Quantitative Portfolio Optimization - Miquel Noguer, Julian Camarena, Alberto Guerrero

Quantitative Portfolio Optimization

Theory and Practice
Buch | Hardcover
384 Seiten
2025
John Wiley & Sons Inc (Verlag)
978-1-394-28131-2 (ISBN)
99,75 inkl. MwSt
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

 

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    1

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 1

 

1 Introduction                                                                                                        3

        1.1 Evolution of Portfolio Optimization . . . . . . . . . . . . . . .. . . . . . . . . . . . . . 3

        1.2 Role of Quantitative Techniques . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . 3

        1.3 Organization of the Book . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .7

 

2 History of Portfolio Optimization                                                                     9

        2.1 Early beginnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  9

        2.2 Harry Markowitz’s Modern Portfolio Theory (1952) . . . . . . . . . . . . . .  12

        2.3 Black-Litterman Model (1990s) . . . . . . . . . . . . . . . ……………………16

        2.4 Alternative Methods: Risk Parity, Hierarchical Risk Parity and

                 Machine Learning . . . . . . . . . . . . . . . . . . .  … .. . . .. . .. . .. ………. . 21

                 2.4.1 Risk Parity . . . . . . . . . . . . . . . . . . . . . . . . .. . .. . . .. . . . . . .  …...21

                 2.4.2 Hierarchical Risk Parity . . . . . . . . . . . . . . . . . …………………28

                 2.4.3 Machine Learning . . . . . . . . . . . . . . . . . . . . . ………………. ...30

       2.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . …………………. . . . . . 35

 

I Foundations of Portfolio Theory                                                   37

 

3 Modern Portfolio Theory                                                                                 38

      3.1 Efficient Frontier and Capital Market Line . . . . . . . . . . . ……………..  38

                     3.1.1 Case without riskless asset . . . . . . . . . . . . . . . . . . . .. . . . . . . 39

                     3.1.2 Case with a riskless asset . . . . . . . . . . . . . . . .. . . . . . . . . . . .  44

      3.2 Capital Asset Pricing Model . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .   50

                     3.2.1 Case without riskless asset . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

                     3.2.2 Case with a riskless asset . . . . . . . . . . . . . . . . .. . . . . . . . . . . .54

 

     3.3 Multi-factor Models . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . 57

     3.4 Challenges of Modern Portfolio Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 62

                    3.4.1 Estimation Techniques in Portfolio Allocation . . . . . .. . . . . . .62

                    3.4.2 Non-Elliptical Distributions and Conditional Value-at-

                             Risk (CVaR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66

     3.5 Quantum Annealing in Portfolio Management . . . . . . . . . . . . . . . . . . . . . 68

     3.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70

 

 

CONTENTS

 

4 Bayesian Methods in Portfolio Optimization                                                           73

         4.1 The Prior . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .  75

         4.2 The Likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80

         4.3 The Posterior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

         4.4 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

         4.5 Hierarchical Bayesian Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90

        4.6 Bayesian Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

                        4.6.1 Gaussian Processes in a Nutshell . . . . . . . . . . . . . . . . . . . . . . . . . .93

                        4.6.2 Uncertainty Quantification and Bayesian Decision Theory . . . . . 97

         4.7 Applications to Portfolio Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

                       4.7.1 GP Regression for Asset Returns . . . . . . . . . . . . . . . . . . . . . . . . . . 99

                       4.7.2 Decision Theory in Portfolio Optimization . . . . . . . . . . . . . . . . . . 100

                       4.7.3 The Black-Litterman Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103

         4.8 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

 

II Risk Management                                                                                  109

 

5 Risk Models and Measures                                                                                        110

        5.1 Risk Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . 111

        5.2 VaR and CVaR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 113

                      5.2.1 VaR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. .  .114

                      5.2.2 CVaR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 116

        5.3 Estimation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119

                       5.3.1 Variance-Covariance Method . . . . . . . . . . . . . . . . . . . . . . . . . .. . .120

                       5.3.2 Historical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120

                       5.3.3 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121

        5.4 Advanced Risk Measures: Tail Risk and Spectral Measures . . . . . . . . . . . . . .121

                       5.4.1 Tail Risk Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  121

                       5.4.2 Spectral Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

        5.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

 

