty with the ADX is that it has two levels of smoothing, which produces disconcerting lags between price movement and indicator response. Chapter 5 shows that the absolute level of the ADX indicator is not as useful for system design as is its trend. An indicator that is more directly based on market momentum, and that responds more predictably than the ADX, is the range action verification index (RAVI). This strategy, which focuses on identifying ranging markets, is different from the ADX, which looks at how much of today's price action is beyond yesterday's price bar. To define RAVI, we begin by selecting the 13-week simple moving average, since it represents a quarter of a year. Because we want to use daily data, we convert the 13-week SMA into the equivalent 65-day SMA of the close. This is the long moving average. The short moving average is chosen as only 10 percent of the long moving average, which is 6.5 days, or, rounding up, 7 days. Thus, we use 7-day and 65-day simple moving averages. This choice of lengths is purely arbitrary. Next, the RAVI is defined as the absolute value of the percentage difference between the 7-day SMA (7-SMA) and the 65-day SMA (65-SMA): RAVI = Absolute value (100 x (7-SMA-65-SMA)/65-SMA) An arbitrary reference level of 3 percent means a market is ranging if the RAVI is less than 3 percent, and trending strongly if the RAVI is greater than 3 percent. In some markets, such as Eurodollars, this is too high a hurdle. Hence, you may want to experiment with a smaller level, such as 1 percent, or use a relative measure, such as a 65-day SMA of the RAVI. You can also require that the RAVI be above 3 percent and rising for there to be a strong trend.

I I I

Foundations of System Design Note the following design features of the RAVI: (1) There is only one level of smoothing. (2) The 7-day moving average is relatively sensitive, so that the lags between price action and indicator action should be small. (3) Markets can still move more quickly than the RAVI indicates. You can verify this by looking at the currency markets. (4) Markets in a slowly drifting, choppy trend will pin the RAVI below 3 percent, indicating ranging action. Figure 3.1 compares the 18-day ADX (bottom graph) to the RAVI (middle graph) with a horizontal line at the 3 percent RAVI level. There is a general similarity between the two indicators, with the RAVI responding more quickly than the ADX because it has only one level of smoothing versus two levels for the ADX. A double-smoothed RAVI indicator created by smoothing the RAVI with a 14-day SMA is very similar to the 18-day ADX, as shown in Figure 3.2. Thus the ADX closely describes double-smoothed momentum and can lag price movements. We now compare the ADX and RAVI and use them both to measure how often trends occur. In this example, we use continuous contracts from January 1, 1989, through June 30, 1995, a rising 18-day ADX above 20, and a rising RAVI greater than 3 percent. The ADX and RAVI are considered to be rising if today's value is greater than the value 10 days ago. These choices of length and reference levels are arbitrary.

Figure 3.1 Comparison between the ADX (bottom) and RAVI (middle) to measure ranging behavior.

Diagnosing Market Trends 43

in

Jul

Aug

Sep

Oct

Nov

Dec

Figure 3.2 A double-smoothed RAVI (solid line) compared to the 18day ADX (dotted line) shows that the two indicators are very similar. The calculations shown in Table 3.1 suggest that markets seem to show some form oftrendiness about 20 to 40 percent of the time. Some markets, such as the 10-year T-note, have not shown very strong trends as measured by the RAVI. However, this may just be due to using a 3 percent barrier with the RAVI to measure trend strength. The "soft" markets, such as coffee and sugar, show the highest tendency to trend. Other fundamentals-driven markets, such as cotton, copper, and crude oil, also show a tendency to have strong trends, with a RAVI rating above 35 percent. The more mature markets, such as S&P-500 and U.S. bond markets, show fewer strong trends than the softs. RAVI calculations correctly tagged the prolonged sideways ranging action in gold with a low rating of 15.8. A separate calculation showed that the average length of these trending intervals was about 15 to 18 days in most markets, with values ranging from as low as 1 to more than 30. Thus, the trending phase of these markets was long enough to allow profitable trading. These calculations show that markets have provided sufficient opportunities for trend-following systems in the "trendless nineties." In summary, you can use momentum-based indicators to measure ranging or trending action. The calculations show that markets have trends lasting 15 to 18 days on average. Hence, trend-following strate-

