Multi-period portfolio optimization: with emphasis on a mean-variance criterion
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | German |
| Veröffentlicht: |
2000
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 195 S. graph. Darst. |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Contents
Preface v
Contents vii
List of figures ix
List of tables xi
1 Introduction 1
1.1 Uncertainty dynamics multi period approach 1
1.2 Organization 10
2 One period optimization 13
2.1 General setting 13
2.2 Utility based approach 18
2.3 Mean variance approach 28
2.4 Alternative one period approaches 36
2.5 Portfolio in proportional terms 39
3 Multi period asset allocation 43
3.1 Probabilistic structure 45
3.2 Evolution of wealth 48
3.3 General problem formulation 51
3.4 The mean variance criterion 54
3.5 A first approach: TOBlN s optimization 59
4 Dynamic programming approaches 65
4.1 The consumption/investment problem 66
4.2 The investment problem 72
4.3 Extension to continuous time 77
viii Contents
5 Stochastic programming in portfolio optimization 85
5.1 Scenario tree 86
5.2 Deterministic equivalent 88
5.3 Discretizations 94
5.4 Solving procedures and exemplary1 applications 96
5.4.1 Progressive hedging algorithm 96
5.4.2 Bi:ndi;rs decomposition 100
5.4.3 Direct method an example 103
6 Multistage mean variance optimization 107
6.1 Formulation of the model 108
6.2 Handling inequalities 109
6.3 Solving the problem 117
6.3.1 Without transaction costs 118
6.3.2 With transaction costs 126
6.3.3 Supplementary comments 131
7 Scenario generation 135
7.1 Return models in stochastic programming 135
7.2 Specification of return models 142
7.3 A specific discretization 145
Appendix 7: ARCH Modelling 148
8 Computational experiments 155
8.1 Estimations from historical data 156
8.2 A single optimization 160
8.2.1 Analyzing portfolio revisions 160
8.2.2 Analyzing final wealth 162
8.3 Rolling horizon 166
8.3.1 Description of the case study 166
8.3.2 Results 170
9 Conclusions 181
Bibliography 185
List of Figures
2.1 Modelling aspects of transaction costs 16
2.2 Quadratic utility function U (W) W aW2 27
2.3 Capital market line and efficient frontier. 33
3.1 Representation of scenarios 46
3.2 Multi stage network for the last periods 50
3.3 Quadratic utility function U(WT) = WT a W $ 58
5.1 Scenario tree of example 5.1 88
6.1 Barrier function (6.6) for /z = 1 (left) and /z = 01 (right) over the
feasible set Ill
6.2 Central path 112
6.3 Scenario aggregation of the tree 5.1 116
7.1 Process of quadratic quarterly return of the Swiss market index (MSCI
Switzerland) 141
7.2 Normal and log normal distribution vis a vis fat tails for the Swiss
stock index of the last quarter 1999 144
7.3 Transformation of the Hyperplane H under r with n = 2 146
7.4 Discretizations with/ = 1 for two different transformation matrices. . 149
7.5 Discretization with Z = 12 149
8.1 Expected log returns for individual assets given by the expected return
of their respective category from the first quarter of 1994 to the last
quarter of 1999 157
8.2 Observed and estimated volatilities 158
8.3 Observed and estimated volatilities 159
8.4 Two stage scenario tree 160
x List of figures
8.5 Cumulated distribution (upper figure) and density functions (lower
figure) of Wt for the optimal buy and hold (MARKOWITZ) strategy
and the optimal minimum variance strategy 165
8.6 Representation of time intervals within a two year horizon 168
8.7 Portfolio path of a 4 period optimization with an annual risk of 10%
(above: (b); below: (c)) 177
8.8 Portfolio path of a 4 and one period optimization (model (d)) with an
annual risk of 5% (above: one period; below: 4 period) 179
List of Tables
5.1 Progressive hedging algorithm 97
5.2 Benders decomposition for a two stage problem 101
6.1 Node wise factorization, transformation, and substitution for generat¬
ing z = # 1a 122
6.2 Node wise factorization, transformation, and substitution for generat¬
ing z = * xa 132
8.1 Optimization Results with three scenarios in monetary terms 161
8.2 Optimization Results with four scenarios in monetary terms 163
8.3 Set of efficient mean volatility combinations 163
8.4 Ex post statistics of individual assets 170
8.5 Efficient expected returns in per cent for four different levels of vola¬
tility 171
8.6 Performances of considered models 173
8.7 Comparison of the 4 period multistage model and the quarterly Mar
KOWITZ optimization 175
8.8 Transaction costs in monetary terms arising during the considered 24
periods 176
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:45:39Z |
| institution | BVB |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009160758 |
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| spelling | Siede, Heiko Verfasser aut Multi-period portfolio optimization with emphasis on a mean-variance criterion Heiko Siede 2000 X, 195 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier St. Gallen, Univ., Diss., 2000 Portfolio Selection (DE-588)4046834-3 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Mehr-Perioden-Modell (DE-588)4388956-6 gnd rswk-swf Methode der kleinsten Quadrate (DE-588)4038974-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Portfolio Selection (DE-588)4046834-3 s Optimierung (DE-588)4043664-0 s Mehr-Perioden-Modell (DE-588)4388956-6 s Methode der kleinsten Quadrate (DE-588)4038974-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009160758&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Siede, Heiko Multi-period portfolio optimization with emphasis on a mean-variance criterion Portfolio Selection (DE-588)4046834-3 gnd Optimierung (DE-588)4043664-0 gnd Mehr-Perioden-Modell (DE-588)4388956-6 gnd Methode der kleinsten Quadrate (DE-588)4038974-1 gnd |
| subject_GND | (DE-588)4046834-3 (DE-588)4043664-0 (DE-588)4388956-6 (DE-588)4038974-1 (DE-588)4113937-9 |
| title | Multi-period portfolio optimization with emphasis on a mean-variance criterion |
| title_auth | Multi-period portfolio optimization with emphasis on a mean-variance criterion |
| title_exact_search | Multi-period portfolio optimization with emphasis on a mean-variance criterion |
| title_full | Multi-period portfolio optimization with emphasis on a mean-variance criterion Heiko Siede |
| title_fullStr | Multi-period portfolio optimization with emphasis on a mean-variance criterion Heiko Siede |
| title_full_unstemmed | Multi-period portfolio optimization with emphasis on a mean-variance criterion Heiko Siede |
| title_short | Multi-period portfolio optimization |
| title_sort | multi period portfolio optimization with emphasis on a mean variance criterion |
| title_sub | with emphasis on a mean-variance criterion |
| topic | Portfolio Selection (DE-588)4046834-3 gnd Optimierung (DE-588)4043664-0 gnd Mehr-Perioden-Modell (DE-588)4388956-6 gnd Methode der kleinsten Quadrate (DE-588)4038974-1 gnd |
| topic_facet | Portfolio Selection Optimierung Mehr-Perioden-Modell Methode der kleinsten Quadrate Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009160758&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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