The Evaluation and Optimization of Trading Strategies

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1 The Evaluation and Optimization of Trading Strategies Second Edition ROBERT PARDO WILEY John Wiley & Sons, Inc.

2 Contents Foreword Preface Acknowledgments xv xvii v\i\ Introduction 1 CHAPTER 1 On Trading Strategies 5 Why This Book Was Written 7 Who Will Benefit from This Book? 8 The Goals of This Book 10 The Lay of the Land 10 CHAPTER 2 The Systematic Trading tfge 17 Discretionary Trading 18 Raising the Bar 19 Verification 22 Quantification 24 Risk and Reward 24 The Performance Profile 26 Objectivity 27 Consistency 29 Extensibility 32 The Benefits of the Historical Simulation 33 Positive Expectancy 34 The Likelihood of Future Profit 34 The Performance Profile 35 Proper Capitalization 35 vii

3 ViH CONTENTS A Measure of Real-Time Trading Performance 36 The Benefits of Optimization 37 The Benefits of the Walk-Forward Analysis 38 The Advantages of a Thorough Understanding 39 Confidence 40 Strategy Refinement 41 CHAPTER 3 The Trading Strategy Development Process 43 Two Philosophical Approaches to Strategy Development 44 The Scientific Approach 44 The Path of Empirical Development 45 An Overview of the Trading Strategy Design Process 47 Step 1: Formulate the Trading Strategy 49 Step 2: Translate the Rules into a Definitive Form 49 Step 3: Preliminary Testing 50 Step 4: Optimize the Trading Strategy 51 Step 5: The Walk-Forward Analysis 52 Step 6: Trade the System 53 Step 7: Evaluate Real-Time Performance 54 Step 8: Improving the System 55 CHAPTER 4 The Strategy Development Platform 57 The Scripting Language 58 Diagnostics 59 Reporting 62 Optimization 68 The Objective Function 68 Speed 68 Automation 69 Walk-Forward Analysis 69 Portfolio Analysis 70 In Conclusion 71 CHAPTER 5 The Elements of Strategy Design 73 The Three Principal Components of a Strategy 74 Entry and Exit 74 Risk Management 74 Position Sizing 75

4 Contents ix An Overview of a Typical Trading Strategy 75 A Trade Equals an Entry and an Exit 76 Entry Filters 78 The Management of Risk 79 Trade Risk 80 Strategy Risk 82 Portfolio Risk 84 The Management of Profit 85 The Trailing Stop 85 The Impact of Overnight Change on the Trailing Stop 87 Profit Targets 87 The Impact of Overnight Change on Target Orders 88 Position Sizing 89 Advanced Strategies 91 Summary 92 CHAPTER 6 The Historical Simulation 93 The Essential Reports 94 The Performance Summary 94 The Trade List 94 The Equity Curve 107 Performance by Period 1 08 The Importance of Accuracy 109 Software Limitations 109 Rounding Issues 109 Phantom Trades 111 Price Orders 112 Realistic Assumptions 113 Price and Trade Slippage 11 3 Opening Cap Slippage 11 5 Opening and Closing Range Slippage 11 6 Slippage Due to Size 11 7 The Significance of Slippage * 117 Limit Moves 118 Major Events and Dates 118 Historical Data 120 Stock Prices 120 Cash Markets 120 Futures Markets 121

5 The Continuous Contract The Perpetual Contract Adjusted Continuous Contracts The Size of the Test Window Statistical Requirements Sample Size and Statistical Error How Many Trades? Stability Degrees of Freedom Frequency of Trading Types of Markets The Bull Market The Bear Market The Cyclic Market The Congested Market Efficient Markets The Life Cycle of a Trading Strategy Window Size and Model Life CHAPTER 7 Formulation and Specification Formulate the Trading Strategy Specification Translate the Idea into a Testable Strategy Make a Vague Idea Precise CHAPTER 8 Preliminary Testing Verification of Calculations and Trades Calculations Trading Rules In Summary Theoretical Expectations Preliminary Profitability The Multimarket and Multiperiod Test Selecting the Basket Determining the Length of the Test Period Segmenting the Data The Test The Results of the Test

