Financial Risk Modelling and Portfolio Optimization With R

A must have text for risk modelling and portfolio optimization using R.

This book introduces the latest techniques advocated for measuring financial market risk and portfolio optimization, and provides a plethora of R code examples that enable the reader to replicate the results featured throughout the book.  This edition has been extensively revised to include new topics on risk surfaces and probabilistic utility optimization as well as an extended introduction to R language.

Financial Risk Modelling and Portfolio Optimization with R:

• Demonstrates techniques in modelling financial risks and applying portfolio optimization techniques as well as recent advances in the field.
• Introduces stylized facts, loss function and risk measures, conditional and unconditional modelling of risk; extreme value theory, generalized hyperbolic distribution, volatility modelling and concepts for capturing dependencies.
• Explores portfolio risk concepts and optimization with risk constraints.
• Is accompanied by a supporting website featuring examples and case studies in R.
• Includes updated list of R packages for enabling the reader to replicate the results in the book.

Graduate and postgraduate students in finance, economics, risk management as well as practitioners in finance and portfolio optimization will find this book beneficial. It also serves well as an accompanying text in computer-lab classes and is therefore suitable for self-study.

Preface to the Second Edition xi

Preface xiii

Abbreviations xv

About the Companion Website xix

PART I MOTIVATION 1

1 Introduction 3

Reference 5

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 22

References 28

3 Financial market data 29

3.1 Stylized facts of financial market returns 29

3.1.1 Stylized facts for univariate series 29

3.1.2 Stylized facts for multivariate series 32

3.2 Implications for risk models 35

References 36

4 Measuring risks 37

4.1 Introduction 37

4.2 Synopsis of risk measures 37

4.3 Portfolio risk concepts 42

References 44

5 Modern portfolio theory 46

5.1 Introduction 46

5.2 Markowitz portfolios 47

5.3 Empirical mean-variance portfolios 50

References 52

PART II RISK MODELLING 55

6 Suitable distributions for returns 57

6.1 Preliminaries 57

6.2 The generalized hyperbolic distribution 57

6.3 The generalized lambda distribution 60

6.4 Synopsis of R packages for GHD 66

6.4.1 The package fBasics 66

6.4.2 The package GeneralizedHyperbolic 67

6.4.3 The package ghyp 69

6.4.4 The package QRM 70

6.4.5 The package SkewHyperbolic 70

6.4.6 The package VarianceGamma 71

6.5 Synopsis of R packages for GLD 71

6.5.1 The package Davies 71

6.5.2 The package fBasics 72

6.5.3 The package gld 73

6.5.4 The package lmomco 73

6.6 Applications of the GHD to risk modelling 74

6.6.1 Fitting stock returns to the GHD 74

6.6.2 Risk assessment with the GHD 77

6.6.3 Stylized facts revisited 80

6.7 Applications of the GLD to risk modelling and data analysis 82

6.7.1 VaR for a single stock 82

6.7.2 Shape triangle for FTSE 100 constituents 84

References 86

7 Extreme value theory 89

7.1 Preliminaries 89

7.2 Extreme value methods and models 90

7.2.1 The block maxima approach 90

7.2.2 The rth largest order models 91

7.2.3 The peaks-over-threshold approach 92

7.3 Synopsis of R packages 94

7.3.1 The package evd 94

7.3.2 The package evdbayes 95

7.3.3 The package evir 96

7.3.4 The packages extRemes and in2extRemes 98

7.3.5 The package fExtremes 99

7.3.6 The package ismev 101

7.3.7 The package QRM 101

7.3.8 The packages Renext and RenextGUI 102

7.4 Empirical applications of EVT 103

7.4.1 Section outline 103

7.4.2 Block maxima model for Siemens 103

7.4.3 r-block maxima for BMW 107

7.4.4 POT method for Boeing 110

References 115

8 Modelling volatility 116

8.1 Preliminaries 116

8.2 The class of ARCH models 116

8.3 Synopsis of R packages 120

8.3.1 The package bayesGARCH 120

8.3.2 The package ccgarch 121

8.3.3 The package fGarch 122

8.3.4 The package GEVStableGarch 122

8.3.5 The package gogarch 123

8.3.6 The package lgarch 123

8.3.7 The packages rugarch and rmgarch 125

8.3.8 The package tseries 127

8.4 Empirical application of volatility models 128

References 130

9 Modelling dependence 133

9.1 Overview 133

9.2 Correlation, dependence, and distributions 133

9.3 Copulae 136

9.3.1 Motivation 136