44 Foundations of System Design Table 3.1 Proportion of market days showing definite trend, using ADX and RAVI Percentage of Days Percentage of Days ADX Rising, RAVI Rising, Market (1/1/89-6/30/95) ADX>20 RAVI > 3 Coffee 30.2 43.3 Copper, high-grade 27.0 35.3 Cotton 29.2 39.4 Crude oil 30.2 39.9 Deutsche mark 32.6 25.7 Gold, Comex 25.0 15.8 Japanese yen 27.7 20.6 Soybeans 30.1 23.9 S&P-500 24.0 17.9 31.3 41.7 Sugar 30.7 28.9 Swiss franc 32.8 6.0 10-year T-note U.S. bond 37.5 16.0

gies are worth considering for system design. The next section examines whether you should use trend-following strategies over the long run. To Follow the Trend or Not? If you are not a large hedger or an institutional trader, you can follow either of two basic strategies when you design a trading system. You can be a trend follower, or you can take antitrend positions. If you are a trend follower, you will typically take intermediate-term positions. In contrast, with a countertrend strategy, you take shorter-term positions that anticipate trends. This section explores both strategies and shows that a trend-following approach is more likely to be profitable over the long run than an antitrend approach. Table 3.2 shows test results for a stochastic-oscillator-based antitrend trading system provided with System Writer Plus™ software from Omega Research. The stochastic oscillator is a range-location oscillator that shows where today's close is within its trading range over the last x days. If the close is near the top of the range, then oscillator values are greater than 80. The next move in prices will probably be toward the lower end of the range. Similarly, if the close is near the lower

To Follow the Trend or Not? 45 Table 3.2 Stochastic-oscillator antitrend trading system results

Coffee Cotton Crude light Gold, Comex Japane yen Swiss U.S.

Max imum Maximum Paper Number Percent- Largest Biggest ConsecuIntraday Profits of age of Winner Loser tive Drawdown ($) Trades Winners ($) ($) Losers ($) 1,837 276 32 27,065 -11,215 9 ^4,931 -98,725 296 24 4,955 -2,800 14 -102,205 -61,940 301 29 5,210 -7,850 17 -63,180 -29,830 256 -47,713 309 -55,350 285 -49,313 310 29 32 32 28 2,630 8,633 9,175 4,400 -2,920 -2,762 -3,225 -1,694 21 9 10 13 -31,150 -60,81 3 -63,51 3 -61,469

end of the range, then oscillator values are below 20. We assume that the next move will take prices toward the top of the range. The "range" between the .r-day high and low changes continuously. Hence, this oscillator cannot predict the amplitude of the next move. The system tested uses a 10-day period to calculate the so-called fast-K and fast-D moving averages. When the fast-K is above the fastD line, the system buys on the open and vice versa. The System Writer Plus™ software guide gives the exact method for the calculations. This example uses continuous contracts for seven unrelated markets, allows $100 for slippage and commissions, and uses a $1,500 initial money management stop. The test period was from May 26, 1989, through June 30, 1995. This simple system was a net loser over these markets. It also had substantial drawdowns, largely due to the many successive losing trades. Note the large number of trades and the relatively low proportion of winners. The main implication of these calculations is that although markets may trend for short periods only, the profits during trending periods can far exceed the profits during trading ranges. The reason for this is that the amplitude of price moves during trends is many times the amplitude during trading ranges. This example assumes that you pay the "discounted" trading commissions offered on the street. If your trading commissions are very low or negligible, then the antitrend strategy, with its high trading fre-

quency, takes on a different dimension.

