Contents
List of Figures ix
List of Tables xi
List of Notations xiii
Preface xv
Acknowledgments xvii
Authors xix
I Introduction 1
1 Introduction 3
1.1 Background 4
1.1.1 Challenge 1: Voluminous Financial Instruments 4
1.1.2 Challenge 2: Human Behavioral Biases 4
1.1.3 Challenge 3: High-Frequency Trading 4
1.1.4 Algorithmic Trading and Machine Learning 4
1.2 What Is Online Portfolio Selection? 5
1.3 Methodology 7
1.4 Book Overview 7
2 Problem formulation 11
2.1 Problem Settings 11
2.2 Transaction Costs and Margin Buying Models 13
2.3 Evaluation 14
2.4 Summary 16
II Principles 17
3 Benchmarks 21
3.1 Buy-and-Hold Strategy 21
3.2 Best Stock Strategy 21
3.3 Constant Rebalanced Portfolios 22
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4 Follow the Winner 23
4.1 Universal Portfolios 23
4.2 Exponential Gradient 25
4.3 Follow the Leader 26
4.4 Follow the Regularized Leader 27
4.5 Summary 29
5 Follow the Loser 31
5.1 Mean Reversion 31
5.2 Anticorrelation 32
5.3 Summary 33
6 Pattern Matching 35
6.1 Sample Selection Techniques 36
6.2 Portfolio Optimization Techniques 37
6.3 Combinations 38
6.4 Summary 39
7 Meta-Learning 41
7.1 Aggregating Algorithms 41
7.2 Fast Universalization 42
7.3 Online Gradient and Newton Updates 43
7.4 Follow the Leading History 43
7.5 Summary 43
III Algorithms 45
8 Correlation-Driven Nonparametric Learning 47
8.1 Preliminaries 48
8.1.1 Motivation 48
8.2 Formulations 50
8.3 Algorithms 51
8.4 Analysis 56
8.5 Summary 57
9 Passive–Aggressive Mean Reversion 59
9.1 Preliminaries 59
9.1.1 Related Work 59
9.1.2 Motivation 60
9.2 Formulations 62
9.3 Algorithms 65
9.4 Analysis 67
9.5 Summary 69
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CONTENTS vii
10 Confidence-Weighted Mean Reversion 71
10.1 Preliminaries 71
10.1.1 Motivation 71
10.2 Formulations 73
10.3 Algorithms 76
10.4 Analysis 78
10.5 Summary 81
11 Online Moving Average Reversion 83
11.1 Preliminaries 83
11.1.1 Related Work 83
11.1.2 Motivation 84
11.2 Formulations 88
11.3 Algorithms 90
11.4 Analysis 91
11.5 Summary 92
IV Empirical Studies 93
12 Implementations 95
12.1 The OLPS Platform 95
12.1.1 Preprocess 96
12.1.2 Algorithmic Trading 96
12.1.3 Postprocess 97
12.2 Data 97
12.3 Setups 99
12.3.1 Comparison Approaches and Their Setups 100
12.4 Performance Metrics 100
12.5 Summary 101
13 Empirical Results 103
13.1 Experiment 1: Evaluation of Cumulative Wealth 103
13.2 Experiment 2: Evaluation of Risk and Risk-Adjusted Return 105
13.3 Experiment 3: Evaluation of Parameter Sensitivity 109
13.3.1 CORN’s Parameter Sensitivity 109
13.3.2 PAMR’s Parameter Sensitivity 109
13.3.3 CWMR’s Parameter Sensitivity 114
13.3.4 OLMAR’s Parameter Sensitivity 114
13.4 Experiment 4: Evaluation of Practical Issues 116
13.5 Experiment 5: Evaluation of Computational Time 120
13.6 Experiment 6: Descriptive Analysis of Assets and Portfolios 122
13.7 Summary 126
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14 Threats to Validity 129
14.1 On Model Assumptions 129
14.2 On Mean Reversion Assumptions 130
14.3 On Theoretical Analysis 131
14.4 On Back-Tests 131
14.5 Summary 133
V Conclusion 135
15 Conclusions 137
15.1 Conclusions 137
15.2 Future Directions 138
15.2.1 On Existing Work 138
15.2.2 On Practical Issues 140
15.2.3 Learning for Index Tracking 140
Appendix A OLPS: A Toolbox for Online Portfolio Selection 143
Appendix B Proofs and Derivations 171
Appendix C Supplementary Data and Portfolio Statistics 187
Bibliography 193
Index 205
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