Financial Risk Modelling and Portfolio Optimization with R Book

Preface xi

List of abbreviations xiii

Part I MOTIVATION 1

1 Introduction 3

2 A brief course in R 6

2.1 Origin and development 6

2.2 Getting help 7

2.3 Working with R 10

2.4 Classes, methods and functions 12

2.5 The accompanying package FRAPO 20

3 Financial market data 26

3.1 Stylized facts on financial market returns 26

3.2 Implications for risk models 32

4 Measuring risks 34

4.1 Introduction 34

4.2 Synopsis of risk measures 34

4.3 Portfolio risk concepts 39

5 Modern portfolio theory 43

5.1 Introduction 43

5.2 Markowitz portfolios 43

5.3 Empirical mean–variance portfolios 47

Part II RISK MODELLING 51

6 Suitable distributions for returns 53

6.1 Preliminaries 53

6.2 The generalized hyperbolic distribution 53

6.3 The generalized lambda distribution 56

6.4 Synopsis of R packages for the GHD 62

6.5 Synopsis of R packages for GLD 67

6.6 Applications of the GHD to risk modelling 69

6.7 Applications of the GLD to risk modelling and data analysis 78

7 Extreme value theory 84

7.1 Preliminaries 84

7.2 Extreme value methods and models 85

7.3 Synopsis of R packages 89

7.4 Empirical applications of EVT 98

8 Modelling volatility 112

8.1 Preliminaries 112

8.2 The class of ARCH models 112

8.3 Synopsis of R packages 116

8.4 Empirical application of volatility models 123

9 Modelling dependence 127

9.1 Overview 127

9.2 Correlation, dependence and distributions 127

9.3 Copulae 130

9.4 Synopsis of R packages 136

9.5 Empirical applications of copulae 142

Part III PORTFOLIO OPTIMIZATION APPROACHES 153

10 Robust portfolio optimization 155

10.1 Overview 155

10.2 Robust statistics 156

10.3 Robust optimization 160

10.4 Synopsis of R packages 166

10.5 Empirical applications 171

11 Diversification reconsidered 189

11.1 Introduction 189

11.2 Most diversified portfolio 190

11.3 Risk contribution constrained portfolios 192

11.4 Optimal tail-dependent portfolios 195

11.5 Synopsis of R packages 197

11.6 Empirical applications 201

12 Risk-optimal portfolios 217

12.1 Overview 217

12.2 Mean–VaR portfolios 218

12.3 Optimal CVaR portfolios 223

12.4 Optimal draw-down portfolios 227

12.5 Synopsis of R packages 229

12.6 Empirical applications 238

13 Tactical asset allocation 255

13.1 Overview 255

13.2 Survey of selected time series models 256

13.3 Black–Litterman approach 270

13.4 Copula opinion and entropy pooling 273

13.5 Synopsis of R packages 276

13.6 Empirical applications 288

Appendix A Package overview 314

A.1 Packages in alphabetical order 314

A.2 Packages ordered by topic 317

Appendix B Time series data 324

B.1 Date-time classes 324

B.2 The ts class in the base package stats 327

B.3 Irregular-spaced time series 328

B.4 The package timeSeries 330

B.5 The package zoo 332

B.6 The packages tframe and xts 334

Appendix C Back-testing and reporting of portfolio strategies 338

C.1 R packages for back-testing 338

C.2 R facilities for reporting 339

C.3 Interfacing databases 339

Appendix D Technicalities 342

Index 343