Holdings: Risk and asset allocation

Risk and asset allocation:

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Bibliographic Details
Main Author:	Meucci, Attilio (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2007
Edition:	Corr. 3. print.
Series:	Springer finance
Subjects:	Asset allocation Portfolio management Risk management Multivariate analysis Portfolio Selection Risikomanagement Finanzmathematik
Online Access:	Inhaltsverzeichnis
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references (p. [505]-513) and index
Physical Description:	XXVI, 532 S. zahlr. graph. Darst. 25 cm
ISBN:	9783540222132 9783642009648

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adam_text	Contents Preface .................................................... XV Audience and style ...................................... XVII Structure of the work ....................................XVIII A guided tour by means of a simplistic example .............XIX Acknowledgments .......................................XXVI Part I The statistics of asset allocation 1 Univariate statistics ....................................... 3 1.1 Building blocks .......................................... 3 1.2 Summary statistics ...................................... 9 1.2.1 Location ......................................... 9 1.2.2 Dispersion ........................................ 11 1.2.3 Higher-order statistics ............................. 14 1.2.4 Graphical representations .......................... 15 1.3 Taxonomy of distributions ................................ 16 1.3.1 Uniform distribution ............................... 16 1.3.2 Normal distribution ............................... 18 .1.3.3 Cauchy distribution ............................... 20 1.3.4 Student t distribution .............................. 22 1.3.5 Lognormal distribution ............................. 24 1.3.6 Gamma distribution ............................... 26 1.3.7 Empirical distribution .............................. 28 l.T Technical appendix ...................................... www l.E Exercises ............................................ www 2 Multivariate statistics ..................................... 33 2.1 Building blocks .......................................... 34 2.2 Factorization of a distribution ............................. 38 2.2.1 Marginal distribution .............................. 38 2.2.2 Copulas .......................................... 40 Vili Contents 2.3 Dependence ............................................. 45 2.4 Shape summary statistics ................................. 48 2.4.1 Location ......................................... 48 2.4.2 Dispersion ........................................ 50 2.4.3 Location-dispersion ellipsoid ........................ 54 2.4.4 Higher-order statistics ............................. 57 2.5 Dependence summary statistics ........................... 59 2.5.1 Measures of dependence ............................ 59 2.5.2 Measures of concordance ........................... 64 2.5.3 Correlation ....................................... 67 2.6 Taxonomy of distributions ................................ 70 2.6.1 Uniform distribution ............................... 70 2.6.2 Normal distribution ............................... 72 2.6.3 Student t distribution .............................. 77 2.6.4 Cauchy distribution ............................... 81 2.6.5 Log-distributions .................................. 82 2.6.6 Wishart distribution ............................... 84 2.6.7 Empirical distribution .............................. 87 2.6.8 Order statistics ................................... 89 2.7 Special classes of distributions ............................ 91 2.7.1 Elliptical distributions ............................. 91 2.7.2 Stable distributions ................................ 96 2.7.3 Infinitely divisible distributions ..................... 98 2. T Technical appendix ...................................... www 2. E Exercises ............................................ www 3 Modeling the market ......................................101 3.1 The quest for invariance ..................................103 3.1.1 Equities, commodities, exchange rates ................105 3.1.2 Fixed-income market ..............................109 3.1.3 Derivatives .......................................114 3.2 Projection of the invariants to the investment horizon ........122 3.3 From invariants to market prices ..........................126 3.3.1 Raw securities ....................................126 3.3.2 Derivatives .......................................129 3.4 Dimension reduction .....................................131 3.1.1 Explicit factors ....................................133 3.4.2 Hidden factors ....................................138 3.4.3 Explicit vs. hidden factors ..........................143 3.4.4 Notable examples .................................145 3.4.5 Λ useful routine ...................................147 3.5 Case study: modeling the swap market .....................150 3.5.1 The market invariants .............................150 3.5.2 Dimension reduction ...............................151 3.5.3 The invariants at the investment horizon .............160 3.5.4 From invariants to prices ...........................162 Contents IX З.Т Technical appendix ...................................... www 3-Е Exercises ............................................ www Part II Classical asset allocation 4 Estimating the distribution of the market invariants .......169 4.1 Estimators .............................................171. 4.1.1 Definition ........................................172 4.1.2 Evaluation .......................................173 4.2 Nonparametric estimators ................................178 4.2.1 Location, dispersion and hidden factors ..............181 4.2.2 Explicit factors ....................................184 4.2.3 Kernel estimators .................................185 4.3 Maximum likelihood estimators ...........................186 4.3.1 Location, dispersion and hidden factors ..............190 4.3.2 Explicit factors ....................................192 4.3.3 The normal case ..................................1.93 4.4 Shrinkage estimators .....................................200 4.4.1 Location .........................................201 4.4.2 Dispersion and hidden factors .......................204 4.4.3 Explicit factors ....................................209 4.5 Robustness .............................................209 4.5.1 Measures of robustness .............................21.1 4.5.2 Robustness of previously introduced estimators ........216 4.5.3 Robust estimators .................................221 4.6 Practical tips ...........................................223 4.6.1 Detection of outliers ...............................223 4.6.2 Missing data ......................................229 4.6.3 Weighted estimates ................................232 4.6.4 Overlapping data ..................................234 4.6.5 Zero-mean invariants ..............................234 4.6.6 Model-implied estimation ...........................235 4.T Technical appendix ...................................... www 4. E Exercises ............................................ www 5 Evaluating allocations .....................................237 5.1 Investor s objectives .....................................239 5.2 Stochastic dominance ....................................243 5.3 Satisfaction .............................................249 5.4 Certainty-equivalent (expected utility) .....................260 5.4.1 Properties ........................................262 5.4.2 Building utility functions ...........................270 5.4.3 Explicit dependence on allocation ...................274 5.4.4 Sensitivity analysis ................................276 5.5 Quantile (value at risk) ..................................277 5.5.1 Properties ........................................278 X Contents 5.5.2 Explicit dependence on allocation ...................282 5.5.3 Sensitivity analysis ................................285 5.6 Coherent indices (expected shortfall) .......................287 5.6.1 Properties ........................................288 5.6.2 Building coherent indices ...........................292 5.6.3 Explicit dependence on allocation ...................296 5.6.4 Sensitivity analysis ................................298 5.Ϊ Technical appendix ...................................... www 5.E Exercises ............................................ www 6 Optimizing allocations .....................................301 6.1 The general approach ....................................302 6.1.1 Collecting information on the investor ................303 6.1.2 Collecting information on the market ................305 6.1.3 Computing the optimal allocation ...................306 6.2 Constrained optimization .................................311 6.2.1 Positive orthants: linear programming ................313 6.2.2 Ice-cream cones: second-order cone programming ......313 6.2.3 Semidefinite cones: semidefmite programming .........315 6.3 The mean-variance approach ..............................315 6.3.1 The geometry of allocation optimization ..............316 6.3.2 Dimension reduction: the mean-variance framework .... 