46 Foundations of System Design Table 3.3 Impact of trading costs on profitability of antitrend trading strategies (dollars) Market Paper Profit $100SScC Paper Profit noS&C Coffee 1,837 29,438 Cotton -98,725 -69,125 Crude oil, light -61,940 -31,840 Gold, Comex -29,830 -A,230 Japanese yen ^7,713 -16,813 Swiss franc -55,350 -26,850 U.S. bond -t9,313 -18,313

Table 3.3 compares paper profits with and without slippage and commissions (S&C). The difference in profitability is striking. The stochastic oscillator system performance improved significantly with low commissions. This result indicates that an antitrend strategy would not be attractive if you had to pay high commissions. There are a number of "antitrend" strategies. Table 3.4 presents another set of calculations using a different trading strategy to illustrate this point. The moving average crossover (MAXO) system is the simplest trend-following strategy, but it can also be used as an antitrend strategy. For example, if the shorter moving average crosses over the longer moving average, you can go short in an antitrend strategy. Of course, this "upside" crossover would be a signal to buy long in a trend-following strategy. Table 3.4 Comparison of trading systems using 5-day and 20day simple MAXO tests, 5/89-6/95 (dollars) Antitrend Trading MAXO Paper Profit, $100SStC Coffee ^2,719 Cotton -14,670 Crude oil, 2,580 Gold, -12,740 Japanese -34,650 Swiss franc -7,812 U.S. bond -28,119 Average -19,733 Maximum Intraday Drawdown -59,344 -36,895 -21,500 -21,780 -58,540 -45,688 -33,019 -39,538 Trend-Following MAXO Paper Profit, Maximum $100 S&C Intraday Drawdown 59,241 -17,216 -6,845 -18,010 -30,730 -35,460 -8,560 -12,950 -9,025 -22,738 -23,500 -40,175 -9,643 -23,568 -4,152 -24,302

To Follow the Trend or Not? 47 Here we have arbitrarily picked 5-day and 20-day moving averages as examples of short- to intermediate-term averages. The test period was from May 26, 1989, through June 30, 1995, with $100 for slippage and commissions and a $1,500 initial stop. The antitrend strategy was a net loser on average, with significant potential for intraday drawdowns. The trend-following strategy cut the average loss by 79 percent and drawdown is lower by 39 percent—a better situation on both counts. Table 3.5 presents another combination: the moving average antitrend and trend-following strategies with 7-day and 50-day simple moving averages. This combination is good for no-nonsense trend following. The assumptions are the same as before: $100 for slippage and commissions and a $1,500 initial stop with the calculations performed from May 26, 1989, through June 30, 1995. Under antitrend trading, the 7/50-day SMA combination was also a net loser. On the other hand, it was a net winner with trend following, with profitability across all seven markets. The trendfollowing strategy had approximately one-fifth the drawdowns of the antitrend approach. Thus, the trend-following approach was the better choice on both counts. These calculations show that a trend-following strategy is probably the better choice for the average position trader. However, the antitrend strategy may be attractive if you have low commission costs and little slippage. The example tests in this chapter used arbitrary combinations of moving averages. However, you can test your system over historical data Table 3.5 Comparison of performance for 7-day and 50-day simple MAXO tests, 5/89-6/95 (dollars) Antitrend Trading MAXO Paper Profit $100 S&C Coffee -22,716 Cotton -44,375 Crude oil, ^t3,440 Gold, -14,540 Japanese -39,663 Swiss franc -49,325 U.S. bond -34,606 Average -37,658 Maximum Intraday Drawdown -68,534 -52,275 -47,570 -20,980 -71,225 -70,800 -36,756 -49,934 Trend-Following MAXO Paper Profit Maximum $100 SScC Intraday Drawdown 38,689 -27,615 23,155 -9,795 20,430 -5,020 4,560 -5,730 23,662 -23,075 32,988 -13,163 18,131 -14,619 20,488 -11,900

48 Foundations of System Design to find other combinations with better performance. Optimization is the process of finding the "best" performing variable set on historical data. The next section examines whether optimization is a good design strategy.