6 Factor Models and Factor Investing                                                                        128

         6.1 Single and Multi-Factor Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    129

                       6.1.1 Statistical Models . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 130

                       6.1.2 Macroeconomic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .131

                        6.1.3 Cross Sectional Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .133

          6.2 Factor Risk and Performance Attribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

          6.3 Machine Learning in Factor Investing . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 145

          6.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

 

7 Market Impact, Transaction Costs and Liquidity                                                 149

         7.1 Market Impact Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ….150

         7.2 Modeling Transaction Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . …153

                        7.2.1 Single asset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . … 156

CONTENTS

                        

                        7.2.2 Multiple assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . …..158

         7.3 Optimal Trading Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . …...160

                       7.3.1 Mei, DeMiguel and Nogales (2016) . . . . . . . . . . . . . .. . . . . … .. 161

                       7.3.2 Skaf and Boyd (2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . …..164

         7.4 Liquidity Considerations in Portfolio Optimization . . . . . . . . . . . . . . . …...166

                       7.4.1 MV and Liquidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

                       7.4.2 CAPM and Liquidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 168

                       7.4.3 APT and Liquidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 170

         7.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 172

 

III Dynamic Models and Control                                                           174

 

8 Optimal Control                                                                                                       175

        8.1 Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .175

        8.2 Approximate Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

        8.3 The Hamilton-Jacobi-Bellman Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

        8.4 Sufficiently Smooth Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .179

        8.5 Viscosity Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181

        8.6 Applications to Portfolio Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

                      8.6.1 Classical Merton Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .185

                      8.6.2 Multi-Asset Portfolio with Transaction Costs . . . . . . . . . . . . . . . 186

                      8.6.3 Risk-Sensitive Portfolio Optimization . . . . . . . . . . . . . . . . . . . . . 188

                                8.6.4 Optimal Portfolio Allocation with Transaction Costs . . . . . . . . . 189

                       8.6.5 American Option Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .189

                       8.6.6 Portfolio Optimization with Constraints . . . . . . . . . . . . . . . . . . . 190

                       8.6.7 Mean-Variance Portfolio Optimization . . . . . . . . . . . . . . . . . . . .190

                       8.6.8 Sch¨odinger Control in Wealth Management . . . . . . . . . . . . . . . 191

         8.7 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .193

 

9 Markov Decision Processes                                                                                    195

          9.1 Fully Observed MDPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  197

          9.2 Partially Observed MDPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 199

          9.3 Infinite Horizon Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .202

          9.4 Finite Horizon Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .206

          9.5 The Bellman Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . 208

          9.6 Solving the Bellman Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .212

          9.7 Examples in Portfolio Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

                        9.7.1 An MDP in Multi-Asset Allocation with Transaction

                                   Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

                         9.7.2 A POMDP for Asset Allocation with Regime Switching . . . . . 214

                         9.7.3 An MDP with Continuous State and Action Spaces for

                                    Option Hedging with Stochastic Volatility . . . . . . . . . . . . . . . 215

          9.8 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

 

CONTENTS

 

10 Reinforcement Learning                                                                                       219

          10.1 Connections to Optimal Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

                     10.1.1 Policy Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

                     10.1.2 Value Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  225

                     10.1.3 Continuous vs. Discrete Formulations . . . . . . . . . . . . . . . . . . . . .226

           10.2 The Environment and The Reward Function . . . . . . . . . . . . . . . . . . . . . . 228

                      10.2.1 The Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

                      10.2.2 The Reward Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .232

           10.3 Agents Acting in an Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

           10.4 State-Action and Value Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .238

                        10.4.1 Value Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .238

                        10.4.2 Gradients and Policy Improvement . . . . . . . . . . . . . . . . . . . . .240

           10.5 The Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. . . . . . . . . . . . 243

           10.6 On-Policy Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

           10.7 Off-Policy Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  249

            10.8 Applications to Portfolio Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 253

                          10.8.1 Mean-Variance Optimization . . . . . . . . . . . . . . . . . . . . . . . . 253

                          10.8.2 Reinforcement Learning Comparison with Mean-Variance

                                      Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .254

                           10.8.3 G-Learning and GIRL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

                           10.8.4 Continuous-time Penalization in Portfolio Optimization . . .259

                           10.8.5 Reinforcement Learning for Utility Maximization . . . . . . . .260

                           10.8.6 Continuous-Time Portfolio Optimization with Transaction

                                       Costs . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .261

            10.9 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 262

 

IV Machine Learning and Deep Learning                                          265


