Science of Algorithmic Trading and Portfolio Management (eBook)

Front Cover 1
The Science of Algorithmic Trading and Portfolio Management 4
Copyright Page 5
Contents 8
Preface 16
Acknowledgments 18
1 Algorithmic Trading 20
Introduction 20
Advantages 22
Disadvantages 23
Changing Trading Environment 24
Recent Growth in Algorithmic Trading 30
Investment Cycle 34
Classifications of Algorithms 35
Types of Algorithms 36
Algorithmic Trading Trends 39
Trading Venue Classification 40
Displayed Market 40
Dark Pool 40
Grey Pool 40
Dark Pool Controversies 41
Types of Orders 42
Execution Options 42
The Trading Floor 44
Research Function 45
Sales Function 46
Algorithmic Trading Decisions 48
Macro-Level Strategies 48
Step 1—Choose Implementation Benchmark 49
Step 2—Select Optimal Execution Strategy 49
Step 3—Specify Adaptation Tactic 51
Micro-Level Decisions 52
Limit Order Models 53
Smart Order Routers 54
Algorithmic Analysis Tools 56
Pre-Trade Analysis 56
Intraday Analysis 56
Post-Trade Analysis 57
Rule-Based Trading 57
Quantitative Techniques 57
High Frequency Trading 58
Auto Market Making 58
Quantitative Trading/Statistical Arbitrage 60
Rebate/Liquidity Trading 60
Direct Market Access 62
Advantages 63
Disadvantages 63
2 Market Microstructure 66
Introduction 66
Market Microstructure Literature 68
The New Market Structure 70
Pricing Models 75
Order Priority 76
Equity Exchanges 76
New NYSE Trading Model 76
Designated Market Makers 77
Supplemental Liquidity Providers 78
Trading Floor Brokers 79
NASDAQ Select Market Maker Program 79
Empirical Evidence 80
Trading Volumes 80
Market Share 80
Large and Small Cap Trading 81
Do Stocks Trade Differently Across the Exchanges and Venues? 82
Volume Distribution Statistics 82
Day of Week Effect 84
Intraday Trading Profiles 86
Spreads 86
Volumes 87
Volatility 89
Intraday Trading Stability—Coefficient of Variation 91
Special Event Days 92
Flash Crash 95
Empirical Evidence from the Flash Crash 98
What Should Regulators do to SafeGuard Investors from Potential Future Flash Crashes? 102
Comparison with Previous Crashes 103
Conclusion 104
3 Algorithmic Transaction Cost Analysis 106
Introduction 106
What Are Transaction Costs? 107
What Is Best Execution? 107
What Is the Goal of Implementation? 108
Unbundled Transaction Cost Components 108
1. Commission 108
2. Fees 108
3. Taxes 108
4. Rebates 109
5. Spreads 109
6. Delay Cost 110
7. Price Appreciation 110
8. Market Impact 110
9. Timing Risk 111
10. Opportunity Cost 111
Transaction Cost Classification 111
Transaction Cost Categorization 113
Transaction Cost Analysis 113
Measuring/Forecasting 115
Cost versus Profit and Loss 116
Implementation Shortfall 116
Complete Execution 118
Opportunity Cost (Andre Perold) 119
Expanded Implementation Shortfall (Wayne Wagner) 120
Implementation Shortfall Formulation 123
Trading Cost/Arrival Cost 123
Evaluating Performance 124
Trading Price Performance 124
Benchmark Price Performance 125
VWAP Benchmark 125
Participation Weighted Price (PWP) Benchmark 127
Relative Performance Measure (RPM) 128
Pre-Trade Benchmark 129
Index Adjusted Performance Metric 130
Z-Score Evaluation Metric 131
Market Cost Adjusted Z-Score 132
Adaptation Tactic 133
Comparing Algorithms 134
Non-Parametric Tests 135
Paired Samples 136
Sign Test 136
Wilcoxon Signed Rank Test 137
Independent Samples 139
Mann-Whitney U Test 139
Median Test 141
Distribution Analysis 142
Chi-Square Goodness of Fit 142
Kolmogorov-Smirnov Goodness of Fit 143
Experimental Design 144
Proper Statistical Tests 145
Small Sample Size 145
Data Ties 145
Proper Categorization 146
Balanced Data Sets 146
Final Note on Post-Trade Analysis 146
4 Market Impact Models 148
Introduction 148
Definition 148
Example 1: Temporary Market Impact 149
Example 2: Permanent Market Impact 149
Graphical Illustrations of Market Impact 150
Illustration 1—Price Trajectory 150
Illustration 2—Supply-Demand Equilibrium 151
