Financial Risk Modelling and. Portfolio Optimization with R. Second Edition. Bernhard Pfaff

Transcription

1 Financial Risk Modelling and Portfolio Optimization with R Second Edition Bernhard Pfaff WILEY

2 Contents Preface to the Second Edition Preface Abbreviations About the Companion Website xi xiii xv xix PART I MOTIVATION 1 1 Introduction 3 Reference 5 2 A brief course in R Origin and development Gelting help Working with R Classes, methods, and functions The accompanying package FRAPO 22 References 28 3 Financial market data Stylized facts of financial market returns Stylized facts for univariate series Stylized facts for multivariate series Implications for risk models 35 References 36 4 Measuring risks Introduction Synopsis of risk measures Portfolio risk concepts 42 References 44 5 Modern portfolio theory Introduction 46

3 vi CONTENTS 5.2 Markowitz portfolios Empirical mean-variance portfolios 50 References 52 PART II RISK MODELLING 55 6 Suitable distributions for returns Preliminaries The generalized hyperbolic distribution The generalized lambda distribution Synopsis of R packages for GHD The package (Basics The package GeneralizedHyperbolic The package ghyp The package QRM The package SkewHyperbolic The package VarianceGamma Synopsis of R packages for GLD The package Davies The package (Basics The package gld The package lmomco Applications ofthe GHD to risk modelling Eitting stock returns to the GHD Risk assessment with the GHD Stylized facts revisited Applications of the GLD to risk modelling and data analysis VaR for a single stock Shape triangle for FTSE 100 constituents 84 References 86 7 Extreme value theory Preliminaries Extreme value methods and models The block maxima approach The rth largest order models The peaks-over-threshold approach Synopsis of R packages The package evd The package evdbayes The package evir The packages extremes and in2extremes 98

4 CONTENTS vii The package (Extremes The package ismev The package QRM The packages Renext and RenextGUI Empirical applications of EVT Section outline Block maxima model for Siemens r-block maxima for BMW POT method for Boeing 110 References Modelling volatility Preliminaries The class of ARCH models Synopsis of R packages The package bayesgarch The package ccgarch The package fgarch The package GEVStableGarch The package gogarch The package lgarch The packages rugarch and rmgarch The package tseries Empirical application of volatility models 128 References Modelling dependence Overview Correlation, dependence, and distributions Copulae Motivation Correlations and dependence revisited Classification of copulae Synopsis of R packages The package BLCOP The package copula The package fcopulae The package gumbel The package QRM Empirical applications of copulae GARCH-copula model Mixed copula approaches 155 References 157

5 CONTENTS PART III PORTFOLIO OPTIMIZATION APPROACHES Robust portfolio optimization Overview Robust statistics Motivation Selected robust estimators Robust optimization Motivation Uncertainty sets and problem formulation Synopsis of R packages The package covrobust The package fportfolio The package MASS The package robustbase The package robust The package rrcov Packages for solving SOCPs Empirical applications Portfolio Simulation: robust versus classical statistics Portfolio back test: robust versus classical statistics Portfolio back test: robust optimization 190 References Diversification reconsidered Introduction Most-diversified portfolio Risk contribution constrained portfolios Optimal tail-dependent portfolios Synopsis of R packages The package cccp The packages DEoptim, DEoptimR, and RcppDE The package FRAPO The package PortfolioAnalytics Empirical applications Comparison of approaches Optimal tail-dependent portfolio against benchmark Limiting contributions to expected shortfall 221 References Risk-optimal portfolios Overview Mean-VaR portfolios Optimal CVaR portfolios Optimal draw-down portfolios 238

6 CONTENTS ix 12.5 Synopsis of R packages The package fportfolio The package FRAPO Packages for linear programming The package PerformanceAnalytics Empirical applications Minimum-CVaR versus minimum-variance portfolios Draw-down constrained portfolios Back-test comparison for stock portfolio Risk surface plots 265 References Tactical asset allocation Overview Survey of selected time series models Univariate time series models Multivariate time series models The Black-Litterman approach Copula opinion and entropy pooling Introduction The COP model The EP model Synopsis of R packages The package BLCOP The package dse The package farma The package forecast The package MSBVAR The package PortfolioAnalytics The packages urca and vars Empirical applications Black-Litterman portfolio optimization Copula opinion pooling Entropy pooling Protection strategies 324 References Probabilistic utility Overview The concept of probabilistic Utility Markov chain Monte Carlo Introduction Monte Carlo approaches Markov chains Metropolis-Hastings algorithm 349

7 x CONTENTS 14.4 Synopsis of R packages Packages for conducting MCMC Packages for analyzing MCMC Empirical application Exemplary Utility function Probabilistic versus maximized expected Utility Simulation of asset allocations 369 References 375 Appendix A Package overview 378 A.l Packages in alphabetical order 378 A.2 Packages ordered by topic 382 References 386 Appendix B Time series data 391 B.l 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