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Machine learning (ML) is changing virtually every aspect of our lives. Today ML algorithms accomplish tasks that until recently only expert humans could perform. As it relates to finance, this is the most exciting time to adopt a disruptive technology that will transform how everyone invests for generations. Readers will learn how to structure Big data in a way that is amenable to ML algorithms; how to conduct research with ML algorithms on that data; how to use supercomputing methods; how to backtest your discoveries while avoiding false positives. The book addresses real-life problems faced by practitioners on a daily basis, and explains scientifically sound solutions using math, supported by code and examples. Readers become active users who can test the proposed solutions in their particular setting. Written by a recognized expert and portfolio manager, this book will equip investment professionals with the groundbreaking tools needed to succeed in modern finance.

Advances in Financial Machine Learning

About the Author xxi





PREAMBLE 1





1 Financial Machine Learning as a Distinct Subject 3





1.1 Motivation, 3





1.2 The Main Reason Financial Machine Learning Projects Usually Fail, 4





1.2.1 The Sisyphus Paradigm, 4





1.2.2 The Meta-Strategy Paradigm, 5





1.3 Book Structure, 6





1.3.1 Structure by Production Chain, 6





1.3.2 Structure by Strategy Component, 9





1.3.3 Structure by Common Pitfall, 12





1.4 Target Audience, 12





1.5 Requisites, 13





1.6 FAQs, 14





1.7 Acknowledgments, 18





Exercises, 19





References, 20





Bibliography, 20





PART 1 DATA ANALYSIS 21





2 Financial Data Structures 23





2.1 Motivation, 23





2.2 Essential Types of Financial Data, 23





2.2.1 Fundamental Data, 23





2.2.2 Market Data, 24





2.2.3 Analytics, 25





2.2.4 Alternative Data, 25





2.3 Bars, 25





2.3.1 Standard Bars, 26





2.3.2 Information-Driven Bars, 29





2.4 Dealing with Multi-Product Series, 32





2.4.1 The ETF Trick, 33





2.4.2 PCA Weights, 35





2.4.3 Single Future Roll, 36





2.5 Sampling Features, 38





2.5.1 Sampling for Reduction, 38





2.5.2 Event-Based Sampling, 38





Exercises, 40





References, 41





3 Labeling 43





3.1 Motivation, 43





3.2 The Fixed-Time Horizon Method, 43





3.3 Computing Dynamic Thresholds, 44





3.4 The Triple-Barrier Method, 45





3.5 Learning Side and Size, 48





3.6 Meta-Labeling, 50





3.7 How to Use Meta-Labeling, 51





3.8 The Quantamental Way, 53





3.9 Dropping Unnecessary Labels, 54





Exercises, 55





Bibliography, 56





4 Sample Weights 59





4.1 Motivation, 59





4.2 Overlapping Outcomes, 59





4.3 Number of Concurrent Labels, 60





4.4 Average Uniqueness of a Label, 61





4.5 Bagging Classifiers and Uniqueness, 62





4.5.1 Sequential Bootstrap, 63





4.5.2 Implementation of Sequential Bootstrap, 64





4.5.3 A Numerical Example, 65





4.5.4 Monte Carlo Experiments, 66





4.6 Return Attribution, 68





4.7 Time Decay, 70





4.8 Class Weights, 71





Exercises, 72





References, 73





Bibliography, 73





5 Fractionally Differentiated Features 75





5.1 Motivation, 75





5.2 The Stationarity vs. Memory Dilemma, 75





5.3 Literature Review, 76





5.4 The Method, 77





5.4.1 Long Memory, 77





5.4.2 Iterative Estimation, 78





5.4.3 Convergence, 80





5.5 Implementation, 80





5.5.1 Expanding Window, 80





5.5.2 Fixed-Width Window Fracdiff, 82





5.6 Stationarity with Maximum Memory Preservation, 84





5.7 Conclusion, 88





Exercises, 88





References, 89





Bibliography, 89





PART 2 MODELLING 91





6 Ensemble Methods 93





6.1 Motivation, 93





6.2 The Three Sources of Errors, 93





6.3 Bootstrap Aggregation, 94





6.3.1 Variance Reduction, 94





6.3.2 Improved Accuracy, 96





6.3.3 Observation Redundancy, 97





6.4 Random Forest, 98





6.5 Boosting, 99





6.6 Bagging vs. Boosting in Finance, 100





6.7 Bagging for Scalability, 101





Exercises, 101





References, 102





Bibliography, 102





7 Cross-Validation in Finance 103





7.1 Motivation, 103





7.2 The Goal of Cross-Validation, 103





7.3 Why K-Fold CV Fails in Finance, 104





7.4 A Solution: Purged K-Fold CV, 105





7.4.1 Purging the Training Set, 105





7.4.2 Embargo, 107





7.4.3 The Purged K-Fold Class, 108





