Asset and risk management risk oriented finance

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Summary

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

Author Notes

Thierry Lopez is Certificated Business Engineer at the High Business School in Liege (HEC), and Head of the Group Risk Management at Kredietbank SA in Luxembourg, lecturer at the University of Liege, Professor of Honour at the High Business School in Liege, lecturer at the Luxembourg Institute of Banking Training and at the Luxembourg Finance Technology Transfer Agency, Honorary President and Vice-President of PRiM (Luxembourg Association of Risk Management Professionals).

Philippe Jorion

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

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