To Optimize or Not to Optimize? If you have a computer, you can easily set up a search to find the "optimum" values for a system over historical data. The results can be truly astonishing. Imagine your profits if you could only have known ahead of time what the most profitable parameter combination was going to be. Therein lies the rub. The unfortunate fact is that parameters that work best on past data rarely provide similar performance in the future. The term "optimization" is used rather loosely here to include all the activities affecting selection of parameter values in a trading system. We have already seen the difficulties of curve-fitting a model. You can also consider lower levels of optimization, in which you test variables over a broad range of values and markets, and try to select the one you like "best." But the real issue is not whether a particular set is the best. It is whether you believe sufficiently in the system to trade it without deviations. The primary benefit of optimization may be that you improve your comfort level with a particular system. The problem with system optimization is that past price patterns do not repeat exactly in the future. The same is true of intermarket relationships. Although broad relationships follow from historical data, there can be differences in the time-lags between events and the relative magnitudes of the effects. You must also resolve other conflicts. For example, you must choose the period you will use to optimize your trading system values. As you will quickly discover, the values you choose depend on the length of the test period. You must also determine how often you will reop-timize your system in the future. You must then prescribe the time for which the optimized values are valid. For example, you may decide to use 3 years of data to optimize the values and recalculate them after 3 months. Thus, one solution may be to reoptimize after 3 months on the latest 3 years of data available. This is equivalent to retraining your favorite neural net. If you do reoptimize, you must determine how to treat trades that may be open from the previous period or values of the trading system.

To Optimize or Not to Optimize? 49 You must also decide if you want to use the same values of your system parameters on all markets. If not, you will have to optimize the system on each market separately. In that case, you must keep up a program of reoptimization and recalibration for each of your systems over every market that you trade. Is all this effort worth the trouble? The results of deterministic testing do not support any attempts at finding the "best" or optimized variables. Consider the following test using actual deutsche mark futures contracts. The rollover dates are the twenty-first day of the month before expiration. For simplicity, we will trade just one contract, allowing $100 for slippage and commissions, with a $1,500 initial money management stop. We will use a variation of the moving average crossover system, trading not the crossover, but a 5-day breakout in prices after the crossover. Thus, if the shorter moving average was above the longer moving average, then a 5-day breakout above the highs would trigger a long entry. Also included is a simple exit condition, ending the trade on the close of the twentieth day in the trade. One attractive feature of this arbitrary system is that the lengths of the short and long moving average can be optimized. The calculations are simplified by fixing the length of the short average to a 3-day simple moving average of the close. The length of the longer simple moving average varies from 20 to 50 days, with an increment of 5 days. The test period was from November 14, 1983, through November 21, 1989. The performance of the various models was observed 3, 6, 9, and 12 months into the future. As Tables 3.6 and 3.7 show, there is no predicting how the model will do over a future period. The relative rankings change from period to period without any pattern or consistency. Table 3.6 Data showing that past performance does not predict future performance Length of Optimized 3 mo. 1990 6mo.1990 9 mo. 1990 12 mo. 1990 SMA Profit Profit Profit Profit ($)______(S)______($)______($)______(S) Profit (Days) 20 28,275 24,175 338 -525 2,038 -238 31,238 -2,475 338 63 2,625 3,600 50 2,175 4,000 45 7,013 -2,200 -300 -1,538 2,325 1,963 40 7,950 338 1,863 -488 2,113 35 15,475 338 -4,363 650 25 -2,300 30 18,088 338 -4,363 -1,800 -3,112

50 Foundations of System Design Table 3.7 Data showing that relative rankings from the past do not predict future relative ranks Length of Optimized 3 mo. 1990 6 mo. 1990 9 mo. 1990 12mo.1990 SMA Relative Relative Relative Relative Relative (days) Rank Rank Rank Rank Rank 20 1 6 4 5 5 25 2 7 6 6 7 30 3 1 2 2 3 35 4 1 1 3 4 40 5 1 3 1 1 45 6 1 6 4 2 50 7 1 6 7 6

