The Evaluation and Optimization of Trading Strategies

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 Edge 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

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

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 108

The Importance of Accuracy 109

Software Limitations 109

Rounding Issues 109

Phantom Trades 111

Price Orders 112

Realistic Assumptions 113

Price and Trade Slippage 113

Opening Gap Slippage 115

Opening and Closing Range Slippage 116

Slippage Due to Size 117

The Significance of Slippage 117

Limit Moves 118

Major Events and Dates 118

Historical Data 120

Stock Prices 120

Cash Markets 120

Futures Markets

The Continuous Contract 124

The Perpetual Contract 124

Adjusted Continuous Contracts 125

The Size of the Test Window 126

Statistical Requirements 127

Sample Size and Statistical Error 127

How Many Trades? 129

Stability 129

Degrees of Freedom 130

Frequency of Trading 131

Types of Markets 132

The Bull Market 132

The Bear Market 134

The Cyclic Market 135

The Congested Market 137

Efficient Markets 137

The Life Cycle of a Trading Strategy 140

Window Size and Model Life 141

CHAPTER 7 Formulation and Specification 145

Formulate the Trading Strategy 145

Specification—Translate the Idea into a Testable

Strategy 147

Make a Vague Idea Precise 150

CHAPTER 8 Preliminary Testing 157

Verification of Calculations and Trades 158

Calculations 159

Trading Rules 159

In Summary 164

Theoretical Expectations 164

Preliminary Profitability 166

The Multimarket and Multiperiod Test 169

Selecting the Basket 169

Determining the Length of the Test Period 171

Segmenting the Data 171

The Test 172

The Results of the Test

CHAPTER 9 Search and Judgment 179

Search Methods 180

The Grid Search 181

The Prioritized Step Search 185

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

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 Overfitting 281

What Is Overfitting? 282

The Abuse of Hindsight 284