Illustration 3—Temporary Impact Decay Function 154
Example—Temporary Decay Formulation 156
Illustration 4—Various Market Impact Price Trajectories 157
Developing a Market Impact Model 158
Essential Properties of a Market Impact Model 159
Derivation of Models 161
Almgren & Chriss—Market Impact Model
Random Walk with Price Drift—Discrete Time Periods 162
Random Walk with Market Impact (No price drift) 163
I-Star Market Impact Model 165
Model Formulation 166
I-Star: Instantaneous Impact Equation 166
Market Impact Equation 167
Derivation of the Model 167
Cost Allocation Method 168
I* Formulation 170
Comparison of Approaches 172
Underlying Data Set 173
Imbalance/Order Size 173
Parameter Estimation Techniques 176
Technique 1: Two-Step Process 176
Step 1: Estimate Temporary Impact Parameter 176
Step 2: Estimate ai Parameters 177
Technique 2: Guesstimate Technique 179
Technique 3: Non-Linear Optimization 179
Model Verification 179
Model Verification 1: Graphical Illustration 180
Model Verification 2: Regression Analysis 180
Model Verification 3: Z-Score Analysis 180
Model Verification 4: Error Analysis 181
5 Estimating I-Star Model Parameters 182
Introduction 182
Scientific Method 183
Step 1: Ask a Question 183
Step 2: Research the Problem 183
Step 3: Construct the Hypothesis 183
Step 4: Test the Hypothesis 183
Step 5: Analyze the Data 184
Step 6: Conclusion and Communication 184
Solution Technique 185
The Question 185
Research the Problem 185
Construct the Hypothesis 190
Test the Hypothesis 192
Data Definitions 194
Universe of Stocks 195
Analysis Period 195
Time Period 195
Number of Data Points 195
Imbalance 195
Side 196
Volume 196
Turnover 196
VWAP 197
First Price 197
Average Daily Volume 197
Annualized Volatility 197
Size 198
POV Rate 198
Cost 198
Estimating Model Parameters 198
Sensitivity Analysis 200
Cost Curves 205
Statistical Analysis 206
Error Analysis 206
Stock Specific Error Analysis 208
6 Price Volatility 212
Introduction 212
Definitions 213
Price Returns/Price Change 213
Average Return 213
Volatility 215
Covariance 215
Correlation 216
Dispersion 216
Value-at-Risk 216
Implied Volatility 217
Beta 217
Market Observations—Empirical Findings 218
Forecasting Stock Volatility 221
Volatility Models 221
Price Returns 222
Data Sample 222
Historical Moving Average (HMA) 223
Exponential Weighted Moving Average (EWMA) 224
Arch Volatility Model 224
GARCH Volatility Model 225
HMA-VIX Adjustment Model 225
Determining Parameters via Maximum Likelihood Estimation 227
Likelihood Function 227
Estimation Results 228
Measuring Model Performance 228
Root Mean Square Error (RMSE) 229
Root Mean Z-Score Squared Error (RMZSE) 229
Outlier Analysis 230
Results 230
Problems Resulting from Relying on Historical Market Data for Covariance Calculations 233
False Relationships 233
Degrees of Freedom 238
Factor Models 240
Matrix Notation 242
Constructing Factor Independence 243
Estimating Covariance Using a Factor Model 244
Types of Factor Models 246
Multi-Index Models 247
Macroeconomic Factor Models 247
Cross-Sectional Multi-Factor Models 248
Index Model 246
Single Index Model 246
Statistical Factor Models 250
7 Advanced Algorithmic Forecasting Techniques 254
Introduction 254
Trading Cost Equations 255
Model Inputs 255
Trading Strategy 256
Percentage of Volume 256
Trading Rate 257
Trade Schedule 257
Comparison of POV rate to Trade Rate 258
Trading Time 258
Trading Risk Components 259
Trading Cost Models—Reformulated 260
Market Impact Expression 260
I-Star 260
Market Impact for a Single Stock Order 260
Market Impact for a Basket of Stock 262
Timing Risk Equation 262
Timing Risk for a Basket of Stock 267
Comparison of Market Impact Estimates 267
Volume Forecasting Techniques 270
Daily Volumes 270
Definitions 270
Daily Forecasting Analysis—Methodology 271
Variable Notation 271
ARMA Daily Forecasting Model 271
Analysis Goal 272
Forecast Improvements 276
