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