11 Deep Learning in Portfolio Management                                                          266

             11.1 Neurons and Activation Functions . . . . . . . . . . . . . . . .. . . . . . . . . . .  . 266

             11.2 Neural Networks and Function Approximation . . . . . . . . . . . . . . . . . . 269

             11.3 Review of Some Important Architectures . . . . . . . . . . . . . . .. . . . . . . . 273

             11.4 Physics-Informed Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

             11.5 Applications to Portfolio Optimization . . . . . . . . . . . . . . . . . . . . . . . . .292

                          11.5.1 Dynamic Asset Allocation Using the Heston Model . . . . . . 292

                          11.5.2 Option-Based Portfolio Insurance Using the Bates Model . .293

                          11.5.3 Factor Learning Approach to Generative Modeling of

                                      Equities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

             11.6 The Case for and Against Deep Learning . . . . . . . . . . . . . . . . . . . . . . 296

             11.7 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . .   298

12 Graph Based Portfolios                                                                                       300

            12.1 Graph Theory Based Portfolios . . . . . . . . . . . . . . . . .                            300

                            12.1.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .300

                            12.1.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  300

CONTENTS

 

            12.2 Equations and Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

                               12.2.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .302

            12.3 Hierarchical Risk Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

            12.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .309

 

13 Sensitivity-based Portfolios                                                                                  310

           13.1 Modelling Portfolios Dynamics with PDEs . . . . . . . . . . . . . . . . . . . . . .  312

           13.2 Optimal Drivers Selection: Causality and Persistence . . . . . . . . . . .  . . . 313

           13.3 AAD Sensitivities Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .319

                               13.3.1 Optimal Network Selection . . . . . . . . . . . . . . . . . . . . . . .  319

                               13.3.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .320

                               13.3.3 Sensitivity Distance Matrix . . . . . . . . . . . . . . . . . . . . . . . .320

                               13.4 Hierarchical Sensitivity Parity . . . . . . . . . . . . . . . . . . . . . . .322

           13.5 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

                                13.5.1 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

                                13.5.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  323

                                13.5.3 Short-to-medium investments . . . . . . . . . . . . . . . . . . . . . 324

                                13.5.4 Long-term investments . . . . . . . . . . . . . . . . . . . . . . . . . . 328

            13.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

 

V Backtesting                                                                                         333

 

14 Backtesting in Portfolio Management                                                                334

            14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . …………….. .. . . . . ..334

            14.2 Data Preparation and Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

             14.3 Implementation of Trading Strategies . . . . . . . . . . . . . . . . . . . . . . . . . 335

             14.4 Types of Backtests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

                                  14.4.1 Walk-Forward Backtest . . . . . . . . . . . . . . . . . . . . . . . . 336

                                  14.4.2 Resampling Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

                                  14.4.3 Monte Carlo Simulations and Generative Models . . . . 337

             14.5 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .337

             14.6 Avoiding Common Pitfalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  338

             14.7 Advanced Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  339

             14.8 Case Study: Applying Backtesting to a Real-World Strategy . . . . . . . 339

             14.9 Impact of Market Conditions on Backtest Results . . . . . . . . . . . . . . .  .340

             14.10 Integration with Portfolio Management . . . . . . . . . . . . . . . . . . . . . .. . 340

             14.11 Tools and Software for Backtesting . . . . . . . . . . . . . . . . . . . . . . .. . .   341

             14.12 Regulatory Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

             14.13Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  342

 

15 Scenario Generation                                                                                            344

             15.1 Historical Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344

             15.2 Bootstrapping Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

             15.3 Copula Based Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

CONTENTS

 

               15.4 Risk Factor Model Based Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . .345

               15.5 Time Series Model Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .346

                15.6 Variational Autoencoders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346

                15.7 Generative Adversarial Networks (GANs) . . . . . . . . . . . . . . . . . .. . . .347

 

Appendices                                                                                                                  348

                          15.8 Software and Tools for Portfolio Optimization . . . . . . . . . . . . . . . . . 348

 

Erscheint lt. Verlag 25.3.2025
Reihe/Serie Wiley Finance
Verlagsort New York
Sprache englisch
Themenwelt Wirtschaft Betriebswirtschaft / Management Finanzierung
ISBN-10 1-394-28131-5 / 1394281315
ISBN-13 978-1-394-28131-2 / 9781394281312
Zustand Neuware
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