Daily Volume Forecasting Model 276
Forecasting Monthly Volumes 277
Forecasting Covariance 282
Efficient Trading Frontier 284
Single Stock Trade Cost Objective Function 286
Portfolio Trade Cost Objective Function 286
8 Algorithmic Decision Making Framework 288
Introduction 288
Equations 289
Algorithmic Decision Making Framework 291
1) Select Benchmark Price 291
Arrival Price Benchmark 291
Historical Price Benchmark 292
Future Price Benchmark 294
Comparison of Benchmark Prices 295
2) Specify Trading Goal 295
1. Minimize Cost 296
2. Minimize Cost with Risk Constraint 298
3. Minimize Risk with Cost Constraint 299
4. Balance Trade-off between Cost and Risk 299
5. Price Improvement 300
Further Insight 302
3) Specify Adaptation Tactic 303
Projected Cost 304
Target Cost Tactic 307
Aggressive-in-the-Money 308
Passive-in-the-Money 310
Comparison across Adaptation Tactics 312
Modified Adaptation Tactics 313
How Often Should We Re-Optimize Our Tactics? 313
9 Portfolio Algorithms 316
Introduction 316
Trader’s Dilemma 317
Variables 318
Transaction Cost Equations 319
Market Impact 320
Price Appreciation 320
Timing Risk 321
One-Sided Optimization Problem 321
Optimization Formulation 321
Constraint Description 322
Objective Function Difficulty 324
Optimization Objective Function Simplification 324
Portfolio Optimization Techniques 325
Quadratic Programming Approach 325
Trade Schedule Exponential 327
Residual Schedule Exponential 328
Trading Rate Parameter 329
Market Impact Expression 329
Timing Risk Expression 330
Comparison of Optimization Techniques 331
Portfolio Adaptation Tactics 335
Description of AIM and PIM for Portfolio Trading 336
How Often Should We Re-Optimize? 338
Managing Portfolio Risk 339
Residual Risk Curve 339
Minimum Trading Risk Quantity 341
Maximum Trading Opportunity 342
When to Use These Values? 343
Program-Block Decomposition 344
Appendix 347
10 Portfolio Construction 350
Introduction 350
Portfolio Optimization and Constraints 351
Transaction Costs in Portfolio Optimization 354
Portfolio Management Process 358
Example: Efficient Trading Frontier w/ and w/o Short Positions 359
Example: Maximizing Investor Utility 359
Trading Decision Process 360
Unifying the Investment and Trading Theories 362
Cost-Adjusted Frontier 367
Determining the Appropriate Level of Risk Aversion 369
Best Execution Frontier 370
Portfolio Construction with Transaction Costs 371
Quest for best execution frontier 373
Return 374
Risk 374
Conclusion 378
11 Quantitative Portfolio Management Techniques 380
Introduction 380
Are the Existing Models Useful Enough for Portfolio Construction? 382
Current State of Vendor Market Impact Models 383
Pre-Trade of Pre-Trades 386
Estimation Process 387
Applications 391
Example 1 391
Example 2 392
Example 3 392
Example 4 392
How Expensive Is It to Trade? 393
Acquisition and Liquidation Costs 396
Portfolio Management—Screening Techniques 399
MI Factor Scores 403
Derivation of the MI Factor Score for Shares 403
Current State of MI Factor Scores 405
MI Factor Score Analysis 405
Alpha Capture Program 407
Example 5 408
Example 6 409
Alpha Capture Curves 412
12 Cost Index & Multi-Asset Trading Costs
Introduction 414
Cost Index 415
Cost Basis 416
Cost Strategy 417
Normalization Process 419
Customized Indexes 421
Real-Time Cost Index 422
Back-Testing 427
Market Impact Simulation 429
Simulation Scenario 431
Multi-Asset Class Investing 434
Investing in Beta Exposure and Other Factors 434
Beta Investment Allocation 438
Multi-Asset Trading Costs 439
Global Equity Markets 440
Multi-Asset Classes 441
13 High Frequency Trading and Black Box Models 448
Introduction 448
Data and Research 450
Strategies 451
Statistical Arbitrage 451
Triangular Arbitrage 455
Liquidity Trading 458
Market-Neutral Arbitrage 459
Index and Exchange Traded Fund Arbitrage 461
Merger Arbitrage 462
Evaluation 465
Summary 469
References 472
Index 484