风险和资产配置 英文版【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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Part Ⅰ The statistics of asset allocation3

1 Univariate statistics3

1.1 Building blocks3

1.2 Summary statistics9

1.2.1 Location9

1.2.2 Dispersion11

1.2.3 Higher-order statistics14

1.2.4 Graphical representations15

1.3 Taxonomy of distributions16

1.3.1 Uniform distribution16

1.3.2 Normal distribution18

1.3.3 Cauchy distribution20

1.3.4 Student t distribution22

1.3.5 Lognormal distribution24

1.3.6 Gamma distribution26

1.3.7 Empirical distribution28

2 Multivariate statistics33

2.1 Building blocks34

2.2 Factorization of a distribution38

2.2.1 Marginal distribution38

2.2.2 Copulas40

2.3 Dependence45

2.4 Shape summary statistics48

2.4.1 Location48

2.4.2 Dispersion50

2.4.3 Location-dispersion ellipsoid54

2.4.4 Higher-order statistics57

2.5 Dependence summary statistics59

2.5.1 Measures of dependence59

2.5.2 Measures of concordance64

2.5.3 Correlation67

2.6 Taxonomy of distributions70

2.6.1 Uniform distribution70

2.6.2 Normal distribution72

2.6.3 Student t distribution77

2.6.4 Cauchy distribution81

2.6.5 Log-distributions82

2.6.6 Wishart distribution84

2.6.7 Empirical distribution87

2.6.8 Order statistics89

2.7 Special classes of distributions91

2.7.1 Elliptical distributions91

2.7.2 Stable distributions96

2.7.3 Infinitely divisible distributions98

3 Modeling the market101

3.1 The quest for invariance103

3.1.1 Equities,commodities,exchange rates105

3.1.2 Fixed-income market109

3.1.3 Derivatives114

3.2 Projection of the invariants to the investment horizon122

3.3 From invariants to market prices126

3.3.1 Raw securities126

3.3.2 Derivatives129

3.4 Dimension reduction131

3.4.1 Explicit factors133

3.4.2 Hidden factors138

3.4.3 Explicit vs. hidden factors143

3.4.4 Notable examples145

3.4.5 A nseful routine147

3.5 Case study:modeling the swap market150

3.5.1 The market invariants150

3.5.2 Dimension reduction151

3.5.3 The invariants at the investment horizon160

3.5.4 From invariants to prices162

Part Ⅱ Classical asset allocation169

4 Estimating the distribution of the market invariants169

4.1 Estimators171

4.1.1 Definition172

4.1.2 Evaluation173

4.2 Nonparametric estimators178

4.2.1 Location,dispersion and hidden factors181

4.2.2 Explicit factors184

4.2.3 Kernel estimators185

4.3 Maximum likelihood estimators186

4.3.1 Location,dispersion and hidden factors190

4.3.2 Explicit factors192

4.3.3 The normal case193

4.4 Shrinkage estimators200

4.4.1 Location201

4.4.2 Dispersion and hidden factors204

4.4.3 Explicit factors209

4.5 Robustness209

4.5.1 Measures of robustness211

4.5.2 Robustness of previously introduced estimators216

4.5.3 Robust estimators221

4.6 Practical tips223

4.6.1 Detection of outliers223

4.6.2 Missing data229

4.6.3 Weighted estimates232

4.6.4 Overlapping data234

4.6.5 Zero-mean invariants234

4.6.6 Model-implied estimation235

5 Evaluating allocations237

5.1 Investor's objectives239

5.2 Stochastic dominance243

5.3 Satisfaction249

5.4 Certainty-equivalent(expected utility)260

5.4.1 Properties262

5.4.2 Building utility functions270

5.4.3 Explicit dependence on allocation274

5.4.4 Sensitivity analysis276

5.5 Quantile(value at risk)277

5.5.1 Properties278

5.5.2 Explicit dependence on allocation282

5.5.3 Sensitivity analysis285

5.6 Coherent indices(expected shortfall)287

5.6.1 Properties288

5.6.2 Building coherent indices292

5.6.3 Explicit dependence on allocation296

5.6.4 Sensitivity analysis298

6 Optimizing allocations301

6.1 The general approach302

6.1.1 Collecting information on the investor303

6.1.2 Collecting information on the market305

6.1.3 Computing the optimal allocation306

6.2 Constrained optimization311

