PRAISE FOR
QUANTITATIVE PORTFOLIO OPTIMIZATIONOPTIMIZATION "This book provides an excellent exposition on portfolio optimization, serving not only as a self-contained guide to this important topic, but also modernizing the field with the latest advances in battle-tested machine learning approaches. The book is well structured and application centric. This is a must read for every quantitative portfolio manager."
- Matthew Dixon, FRM, Ph. D. , Associate Professor of Applied Math at the Illinois Institute of Technology and an Affiliate Associate Professor of the Stuart School of Business "Quantitative Portfolio Optimization: Advanced Techniques and Applications is an essential guide for anyone seeking to navigate the complex world of modern portfolio management. This book masterfully blends the foundational principles of portfolio theory with cutting-edge advancements in risk management, dynamic models, and control systems. Its integration of machine learning and deep learning offers readers a forward-looking perspective on leveraging AI-driven techniques for optimization. What truly sets this book apart is its comprehensive approach. From theoretical insights to practical backtesting applications, it equips professionals, researchers, and students with the tools to design and refine robust investment strategies. Whether you're delving into the nuances of risk modelling or exploring dynamic portfolio control with the latest AI methodologies, this text is an invaluable resource. This book isn't just about managing portfolios-it's about mastering the art and science behind it. Highly recommended for anyone aiming to achieve excellence in quantitative finance and portfolio optimization."
-Daniel Bloch, Director, Quant Finance Limited
Inhaltsverzeichnis
Contents Preface xiii Acknowledgements xv About the Authors xvii CHAPTER 1 Introduction 1 1. 1 Evolution of Portfolio Optimization 1 1. 2 Role of Quantitative Techniques 1 1. 3 Organization of the Book 4 Contents
Preface xiii Acknowledgements xv About the Authors xvii
CHAPTER 1 Introduction 1 1. 1 Evolution of Portfolio Optimization 1 1. 2 Role of Quantitative Techniques 1 1. 3 Organization of the Book 4 CHAPTER 2 History of Portfolio Optimization 7 2. 1 Early beginnings 7 2. 2 Harry Markowitz's Modern Portfolio Theory (1952) 9 2. 3 Black-Litterman Model (1990s) 13 2. 4 Alternative Methods: Risk Parity, Hierarchical Risk Parity and Machine Learning 19 2. 4. 1 Risk Parity 19 2. 4. 2 Hierarchical Risk Parity 26 2. 4. 3 Machine Learning 27 2. 5 Notes 31
PART ONE Foundations of Portfolio Theory CHAPTER 3 Modern Portfolio Theory 35 3. 1 Efficient Frontier and Capital Market Line 35 3. 1. 1 Case Without Riskless Asset 35 3. 1. 2 Case With a Riskless Asset 41 3. 2 Capital Asset Pricing Model 48 3. 2. 1 Case Without Riskless Asset 48 3. 2. 2 Case With a Riskless Asset 52 3. 3 Multifactor Models 54 3. 4 Challenges of Modern Portfolio Theory 59 3. 4. 1 Estimation Techniques in Portfolio Allocation 60 3. 4. 2 Non-Elliptical Distributions and Conditional Value-at-Risk (CVaR) 63 3. 5 Quantum Annealing in Portfolio Management 65 3. 6 Mean-Variance Optimization with CVaR Constraint 67 3. 6. 1 Problem Formulation 67 3. 6. 2 Optimization Problem 68 3. 6. 3 Clarification of Optimization Classes 68 3. 6. 4 Numerical Example 69 3. 7 Notes 70
