Introduction to risk parity and budgeting:
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| Format: | Book |
| Language: | English |
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Boca Raton
CRC Press, Taylor & Francis
2014
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| Series: | Chapman & Hall/CRC financial mathematics series
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIII, 410 S. graph. Darst. |
| ISBN: | 9781482207156 |
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| 245 | 1 | 0 | |a Introduction to risk parity and budgeting |c Thierry Roncalli |
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| adam_text | Titel: Introduction to risk parity and budgeting
Autor: Roncalli, Thierry
Jahr: 2014
Contents
Introduction i
List of Figures xiii
List of Tables xvii
List of Symbols and Notations xxi
I From Portfolio Optimization to Risk Parity 1
1 Modern Portfolio Theory 3
1.1 From optimized portfolios to the market portfolio ............4
1.1.1 The efficient frontier......................................4
1.1.1.1 Introducing the quadratic utility function . . 6
1.1.1.2 Adding some constraints......................9
1.1.1.3 Analytical solution..............................11
1.1.2 The tangency portfolio....................................12
1.1.3 Market equilibrium and CAPM..........................16
1.1.4 Portfolio optimization in the presence of a benchmark 19
1.1.5 The Black-Litterman model..............................22
1.1.5.1 Computing the implied risk premia..........23
1.1.5.2 The optimization problem......................24
1.1.5.3 Numerical implementation of the model ... 25
1.2 Practice of portfolio optimization ..............................27
1.2.1 Estimation of the covariance matrix....................27
1.2.1.1 Empirical covariance matrix estimator .... 27
1.2.1.2 Hayashi-Yoshida estimator....................29
1.2.1.3 G ARCH approach..............................32
1.2.1.4 Factor models..................................35
1.2.2 Designing expected returns..............................40
1.2.3 Regularization of optimized portfolios..................44
1.2.3.1 Stability issues..................................45
1.2.3.2 Resampling techniques ........................45
1.2.3.3 Denoising the covariance matrix..............47
1.2.3.4 Shrinkage methods..............................49
1.2.4 Introducing constraints ..................................53
1.2.4.1 Why regularization techniques are not suffi-
cient ..............................................54
1.2.4.2 How to specify the constraints................57
1.2.4.3 Shrinkage interpretation of the constrained so-
lution ............................................65
2 Risk Budgeting Approach 71
2.1 Risk allocation principle..........................................72
2.1.1 Properties of a risk measure..............................72
2.1.1.1 Coherency and convexity of risk measures . . 72
2.1.1.2 Euler allocation principle......................77
2.1.2 Risk contribution of portfolio assets ....................79
2.1.2.1 Computing the risk contributions ............79
2.1.2.2 Interpretation of risk contributions............82
2.1.3 Application to non-normal risk measures................84
2.1.3.1 Non-normal value-at-risk and expected short-
fall ..............................................84
2.1.3.2 Historical value-at-risk ........................92
2.2 Analysis of risk budgeting portfolios............................97
2.2.1 Definition of a risk budgeting portfolio..................98
2.2.1.1 The right specification of the RB portfolio . 99
2.2.1.2 Solving the non-linear system of risk budget-
ing contraints....................................102
2.2.2 Some properties of the RB portfolio....................102
2.2.2.1 Particular solutions with the volatility risk
measure..........................................102
2.2.2.2 Existence and uniqueness of the RB portfolio 108
2.2.3 Optimality of the risk budgeting portfolio..............113
2.2.4 Stability of the risk budgeting approach................116
2.3 Special case: the ERC portfolio..................................119
2.3.1 The two-asset case (n = 2) ..............................119
2.3.2 The general case (n 2)..................................121
2.3.3 Optimality of the ERC portfolio........................123
2.3.4 Back to the notion of diversification....................125
2.3.4.1 Diversification index............................125
2.3.4.2 Concentration indices..........................126
2.3.4.3 Difficulty of reconciling the different diversifi-
cation concepts..................................128
2.4 Risk budgeting versus weight budgeting........................130
2.4.1 Comparing weight budgeting and risk budgeting port-
folios ........................................................130
2.4.2 New construction of the minimum variance portfolio . 131
2.5 Using risk factors instead of assets..............................135
2.5.1 Pitfalls of the risk budgeting approach based on assets 135
2.5.1.1 Duplication invariance property..............135
2.5.1.2 Polico invariance property ....................137
2.5.1.3 Impact of the reparametrization on the asset
universe..........................................138
2.5.2 Risk decomposition with respect to the risk factors . . 141
2.5.3 Some illustrations ........................................144
2.5.3.1 Matching the risk budgets ....................144
