Collaborators p. xiii
Foreword p. xv
Acknowledgements p. xvii
Introduction p. xix
Areas covered p. xix
Who is this book for? p. xxi
The Massive Changes in the World of Finance p. 1
Introduction p. 2
The Regulatory Context p. 3
Precautionary surveillance p. 3
The Basle Committee p. 3
General information p. 3
Basle II and the philosophy of operational risk p. 5
Accounting standards p. 9
Standard-setting organisations p. 9
The IASB p. 9
Changes in Financial Risk Management p. 11
Definitions p. 11
Typology of risks p. 11
Risk management methodology p. 19
Changes in financial risk management p. 21
Towards an integrated risk management p. 21
The 'cost' of risk management p. 25
A new risk-return world p. 26
Towards a minimisation of risk for an anticipated return p. 26
Theoretical formalisation p. 26
Evaluating Financial Assets p. 29
Introduction p. 30
Equities p. 35
The basics p. 35
Return and risk p. 35
Market efficiency p. 44
Equity valuation models p. 48
Portfolio diversification and management p. 51
Principles of diversification p. 51
Diversification and portfolio size p. 55
Markowitz model and critical line algorithm p. 56
Sharpe's simple index model p. 69
Model with risk-free security p. 75
The Elton, Gruber and Padberg method of portfolio management p. 79
Utility theory and optimal portfolio selection p. 85
The market model p. 91
Model of financial asset equilibrium and applications p. 93
Capital asset pricing model p. 93
Arbitrage pricing theory p. 97
Performance evaluation p. 99
Equity portfolio management strategies p. 103
Equity dynamic models p. 108
Deterministic models p. 108
Stochastic models p. 109
Bonds p. 115
Characteristics and valuation p. 115
Definitions p. 115
Return on bonds p. 116
Valuing a bond p. 119
Bonds and financial risk p. 119
Sources of risk p. 119
Duration p. 121
Convexity p. 127
Deterministic structure of interest rates p. 129
Yield curves p. 129
Static interest rate structure p. 130
Dynamic interest rate structure p. 132
Deterministic model and stochastic model p. 134
Bond portfolio management strategies p. 135
Passive strategy: immunisation p. 135
Active strategy p. 137
Stochastic bond dynamic models p. 138
Arbitrage models with one state variable p. 139
The Vasicek model p. 142
The Cox, Ingersoll and Ross model p. 145
Stochastic duration p. 147
Options p. 149
Definitions p. 149
Characteristics p. 149
Use p. 150
Value of an option p. 153
Intrinsic value and time value p. 153
Volatility p. 154
Sensitivity parameters p. 155
General properties p. 157
Valuation models p. 160
Binomial model for equity options p. 162
Black and Scholes model for equity options p. 168
Other models of valuation p. 174
Strategies on options p. 175
Simple strategies p. 175
More complex strategies p. 175
General Theory of VaR p. 179
Introduction p. 180
Theory of VaR p. 181
The concept of 'risk per share' p. 181
Standard measurement of risk linked to financial products p. 181
Problems with these approaches to risk p. 181
Generalising the concept of 'risk' p. 184
VaR for a single asset p. 185
Value at Risk p. 185
Case of a normal distribution p. 188
VaR for a portfolio p. 190
General results p. 190
Components of the VaR of a portfolio p. 193
Incremental VaR p. 195
VaR Estimation Techniques p. 199
General questions in estimating VaR p. 199
The problem of estimation p. 199
Typology of estimation methods p. 200
Estimated variance-covariance matrix method p. 202
Identifying cash flows in financial assets p. 203
Mapping cashflows with standard maturity dates p. 205
Calculating VaR p. 209
Monte Carlo simulation p. 216
The Monte Carlo method and probability theory p. 216
Estimation method p. 218
Historical simulation p. 224
Basic methodology p. 224
The contribution of extreme value theory p. 230
Advantages and drawbacks p. 234
The theoretical viewpoint p. 235
The practical viewpoint p. 238
Synthesis p. 241
Setting Up a VaR Methodology p. 243
Putting together the database p. 243
Which data should be chosen? p. 243
The data in the example p. 244
Calculations p. 244
