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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.
Bernhard Eugen Heinrich Pfaff, Director, Invesco Asset Management Deutschland GmbH, Germany.
Preface to the Second Edition xiPreface xiiiAbbreviations xvAbout the Companion Website xixPART I MOTIVATION 11 Introduction 3Reference 52 A brief course in R 62.1 Origin and development 62.2 Getting help 72.3 Working with R 102.4 Classes, methods, and functions 122.5 The accompanying package FRAPO 22References 283 Financial market data 293.1 Stylized facts of financial market returns 293.1.1 Stylized facts for univariate series 293.1.2 Stylized facts for multivariate series 323.2 Implications for risk models 35References 364 Measuring risks 374.1 Introduction 374.2 Synopsis of risk measures 374.3 Portfolio risk concepts 42References 445 Modern portfolio theory 465.1 Introduction 465.2 Markowitz portfolios 475.3 Empirical mean-variance portfolios 50References 52PART II RISK MODELLING 556 Suitable distributions for returns 576.1 Preliminaries 576.2 The generalized hyperbolic distribution 576.3 The generalized lambda distribution 606.4 Synopsis of R packages for GHD 666.4.1 The package fBasics 666.4.2 The package GeneralizedHyperbolic 676.4.3 The package ghyp 696.4.4 The package QRM 706.4.5 The package SkewHyperbolic 706.4.6 The package VarianceGamma 716.5 Synopsis of R packages for GLD 716.5.1 The package Davies 716.5.2 The package fBasics 726.5.3 The package gld 736.5.4 The package lmomco 736.6 Applications of the GHD to risk modelling 746.6.1 Fitting stock returns to the GHD 746.6.2 Risk assessment with the GHD 776.6.3 Stylized facts revisited 806.7 Applications of the GLD to risk modelling and data analysis 826.7.1 VaR for a single stock 826.7.2 Shape triangle for FTSE 100 constituents 84References 867 Extreme value theory 897.1 Preliminaries 897.2 Extreme value methods and models 907.2.1 The block maxima approach 907.2.2 The rth largest order models 917.2.3 The peaks-over-threshold approach 927.3 Synopsis of R packages 947.3.1 The package evd 947.3.2 The package evdbayes 957.3.3 The package evir 967.3.4 The packages extRemes and in2extRemes 987.3.5 The package fExtremes 997.3.6 The package ismev 1017.3.7 The package QRM 1017.3.8 The packages Renext and RenextGUI 1027.4 Empirical applications of EVT 1037.4.1 Section outline 1037.4.2 Block maxima model for Siemens 1037.4.3 r-block maxima for BMW 1077.4.4 POT method for Boeing 110References 1158 Modelling volatility 1168.1 Preliminaries 1168.2 The class of ARCH models 1168.3 Synopsis of R packages 1208.3.1 The package bayesGARCH 1208.3.2 The package ccgarch 1218.3.3 The package fGarch 1228.3.4 The package GEVStableGarch 1228.3.5 The package gogarch 1238.3.6 The package lgarch 1238.3.7 The packages rugarch and rmgarch 1258.3.8 The package tseries 1278.4 Empirical application of volatility models 128References 1309 Modelling dependence 1339.1 Overview 1339.2 Correlation, dependence, and distributions 1339.3 Copulae 1369.3.1 Motivation 1369.3.2 Correlations and dependence revisited 1379.3.3 Classification of copulae 1399.4 Synopsis of R packages 1429.4.1 The package BLCOP 1429.4.2 The package copula 1449.4.3 The package fCopulae 1469.4.4 The package gumbel 1479.4.5 The package QRM 1489.5 Empirical applications of copulae 1489.5.1 GARCH–copula model 1489.5.2 Mixed copula approaches 155References 157PART III PORTFOLIO OPTIMIZATION APPROACHES 16110 Robust portfolio optimization 16310.1 Overview 16310.2 Robust statistics 16410.2.1 Motivation 16410.2.2 Selected robust estimators 