2.5.3.2 Minimizing the risk concentration between the
risk factors......................................145
2.5.3.3 Solving the duplication and polico invariance
properties........................................146
II Applications of the Risk Parity Approach 149
3 Risk-Based Indexation 151
3.1 Capitalization-weighted indexation..............................152
3.1.1 Theory support............................................152
3.1.2 Constructing and replicating an equity index..........153
3.1.3 Pros and cons of CW indices............................154
3.2 Alternative-weighted indexation ................................157
3.2.1 Desirable properties of AW indices......................159
3.2.2 Fundamental indexation..................................160
3.2.3 Risk-based indexation....................................162
3.2.3.1 The equally weighted portfolio................163
3.2.3.2 The minimum variance portfolio..............164
3.2.3.3 The most diversified portfolio..................168
3.2.3.4 The ERC portfolio..............................172
3.2.3.5 Comparison of the risk-based allocation ap-
proaches ........................................173
3.3 Some illustrations ................................................181
3.3.1 Simulation of risk-based indices..........................181
3.3.2 Practical issues of risk-based indexation................183
3.3.3 Findings of other empirical works........................187
3.3.3.1 What is the best alternative-weighted indexa-
tion? ............................................187
3.3.3.2 Style analysis of alternative-weighted indexa-
tion ..............................................189
4 Application to Bond Portfolios 191
4.1 Some issues in bond management ..............................191
4.1.1 Debt-weighted indexation................................191
4.1.2 Yield versus risk..........................................193
4.2 Bond portfolio management ....................................194
4.2.1 Term structure of interest rates..........................194
4.2.2 Pricing of bonds..........................................197
4.2.2.1 Without default risk............................197
4.2.2.2 With default risk................................200
4.2.3 Risk management of bond portfolios....................203
4.2.3.1 Using the yield curve as risk factors..........204
4.2.3.2 Taking into account the default risk..........209
4.3 Some illustrations ................................................215
4.3.1 Managing risk factors of the yield curve................216
4.3.2 Managing sovereign credit risk..........................220
4.3.2.1 Measuring the credit risk of sovereign bond
portfolios........................................222
4.3.2.2 Comparing debt-weighted, gdp-weighted and
risk-based indexations..........................231
5 Risk Parity Applied to Alternative Investments 243
5.1 Case of commodities..............................................244
5.1.1 Why investing in commodities is different..............244
5.1.1.1 Commodity futures markets ..................244
5.1.1.2 How to define the commodity risk premium . 246
5.1.2 Designing an exposure to the commodity asset class . 247
5.1.2.1 Diversification return..........................247
5.1.2.2 Comparing EW and ERC portfolios..........251
5.2 Hedge fund strategies ............................................254
5.2.1 Position sizing ............................................254
5.2.2 Portfolio allocation of hedge funds......................257
5.2.2.1 Choosing the risk measure ....................258
5.2.2.2 Comparing ERC allocations ..................258
5.2.2.3 Budgeting the risk factors......................262
5.2.2.4 Limiting the turnover..........................265
6 Portfolio Allocation with Multi-Asset Classes 269
6.1 Construction of diversified funds................................270
6.1.1 Stock/bond asset mix policy ............................270
6.1.2 Growth assets versus hedging assets....................273
6.1.2.1 Are bonds growth assets or hedging assets? . 273
6.1.2.2 Analytics of these results......................277
6.1.3 Risk-balanced allocation..................................278
6.1.4 Pros and cons of risk parity funds ......................280
6.2 Long-term investment policy ....................................284
6.2.1 Capturing the risk premia................................285
6.2.2 Strategic asset allocation ................................286
6.2.2.1 Allocation between asset classes..............286
6.2.2.2 Asset classes or risk factor classes............288
6.2.2.3 Allocation within an asset class ..............291
6.2.3 Risk budgeting with liability constraints................294
6.3 Absolute return and active risk parity..........................294
Conclusion 299
A Technical Appendix 301
A.l Optimization problems ..........................................301
A. 1.1 Quadratic programming problem........................301
A.1.2 Non-linear unconstrained optimization..................303
A.1.3 Sequential quadratic programming algorithm..........306
A. 1.4 Numerical solutions of the RB problem ................307
A.2 Copula functions..................................................308
A.2.1 Definition and main properties..........................308
A.2.2 Parametric functions......................................312
A.2.3 Simulation of copula models..............................314
