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Quantitative Portfolio Management

E-BookPDF1 - PDF WatermarkE-Book
205 Seiten
Englisch
Springer Nature Switzerlanderschienen am28.03.20201st ed. 2020
This self-contained book presents the main techniques of quantitative portfolio management and associated statistical methods in a very didactic and structured way, in a minimum number of pages. The concepts of investment portfolios, self-financing portfolios and absence of arbitrage opportunities are extensively used and enable the translation of all the mathematical concepts in an easily interpretable way.


All the results, tested with Python programs, are demonstrated rigorously, often using geometric approaches for optimization problems and intrinsic approaches for statistical methods, leading to unusually short and elegant proofs. The statistical methods concern both parametric and non-parametric estimators and, to estimate the factors of a model, principal component analysis is explained. The presented Python code and web scraping techniques also make it possible to test the presented concepts on market data.

This book will be useful for teaching Masters students and for professionals in asset management, and will be of interest to academics who want to explore a field in which they are not specialists. The ideal pre-requisites consist of undergraduate probability and statistics and a familiarity with linear algebra and matrix manipulation. Those who want to run the code will have to install Python on their pc, or alternatively can use Google Colab on the cloud.  Professionals will need to have a quantitative background, being either portfolio managers or risk managers, or potentially quants wanting to double check their understanding of the subject.





Pierre Brugière is currently Associate Professor at University Paris 9 Dauphine. Previously he spent 19 years working in investment banking in London, in international banks, and 4 years in Paris in an arbitrage bank. During his career in finance he has been responsible for quant groups in fixed income, asset management and equity derivatives. In addition, in his role working for corporate equity derivatives businesses, he has been involved in structuring marketing and executing very large and strategic transactions for large companies and institutions, mainly in Europe, but also in Emerging Markets.mehr
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Produkt

KlappentextThis self-contained book presents the main techniques of quantitative portfolio management and associated statistical methods in a very didactic and structured way, in a minimum number of pages. The concepts of investment portfolios, self-financing portfolios and absence of arbitrage opportunities are extensively used and enable the translation of all the mathematical concepts in an easily interpretable way.


All the results, tested with Python programs, are demonstrated rigorously, often using geometric approaches for optimization problems and intrinsic approaches for statistical methods, leading to unusually short and elegant proofs. The statistical methods concern both parametric and non-parametric estimators and, to estimate the factors of a model, principal component analysis is explained. The presented Python code and web scraping techniques also make it possible to test the presented concepts on market data.

This book will be useful for teaching Masters students and for professionals in asset management, and will be of interest to academics who want to explore a field in which they are not specialists. The ideal pre-requisites consist of undergraduate probability and statistics and a familiarity with linear algebra and matrix manipulation. Those who want to run the code will have to install Python on their pc, or alternatively can use Google Colab on the cloud.  Professionals will need to have a quantitative background, being either portfolio managers or risk managers, or potentially quants wanting to double check their understanding of the subject.





Pierre Brugière is currently Associate Professor at University Paris 9 Dauphine. Previously he spent 19 years working in investment banking in London, in international banks, and 4 years in Paris in an arbitrage bank. During his career in finance he has been responsible for quant groups in fixed income, asset management and equity derivatives. In addition, in his role working for corporate equity derivatives businesses, he has been involved in structuring marketing and executing very large and strategic transactions for large companies and institutions, mainly in Europe, but also in Emerging Markets.
Details
Weitere ISBN/GTIN9783030377403
ProduktartE-Book
EinbandartE-Book
FormatPDF
Format Hinweis1 - PDF Watermark
FormatE107
Erscheinungsjahr2020
Erscheinungsdatum28.03.2020
Auflage1st ed. 2020
ReiheSpringer Texts in Business and Economics
Seiten205 Seiten
SpracheEnglisch
Dateigrösse3148 Kbytes
IllustrationenXII, 205 p. 23 illus., 22 illus. in color.
Artikel-Nr.5135238
Rubriken
Genre9200

