Financial Risk Modelling and Portfolio Optimization with R

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