Quantitative Portfolio Management: with Applications in Python

Preface\nContents\n1 Returns and the Gaussian Hypothesis\n	1.1 Measure of the Performance\n		1.1.1 Return\n		1.1.2 Rate of Return\n	1.2 Probabilistic and Empirical Definitions\n	1.3 Goodness of Fit Tests\n		1.3.1 Example: Testing the Normality of the Returns of the DAX 30\n	1.4 Further Statistical Results\n		1.4.1 Convergence of the Density Function Estimate\n		1.4.2 Tests Based on Cumulative Distribution Function Estimates\n		1.4.3 Tests Based on Order Statistics\n		1.4.4 Parameter Estimation and Confidence Intervals\n	1.5 Market Data with Python\n		1.5.1 Data Extraction for the DAX 30\n		1.5.2 Statistical Analysis for the DAX 30\n	A Few References\n2 Utility Functions and the Theory of Choice\n	2.1 Utility Functions and Preferred Investments\n		2.1.1 Risk Appetite and Concavity\n	2.2 Gaussian Laws and Mean-Variance Implications\n	2.3 Efficient Investment Strategies\n	A Few References\n3 The Markowitz Framework\n	3.1 Investment and Self-Financing Portfolios\n		3.1.1 Notations and Definitions\n		3.1.2 Representations of the Portfolios\n		3.1.3 Return of a Portfolio\n	3.2 Absence of Arbitrage Opportunities\n		3.2.1 Analysis of the Variance-Covariance Matrix\n		3.2.2 The Correlation Matrix\n	3.3 Multidimensional Estimations\n		3.3.1 Wishart, Hotelling\'s T2 and Fisher–Snedecor Distributions\n		3.3.2 Mean Vector and Variance-Covariance Matrix Estimates\n		3.3.3 Confidence Domain and Statistical Tests\n	3.4 Maket Data with Python\n	A Few References\n4 Markowitz Without a Risk-Free Asset\n	4.1 The Optimisation Problem\n	4.2 The Geometric Nature of the Set F(σ,m)\n	4.3 The Two Fund Theorem\n		4.3.1 Example with Two Assets: Importance of the Correlation\n	4.4 Alternative Parametrisation of F(σ, m) and Conclusion\n	A Few References\n5 Markowitz with a Risk-Free Asset\n	5.1 The Optimisation Problem\n	5.2 Capital Market Line and Limit Cone C(σ, m)\n		5.2.1 The Market Portfolio\n		5.2.2 The Tangent Portfolio\n		5.2.3 More Geometric Properties\n	5.3 The Security Market Line\n		5.3.1 The Security Market Line and ``Arbitrage\'\' Detections\n	5.4 Market Data with Python\n		5.4.1 The Frontier and Capital Market Line for the DAX 30 Components\n		5.4.2 Adding Additional Constraints\n	5.5 Stability of the Solutions\n		5.5.1 Stabilisation by Correlation Adjustment\n	5.6 The Bayesian Approach\n		5.6.1 Jeffrey\'s Prior μ0 on M and\n		5.6.2 Gaussian Prior μ0 on M\n		5.6.3 The Black–Litterman Model\n	A Few References\n6 Performance and Diversification Indicators\n	6.1 The Sharpe Ratio\n	6.2 The Jensen Index\n	6.3 The Treynor Index\n	6.4 Other Risk/Return Indicators\n	6.5 The Diversification Ratio\n	A Few References\n7 Risk Measures and Capital Allocation\n	7.1 Definition of a Risk Measure\n	7.2 Risk Measure in the Markowitz Framework\n		7.2.1 The Markowitz Risk Measure\n		7.2.2 Value at Risk\n		7.2.3 Expected Shortfall\n	7.3 Euler\'s Formula and Capital Allocation\n		7.3.1 Example of Risk Measure and Capital Allocation\n	7.4 Return on Risk-Adjusted Capital\n		7.4.1 Maximising the RORAC\n		7.4.2 Capital Allocation for a Positive Homogeneous Risk Measure\n		7.4.3 Example: Euler Allocation\n		7.4.4 Example: RORAC for Optimal Portfolios\n		7.4.5 Calculation of a Portfolio VaR, from Observed Asset Prices\n		7.4.6 Example: Boostrap Historical Simulation for a Portfolio VaR\n	A Few References\n8 Factor Models\n	8.1 Definitions and Notations\n		8.1.1 The Tangent Portfolio as a Factor\n		8.1.2 Endogenous and Exogenous Factors\n		8.1.3 Standard Form for a Factor Model\n	8.2 Identifying the Coefficients When the Factors Are Known\n		8.2.1 Regression on the Factors\n	8.3 Example of a Factor Model\n	8.4 APT Models\n		8.4.1 Example of an APT Model\n		8.4.2 Further Remarks\n		8.4.3 Standard Form for an APT Model\n	8.5 Alternative Definition of an APT Model\n		8.5.1 Estimation of the Risk Premia in an APT Model\n	A Few References\n9 Identification of the Factors\n	9.1 Total Inertia and Trace of the Variance-Covariance Matrix\n	9.2 Total Inertia of the Projection\n	9.3 Principal Component Analysis and Factors\n		9.3.1 PCA of the Matrix of Variance-Covariance\n		9.3.2 PCA of the Correlation Matrix\n	9.4 Principal Components and Eigenvalues Visualisation\n	9.5 Python: Application to the DAX 30 Components\n		9.5.1 Factors Explaining the Variance for the DAX 30 Components\n		9.5.2 Explanation of the Factors for the DAX 30 Components\n	A Few References\n10 Exercises and Problems\n	10.1 Midterm Exam, November 2015\n		Master M1: Mido 2nd November 2015 (Midterm Exam: Portfolio Management)\n		10.1.1 Solutions: Midterm Exam, November 2015\n		Master M1: Mido 2015–2016 (Midterm Exam: Portfolio Management)\n	10.2 Exam, January 2016\n		Master M1: Mido 5th January 2016 (Exam: Portfolio Management: Time 1h 30min)\n		10.2.1 Solutions: Exam, January 2016\n		Master M1: Mido 5th January 2016 (Exam: Portfolio Management)\n	10.3 Midterm Exam, November 2016\n		Master M1: Mido 3rd November 2016 (Exam: Portfolio Management: Time 2h)\n		10.3.1 Solutions: Midterm Exam, November 2016\n	10.4 Exam, January 2017\n		Master M1: Mido 11th January 2017 (Exam: Portfolio Management: Time 2h)\n		10.4.1 Solutions: Exam, January 2017\n	10.5 Midterm Exam, November 2017\n		Master M1: Mido 2nd November 2017 (Midterm Exam: Portfolio Management: Time 2h)\n		10.5.1 Solutions: Midterm Exam, November 2017\n	10.6 Exam, January 2018\n		Master M1: Mido 15th January 2018 (Exam: Portfolio Management: Time 2h)\n		10.6.1 Solutions: Exam, January 2018\n	10.7 Midterm Exam, October 2018\n		Master M1: Mido 29th October 2018 (Midterm Exam: Portfolio Management: Time 2h)\n		10.7.1 Solutions: Midterm Exam October 2018\nA The Lagrangian\n	A.1 Main Results\n		A.1.1 Solution of the Markowitz Problem\nB Parametrisations\n	B.1 Confidence Domain for an Estimator of M\n	B.2 Confidence Domain for an Observation Ri\nBibliography\nIndex