Expert guidance on implementing quantitative portfolio optimization techniques
In Quantitative Portfolio Optimization: Theory and Practice, renowned financial practitioner Miquel Noguer, alongside physicists Alberto Bueno Guerrero and Julian Antolin Camarena, who possess excellent knowledge in finance, delve into advanced mathematical techniques for portfolio optimization. The book covers a range of topics including mean-variance optimization, the Black-Litterman Model, risk parity and hierarchical risk parity, factor investing, methods based on moments, and robust optimization as well as machine learning and reinforcement technique. These techniques enable readers to develop a systematic, objective, and repeatable approach to investment decision-making, particularly in complex financial markets.
Readers will gain insights into the associated mathematical models, statistical analyses, and computational algorithms for each method, allowing them to put these techniques into practice and identify the best possible mix of assets to maximize returns while minimizing risk. Topics explored in this book include:
- Specific drivers of return across asset classes
- Personal risk tolerance and it#s impact on ideal asses allocation
- The importance of weekly and monthly variance in the returns of specific securities
Serving as a blueprint for solving portfolio optimization problems, Quantitative Portfolio Optimization: Theory and Practice is an essential resource for finance practitioners and individual investors It helps them stay on the cutting edge of modern portfolio theory and achieve the best returns on investments for themselves, their clients, and their organizations.
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 Schödinger 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
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.
Quantitative Portfolio Optimization: Advanced Techniques and Applications is an authoritative guide on using mathematical models, statistical analyses, and computational algorithms to optimize the composition of an investment portfolio and allow for a systematic, objective, and repeatable approach to investment decision-making, especially in complex financial markets. In this book, readers will learn to identify the best possible mix of assets that can maximize returns while minimizing risk based on the investor’s specific objectives and constraints.
Written by Miquel Noguer Alonso, an experienced financial markets practitioner and pioneer in the field, Julián Antolín Camarena, experienced AI researcher and physicist, and Alberto Bueno Guerrero, accomplished researcher in mathematical finance, this book takes a deep dive into various methods in quantitative portfolio optimization, including mean-variance optimization, the Black-Litterman Model, risk parity and hierarchical risk parity, factor investing, machine learning models, methods based on moments, and robust optimization. Readers will learn about the unique approach and application of each of these methods and receive a variety of tools that can be used in their efforts to practically construct and manage their portfolios.
Providing key knowledge on advanced mathematical techniques for portfolio optimization to solve one of the central problems in finance, Quantitative Portfolio Optimization: Advanced Techniques and Applications earns a well-deserved spot on the bookshelves of finance practitioners and academics interested in portfolio management, along with all investors looking to stay on the cutting edge of modern investment techniques.
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