CHAPTER 4 Bayesian Methods in Portfolio Optimization 73 4. 1 The Prior 75 4. 2 The Likelihood 79 4. 3 The Posterior 80 4. 4 Filtering 83 4. 5 Hierarchical Bayesian Models 87 4. 6 Bayesian Optimization 89 4. 6. 1 Gaussian Processes in a Nutshell 90 4. 6. 2 Uncertainty Quantification and Bayesian Decision Theory 94 4. 7 Applications to Portfolio Optimization 96 4. 7. 1 GP Regression for Asset Returns 96 4. 7. 2 Decision Theory in Portfolio Optimization 96 4. 7. 3 The Black-Litterman Model 99 4. 8 Notes 103
PART TWO Risk Management CHAPTER 5 Risk Models and Measures 107 5. 1 Risk Measures 107 5. 2 VaR and CVaR 109 5. 2. 1 VaR 110 5. 2. 2 CVaR 112 5. 3 Estimation Methods 116 5. 3. 1 Variance-Covariance Method 116 5. 3. 2 Historical Simulation 116 5. 3. 3 Monte Carlo Simulation 117 5. 4 Advanced Risk Measures: Tail Risk and Spectral Measures 118 5. 4. 1 Tail Risk Measures 118 5. 4. 2 Spectral Measures 120 5. 5 Notes 123
CHAPTER 6 Factor Models and Factor Investing 125 6. 1 Single and Multifactor Models 126 6. 1. 1 Statistical Models 127 6. 1. 2 Macroeconomic Models 128 6. 1. 3 Cross-sectional Models 130 6. 2 Factor Risk and Performance Attribution 135 6. 3 Machine Learning in Factor Investing 141 6. 4 Notes 144 CHAPTER 7 Market Impact, Transaction Costs, and Liquidity 145 7. 1 Market Impact Models 145 7. 2 Modeling Transaction Costs 148 7. 2. 1 Single Asset 151 7. 2. 2 Multiple Assets 154 7. 3 Optimal Trading Strategies 155 7. 3. 1 Mei, DeMiguel, and Nogales (2016) 156 7. 3. 2 Skaf and Boyd (2009) 159 7. 4 Liquidity Considerations in Portfolio Optimization 161 7. 4. 1 MV and Liquidity 162 7. 4. 2 CAPM and Liquidity 163 7. 4. 3 APT and Liquidity 165 7. 5 Notes 167
PART THREE Dynamic Models and Control CHAPTER 8 Optimal Control 171 8. 1 Dynamic Programming 171 8. 2 Approximate Dynamic Programming 171 8. 3 The Hamilton-Jacobi-Bellman Equation 172 8. 4 Sufficiently Smooth Problems 174 8. 5 Viscosity Solutions 176 8. 6 Applications to Portfolio Optimization 180 8. 6. 1 Classical Merton Problem 180 8. 6. 2 Multi-asset Portfolio with Transaction Costs 181 8. 6. 3 Risk-sensitive Portfolio Optimization 183 8. 6. 4 Optimal Portfolio Allocation with Transaction Costs 184 8. 6. 5 American Option Pricing 184 8. 6. 6 Portfolio Optimization with Constraints 184 8. 6. 7 Mean-variance Portfolio Optimization 185 8. 6. 8 Schö dinger Control in Wealth Management 185 8. 7 Notes 187
CHAPTER 9 Markov Decision Processes 189 9. 1 Fully Observed MDPs 191 9. 2 Partially Observed MDPs 192 9. 3 Infinite Horizon Problems 194 9. 4 Finite Horizon Problems 198 9. 5 The Bellman Equation 200 9. 6 Solving the Bellman Equation 203 9. 7 Examples in Portfolio Optimization 205 9. 7. 1 An MDP in Multi-asset Allocation with Transaction Costs 205 9. 7. 2 A POMDP for Asset Allocation with Regime Switching 205 9. 7. 3 An MDP with Continuous State and Action Spaces for Option Hedging with Stochastic Volatility 206 9. 8 Notes 207 CHAPTER 10 Reinforcement Learning 209 10. 1 Connections to Optimal Control 211 10. 1. 1 Policy Iteration 212 10. 1. 2 Value Iteration 214 10. 1. 3 Continuous vs. Discrete Formulations 215 10. 2 The Environment and The Reward Function 217 10. 