319 6.3.3 Setting up the mean-variance optimization ............320 6.3.4 Mean-variance in terms of returns ...................323 6.4 Analytical solutions of the mean-variance problem ...........326 6.4.1 Efficient frontier with affine constraints ...............327 6.4.2 Efficient frontier with linear constraints ..............330 6.4.3 Effects of correlations and other parameters ..........332 6.4.4 Effects of the market dimension .....................335 6.5 Pitfalls of the mean-variance framework ....................336 6.5.1 MV as an approximation ...........................336 6.5.2 MV as an index of satisfaction ......................338 6.5.3 Quadratic programming and dual formulation .........340 6.5.4 MV on returns: estimation versus optimization ........342 6.5.5 MV on returns: investment at different horizons .......343 6.6 Total-return versus benchmark allocation ...................347 6.7 Case study: allocation in stocks ...........................354 6.7.1 Collecting information on the investor ................355 6.7.2 Collecting information on the market ................355 6.7.3 Computing the optimal allocation ...................357 6. Τ Technical appendix ...................................... www 6. E Exercises ............................................ www Contents XI Part III Accounting for estimation risk Estimating the distribution of the market invariants .......363 7.1 Bayesian estimation ......................................364 7.1.1 Baycsian posterior distribution ......................364 7.1.2 Summarizing the posterior distribution ...............366 7.1.3 Computing the posterior distribution ................369 7.2 Location and dispersion parameters ........................370 7.2.1 Computing the posterior distribution ................370 7.2.2 Summarizing the posterior distribution ...............373 7.3 Explicit factors ..........................................377 7.3.1 Computing the posterior distribution ................377 7.3.2 Summarizing the posterior distribution ...............380 7.4 Determining the prior ....................................383 7.4.1 Allocation-implied parameters ......................385 7.4.2 Likelihood maximization ...........................387 7.T Technical appendix ...................................... www 7.E Exercises ............................................ www Evaluating allocations .....................................389 8.1 Allocations as decisions ..................................390 8.1.1 Opportunity cost of a sub-optimal allocation ..........390 8.1.2 Opportunity cost as function of the market parameters . 394 8.1.3 Opportunity cost as loss of an estimator ..............397 8.1.4 Evaluation of a generic allocation decision ............401 8.2 Prior allocation .........................................403 8.2.1 Definition ........................................403 8.2.2 Evaluation .......................................404 8.2.3 Discussion ........................................406 8.3 Sample-based allocation ..................................407 8.3.1 Definition ........................................407 8.3.2 Evaluation .......................................408 8.3.3 Discussion ........................................412 8.T Technical appendix ...................................... www 8. E Exercises ............................................ www Optimizing allocations .....................................417 9.1 Bayesian allocation ......................................418 9.1.1 Utility maximization ...............................419 9.1.2 Classical-equivalent maximization ...................421 9.1.3 Evaluation .......................................422 9.1.4 Discussion ........................................425 9.2 Black-Litterman allocation ...............................426 9.2.1 General definition .................................426 9.2.2 Practicable definition: linear expertise on normal markets ..........................................429 9.2.3 Evaluation .......................................433 9.2.4 Discussion ........................................436 XII Contents 9.3 Resampled allocation ....................................437 9.3.1 Practicable definition: the mean-variance setting ......438 9.3.2 General definition .................................440 9.3.3 Evaluation .......................................443 9.3.4 Discussion ........................................445 9.4 Robust allocation ........................................445 9.4.1 General definition .................................445 9.4.2 Practicable definition: the mean-variance setting ......450 9.4.3 Discussion ........................................453 9.5 Robust Bavesian allocation ...............................454 9.5.1 General definition .................................455 9.5.2 Practicable definition: the mean-variance setting ......457 9.5.3 Discussion ........................................459 9. Τ Technical appendix ...................................... www 9.E Exercises ............................................ www Part IV Appendices A Linear algebra .............................................465 A.I Vector space ............................................465 A.2 Basis ..................................................468 A.3 Linear transformations ...................................469 A.3.1 Matrix representation ..............................470 A.3.2 Rotations ........................................471 A.4 Invariants ..............................................472 A.4.1 Determinant ......................................472 A.4.2 Trace ............................................474 A.4.3 Eigenvalues .......................................474 A. 5 Spectral theorem ........................................475 A. 5.1 Analytical result ..................................475 A. 5.2 Geometrical interpretation ..........................478 A.6 Matrix operations .......................................480 A.6.1 useful identities ...................................480 A.6. 2 Tensors and Kronecker product .....................482 A.6.3 The vec and vech operators .....................483 A. 6.4 Matrix calculus ...................................485 В Functional Analysis ........................................487 B.I Vector space ............................................487 B.2 Basis ..................................................490 B.3 Linear operators .........................................493 B.3.1 Kernel representations .............................494 B.3. 2 Unitary operators .................................494 B.4 Régularisation ..........................................496 B.5 Expectation operator ....................................499 B.6 Some special functions ...................................501 Contents XIII References .....................................................505 List of figures ..................................................515 Notation .......................................................519 Index ..........................................................525
adam_txt	Contents Preface . XV Audience and style . XVII Structure of the work .XVIII A guided tour by means of a simplistic example .XIX Acknowledgments .XXVI Part I The statistics of asset allocation 1 Univariate statistics . 3 1.1 Building blocks . 3 1.2 Summary statistics . 9 1.2.1 Location . 9 1.2.2 Dispersion . 11 1.2.3 Higher-order statistics . 14 1.2.4 Graphical representations . 15 1.3 Taxonomy of distributions . 16 1.3.1 Uniform distribution . 16 1.3.2 Normal distribution . 18 .1.3.3 Cauchy distribution . 20 1.3.4 Student t distribution . 22 1.3.5 Lognormal distribution . 24 1.3.6 Gamma distribution . 26 1.3.7 Empirical distribution . 28 l.T Technical appendix . www l.E Exercises . www 2 Multivariate statistics . 33 2.1 Building blocks . 34 2.2 Factorization of a distribution . 38 2.2.1 Marginal distribution . 38 2.2.2 Copulas . 40 Vili Contents 2.3 Dependence . 45 2.4 Shape summary statistics . 48 2.4.1 Location . 48 2.4.2 Dispersion . 50 2.4.3 Location-dispersion ellipsoid . 54 2.4.4 Higher-order statistics . 57 2.5 Dependence summary statistics . 59 2.5.1 Measures of dependence . 59 2.5.2 Measures of concordance . 64 2.5.3 Correlation . 67 2.6 Taxonomy of distributions . 70 2.6.1 Uniform distribution . 70 2.6.2 Normal distribution . 72 2.6.3 Student t distribution . 77 2.6.4 Cauchy distribution . 81 2.6.5 Log-distributions . 82 2.6.6 Wishart distribution . 84 2.6.7 Empirical distribution . 87 2.6.8 Order statistics . 89 2.7 Special classes of distributions . 91 2.7.1 Elliptical distributions . 91 2.7.2 Stable distributions . 96 2.7.3 Infinitely divisible distributions . 