The aim of this book is to study three essential components of modern finance – Risk Management, Asset Management and Asset and Liability Management, as well as the links that bind them together. It is divided into five parts: Part I sets out the financial and regulatory contexts that explain the rapid development of these three areas during the last few years and shows the ways in which the Risk Management function has developed recently in financial institutions. Part II is dedicated to the underlying theories of Asset Management and deals in depth with evaluation of financial assets and with theories relating to equities, bonds and options. Part III deals with a central theory of Risk Management, the general theory of Value at Risk or VaR, its estimation techniques and the setting up of the methodology. Part IV is the point at which Asset Management and Risk Management meet. It deals with Portfolio Risk Management (the application of risk management methods to private asset management), with an adaptation of Sharpe’s simple index method and the EGP method to suit VaR and application of the APT method to investment funds in terms of behavioural analysis. Part V is the point at which Risk Management and Asset and Liability Management (ALM) meet, and touches on techniques for measuring structural risks within the on and off balance sheet. The book is aimed both at financial professionals and at students whose studies contain a financial aspect. "Esch, Kieffer and Lopez have provided us with a comprehensive and well written treatise on risk. This is a must read, must keep volume for all those who need or aspire to a professional understanding of risk and its management." —Harry M Markowitz, San Diego, USA

Table of Contents:
Collaborators xiii Foreword by Philippe Jorion xv Acknowledgements xvii Introduction xix Areas covered xix Who is this book for? xxi Part I The Massive Changes in the World of Finance 1 Introduction 2 1 The Regulatory Context 3 1.1 Precautionary surveillance 3 1.2 The Basle Committee 3 1.2.1 General information 3 1.2.2 Basle II and the philosophy of operational risk 5 1.3 Accounting standards 9 1.3.1 Standard-setting organisations 9 1.3.2 The IASB 9 2 Changes in Financial Risk Management 11 2.1 Definitions 11 2.1.1 Typology of risks 11 2.1.2 Risk management methodology 19 2.2 Changes in financial risk management 21 2.2.1 Towards an integrated risk management 21 2.2.2 The ‘cost’ of risk management 25 2.3 A new risk-return world 26 2.3.1 Towards a minimisation of risk for an anticipated return 26 2.3.2 Theoretical formalisation 26 Part II Evaluating Financial Assets 29 Introduction 30 3 Equities 35 3.1 The basics 35 3.1.1 Return and risk 35 3.1.2 Market efficiency 44 3.1.3 Equity valuation models 48 3.2 Portfolio diversification and management 51 3.2.1 Principles of diversification 51 3.2.2 Diversification and portfolio size 55 3.2.3 Markowitz model and critical line algorithm 56 3.2.4 Sharpe’s simple index model 69 3.2.5 Model with risk-free security 75 3.2.6 The Elton, Gruber and Padberg method of portfolio management 79 3.2.7 Utility theory and optimal portfolio selection 85 3.2.8 The market model 91 3.3 Model of financial asset equilibrium and applications 93 3.3.1 Capital asset pricing model 93 3.3.2 Arbitrage pricing theory 97 3.3.3 Performance evaluation 99 3.3.4 Equity portfolio management strategies 103 3.4 Equity dynamic models 108 3.4.1 Deterministic models 108 3.4.2 Stochastic models 109 4 Bonds 115 4.1 Characteristics and valuation 115 4.1.1 Definitions 115 4.1.2 Return on bonds 116 4.1.3 Valuing a bond 119 4.2 Bonds and financial risk 119 4.2.1 Sources of risk 119 4.2.2 Duration 121 4.2.3 Convexity 127 4.3 Deterministic structure of interest rates 129 4.3.1 Yield curves 129 4.3.2 Static interest rate structure 130 4.3.3 Dynamic interest rate structure 132 4.3.4 Deterministic model and stochastic model 134 4.4 Bond portfolio management strategies 135 4.4.1 Passive strategy: immunisation 135 4.4.2 Active strategy 137 4.5 Stochastic bond dynamic models 138 4.5.1 Arbitrage models with one state variable 139 4.5.2 The Vasicek model 142 4.5.3 The Cox, Ingersoll and Ross model 145 4.5.4 Stochastic duration 147 5 Options 149 5.1 Definitions 149 5.1.1 Characteristics 149 5.1.2 Use 150 5.2 Value of an option 153 5.2.1 Intrinsic value and time value 153 5.2.2 Volatility 154 5.2.3 Sensitivity parameters 155 5.2.4 General properties 157 5.3 Valuation models 160 5.3.1 Binomial model for equity options 162 5.3.2 Black and Scholes model for equity options 168 5.3.3 Other models of valuation 174 5.4 Strategies on options 175 5.4.1 Simple strategies 175 5.4.2 More complex strategies 175 Part III General Theory of VaR 179 Introduction 180 6 Theory of VaR 181 6.1 The concept of ‘risk per share’ 181 6.1.1 Standard measurement of risk linked to financial products 181 6.1.2 Problems with these approaches to risk 181 6.1.3 Generalising the concept of ‘risk’ 184 6.2 VaR for a single asset 185 6.2.1 Value at Risk 185 6.2.2 Case of a normal distribution 188 6.3 VaR for a portfolio 190 6.3.1 General results 190 6.3.2 Components of the VaR of a portfolio 193 6.3.3 Incremental