We next test the hypothesis that if the optimization period were closer to the actual trading period, the predictions would be more reliable. However, as Tables 3.8 and 3.9 show, there is again no way to predict what the model will do in the succeeding periods. This should be expected because there is no cause-and-effect relationship between our optimized model and market forces. Since we are merely fitting a model to past data, we are not capturing all the fundamental and psychological forces driving the market. Our poor ability to predict the future based only on past price data is not surprising. Let us carry our argument one step forward. Because we do not capture any cause-and-effect relationships, optimization on one market should have little or no benefit for trading other markets. Indeed, as Table 3.10 shows, optimizing a system on one market (here the deutsche mark) does little to improve performance in other markets. Table 3.8 Data showing that bringing the optimization period closer to the trading period (11 /88-11 /89) does not predict future performance Length of Optimized 3 mo. 1990 6mo.1990 9mo.1990 12mo.1990 SMA Profit Profit Profit Profit Profit (Pays) (S)_____($)_____($)_____($)_____($) 20 3,525 -1,625 -1,000 2,650 2,438 25 5,225 5,338 4,713 6,213 7,638 50 -1,900 4,713 7,213 8,813 45 -1,525 -2,575 7,688 8,000 40 -2,800 5,338 400 8,475 35 ' 63 5,338 913 -^13 30 513 5,338 3,138 2,688 4,250 5,338 4,437 4,913 5,413

To Optimize or Not to Optimize? 51 Table 3.9 Data showing that relative rankings over recent past (11 /88-11 /89) do not predict future relative ranks 6 mo. 9 mo. 12mo. Length of Optimize 3 mo. SMA d 1990 1990 1990 1990 (Days) Rank Rank Rank Rank Rank 20 2 6 6 6 6 25 1 7 7 7 7 30 3 1 1 1 2 35 4 1 1 2 3 40 5 1 3 3 1 45 7 1 4 4 4 50 6 1 5 5 5

Any optimization exercise has many potential benefits. The first benefit is recognition of the type of market conditions under which the trading system is unprofitable. For any rules that you can construct, you can find market action that produces losses. This happens because the market triggers the signal, and then does just the opposite instead of following through. The second benefit is verification of the general ideas underlying the model. For example, you can check to see if the model is profitable in trending markets or trendless markets. You have designed the rules to be profitable under certain market assumptions. The optimization exercise allows you to verify if your broad assumptions are correct. A third benefit is understanding the effect of initial money management stops. You can quantify what level of initial stop allows you to Table 3.10 Data showing that optimization over one market does not predict performance in other markets Deutsche Lengt Mark Japanese Cold Coffee Heating h of 11/88Yen 11/90- 11/90-7/95 11/90-7/95 Oil 11/90SMA 11/89 7/95 P fit P fit P fit 7/95 P fit (Days) ($) (S) (S) ($) (S) 20 25 30 35 40 45 50 3,525 5,225 4,250 513 63 -2,800 -1,525 8,188 7,838 8,938 7,013 3,963 3,250 11,245 -16,190 -15,370 -13,920 -10,860 -11,400 -7,940 -8,310 30,956 29,206 40,781 -5,013 -6,343 6,188 6,625 -26,771 -21,938 -21,230 -18,028 -14,316 -18,873 -13,773

52 Foundations of System Design capture the majority of potential profits. For example, if your stop is too wide, your losing trades will be relatively large. On the other hand, if your stop is too close to the starting position, you will be stopped out frequently. Your loss per trade will be small. However, the higher frequency of losing trades means your total drawdown could exceed a larger initial stop. The biggest benefit of optimization is reinforcing your beliefs about a particular trading system. Ultimately, it is more important for you to implement the trading system exactly as planned. Hence, any testing you do that allows you to understand system performance and become more comfortable with its profit and loss characteristics will help you to execute it with greater confidence in actual trading. The main point of this section is that you cannot assume your system is going to be as profitable in the future as it has been in the past. This raises the issue of how you control your risks to cope with uncertain future performance. The next section presents risk-control ideas.