7.5 Bugs in Sklearn's Cross-Validation, 109





Exercises, 110





Bibliography, 111





8 Feature Importance 113





8.1 Motivation, 113





8.2 The Importance of Feature Importance, 113





8.3 Feature Importance with Substitution Effects, 114





8.3.1 Mean Decrease Impurity, 114





8.3.2 Mean Decrease Accuracy, 116





8.4 Feature Importance without Substitution Effects, 117





8.4.1 Single Feature Importance, 117





8.4.2 Orthogonal Features, 118





8.5 Parallelized vs. Stacked Feature Importance, 121





8.6 Experiments with Synthetic Data, 122





Exercises, 127





References, 127





9 Hyper-Parameter Tuning with Cross-Validation 129





9.1 Motivation, 129





9.2 Grid Search Cross-Validation, 129





9.3 Randomized Search Cross-Validation, 131





9.3.1 Log-Uniform Distribution, 132





9.4 Scoring and Hyper-parameter Tuning, 134





Exercises, 135





References, 136





Bibliography, 137





PART 3 BACKTESTING 139





10 Bet Sizing 141





10.1 Motivation, 141





10.2 Strategy-Independent Bet Sizing Approaches, 141





10.3 Bet Sizing from Predicted Probabilities, 142





10.4 Averaging Active Bets, 144





10.5 Size Discretization, 144





10.6 Dynamic Bet Sizes and Limit Prices, 145 Exercises, 148





References, 149





Bibliography, 149





11 The Dangers of Backtesting 151





11.1 Motivation, 151





11.2 Mission Impossible: The Flawless Backtest, 151





11.3 Even If Your Backtest Is Flawless, It Is Probably Wrong, 152





11.4 Backtesting Is Not a Research Tool, 153





11.5 A Few General Recommendations, 153





11.6 Strategy Selection, 155





Exercises, 158





References, 158





Bibliography, 159





12 Backtesting through Cross-Validation 161





12.1 Motivation, 161





12.2 The Walk-Forward Method, 161





12.2.1 Pitfalls of the Walk-Forward Method, 162





12.3 The Cross-Validation Method, 162





12.4 The Combinatorial Purged Cross-Validation Method, 163





12.4.1 Combinatorial Splits, 164





12.4.2 The Combinatorial Purged Cross-Validation Backtesting Algorithm, 165





12.4.3 A Few Examples, 165





12.5 How Combinatorial Purged Cross-Validation Addresses Backtest Overfitting, 166





Exercises, 167





References, 168





13 Backtesting on Synthetic Data 169





13.1 Motivation, 169





13.2 Trading Rules, 169





13.3 The Problem, 170





13.4 Our Framework, 172





13.5 Numerical Determination of Optimal Trading Rules, 173





13.5.1 The Algorithm, 173





13.5.2 Implementation, 174





13.6 Experimental Results, 176





13.6.1 Cases with Zero Long-Run Equilibrium, 177





13.6.2 Cases with Positive Long-Run Equilibrium, 180





13.6.3 Cases with Negative Long-Run Equilibrium, 182





13.7 Conclusion, 192





Exercises, 192





References, 193





14 Backtest Statistics 195





14.1 Motivation, 195





14.2 Types of Backtest Statistics, 195





14.3 General Characteristics, 196





14.4 Performance, 198





14.4.1 Time-Weighted Rate of Return, 198





14.5 Runs, 199





14.5.1 Returns Concentration, 199





14.5.2 Drawdown and Time under Water, 201





14.5.3 Runs Statistics for Performance Evaluation, 201





14.6 Implementation Shortfall, 202





14.7 Efficiency, 203





14.7.1 The Sharpe Ratio, 203





14.7.2 The Probabilistic Sharpe Ratio, 203





14.7.3 The Deflated Sharpe Ratio, 204





14.7.4 Efficiency Statistics, 205





14.8 Classification Scores, 206





14.9 Attribution, 207





Exercises, 208





References, 209





Bibliography, 209





15 Understanding Strategy Risk 211





15.1 Motivation, 211





15.2 Symmetric Payouts, 211





15.3 Asymmetric Payouts, 213





15.4 The Probability of Strategy Failure, 216





15.4.1 Algorithm, 217





15.4.2 Implementation, 217





Exercises, 219





References, 220





16 Machine Learning Asset Allocation 221





16.1 Motivation, 221





16.2 The Problem with Convex Portfolio Optimization, 221





16.3 Markowitz's Curse, 222





16.4 From Geometric to Hierarchical Relationships, 223





16.4.1 Tree Clustering, 224





16.4.2 Quasi-Diagonalization, 229





16.4.3 Recursive Bisection, 229





16.5 A Numerical Example, 231





16.6 Out-of-Sample Monte Carlo Simulations, 234





16.7 Further Research, 236





16.8 Conclusion, 238





Appendices, 239





16.A.1 Correlation-based Metric, 239





16.A.2 Inverse Variance Allocation, 239





16.A.3 Reproducing the Numerical Example, 240