98 2. T Technical appendix . www 2. E Exercises . www 3 Modeling the market .101 3.1 The quest for invariance .103 3.1.1 Equities, commodities, exchange rates .105 3.1.2 Fixed-income market .109 3.1.3 Derivatives .114 3.2 Projection of the invariants to the investment horizon .122 3.3 From invariants to market prices .126 3.3.1 Raw securities .126 3.3.2 Derivatives .129 3.4 Dimension reduction .131 3.1.1 Explicit factors .133 3.4.2 Hidden factors .138 3.4.3 Explicit vs. hidden factors .143 3.4.4 Notable examples .145 3.4.5 Λ useful routine .147 3.5 Case study: modeling the swap market .150 3.5.1 The market invariants .150 3.5.2 Dimension reduction .151 3.5.3 The invariants at the investment horizon .160 3.5.4 From invariants to prices .162 Contents IX З.Т Technical appendix . www 3-Е Exercises . www Part II Classical asset allocation 4 Estimating the distribution of the market invariants .169 4.1 Estimators .171. 4.1.1 Definition .172 4.1.2 Evaluation .173 4.2 Nonparametric estimators .178 4.2.1 Location, dispersion and hidden factors .181 4.2.2 Explicit factors .184 4.2.3 Kernel estimators .185 4.3 Maximum likelihood estimators .186 4.3.1 Location, dispersion and hidden factors .190 4.3.2 Explicit factors .192 4.3.3 The normal case .1.93 4.4 Shrinkage estimators .200 4.4.1 Location .201 4.4.2 Dispersion and hidden factors .204 4.4.3 Explicit factors .209 4.5 Robustness .209 4.5.1 Measures of robustness .21.1 4.5.2 Robustness of previously introduced estimators .216 4.5.3 Robust estimators .221 4.6 Practical tips .223 4.6.1 Detection of outliers .223 4.6.2 Missing data .229 4.6.3 Weighted estimates .232 4.6.4 Overlapping data .234 4.6.5 Zero-mean invariants .234 4.6.6 Model-implied estimation .235 4.T Technical appendix . www 4. E Exercises . www 5 Evaluating allocations .237 5.1 Investor's objectives .239 5.2 Stochastic dominance .243 5.3 Satisfaction .249 5.4 Certainty-equivalent (expected utility) .260 5.4.1 Properties .262 5.4.2 Building utility functions .270 5.4.3 Explicit dependence on allocation .274 5.4.4 Sensitivity analysis .276 5.5 Quantile (value at risk) .277 5.5.1 Properties .278 X Contents 5.5.2 Explicit dependence on allocation .282 5.5.3 Sensitivity analysis .285 5.6 Coherent indices (expected shortfall) .287 5.6.1 Properties .288 5.6.2 Building coherent indices .292 5.6.3 Explicit dependence on allocation .296 5.6.4 Sensitivity analysis .298 5.Ϊ Technical appendix . www 5.E Exercises . www 6 Optimizing allocations .301 6.1 The general approach .302 6.1.1 Collecting information on the investor .303 6.1.2 Collecting information on the market .305 6.1.3 Computing the optimal allocation .306 6.2 Constrained optimization .311 6.2.1 Positive orthants: linear programming .313 6.2.2 Ice-cream cones: second-order cone programming .313 6.2.3 Semidefinite cones: semidefmite programming .315 6.3 The mean-variance approach .315 6.3.1 The geometry of allocation optimization .316 6.3.2 Dimension reduction: the mean-variance framework . 319 6.3.3 Setting up the mean-variance optimization .320 6.3.4 Mean-variance in terms of returns .323 6.4 Analytical solutions of the mean-variance problem .326 6.4.1 Efficient frontier with affine constraints .327 6.4.2 Efficient frontier with linear constraints .330 6.4.3 Effects of correlations and other parameters .332 6.4.4 Effects of the market dimension .335 6.5 Pitfalls of the mean-variance framework .336 6.5.1 MV as an approximation .336 6.5.2 MV as an index of satisfaction .338 6.5.3 Quadratic programming and dual formulation .340 6.5.4 MV on returns: estimation versus optimization .342 6.5.5 MV on returns: investment at different horizons .343 6.6 Total-return versus benchmark allocation .347 6.7 Case study: allocation in stocks .354 6.7.1 Collecting information on the investor .355 6.7.2 Collecting information on the market .355 6.7.3 Computing the optimal allocation .357 6. Τ Technical appendix . www 6. E Exercises . www Contents XI Part III Accounting for estimation risk Estimating the distribution of the market invariants .363 7.1 Bayesian estimation .364 7.1.1 Baycsian posterior distribution .364 7.1.2 Summarizing the posterior distribution .366 7.1.3 Computing the posterior distribution .369 7.2 Location and dispersion parameters .370 7.2.1 Computing the posterior distribution .370 7.2.2 Summarizing the posterior distribution .373 7.3 Explicit factors .377 7.3.1 Computing the posterior distribution .377 7.3.2 Summarizing the posterior distribution .380 7.4 Determining the prior .383 7.4.1 Allocation-implied parameters .385 7.4.2 Likelihood maximization .387 7.T Technical appendix . www 7.E Exercises . www Evaluating allocations .389 8.1 Allocations as decisions .390 8.1.1 Opportunity cost of a sub-optimal allocation .390 8.1.2 Opportunity cost as function of the market parameters . 