16510.3 Robust optimization 16810.3.1 Motivation 16810.3.2 Uncertainty sets and problem formulation 16810.4 Synopsis of R packages 17410.4.1 The package covRobust 17410.4.2 The package fPortfolio 17410.4.3 The package MASS 17510.4.4 The package robustbase 17610.4.5 The package robust 17610.4.6 The package rrcov 17810.4.7 Packages for solving SOCPs 17910.5 Empirical applications 18010.5.1 Portfolio simulation: robust versus classical statistics 18010.5.2 Portfolio back test: robust versus classical statistics 18610.5.3 Portfolio back-test: robust optimization 190References 19511 Diversification reconsidered 19811.1 Introduction 19811.2 Most-diversified portfolio 19911.3 Risk contribution constrained portfolios 20111.4 Optimal tail-dependent portfolios 20411.5 Synopsis of R packages 20711.5.1 The package cccp 20711.5.2 The packages DEoptim, DEoptimR, and RcppDE 20711.5.3 The package FRAPO 21011.5.4 The package PortfolioAnalytics 21111.6 Empirical applications 21211.6.1 Comparison of approaches 21211.6.2 Optimal tail-dependent portfolio against benchmark 21611.6.3 Limiting contributions to expected shortfall 221References 22612 Risk-optimal portfolios 22812.1 Overview 22812.2 Mean-VaR portfolios 22912.3 Optimal CVaR portfolios 23412.4 Optimal draw-down portfolios 23812.5 Synopsis of R packages 24112.5.1 The package fPortfolio 24112.5.2 The package FRAPO 24312.5.3 Packages for linear programming 24512.5.4 The package PerformanceAnalytics 24912.6 Empirical applications 25112.6.1 Minimum-CVaR versus minimum-variance portfolios 25112.6.2 Draw-down constrained portfolios 25412.6.3 Back-test comparison for stock portfolio 26012.6.4 Risk surface plots 265References 27213 Tactical asset allocation 27413.1 Overview 27413.2 Survey of selected time series models 27513.2.1 Univariate time series models 27513.2.2 Multivariate time series models 28113.3 The Black–Litterman approach 28913.4 Copula opinion and entropy pooling 29213.4.1 Introduction 29213.4.2 The COP model 29213.4.3 The EP model 29313.5 Synopsis of R packages 29513.5.1 The package BLCOP 29513.5.2 The package dse 29713.5.3 The package fArma 30013.5.4 The package forecast 30113.5.5 The package MSBVAR 30213.5.6 The package PortfolioAnalytics 30413.5.7 The packages urca and vars 30413.6 Empirical applications 30713.6.1 Black–Litterman portfolio optimization 30713.6.2 Copula opinion pooling 31313.6.3 Entropy pooling 31813.6.4 Protection strategies 324References 33414 Probabilistic utility 33914.1 Overview 33914.2 The concept of probabilistic utility 34014.3 Markov chain Monte Carlo 34214.3.1 Introduction 34214.3.2 Monte Carlo approaches 34314.3.3 Markov chains 34714.3.4 Metropolis–Hastings algorithm 34914.4 Synopsis of R packages 35414.4.1 Packages for conducting MCMC 35414.4.2 Packages for analyzing MCMC 35814.5 Empirical application 36214.5.1 Exemplary utility function 36214.5.2 Probabilistic versus maximized expected utility 36614.5.3 Simulation of asset allocations 369References 375Appendix A Package overview 378A.1 Packages in alphabetical order 378A.2 Packages ordered by topic 382References 386Appendix B Time series data 391B.1 Date/time classes 391B.2 The ts class in the base package stats 395B.3 Irregularly spaced time series 395B.4 The package timeSeries 397B.5 The package zoo 399B.6 The packages tframe and xts 401References 404Appendix C Back-testing and reporting of portfolio strategies 406C.1 R packages for back-testing 406C.2 R facilities for reporting 407C.3 Interfacing with databases 407References 408Appendix D Technicalities 411Reference 411Index 413