Initial Stop: Solution or Problem? Many traders have raised stop placement to an art form because it is not clear if the initial stop is a solution or a problem. The answer depends on your experiences. Often, the stop acts as a magnet for prices. It seems the market hits the stop, only to reverse and resume the previous trend. Thus, initial stops can easily test your patience. Even so, initial stops should be an essential part of managing trading risk. This section discusses some general issues related to selecting an initial stop. Detailed examples appear in the following chapters. If you use an initial stop at all, use stops that follow moneymanagement rules but are derived from system design and market volatility. A good idea is to use a 2 percent of equity initial stop, and then use maximum adverse excursion (MAE), a distribution of the worst loss in winning trades, to select the dollar value of the stop for a particular system. Relate the MAE to some measure of market volatility before calculating the number of contracts. Thus, the initial stop meets three criteria: money management, MAE, and volatility. Another issue involves whether you should place your stop loss order with your broker. Many traders will have a well-defined exit price, but will not place an order in the market. They like to monitor the market in real time, and will place the exit order themselves if needed. This is termed the "discretionary initial stop." If you have good discipline and

Initial Stop: Solution or Problem? 53 judgment, the discretionary initial stop could work well for you. However, if you cannot monitor the market continuously, it may be prudent to enter the exit order with your broker. What values of the initial stop should you use during system testing? That depends on the type of data you have and the nature of the system design. The issue is whether to use a tight stop or a loose stop. A tight stop may have a dollar value less than $500 per contract. A loose stop could be as high as $5,000. Let us assume you have only daily data. In this case, it is difficult to test a tight stop accurately because the exact track of prices during the day is unknown. Suppose you are trading the bond market, and the typical daily range is $1000. Now, say you want to test a $100 stop with daily data. Most system-testing software will stop you out on the day of entry because it does not know the exact track of prices. Of course, if you have intraday data, then you can more accurately test a $100 stop. Thus, if your stop is very tight, you need intraday data for accurate tests. There are two broad types of systems, those that are selfcorrecting and those that are not self-correcting. Self-correcting systems have rules for long and short entries. Such systems will eventually generate a long signal for short trades and vice versa. Because these systems are self-correcting, the reverse signal will limit losses, even without an initial stop. Of course, the losses will depend on market volatility, and easily could be as large as -$10,000 per contract. Systems that are not self-correcting include those that trade the long side or the short side only. Thus, you could get a false short signal and remain short through a long up trend. The losses in these systems can be unlimited, and hence must be protected by an initial stop. A onesided system with an exit strategy can become selfcorrecting. The exit strategy will limit losses in a one-sided system by closing out the trade at some preselected point. For example, a selfcorrecting, longside-only system has an exit stop at the most recent 14-day low. You can get a better feel for the efficiency of entry rules if you test a self-correcting system without initial stops. However, if the system is not self-correcting, then you must test it with an initial stop. There is still the issue of how wide the stop should be. Relatively wide stops, defined as three times the 10-day average of the daily range, are a good choice. In this way the stop has a smaller influence on results than do the entry rules. If you like tight stops, then use intraday data, or use an amount larger than the recent daily trading range. Your data set will strongly influence the results of your initial stop selection. If your data set has many trading range markets, then a

tight stop will produce whipsaw losses. Even though each loss may be small,

Foundations of System Design the sum of a series of losses can be large. A loose stop will prevent whip-saw losses in a trading range. If the market is trending, then the value of the initial stop is not critical. Thus, a trending market will rescue a system with tight stops, and you can get some astonishing results. Relatively loose stops, between $1,500 and $5,000, work well. If the stops are relatively "loose" then there is little difference between nearby values. Conversely, if the stop is "tight," then small changes in the stop can produce big swings in equity. Hence, the system tests in this book use daily data and stops ranging from $1,000 to $5,000. Often, the point of discussion in this book does not depend on the amount of the stop. Sometimes the loose stop is a necessary design feature. In such cases the reason for choosing the wider stop is stated. Ultimately, if you do not like my stop, you can retest the system to suit your preferences. Some actual calculations will clarify this discussion. Here we use the standard 20-day channel breakout on the close (CHBOC) trading system. This system buys on the close if today's close is higher than the highest high of the last 20 days. The short sale condition is symmetrical. 20-day CHBOC with varying initial stop 2700 00 2500 00 S 2300 2100 00 00 1900 00 1700 00 1500 00 Initial stop ($) Figure 3.3 Profit increases steadily and then levels off as the

initial stop

increases.