394 8.1.3 Opportunity cost as loss of an estimator .397 8.1.4 Evaluation of a generic allocation decision .401 8.2 Prior allocation .403 8.2.1 Definition .403 8.2.2 Evaluation .404 8.2.3 Discussion .406 8.3 Sample-based allocation .407 8.3.1 Definition .407 8.3.2 Evaluation .408 8.3.3 Discussion .412 8.T Technical appendix . www 8. E Exercises . www Optimizing allocations .417 9.1 Bayesian allocation .418 9.1.1 Utility maximization .419 9.1.2 Classical-equivalent maximization .421 9.1.3 Evaluation .422 9.1.4 Discussion .425 9.2 Black-Litterman allocation .426 9.2.1 General definition .426 9.2.2 Practicable definition: linear expertise on normal markets .429 9.2.3 Evaluation .433 9.2.4 Discussion .436 XII Contents 9.3 Resampled allocation .437 9.3.1 Practicable definition: the mean-variance setting .438 9.3.2 General definition .440 9.3.3 Evaluation .443 9.3.4 Discussion .445 9.4 Robust allocation .445 9.4.1 General definition .445 9.4.2 Practicable definition: the mean-variance setting .450 9.4.3 Discussion .453 9.5 Robust Bavesian allocation .454 9.5.1 General definition .455 9.5.2 Practicable definition: the mean-variance setting .457 9.5.3 Discussion .459 9. Τ Technical appendix . www 9.E Exercises . www Part IV Appendices A Linear algebra .465 A.I Vector space .465 A.2 Basis .468 A.3 Linear transformations .469 A.3.1 Matrix representation .470 A.3.2 Rotations .471 A.4 Invariants .472 A.4.1 Determinant .472 A.4.2 Trace .474 A.4.3 Eigenvalues .474 A. 5 Spectral theorem .475 A. 5.1 Analytical result .475 A. 5.2 Geometrical interpretation .478 A.6 Matrix operations .480 A.6.1 useful identities .480 A.6. 2 Tensors and Kronecker product .482 A.6.3 The "vec" and "vech" operators .483 A. 6.4 Matrix calculus .485 В Functional Analysis .487 B.I Vector space .487 B.2 Basis .490 B.3 Linear operators .493 B.3.1 Kernel representations .494 B.3. 2 Unitary operators .494 B.4 Régularisation .496 B.5 Expectation operator .499 B.6 Some special functions .501 Contents XIII References .505 List of figures .515 Notation .519 Index .525
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id	DE-604.BV023305342
illustrated	Illustrated
index_date	2024-07-02T20:48:15Z
indexdate	2024-07-09T21:15:26Z
institution	BVB
isbn	9783540222132 9783642009648
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016489722
oclc_num	191850989
open_access_boolean
owner	DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-1043 DE-521
owner_facet	DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-1043 DE-521
physical	XXVI, 532 S. zahlr. graph. Darst. 25 cm
publishDate	2007
publishDateSearch	2007
publishDateSort	2007
publisher	Springer
record_format	marc
series2	Springer finance
spelling	Meucci, Attilio Verfasser aut Risk and asset allocation Attilio Meucci Corr. 3. print. Berlin [u.a.] Springer 2007 XXVI, 532 S. zahlr. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Springer finance Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references (p. [505]-513) and index Asset allocation Portfolio management Risk management Multivariate analysis Portfolio Selection (DE-588)4046834-3 gnd rswk-swf Risikomanagement (DE-588)4121590-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Portfolio Selection (DE-588)4046834-3 s Finanzmathematik (DE-588)4017195-4 s Risikomanagement (DE-588)4121590-4 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-27904-4 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016489722&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Meucci, Attilio Risk and asset allocation Asset allocation Portfolio management Risk management Multivariate analysis Portfolio Selection (DE-588)4046834-3 gnd Risikomanagement (DE-588)4121590-4 gnd Finanzmathematik (DE-588)4017195-4 gnd
subject_GND	(DE-588)4046834-3 (DE-588)4121590-4 (DE-588)4017195-4
title	Risk and asset allocation
title_auth	Risk and asset allocation
title_exact_search	Risk and asset allocation
title_exact_search_txtP	Risk and asset allocation
title_full	Risk and asset allocation Attilio Meucci
title_fullStr	Risk and asset allocation Attilio Meucci
title_full_unstemmed	Risk and asset allocation Attilio Meucci
title_short	Risk and asset allocation
title_sort	risk and asset allocation
topic	Asset allocation Portfolio management Risk management Multivariate analysis Portfolio Selection (DE-588)4046834-3 gnd Risikomanagement (DE-588)4121590-4 gnd Finanzmathematik (DE-588)4017195-4 gnd
topic_facet	Asset allocation Portfolio management Risk management Multivariate analysis Portfolio Selection Risikomanagement Finanzmathematik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016489722&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT meucciattilio riskandassetallocation

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