6.2.1 Positive orthants:linear programming313

6.2.2 Ice-cream cones:second-order cone programming313

6.2.3 Semidefinite cones:semidefinite programming315

6.3 The mean-variance approach315

6.3.1 The geometry of allocation optimization316

6.3.2 Dimension reduction:the mean-variance framework319

6.3.3 Setting up the mean-variance optimization320

6.3.4 Mean-variance in terms of returns323

6.4 Analytical solutions of the mean-variance problem326

6.4.1 Efficient frontier with affine constraints327

6.4.2 Efficient frontier with linear constraints330

6.4.3 Effects of correlations and other parameters332

6.4.4 Effects of the market dimension335

6.5 Pitfalls of the mean-variance framework336

6.5.1 MV as an approximation336

6.5.2 MV as an index of satisfaction338

6.5.3 Quadratic programming and dual formulation340

6.5.4 MV on returns:estimation versus optimization342

6.5.5 MV on returns:investment at different horizons343

6.6 Total-return versus benchmark allocation347

6.7 Case study:allocation in stocks354

6.7.1 Collecting information on the investor355

6.7.2 Collecting information on the market355

6.7.3 Computing the optimal allocation357

Part Ⅲ Accounting for estimation risk363

7 Estimating the distribution of the market invariants363

7.1 Bayesian estimation364

7.1.1 Bayesian posterior distribution364

7.1.2 Summarizing the posterior distribution366

7.1.3 Computing the posterior distribution369

7.2 Location and dispersion parameters370

7.2.1 Computing the posterior distribution370

7.2.2 Summarizing the posterior distribution373

7.3 Explicit factors377

7.3.1 Computing the posterior distribution377

7.3.2 Summarizing the posterior distribution380

7.4 Determining the prior383

7.4.1 Allocation-implied parameters385

7.4.2 Likelihood maximization387

8 Evaluating allocations389

8.1 Allocations as decisions390

8.1.1 Opportunity cost of a sub-optimal allocation390

8.1.2 Opportunity cost as function of the market parameters394

8.1.3 Opportunity cost as loss of an estimator397

8.1.4 Evaluation of a generic allocation decision401

8.2 Prior allocation403

8.2.1 Definition403

8.2.2 Evaluation404

8.2.3 Discussion406

8.3 Sample-based allocation407

8.3.1 Definition407

8.3.2 Evaluation408

8.3.3 Discussion412

9 Optimizing allocations417

9.1 Bayesian allocation418

9.1.1 Utility maximization419

9.1.2 Classical-equivalent maximization421

9.1.3 Evaluation422

9.1.4 Discussion425

9.2 Black-Litterman allocation426

9.2.1 General definition426

9.2.2 Practicable definition:linear expertise on normal markets429

9.2.3 Evaluation433

9.2.4 Discussion436

9.3 Resampled allocation437

9.3.1 Practicable definition:the mean-variance setting438

9.3.2 General definition440

9.3.3 Evaluation443

9.3.4 Discussion445

9.4 Robust allocation445

9.4.1 General definition445

9.4.2 Practicable definition:the mean-variance setting450

9.4.3 Discussion453

9.5 Robust Bayesian allocation454

9.5.1 General definition455

9.5.2 Practicable definition:the mean-variance setting457

9.5.3 Discussion459

Part Ⅳ Appendices465

A Linear algebra465

A.1 Vector space465

A.2 Basis468

A.3 Linear transformations469

A.3.1 Matrix representation470

A.3.2 Rotations471

A.4 Invariants472

A.4.1 Determinant472

A.4.2 Trace474

A.4.3 Eigenvalues474

A.5 Spectral theorem475

A.5.1 Analytical result475

A.5.2 Geometrical interpretation478

A.6 Matrix operations480

A.6.1 Useful identities480

A.6.2 Tensors and Kronecker product482

A.6.3 The"vec"and"vech"operators483

A.6.4 Matrix calculus485

B Functional Analysis487

B.1 Vector space487

B.2 Basis490

B.3 Linear operators493

B.3.1 Kernel representations494

B.3.2 Unitary operators494

B.4 Regularization496

B.5 Expectation operator499

B.6 Some special functions501

References505

List of figures515

Notation519

Index525