2. 1 The Environment 217 10. 2. 2 The Reward Function 220 10. 3 Agents Acting in an Environment 223 10. 4 State-Action and Value Functions 225 10. 4. 1 Value Functions 226 10. 4. 2 Gradients and Policy Improvement 227 10. 5 The Policy 230 10. 6 On-Policy Methods 233 10. 7 Off-Policy Methods 235 10. 8 Applications to Portfolio Optimization 238 10. 8. 1 Mean-variance Optimization 238 10. 8. 2 Reinforcement Learning Comparison with Mean-variance Optimization 239 10. 8. 3 G-Learning and GIRL 241 10. 8. 4 Continuous-time Penalization in Portfolio Optimization 244 10. 8. 5 Reinforcement Learning for Utility Maximization 246 10. 8. 6 Continuous-time Portfolio Optimization with Transaction Costs 246 10. 9 Notes 247
PART FOUR Machine Learning and Deep Learning CHAPTER 11 Deep Learning in Portfolio Management 253 11. 1 Neurons and Activation Functions 253 11. 2 Neural Networks and Function Approximation 256 11. 3 Review of Some Important Architectures 259 11. 4 Physics-Informed Neural Networks 269 11. 5 Applications to Portfolio Optimization 276 11. 5. 1 Dynamic Asset Allocation Using the Heston Model 276 11. 5. 2 Option-Based Portfolio Insurance Using the Bates Model 277 11. 5. 3 Factor Learning Approach to Generative Modeling of Equities 278 11. 6 The Case for and Against Deep Learning 280 11. 7 Notes 282 CHAPTER 12 Graph-based Portfolios 285 12. 1 Graph Theory-Based Portfolios 285 12. 1. 1 Literature Review 285 12. 2 Graph Theory Portfolios: MST and TMFG 285 12. 2. 1 Equations and Formulas 286 12. 2. 2 Results 287 12. 3 Hierarchical Risk Parity 289 12. 4 Notes 294
CHAPTER 13 Sensitivity-based Portfolios 295 13. 1 Modeling Portfolios Dynamics with PDEs 296 13. 2 Optimal Drivers Selection: Causality and Persistence 297 13. 3 AAD Sensitivities Approximation 303 13. 3. 1 Optimal Network Selection 304 13. 3. 2 Sensitivity Analysis 304 13. 3. 3 Sensitivity Distance Matrix 304 13. 4 Hierarchical Sensitivity Parity 307 13. 5 Implementation 307 13. 5. 1 Datasets 307 13. 5. 2 Experimental Setup 308 13. 5. 3 Short-to-medium Investments 309 13. 5. 4 Long-term Investments 312 13. 6 Conclusion 315
PART FIVE Backtesting CHAPTER 14 Backtesting in Portfolio Management 319 14. 1 Introduction 319 14. 2 Data Preparation and Handling 319 14. 3 Implementation of Trading Strategies 320 14. 4 Types of Backtests 321 14. 4. 1 Walk-forward Backtest 321 14. 4. 2 Resampling Method 321 14. 4. 3 Monte Carlo Simulations and Generative Models 321 14. 5 Performance Metrics 322 14. 6 Avoiding Common Pitfalls 323 14. 7 Advanced Techniques 323 14. 8 Case Study: Applying Backtesting to a Real-World Strategy 324 14. 9 Impact of Market Conditions on Backtest Results 324 14. 10 Integration with Portfolio Management 325 14. 11 Tools and Software for Backtesting 325 14. 12 Regulatory Considerations 326 14. 13 Conclusion 326 CHAPTER 15 Scenario Generation 329 15. 1 Historical Scenarios 329 15. 2 Bootstrapping Scenarios 330 15. 3 Copula-Based Scenarios 330 15. 4 Risk Factor Model-Based Scenarios 330 15. 5 Time Series Model Scenarios 331 15. 6 Variational Autoencoders 331 15. 7 Generative Adversarial Networks (GANs) 332 Appendix 333 A. 1 Software and Tools for Portfolio Optimization 333 Bibliography 335 Index 357