6 Contents xi CHAPTER 9 Search and Judgment 179 Search Methods 180 The Grid Search 181 The Prioritized Step Search 1 85 Hill Climbing Search Algorithms 188 Multipoint Hill Climbing Search 189 Advanced Search Methods 191 Simulated Annealing 193 Genetic Algorithms 195 Particle Swarm Optimization 197 General Problems with Search Methods 198 The Objective Function 201 A Review of a Variety of Evaluation Methods 203 Multiple Evaluation Types 208 CHAPTER 10 Optimization 211 Optimization Contra Overfitting 213 A Simple Optimization 214 The Optimization Framework 216 The Parameters 216 The Scan Range 218 The Historical Sample 220 The Objective Function 222 The Optimization Evaluation 222 A Multimarket and Multiperiod Optimization 223 The Evaluation of the Optimization 225 The Robust Trading Strategy 225 The Robust Optimization 227 The Statistically Significant Optimization Profile 227 The Distribution of the Optimization Profile 229 The Shape of the Optimization Profile 231 How Does the Strategy Respond to Optimization? 235 Does the Strategy Deserve Further Development? 236 CHAPTER 11 Walk-Forward Analysis 237 Is the Trading Strategy Robust? 238 Robustness and Walk-Forward Efficiency 238 The Cure for Overfitting 239

7 Xii CONTENTS A More Reliable Measure of Risk and Return 241 Assessing the Impact of Market Changes 241 The Best Parameter Set for Trading 242 The Theory of Relevant Data 243 Peak Performance 243 Statistical Rigor 244 Shifting Markets 245 The Varieties of Market Conditions 245 The Walk-Forward 247 The Role of the Walk-Forward 247 Setting up a Walk-Forward 248 An Example of a Walk-Forward Test 250 The Walk-Forward Analysis 251 The Purpose of the Walk-Forward Analysis 252 An Example of a Walk-Forward Analysis 255 Is the Strategy Robust? 256 What Rate of Profit Should We Expect? 260 What Is the Risk? 261 Walk-Forward Analysis and the Portfolio 261 CHAPTER 12 The Evaluation of Performance 263 The Trading Strategy as an Investment 263 The Dimension of Risk 264 Compare the Strategy to the Alternatives 264 Maximum Drawdown and Trading Risk 265 Maximum Drawdown in Context 267 Maximum Drawdown and the Trader 268 Maximum Run-up and the Trader 269 Trading Capital and Risk 270 Risk Adjusted Return 272 Reward to Risk Ratio 273 Model Efficiency 273 Consistency 276 Patterns of Profit and Loss 277 CHAPTER 13 The Many Faces of Overfltting 281 What Is Overfitting? 282 The Abuse of Hindsight 284

8 Contents xiii The Case of the Overfit Forecasting Model 286 The Case of the Overfit Trading Model 289 The Symptoms of an Overfit Trading Model 290 The Causes of Overfitting 291 Degrees of Freedom 292 Measuring Degrees of Freedom 292 Degrees of Freedom, Sample Size and Startup Overhead 293 Trade Sample Size 295 Optimization Error 1 Overparameterization 296 Optimization Error 2 Overscanning 297 The Big Fish in a Small Pond Syndrome 298 The Walk-Forward Test 298 CHAPTER 14 Trading the Strategy 301 The Mental Aspects of Trading 302 Return on Investment 303 PoorStrategy 303 Market Contraction 303 Unseen Market Conditions 304 Superior Alternatives 305 Maximum Risk 305 Real-time and Evaluation Performance 308 Comparing the Evaluation and Trade Profile 310 Understanding the Test Profile 311 Performance Quirks 313 The Windfall Profit 315 The Losing Run 316 Flat Production 316 In Conclusion 317 \otes 319 Index 323

Trading strategies have been around for as long as people have traded

CHAPTER 1 On Trading Strategies Trading strategies have been around for as long as people have traded organized markets. Whereas some might quarrel with me in this usage I will state unequivocally that