Initial Stop: Solution or Problem? 55 The system sells short on the close if today's close is lower than the lowest low of the past 20 days. We will test this system on the coffee market, which has seen much volatility as well as strong trends. We will vary the initial stop from $0 to $8,000 in $500 increments and allow $100 for slippage and commissions. Consider for a moment what the $0 initial stop means. The system goes long or short on the close. Thus, the trade will remain open only if prices continue to move strongly beyond today's close. This is the toughest stop you can impose because the only trades that survive are the ones that are profitable immediately. Observe that profits increase steadily as we loosen the initial stop (see Figure 3.3). There was a surprising profit of $158,103 with a $0 initial stop on just 20 (of 434) trades. This confirms a common piece of market wisdom that the best trades are profitable immediately. It also confirms that only 5 percent or so of the trades are the "big ones." So you should work hard not to miss them. Figure 3.4 shows that a tight stop can produce a drawdown greater than using no stop at all. More and more trades recover their losses and Changes In MIDD for 20-day CHBOC on Coffee 2000 0 S 2200 0

2400 0 2600 0 2800 0 3000 0 3200 0 3400 0 3600 0 Initial stop ($) Figure 3.4 As we loosen the initial stop, MIDD first increases and then stops declining.

56 Foundations of System Design close at a profit as the stop widens. Eventually the stops are so large that they have little effect, and so MIDD stabilizes. The initial stop cuts off fewer trades as we loosen it (see Figure 3.5), and hence the total number of trades produced by CHBOC decreases. Once the stop is "too loose" (more than $3,000 or so), it has little effect, and the number of trades stops declining. Only 5 percent of the trades are profitable with a $0 stop. The percentage of winners increases quickly as we loosen the initial stop until the stop has little effect (see Figure 3.6). As we loosen the stop, more of the winning trades can survive the vagaries of market action. As you may expect, the worst losing trade increases as we loosen the stop (see Figure 3.7, page 58). This occurs because the worst case with a $0 stop reflects slippage due to a weak opening. However, as we loosen the stop, the losing trade from a false signal can survive longer. The highest average 10-day trading range in the coffee market over the last 20 years was approximately $5,025. The average value was $1,015 and the standard deviation was $641. The cumulative distribu-

Number of trades for 20-day CHBOC on Coffee

Initial stop ($) Figure 3.5 The number of trades drops and levels off as we loosen the initial stop.

Initial Stop: Solution or Problem? 57 Changes In percent profitable trades, 20-day CHBOC on Coffee

>o o
T-

10 o io o io
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irt co

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ro Figure 3.6 The proportion of profitable trades Ini increases and levels off as tial stop we loosen the initial stop. ($)

tion (Figure 3.8, page 59) shows that a stop of $3,000 exceeds 98.3 percent of all the 10-day average trading range values seen in coffee over the last 20 years. Hence, $3,000 should be a loose stop. Figures 3.3 through 3.7 show that the changes in performance begin to level off beyond $3,000. Thus, you can view stops greater than $3,000 as "very loose" stops. A $500 stop that covers less than 20 percent of all observed values of the 10-day average daily range qualifies as a "tight" stop. You can now use the cumulative frequency distribution to select a stop based on market volatility. An arbitrary stop may be too tight or too loose. This analysis assumes that you use the same dollar stop on every trade. If you vary the initial stop on every trade then this analysis will be of little use to you. We already know that stops are hit more frequently during trading range markets. Hence, you could use some measure of trendiness to vary your initial stop. Many traders feel an aversion to taking a big loss, even though they have no problem taking many small ones. The maximum drawdown usually decreases as the stop increases (see Figure 3.4). Thus, you should

58 Foundations of System Design Variation In biggest losing trade: 20-day CHBOC on Coffee

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How to Develop and Implement a Winning Trading Sytem

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