Inhalt/Kritik

Inhaltsverzeichnis
1;Preface;6
2;Contents;10
3;1 Returns and the Gaussian Hypothesis;14
3.1;1.1 Measure of the Performance;14
3.1.1;1.1.1 Return;14
3.1.2;1.1.2 Rate of Return;15
3.2;1.2 Probabilistic and Empirical Definitions;16
3.3;1.3 Goodness of Fit Tests;18
3.3.1;1.3.1 Example: Testing the Normality of the Returns of the DAX 30;19
3.4;1.4 Further Statistical Results;21
3.4.1;1.4.1 Convergence of the Density Function Estimate;21
3.4.2;1.4.2 Tests Based on Cumulative Distribution Function Estimates;22
3.4.3;1.4.3 Tests Based on Order Statistics;24
3.4.4;1.4.4 Parameter Estimation and Confidence Intervals;25
3.5;1.5 Market Data with Python;29
3.5.1;1.5.1 Data Extraction for the DAX 30;29
3.5.2;1.5.2 Statistical Analysis for the DAX 30;29
3.6;A Few References;31
4;2 Utility Functions and the Theory of Choice;32
4.1;2.1 Utility Functions and Preferred Investments;32
4.1.1;2.1.1 Risk Appetite and Concavity;33
4.2;2.2 Gaussian Laws and Mean-Variance Implications;36
4.3;2.3 Efficient Investment Strategies;37
4.4;A Few References;38
5;3 The Markowitz Framework;39
5.1;3.1 Investment and Self-Financing Portfolios;39
5.1.1;3.1.1 Notations and Definitions;40
5.1.2;3.1.2 Representations of the Portfolios;40
5.1.3;3.1.3 Return of a Portfolio;42
5.2;3.2 Absence of Arbitrage Opportunities;44
5.2.1;3.2.1 Analysis of the Variance-Covariance Matrix;45
5.2.2;3.2.2 The Correlation Matrix;45
5.3;3.3 Multidimensional Estimations;47
5.3.1;3.3.1 Wishart, Hotelling's T2 and Fisher-Snedecor Distributions;47
5.3.2;3.3.2 Mean Vector and Variance-Covariance Matrix Estimates;51
5.3.3;3.3.3 Confidence Domain and Statistical Tests;56
5.4;3.4 Maket Data with Python;57
5.5;A Few References;61
6;4 Markowitz Without a Risk-Free Asset;63
6.1;4.1 The Optimisation Problem;63
6.2;4.2 The Geometric Nature of the Set F(?,m);66
6.3;4.3 The Two Fund Theorem;68
6.3.1;4.3.1 Example with Two Assets: Importance of the Correlation;68
6.4;4.4 Alternative Parametrisation of F(?, m) and Conclusion;69
6.5;A Few References;71
7;5 Markowitz with a Risk-Free Asset;72
7.1;5.1 The Optimisation Problem;73
7.2;5.2 Capital Market Line and Limit Cone C(?, m);74
7.2.1;5.2.1 The Market Portfolio;76
7.2.2;5.2.2 The Tangent Portfolio;79
7.2.3;5.2.3 More Geometric Properties;80
7.3;5.3 The Security Market Line;80
7.3.1;5.3.1 The Security Market Line and ``Arbitrage'' Detections;82
7.4;5.4 Market Data with Python;84
7.4.1;5.4.1 The Frontier and Capital Market Line for the DAX 30 Components;84
7.4.2;5.4.2 Adding Additional Constraints;88
7.5;5.5 Stability of the Solutions;92
7.5.1;5.5.1 Stabilisation by Correlation Adjustment;93
7.6;5.6 The Bayesian Approach;94
7.6.1;5.6.1 Jeffrey's Prior ?0 on M and;97
7.6.2;5.6.2 Gaussian Prior ?0 on M;99
7.6.3;5.6.3 The Black-Litterman Model;102
7.7;A Few References;104
8;6 Performance and Diversification Indicators;106
8.1;6.1 The Sharpe Ratio;106
8.2;6.2 The Jensen Index;107
8.3;6.3 The Treynor Index;108
8.4;6.4 Other Risk/Return Indicators;109
8.5;6.5 The Diversification Ratio;109
8.6;A Few References;112
9;7 Risk Measures and Capital Allocation;114
9.1;7.1 Definition of a Risk Measure;114
9.2;7.2 Risk Measure in the Markowitz Framework;116
9.2.1;7.2.1 The Markowitz Risk Measure;116
9.2.2;7.2.2 Value at Risk;118
9.2.3;7.2.3 Expected Shortfall;119
9.3;7.3 Euler's Formula and Capital Allocation;120
9.3.1;7.3.1 Example of Risk Measure and Capital Allocation;122
9.4;7.4 Return on Risk-Adjusted Capital;123
9.4.1;7.4.1 Maximising the RORAC;123
9.4.2;7.4.2 Capital Allocation for a Positive Homogeneous Risk Measure;124
9.4.3;7.4.3 Example: Euler Allocation;127
9.4.4;7.4.4 Example: RORAC for Optimal Portfolios;128