VaR 195 7 VaR Estimation Techniques 199 7.1 General questions in estimating VaR 199 7.1.1 The problem of estimation 199 7.1.2 Typology of estimation methods 200 7.2 Estimated variance–covariance matrix method 202 7.2.1 Identifying cash flows in financial assets 203 7.2.2 Mapping cashflows with standard maturity dates 205 7.2.3 Calculating VaR 209 7.3 Monte Carlo simulation 216 7.3.1 The Monte Carlo method and probability theory 216 7.3.2 Estimation method 218 7.4 Historical simulation 224 7.4.1 Basic methodology 224 7.4.2 The contribution of extreme value theory 230 7.5 Advantages and drawbacks 234 7.5.1 The theoretical viewpoint 235 7.5.2 The practical viewpoint 238 7.5.3 Synthesis 241 8 Setting Up a VaR Methodology 243 8.1 Putting together the database 243 8.1.1 Which data should be chosen? 243 8.1.2 The data in the example 244 8.2 Calculations 244 8.2.1 Treasury portfolio case 244 8.2.2 Bond portfolio case 250 8.3 The normality hypothesis 252 Part IV From Risk Management to Asset Management 255 Introduction 256 9 Portfolio Risk Management 257 9.1 General principles 257 9.2 Portfolio risk management method 257 9.2.1 Investment strategy 258 9.2.2 Risk framework 258 10 Optimising the Global Portfolio via VaR 265 10.1 Taking account of VaR in Sharpe’s simple index method 266 10.1.1 The problem of minimisation 266 10.1.2 Adapting the critical line algorithm to VaR 267 10.1.3 Comparison of the two methods 269 10.2 Taking account of VaR in the EGP method 269 10.2.1 Maximising the risk premium 269 10.2.2 Adapting the EGP method algorithm to VaR 270 10.2.3 Comparison of the two methods 271 10.2.4 Conclusion 272 10.3 Optimising a global portfolio via VaR 274 10.3.1 Generalisation of the asset model 275 10.3.2 Construction of an optimal global portfolio 277 10.3.3 Method of optimisation of global portfolio 278 11 Institutional Management: APT Applied to Investment Funds 285 11.1 Absolute global risk 285 11.2 Relative global risk/tracking error 285 11.3 Relative fund risk vs. benchmark abacus 287 11.4 Allocation of systematic risk 288 11.4.1 Independent allocation 288 11.4.2 Joint allocation: ‘value’ and ‘growth’ example 289 11.5 Allocation of performance level 289 11.6 Gross performance level and risk withdrawal 290 11.7 Analysis of style 291 Part V From Risk Management to Asset and Liability Management 293 Introduction 294 12 Techniques for Measuring Structural Risks in Balance Sheets 295 12.1 Tools for structural risk analysis in asset and liability management 295 12.1.1 Gap or liquidity risk 296 12.1.2 Rate mismatches 297 12.1.3 Net present value (NPV) of equity funds and sensitivity 298 12.1.4 Duration of equity funds 299 12.2 Simulations 300 12.3 Using VaR in ALM 301 12.4 Repricing schedules (modelling of contracts with floating rates) 301 12.4.1 The conventions method 301 12.4.2 The theoretical approach to the interest rate risk on floating rate products, through the net current value 302 12.4.3 The behavioural study of rate revisions 303 12.5 Replicating portfolios 311 12.5.1 Presentation of replicating portfolios 312 12.5.2 Replicating portfolios constructed according to convention 313 12.5.3 The contract-by-contract replicating portfolio 314 12.5.4 Replicating portfolios with the optimal value method 316 Appendices 323 Appendix 1 Mathematical Concepts 325 1.1 Functions of one variable 325 1.1.1 Derivatives 325 1.1.2 Taylor’s formula 327 1.1.3 Geometric series 328 1.2 Functions of several variables 329 1.2.1 Partial derivatives 329 1.2.2 Taylor’s formula 331 1.3 Matrix calculus 332 1.3.1 Definitions 332 1.3.2 Quadratic forms 334 Appendix 2 Probabilistic Concepts 339 2.1 Random variables 339 2.1.1 Random variables and probability law 339 2.1.2 Typical values of random variables 343 2.2 Theoretical distributions 347 2.2.1 Normal distribution and associated ones 347 2.2.2 Other theoretical distributions 350 2.3 Stochastic processes 353 2.3.1 General considerations 353 2.3.2 Particular stochastic processes 354 2.3.3 Stochastic differential equations 356 Appendix 3 Statistical Concepts 359 3.1 Inferential statistics 359 3.1.1 Sampling 359 3.1.2 Two problems of inferential statistics 360 3.2 Regressions 362 3.2.1 Simple regression 362 3.2.2 Multiple regression 363 3.2.3 Nonlinear regression 364 Appendix 4 Extreme Value Theory 365 4.1 Exact result 365 4.2 Asymptotic results 365 4.2.1 Extreme value theorem 365 4.2.2 Attraction domains 366 4.2.3 Generalisation 367 Appendix 5 Canonical Correlations 369 5.1 Geometric presentation of the method 369 5.2 Search for canonical characters 369 Appendix 6 Algebraic Presentation of Logistic Regression 371 Appendix 7 Time Series Models: ARCH-GARCH and EGARCH 373 7.1 ARCH-GARCH models 373 7.2 EGARCH models 373 Appendix 8 Numerical Methods for Solving Nonlinear Equations 375 8.1 General principles for iterative methods 375 8.1.1 Convergence 375 8.1.2 Order of convergence 376 8.1.3 Stop criteria 376 8.2 Principal methods 377 8.2.1 First order methods 377 8.2.2 Newton–Raphson method 379 8.2.3 Bisection method 380 8.3 Nonlinear equation systems 380 8.3.1 General theory of n-dimensional iteration 381 8.3.2 Principal methods 381 Bibliography 383 Index 389