Treasury portfolio case p. 244
Bond portfolio case p. 250
The normality hypothesis p. 252
From Risk Management to Asset Management p. 255
Introduction p. 256
Portfolio Risk Management p. 257
General principles p. 257
Portfolio risk management method p. 257
Investment strategy p. 258
Risk framework p. 258
Optimising the Global Portfolio via VaR p. 265
Taking account of VaR in Sharpe's simple index method p. 266
The problem of minimisation p. 266
Adapting the critical line algorithm to VaR p. 267
Comparison of the two methods p. 269
Taking account of VaR in the EGP method p. 269
Maximising the risk premium p. 269
Adapting the EGP method algorithm to VaR p. 270
Comparison of the two methods p. 271
Conclusion p. 272
Optimising a global portfolio via VaR p. 274
Generalisation of the asset model p. 275
Construction of an optimal global portfolio p. 277
Method of optimisation of global portfolio p. 278
Institutional Management: APT Applied to Investment Funds p. 285
Absolute global risk p. 285
Relative global risk/tracking error p. 285
Relative fund risk vs. benchmark abacus p. 287
Allocation of systematic risk p. 288
Independent allocation p. 288
Joint allocation: 'value' and 'growth' example p. 289
Allocation of performance level p. 289
Gross performance level and risk withdrawal p. 290
Analysis of style p. 291
From Risk Management to Asset and Liability Management p. 293
Introduction p. 294
Techniques for Measuring Structural Risks in Balance Sheets p. 295
Tools for structural risk analysis in asset and liability management p. 295
Gap or liquidity risk p. 296
Rate mismatches p. 297
Net present value (NPV) of equity funds and sensitivity p. 298
Duration of equity funds p. 299
Simulations p. 300
Using VaR in ALM p. 301
Repricing schedules (modelling of contracts with floating rates) p. 301
The conventions method p. 301
The theoretical approach to the interest rate risk on floating rate products, through the net current value p. 302
The behavioural study of rate revisions p. 303
Replicating portfolios p. 311
Presentation of replicating portfolios p. 312
Replicating portfolios constructed according to convention p. 313
The contract-by-contract replicating portfolio p. 314
Replicating portfolios with the optimal value method p. 316
Appendices p. 323
Mathematical Concepts p. 325
Functions of one variable p. 325
Derivatives p. 325
Taylor's formula p. 327
Geometric series p. 328
Functions of several variables p. 329
Partial derivatives p. 329
Taylor's formula p. 331
Matrix calculus p. 332
Definitions p. 332
Quadratic forms p. 334
Probabilistic Concepts p. 339
Random variables p. 339
Random variables and probability law p. 339
Typical values of random variables p. 343
Theoretical distributions p. 347
Normal distribution and associated ones p. 347
Other theoretical distributions p. 350
Stochastic processes p. 353
General considerations p. 353
Particular stochastic processes p. 354
Stochastic differential equations p. 356
Statistical Concepts p. 359
Inferential statistics p. 359
Sampling p. 359
Two problems of inferential statistics p. 360
Regressions p. 362
Simple regression p. 362
Multiple regression p. 363
Nonlinear regression p. 364
Extreme Value Theory p. 365
Exact result p. 365
Asymptotic results p. 365
Extreme value theorem p. 365
Attraction domains p. 366
Generalisation p. 367
Canonical Correlations p. 369
Geometric presentation of the method p. 369
Search for canonical characters p. 369
Algebraic Presentation of Logistic Regression p. 371
Time Series Models: ARCH-GARCH and EGARCH p. 373
ARCH-GARCH models p. 373
EGARCH models p. 373
Numerical Methods for Solving Nonlinear Equations p. 375
General principles for iterative methods p. 375
Convergence p. 375
Order of convergence p. 376
Stop criteria p. 376
Principal methods p. 377
First order methods p. 377
Newton-Raphson method p. 379
Bisection method p. 380
Nonlinear equation systems p. 380
General theory of n-dimensional iteration p. 381
Principal methods p. 381
Bibliography p. 383
Index p. 389