Preface xi
List of abbreviations xiii
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 20
References 25
3 Financial market data 26
3.1 Stylized facts on financial market returns 26
3.1.1 Stylized facts for univariate series 26
3.1.2 Stylized facts for multivariate series 29
3.2 Implications for risk models 32
References 33
4 Measuring risks 34
4.1 Introduction 34
4.2 Synopsis of risk measures 34
4.3 Portfolio risk concepts 39
References 41
5 Modern portfolio theory 43
5.1 Introduction 43
vi CONTENTS
5.2 Markowitz portfolios 43
5.3 Empirical mean–variance portfolios 47
References 49
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
6.4.1 The package fBasics 62
6.4.2 The package GeneralizedHyperbolic 63
6.4.3 The package ghyp 64
6.4.4 The package QRM 65
6.4.5 The package SkewHyperbolic 66
6.4.6 The package VarianceGamma 67
6.5 Synopsis of R packages for GLD 67
6.5.1 The package Davies 67
6.5.2 The package fBasics 67
6.5.3 The package gld 68
6.5.4 The package lmomco 69
6.6 Applications of the GHD to risk modelling 69
6.6.1 Fitting stock returns to the GHD 69
6.6.2 Risk assessment with the GHD 73
6.6.3 Stylized facts revisited 75
6.7 Applications of the GLD to risk modelling and
data analysis 78
6.7.1 VaR for a single stock 78
6.7.2 Shape triangle for FTSE 100 constituents 79
References 82
7 Extreme value theory 84
7.1 Preliminaries 84
7.2 Extreme value methods and models 85
7.2.1 The block maxima approach 85
7.2.2 rth largest order models 86
7.2.3 The peaks-over-threshold approach 87
7.3 Synopsis of R packages 89
7.3.1 The package evd 89
7.3.2 The package evdbayes 90
7.3.3 The package evir 91
CONTENTS vii
7.3.4 The package fExtremes 93
7.3.5 The packages ismev and extRemes 95
7.3.6 The package POT 96
7.3.7 The package QRM 97
7.3.8 The package Renext 97
7.4 Empirical applications of EVT 98
7.4.1 Section outline 98
7.4.2 Block maxima model for Siemens 99
7.4.3 r block maxima model for BMW 101
7.4.4 POT method for Boeing 105
References 110
8 Modelling volatility 112
8.1 Preliminaries 112
8.2 The class of ARCH models 112
8.3 Synopsis of R packages 116
8.3.1 The package bayesGARCH 116
8.3.2 The package ccgarch 117
8.3.3 The package fGarch 118
8.3.4 The package gogarch 118
8.3.5 The packages rugarch and rmgarch 120
8.3.6 The package tseries 122
8.4 Empirical application of volatility models 123
References 125
9 Modelling dependence 127
9.1 Overview 127
9.2 Correlation, dependence and distributions 127
9.3 Copulae 130
9.3.1 Motivation 130
9.3.2 Correlations and dependence revisited 131
9.3.3 Classification of copulae 133
9.4 Synopsis of R packages 136
9.4.1 The package BLCOP 136
9.4.2 The packages copula and nacopula 138
9.4.3 The package fCopulae 140
9.4.4 The package gumbel 141
9.4.5 The package QRM 142
9.5 Empirical applications of copulae 142
9.5.1 GARCH–copula model 142
9.5.2 Mixed copula approaches 149
References 151
viii CONTENTS
Part III PORTFOLIO OPTIMIZATION APPROACHES 153
10 Robust portfolio optimization 155
10.1 Overview 155
10.2 Robust statistics 156
10.2.1 Motivation 156
10.2.2 Selected robust estimators 157
10.3 Robust optimization 160
10.3.1 Motivation 160
10.3.2 Uncertainty sets and problem formulation 160
10.4 Synopsis of R packages 166
10.4.1 The package covRobust 166
10.4.2 The package fPortfolio 166
10.4.3 The package MASS 167
10.4.4 The package robustbase 168
10.4.5 The package robust 168
10.4.6 The package rrcov 169
10.4.7 The package Rsocp 170
10.5 Empirical applications 171
10.5.1 Portfolio simulation: Robust versus classical statistics 171
10.5.2 Portfolio back-test: Robust versus classical statistics 177
10.5.3 Portfolio back-test: Robust optimization 182
References 187
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
11.5.1 The packages DEoptim and RcppDE 197
11.5.2 The package FRAPO 199
11.5.3 The package PortfolioAnalytics 201
11.6 Empirical applications 201
11.6.1 Comparison of approaches 201
11.6.2 Optimal tail-dependent portfolio against benchmark 206
11.6.3 Limiting contributions to expected shortfall 211
References 215
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
CONTENTS ix
12.5 Synopsis of R packages 229
12.5.1 The package fPortfolio 229
12.5.2 The package FRAPO 230
12.5.3 Packages for linear programming 232
12.5.4 The package PerformanceAnalytics 236
12.6 Empirical applications 238
12.6.1 Minimum-CVaR versus minimum-variance portfolios 238
12.6.2 Draw-down constrained portfolios 242
12.6.3 Back-test comparison for stock portfolio 247
References 253
13 Tactical asset allocation 255
13.1 Overview 255
13.2 Survey of selected time series models 256
13.2.1 Univariate time series models 256
13.2.2 Multivariate time series models 262
13.3 Black–Litterman approach 270
13.4 Copula opinion and entropy pooling 273
13.4.1 Introduction 273
13.4.2 The COP model 273
13.4.3 The EP model 274
13.5 Synopsis of R packages 276
13.5.1 The package BLCOP 276
13.5.2 The package dse 278
13.5.3 The package fArma 281
13.5.4 The package forecast 281
13.5.5 The package MSBVAR 283
13.5.6 The package PairTrading 284
13.5.7 The packages urca and vars 285
13.6 Empirical applications 288
13.6.1 Black–Litterman portfolio optimization 288
13.6.2 Copula opinion pooling 295
13.6.3 Protection strategies 299
References 310
Appendix A Package overview 314
A.1 Packages in alphabetical order 314
A.2 Packages ordered by topic 317
References 320
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
x CONTENTS
B.4 The package timeSeries 330
B.5 The package zoo 332
B.6 The packages tframe and xts 334
References 337
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
References 340
Appendix D Technicalities 342
Index 343
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