16.A.4 Reproducing the Monte Carlo Experiment, 242 Exercises, 244





References, 245





PART 4 USEFUL FINANCIAL FEATURES 247





17 Structural Breaks 249





17.1 Motivation, 249





17.2 Types of Structural Break Tests, 249





17.3 CUSUM Tests, 250





17.3.1 Brown-Durbin-Evans CUSUM Test on Recursive Residuals, 250





17.3.2 Chu-Stinchcombe-White CUSUM Test on Levels, 251





17.4 Explosiveness Tests, 251





17.4.1 Chow-Type Dickey-Fuller Test, 251





17.4.2 Supremum Augmented Dickey-Fuller, 252





17.4.3 Sub- and Super-Martingale Tests, 259





Exercises, 261





References, 261





18 Entropy Features 263





18.1 Motivation, 263





18.2 Shannon's Entropy, 263





18.3 The Plug-in (or Maximum Likelihood) Estimator, 264





18.4 Lempel-Ziv Estimators, 265





18.5 Encoding Schemes, 269





18.5.1 Binary Encoding, 270





18.5.2 Quantile Encoding, 270





18.5.3 Sigma Encoding, 270





18.6 Entropy of a Gaussian Process, 271





18.7 Entropy and the Generalized Mean, 271





18.8 A Few Financial Applications of Entropy, 275





18.8.1 Market Efficiency, 275





18.8.2 Maximum Entropy Generation, 275





18.8.3 Portfolio Concentration, 275





18.8.4 Market Microstructure, 276





Exercises, 277





References, 278





Bibliography, 279





19 Microstructural Features 281





19.1 Motivation, 281





19.2 Review of the Literature, 281





19.3 First Generation: Price Sequences, 282





19.3.1 The Tick Rule, 282





19.3.2 The Roll Model, 282





19.3.3 High-Low Volatility Estimator, 283





19.3.4 Corwin and Schultz, 284





19.4 Second Generation: Strategic Trade Models, 286





19.4.1 Kyle's Lambda, 286





19.4.2 Amihud's Lambda, 288





19.4.3 Hasbrouck's Lambda, 289





19.5 Third Generation: Sequential Trade Models, 290





19.5.1 Probability of Information-based Trading, 290





19.5.2 Volume-Synchronized Probability of Informed Trading, 292





19.6 Additional Features from Microstructural Datasets, 293





19.6.1 Distibution of Order Sizes, 293





19.6.2 Cancellation Rates, Limit Orders, Market Orders, 293





19.6.3 Time-Weighted Average Price Execution Algorithms, 294





19.6.4 Options Markets, 295





19.6.5 Serial Correlation of Signed Order Flow, 295





19.7 What Is Microstructural Information?, 295





Exercises, 296





References, 298





PART 5 HIGH-PERFORMANCE COMPUTING RECIPES 301





20 Multiprocessing and Vectorization 303





20.1 Motivation, 303





20.2 Vectorization Example, 303





20.3 Single-Thread vs. Multithreading vs. Multiprocessing, 304





20.4 Atoms and Molecules, 306





20.4.1 Linear Partitions, 306





20.4.2 Two-Nested Loops Partitions, 307





20.5 Multiprocessing Engines, 309





20.5.1 Preparing the Jobs, 309





20.5.2 Asynchronous Calls, 311





20.5.3 Unwrapping the Callback, 312





20.5.4 Pickle/Unpickle Objects, 313





20.5.5 Output Reduction, 313





20.6 Multiprocessing Example, 315





Exercises, 316





Reference, 317





Bibliography, 317





21 Brute Force and Quantum Computers 319





21.1 Motivation, 319





21.2 Combinatorial Optimization, 319





21.3 The Objective Function, 320





21.4 The Problem, 321





21.5 An Integer Optimization Approach, 321





21.5.1 Pigeonhole Partitions, 321





21.5.2 Feasible Static Solutions, 323





21.5.3 Evaluating Trajectories, 323





21.6 A Numerical Example, 325





21.6.1 Random Matrices, 325





21.6.2 Static Solution, 326





21.6.3 Dynamic Solution, 327





Exercises, 327





References, 328





22 High-Performance Computational Intelligence and Forecasting Technologies 329

Kesheng Wu and Horst D. Simon





22.1 Motivation, 329





22.2 Regulatory Response to the Flash Crash of 2010, 329





22.3 Background, 330





22.4 HPC Hardware, 331





22.5 HPC Software, 335





22.5.1 Message Passing Interface, 335





22.5.2 Hierarchical Data Format 5, 336





22.5.3 In Situ Processing, 336





22.5.4 Convergence, 337





22.6 Use Cases, 337





22.6.1 Supernova Hunting, 337





22.6.2 Blobs in Fusion Plasma, 338





22.6.3 Intraday Peak Electricity Usage, 340





22.6.4 The Flash Crash of 2010, 341





22.6.5 Volume-synchronized Probability of Informed Trading Calibration, 346





22.6.6 Revealing High Frequency Events with Non-uniform Fast Fourier Transform, 347





22.7 Summary and Call for Participation, 349





22.8 Acknowledgments, 350





References, 350





Index 353