Quantitative Portfolio Optimization

MIQUEL NOGUER ALONSO is a financial markets practitioner with 25+ years of experience in asset management. He is the Founder of the Artificial Intelligence Finance Institute and serves as Head of Development at Global AI. He is also the co-editor of the Journal of Machine Learning in Finance. JULIÁN ANTOLÍN CAMARENA holds a Bachelor’s, Master’s and a PhD in physics. For his Master’s he worked on the foundations of quantum mechanics examining alternative quantization schemes and their application to exotic atoms to discover new physics. His PhD dissertation work was on computational and theoretical optics, electromagnetic scattering from random surfaces, and nonlinear optimization. He then went on to a postdoctoral stint with the U.S. Army Research Laboratory working on inverse reinforcement learning for human-autonomy teaming. ALBERTO BUENO GUERRERO has two Bachelor’s degrees in physics and economics, and a PhD in banking and finance. Since he got his doctorate, he has dedicated himself to research in mathematical finance. His work has been presented at various international conferences and published in journals such as Quantitative Finance, Journal of Derivatives, Journal of Mathematics, and Chaos, Solitons and Fractals. His article “Bond Market Completeness Under Stochastic Strings with Distribution-Valued Strategies” has been considered a feature article in Quantitative Finance.

• Preface xiiiAcknowledgements xvAbout the Authors xviiCHAPTER 1 Introduction 11.1 Evolution of Portfolio Optimization 11.2 Role of Quantitative Techniques 11.3 Organization of the Book 4CHAPTER 2 History of Portfolio Optimization 72.1 Early beginnings 72.2 Harry Markowitz's Modern Portfolio Theory (1952) 92.3 Black-Litterman Model (1990s) 132.4 Alternative Methods: Risk Parity, Hierarchical Risk Parity and Machine Learning 192.5 Notes 31PART ONE Foundations of Portfolio TheoryCHAPTER 3 Modern Portfolio Theory 353.1 Efficient Frontier and Capital Market Line 353.2 Capital Asset Pricing Model 483.3 Multifactor Models 543.4 Challenges of Modern Portfolio Theory 593.5 Quantum Annealing in Portfolio Management 653.6 Mean-Variance Optimization with CVaR Constraint 673.7 Notes 70CHAPTER 4 Bayesian Methods in Portfolio Optimization 734.1 The Prior 754.2 The Likelihood 794.3 The Posterior 804.4 Filtering 834.5 Hierarchical Bayesian Models 874.6 Bayesian Optimization 894.7 Applications to Portfolio Optimization 964.8 Notes 103PART TWO Risk ManagementCHAPTER 5 Risk Models and Measures 1075.1 Risk Measures 1075.2 VaR and CVaR 1095.3 Estimation Methods 1165.4 Advanced Risk Measures: Tail Risk and Spectral Measures 1185.5 Notes 123CHAPTER 6 Factor Models and Factor Investing 1256.1 Single and Multifactor Models 1266.2 Factor Risk and Performance Attribution 1356.3 Machine Learning in Factor Investing 1416.4 Notes 144CHAPTER 7 Market Impact, Transaction Costs, and Liquidity 1457.1 Market Impact Models 1457.2 Modeling Transaction Costs 1487.3 Optimal Trading Strategies 1557.4 Liquidity Considerations in Portfolio Optimization 1617.5 Notes 167PART THREE Dynamic Models and ControlCHAPTER 8 Optimal Control 1718.1 Dynamic Programming 1718.2 Approximate Dynamic Programming 1718.3 The Hamilton-Jacobi-Bellman Equation 1728.4 Sufficiently Smooth Problems 1748.5 Viscosity Solutions 1768.6 Applications to Portfolio Optimization 1808.7 Notes 187CHAPTER 9 Markov Decision Processes 1899.1 Fully Observed MDPs 1919.2 Partially Observed MDPs 1929.3 Infinite Horizon Problems 1949.4 Finite Horizon Problems 1989.5 The Bellman Equation 2009.6 Solving the Bellman Equation 2039.7 Examples in Portfolio Optimization 2059.8 Notes 207CHAPTER 10 Reinforcement Learning 20910.1 Connections to Optimal Control 21110.2 The Environment and The Reward Function 21710.3 Agents Acting in an Environment 22310.4 State-Action and Value Functions 22510.5 The Policy 23010.6 On-Policy Methods 23310.7 Off-Policy Methods 23510.8 Applications to Portfolio Optimization 23810.9 Notes 247PART FOUR Machine Learning and Deep LearningCHAPTER 11 Deep Learning in Portfolio Management 25311.1 Neurons and Activation Functions 25311.2 Neural Networks and Function Approximation 25611.3 Review of Some Important Architectures 25911.4 Physics-Informed Neural Networks 26911.5 Applications to Portfolio Optimization 27611.6 The Case for and Against Deep Learning 28011.7 Notes 282CHAPTER 12 Graph-based Portfolios 28512.1 Graph Theory-Based Portfolios 28512.2 Graph Theory Portfolios: MST and TMFG 28512.3 Hierarchical Risk Parity 28912.4 Notes 294CHAPTER 13 Sensitivity-based Portfolios 29513.1 Modeling Portfolios Dynamics with PDEs 29613.2 Optimal Drivers Selection: Causality and Persistence 29713.3 AAD Sensitivities Approximation 30313.4 Hierarchical Sensitivity Parity 30713.5 Implementation 30713.6 Conclusion 315PART FIVE BacktestingCHAPTER 14 Backtesting in Portfolio Management 31914.1 Introduction 31914.2 Data Preparation and Handling 31914.3 Implementation of Trading Strategies 32014.4 Types of Backtests 32114.5 Performance Metrics 32214.6 Avoiding Common Pitfalls 32314.7 Advanced Techniques 32314.8 Case Study: Applying Backtesting to a Real-World Strategy 32414.9 Impact of Market Conditions on Backtest Results 32414.10 Integration with Portfolio Management 32514.11 Tools and Software for Backtesting 32514.12 Regulatory Considerations 32614.13 Conclusion 326CHAPTER 15 Scenario Generation 32915.1 Historical Scenarios 32915.2 Bootstrapping Scenarios 33015.3 Copula-Based Scenarios 33015.4 Risk Factor Model-Based Scenarios 33015.5 Time Series Model Scenarios 33115.6 Variational Autoencoders 33115.7 Generative Adversarial Networks (GANs) 332Appendix 333A.1 Software and Tools for Portfolio Optimization 333Bibliography 335Index 357