A.2.3.1 Distribution approach..........................314
A.2.3.2 Simulation based on conditional copula func-
tions ..............................................315
A.2.4 Copulas and risk management ..........................316
A.2.5 Multivariate survival modeling..........................319
A.3 Dynamic portfolio optimization ................................322
A.3.1 Stochastic optimal control................................322
A.3.1.1 Bellman approach..............................322
A.3.1.2 Martingale approach............................323
A.3.2 Portfolio optimization in continuous-time..............324
A.3.3 Some extensions of the Merton model..................326
A.3.3.1 Lifestyle funds..................................326
A.3.3.2 Lifecycle funds..................................329
A.3.3.3 Liability driven investment....................332
B Tutorial Exercises 337
B.l Exercises related to modern portfolio theory ..................337
B.l.l Markowitz optimized portfolios..........................337
B.l.2 Variations on the efficient frontier ......................338
B.l.3 Sharpe ratio................................................339
B.l.4 Beta coefficient............................................341
B.l.5 Tangency portfolio........................................342
B.l.6 Information ratio..........................................343
B.l.7 Building a tilted portfolio................................344
B.1.8 Implied risk premium ....................................345
B.l.9 Black-Litterman model ..................................346
B.l.10 Portfolio optimization with transaction costs..........347
B.l.11 Impact of constraints on the CAPM theory............348
B.l.12 Generalization of the Jagannathan-Ma shrinkage ap-
proach ......................................................349
B.2 Exercises related to the risk budgeting approach ..............351
B.2.1 Risk measures ............................................351
B.2.2 Weight concentration of a portfolio......................352
B.2.3 ERC portfolio..............................................353
B.2.4 Computing the Cornish-Fisher value-at-risk............354
B.2.5 Risk budgeting when risk budgets are not strictly posi-
tive ........................................................355
B.2.6 Risk parity and factor models............................356
B.2.7 Risk allocation with the expected shortfall risk measure 358
B.2.8 ERC optimization problem..............................359
B.2.9 Risk parity portfolios with skewness and kurtosis . . . 360
B.3 Exercises related to risk parity applications....................362
B.3.1 Computation of heuristic portfolios......................362
B.3.2 Equally weighted portfolio................................362
B.3.3 Minimum variance portfolio..............................363
B.3.4 Most diversified portfolio ................................365
B.3.5 Risk allocation with yield curve factors ................366
B.3.6 Credit risk analysis of sovereign bond portfolios .... 368
B.3.7 Risk contributions of long-short portfolios..............370
B.3.8 Risk parity funds..........................................371
B.3.9 The Frazzini-Pedersen model............................372
B.3.10 Dynamic risk budgeting portfolios......................374
Bibliography 377
Subject Index 399
Author Index 405
|
| any_adam_object | 1 |
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| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.601 |
| dewey-search | 332.601 |
| dewey-sort | 3332.601 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| language | English |
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| physical | XXIII, 410 S. graph. Darst. |
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| spelling | Roncalli, Thierry Verfasser (DE-588)1011210959 aut Introduction to risk parity and budgeting Thierry Roncalli Boca Raton CRC Press, Taylor & Francis 2014 XXIII, 410 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC financial mathematics series Risikomanagement (DE-588)4121590-4 gnd rswk-swf Portfoliomanagement (DE-588)4115601-8 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Risikomanagement (DE-588)4121590-4 s Portfoliomanagement (DE-588)4115601-8 s Finanzmathematik (DE-588)4017195-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026226516&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roncalli, Thierry Introduction to risk parity and budgeting Risikomanagement (DE-588)4121590-4 gnd Portfoliomanagement (DE-588)4115601-8 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4121590-4 (DE-588)4115601-8 (DE-588)4017195-4 |
| title | Introduction to risk parity and budgeting |
| title_auth | Introduction to risk parity and budgeting |
| title_exact_search | Introduction to risk parity and budgeting |
| title_full | Introduction to risk parity and budgeting Thierry Roncalli |
| title_fullStr | Introduction to risk parity and budgeting Thierry Roncalli |
| title_full_unstemmed | Introduction to risk parity and budgeting Thierry Roncalli |
| title_short | Introduction to risk parity and budgeting |
| title_sort | introduction to risk parity and budgeting |
| topic | Risikomanagement (DE-588)4121590-4 gnd Portfoliomanagement (DE-588)4115601-8 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Risikomanagement Portfoliomanagement Finanzmathematik |
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