Market Risk Analysis [vol 2] - Practical Financial Econometrics

430 Pages·2008·5.73 MB·English

by  Carol Alexander

Market Risk Analysis
Volume II
Practical Financial Econometrics

Market Risk Analysis
Volume II
Practical Financial Econometrics
Carol Alexander
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Contents
List of Figures xiii
List of Tables xvii
List of Examples xx
Foreword xxii
Preface to Volume II xxvi
II.1 Factor Models 1
II.1.1 Introduction 1
II.1.2 Single Factor Models 2
II.1.2.1 Single Index Model 2
II.1.2.2 Estimating Portfolio Characteristics using OLS 4
II.1.2.3 Estimating Portfolio Risk using EWMA 6
II.1.2.4 Relationship between Beta, Correlation and Relative
Volatility 8
II.1.2.5 Risk Decomposition in a Single Factor Model 10
II.1.3 Multi-Factor Models 11
II.1.3.1 Multi-factor Models of Asset or Portfolio Returns 11
II.1.3.2 Style Attribution Analysis 13
II.1.3.3 General Formulation of Multi-factor Model 16
II.1.3.4 Multi-factor Models of International Portfolios 17
II.1.4 Case Study: Estimation of Fundamental Factor Models 21
II.1.4.1 Estimating Systematic Risk for a Portfolio of US Stocks 22
II.1.4.2 Multicollinearity: A Problem with Fundamental Factor
Models 23
II.1.4.3 Estimating Fundamental Factor Models by Orthogonal
Regression 25
II.1.5 Analysis of Barra Model 27
II.1.5.1 Risk Indices, Descriptors and Fundamental Betas 28
II.1.5.2 Model Specification and Risk Decomposition 30
II.1.6 Tracking Error and Active Risk 31
II.1.6.1 Ex Post versus Ex Ante Measurement of Risk and Return 32
II.1.6.2 Definition of Active Returns 32
II.1.6.3 Definition of Active Weights 33
II.1.6.4 Ex Post Tracking Error 33
viii Contents
II.1.6.5 Ex Post Mean-Adjusted Tracking Error 36
II.1.6.6 Ex Ante Tracking Error 39
II.1.6.7 Ex Ante Mean-Adjusted Tracking Error 40
II.1.6.8 Clarification of the Definition of Active Risk 42
II.1.7 Summary and Conclusions 44
II.2 Principal Component Analysis 47
II.2.1 Introduction 47
II.2.2 Review of Principal Component Analysis 48
II.2.2.1 Definition of Principal Components 49
II.2.2.2 Principal Component Representation 49
II.2.2.3 Frequently Asked Questions 50
II.2.3 Case Study: PCA of UK Government Yield Curves 53
II.2.3.1 Properties of UK Interest Rates 53
II.2.3.2 Volatility and Correlation of UK Spot Rates 55
II.2.3.3 PCA on UK Spot Rates Correlation Matrix 56
II.2.3.4 Principal Component Representation 58
II.2.3.5 PCA on UK Short Spot Rates Covariance Matrix 60
II.2.4 Term Structure Factor Models 61
II.2.4.1 Interest Rate Sensitive Portfolios 62
II.2.4.2 Factor Models for Currency Forward Positions 66
II.2.4.3 Factor Models for Commodity Futures Portfolios 70
II.2.4.4 Application to Portfolio Immunization 71
II.2.4.5 Application to Asset–Liability Management 72
II.2.4.6 Application to Portfolio Risk Measurement 73
II.2.4.7 Multiple Curve Factor Models 76
II.2.5 Equity PCA Factor Models 80
II.2.5.1 Model Structure 80
II.2.5.2 Specific Risks and Dimension Reduction 81
II.2.5.3 Case Study: PCA Factor Model for DJIA
Portfolios 82
II.2.6 Summary and Conclusions 86
II.3 Classical Models of Volatility and Correlation 89
II.3.1 Introduction 89
II.3.2 Variance and Volatility 90
II.3.2.1 Volatility and the Square-Root-of-Time Rule 90
II.3.2.2 Constant Volatility Assumption 92
II.3.2.3 Volatility when Returns are Autocorrelated 92
II.3.2.4 Remarks about Volatility 93
II.3.3 Covariance and Correlation 94
II.3.3.1 Definition of Covariance and Correlation 94
II.3.3.2 Correlation Pitfalls 95
II.3.3.3 Covariance Matrices 96
II.3.3.4 Scaling Covariance Matrices 97
II.3.4 Equally Weighted Averages 98
II.3.4.1 Unconditional Variance and Volatility 99
II.3.4.2 Unconditional Covariance and Correlation 102
II.3.4.3 Forecasting with Equally Weighted Averages 103