9.4.5;7.4.5 Calculation of a Portfolio VaR, from Observed Asset Prices;130
9.4.6;7.4.6 Example: Boostrap Historical Simulation for a Portfolio VaR;131
9.5;A Few References;134
10;8 Factor Models;135
10.1;8.1 Definitions and Notations;135
10.1.1;8.1.1 The Tangent Portfolio as a Factor;137
10.1.2;8.1.2 Endogenous and Exogenous Factors;137
10.1.3;8.1.3 Standard Form for a Factor Model;138
10.2;8.2 Identifying the Coefficients When the Factors Are Known;139
10.2.1;8.2.1 Regression on the Factors;141
10.3;8.3 Example of a Factor Model;141
10.4;8.4 APT Models;143
10.4.1;8.4.1 Example of an APT Model;146
10.4.2;8.4.2 Further Remarks;147
10.4.3;8.4.3 Standard Form for an APT Model;147
10.5;8.5 Alternative Definition of an APT Model;147
10.5.1;8.5.1 Estimation of the Risk Premia in an APT Model;148
10.6;A Few References;149
11;9 Identification of the Factors;150
11.1;9.1 Total Inertia and Trace of the Variance-Covariance Matrix;150
11.2;9.2 Total Inertia of the Projection;151
11.3;9.3 Principal Component Analysis and Factors;153
11.3.1;9.3.1 PCA of the Matrix of Variance-Covariance;153
11.3.2;9.3.2 PCA of the Correlation Matrix;156
11.4;9.4 Principal Components and Eigenvalues Visualisation;156
11.5;9.5 Python: Application to the DAX 30 Components;157
11.5.1;9.5.1 Factors Explaining the Variance for the DAX 30 Components;158
11.5.2;9.5.2 Explanation of the Factors for the DAX 30 Components;159
11.6;A Few References;162
12;10 Exercises and Problems;164
12.1;10.1 Midterm Exam, November 2015;164
12.1.1;Master M1: Mido 2nd November 2015 (Midterm Exam: Portfolio Management);164
12.1.2;10.1.1 Solutions: Midterm Exam, November 2015;166
12.1.3;Master M1: Mido 2015-2016 (Midterm Exam: Portfolio Management);166
12.2;10.2 Exam, January 2016;168
12.2.1;Master M1: Mido 5th January 2016 (Exam: Portfolio Management: Time 1h 30min);168
12.2.2;10.2.1 Solutions: Exam, January 2016;171
12.2.3;Master M1: Mido 5th January 2016 (Exam: Portfolio Management);171
12.3;10.3 Midterm Exam, November 2016;173
12.3.1;Master M1: Mido 3rd November 2016 (Exam: Portfolio Management: Time 2h);173
12.3.2;10.3.1 Solutions: Midterm Exam, November 2016;175
12.4;10.4 Exam, January 2017;177
12.4.1;Master M1: Mido 11th January 2017 (Exam: Portfolio Management: Time 2h);177
12.4.2;10.4.1 Solutions: Exam, January 2017;181
12.5;10.5 Midterm Exam, November 2017;183
12.5.1;Master M1: Mido 2nd November 2017 (Midterm Exam: Portfolio Management: Time 2h);183
12.5.2;10.5.1 Solutions: Midterm Exam, November 2017;186
12.6;10.6 Exam, January 2018;188
12.6.1;Master M1: Mido 15th January 2018 (Exam: Portfolio Management: Time 2h);188
12.6.2;10.6.1 Solutions: Exam, January 2018;191
12.7;10.7 Midterm Exam, October 2018;193
12.7.1;Master M1: Mido 29th October 2018 (Midterm Exam: Portfolio Management: Time 2h);193
12.7.2;10.7.1 Solutions: Midterm Exam October 2018;196
13;A The Lagrangian;199
13.1;A.1 Main Results;199
13.1.1;A.1.1 Solution of the Markowitz Problem;201
14;B Parametrisations;203
14.1;B.1 Confidence Domain for an Estimator of M;203
14.2;B.2 Confidence Domain for an Observation Ri;204
15;Bibliography;206
16;Index;210mehr

Autor

Pierre Brugière is currently Associate Professor at University Paris 9 Dauphine. Previously he spent 19 years working in investment banking in London, in international banks, and 4 years in Paris in an arbitrage bank. During his career in finance he has been responsible for quant groups in fixed income, asset management and equity derivatives. In addition, in his role working for corporate equity derivatives businesses, he has been involved in structuring marketing and executing very large and strategic transactions for large companies and institutions, mainly in Europe, but also in Emerging Markets.