9.3.2 Correlations and dependence revisited 137

9.3.3 Classification of copulae 139

9.4 Synopsis of R packages 142

9.4.1 The package BLCOP 142

9.4.2 The package copula 144

9.4.3 The package fCopulae 146

9.4.4 The package gumbel 147

9.4.5 The package QRM 148

9.5 Empirical applications of copulae 148

9.5.1 GARCH–copula model 148

9.5.2 Mixed copula approaches 155

References 157

PART III PORTFOLIO OPTIMIZATION APPROACHES 161

10 Robust portfolio optimization 163

10.1 Overview 163

10.2 Robust statistics 164

10.2.1 Motivation 164

10.2.2 Selected robust estimators 165

10.3 Robust optimization 168

10.3.1 Motivation 168

10.3.2 Uncertainty sets and problem formulation 168

10.4 Synopsis of R packages 174

10.4.1 The package covRobust 174

10.4.2 The package fPortfolio 174

10.4.3 The package MASS 175

10.4.4 The package robustbase 176

10.4.5 The package robust 176

10.4.6 The package rrcov 178

10.4.7 Packages for solving SOCPs 179

10.5 Empirical applications 180

10.5.1 Portfolio simulation: robust versus classical statistics 180

10.5.2 Portfolio back test: robust versus classical statistics 186

10.5.3 Portfolio back-test: robust optimization 190

References 195

11 Diversification reconsidered 198

11.1 Introduction 198

11.2 Most-diversified portfolio 199

11.3 Risk contribution constrained portfolios 201

11.4 Optimal tail-dependent portfolios 204

11.5 Synopsis of R packages 207

11.5.1 The package cccp 207

11.5.2 The packages DEoptim, DEoptimR, and RcppDE 207

11.5.3 The package FRAPO 210

11.5.4 The package PortfolioAnalytics 211

11.6 Empirical applications 212

11.6.1 Comparison of approaches 212

11.6.2 Optimal tail-dependent portfolio against benchmark 216

11.6.3 Limiting contributions to expected shortfall 221

References 226

12 Risk-optimal portfolios 228

12.1 Overview 228

12.2 Mean-VaR portfolios 229

12.3 Optimal CVaR portfolios 234

12.4 Optimal draw-down portfolios 238

12.5 Synopsis of R packages 241

12.5.1 The package fPortfolio 241

12.5.2 The package FRAPO 243

12.5.3 Packages for linear programming 245

12.5.4 The package PerformanceAnalytics 249

12.6 Empirical applications 251

12.6.1 Minimum-CVaR versus minimum-variance portfolios 251

12.6.2 Draw-down constrained portfolios 254

12.6.3 Back-test comparison for stock portfolio 260

12.6.4 Risk surface plots 265

References 272

13 Tactical asset allocation 274

13.1 Overview 274

13.2 Survey of selected time series models 275

13.2.1 Univariate time series models 275

13.2.2 Multivariate time series models 281

13.3 The Black–Litterman approach 289

13.4 Copula opinion and entropy pooling 292

13.4.1 Introduction 292

13.4.2 The COP model 292

13.4.3 The EP model 293

13.5 Synopsis of R packages 295

13.5.1 The package BLCOP 295

13.5.2 The package dse 297

13.5.3 The package fArma 300

13.5.4 The package forecast 301

13.5.5 The package MSBVAR 302

13.5.6 The package PortfolioAnalytics 304

13.5.7 The packages urca and vars 304

13.6 Empirical applications 307

13.6.1 Black–Litterman portfolio optimization 307

13.6.2 Copula opinion pooling 313

13.6.3 Entropy pooling 318

13.6.4 Protection strategies 324

References 334

14 Probabilistic utility 339

14.1 Overview 339

14.2 The concept of probabilistic utility 340

14.3 Markov chain Monte Carlo 342

14.3.1 Introduction 342

14.3.2 Monte Carlo approaches 343

14.3.3 Markov chains 347

14.3.4 Metropolis–Hastings algorithm 349

14.4 Synopsis of R packages 354

14.4.1 Packages for conducting MCMC 354

14.4.2 Packages for analyzing MCMC 358

14.5 Empirical application 362

14.5.1 Exemplary utility function 362

14.5.2 Probabilistic versus maximized expected utility 366

14.5.3 Simulation of asset allocations 369

References 375

Appendix A Package overview 378

A.1 Packages in alphabetical order 378

A.2 Packages ordered by topic 382

References 386

Appendix B Time series data 391

B.1 Date/time classes 391

B.2 The ts class in the base package stats 395

B.3 Irregularly spaced time series 395

B.4 The package timeSeries 397

B.5 The package zoo 399

B.6 The packages tframe and xts 401

References 404

Appendix C Back-testing and reporting of portfolio strategies 406

C.1 R packages for back-testing 406

C.2 R facilities for reporting 407

C.3 Interfacing with databases 407

References 408

Appendix D Technicalities 411

Reference 411

Index 413

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