Optimal portfolio choice under parameter uncertainty:
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| Format: | Thesis Book |
| Language: | English |
| Published: |
2011
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| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 235 S. graph. Darst. |
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| 008 | 110404s2011 d||| m||| 00||| eng d | ||
| 028 | 5 | 2 | |a Dissertation Nr. 3837 |
| 035 | |a (OCoLC)729950557 | ||
| 035 | |a (DE-599)BVBBV037317049 | ||
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| 100 | 1 | |a Merz, Rolf |d 1975- |e Verfasser |0 (DE-588)143914855 |4 aut | |
| 245 | 1 | 0 | |a Optimal portfolio choice under parameter uncertainty |c submitted by Rolf Merz |
| 264 | 1 | |c 2011 | |
| 300 | |a XVII, 235 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a St. Gallen, Univ., Diss., 2010 | ||
| 650 | 0 | 7 | |a Portfolio Selection |0 (DE-588)4046834-3 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
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| _version_ | 1804145594541801472 |
|---|---|
| adam_text | Contents
Chapter
1
Introduction
1
1.1
The parameter certainty case
................................ 4
1.2
The parameter uncertainty case
............................... 5
1.3
Baycsian solution
....................................... 9
1.4
Risk function
......................................... 10
1.4.1
Certainty equivalent loss
............................... 11
1.4.2
Alternative measures for assessing parameter uncertainty
............ 12
1.4.2.1
Expected utility
.............................. 12
1.4.2.2
Bayes
risk against frequentist
risk
.................... 13
1.4.2.3
Sharpe
ratio
................................ 13
1.4.2.4
Portfolio weights
.............................. 13
1.5
What is missing?
....................................... 14
1.5.1
Choice of utility function
.............................. 14
1.5.2
Constraint(s) on the portfolio weights
....................... 15
1.5.2.1
Budget constraint
............................. 15
1.5.2.2
Short selling constraint
.......................... 17
1.5.2.3
Four cases of investment conditions
................... 18
1.5.3
Resampling vs.
Bayes
solution
........................... 18
1.5.4
Shrinkage estimation and ambiguity aversion
................... 20
1.5.5
Higher moments in the utility function
....................... 20
1.5.6
Non-normally distributed returns
.......................... 21
1.5.6.1
Estimation of a non-normal multivariatc return model
......... 21
1.5.6.2
Derivation of the Bayesian predictive distribution
........... 22
1.5.7
Expected portfolio weights instead of out-of-sample performance
........ 22
1.6
Data and Software
...................................... 23
1.6.1
Software implementation
.............................. 23
1.6.2
Monthly data
1970-2008............................... 25
1.6.3
Data sub-samples
(1970-1989
and
1989-2008)................... 27
1.7
Outline
............................................ 29
2
Resampling based framework
31
2.1
Introduction
.......................................... 31
2.2
Resampling
.......................................... 32
2.2.1
Resampling based on model parameters
...................... 32
2.2.1.1
Two-fund rules
............................... 33
2.2.1.2
Improved Two-fund rule
.......................... 35
2.2.2
Resampling based on predictive returns
...................... 36
2.2.2.1
Predictive moments
............................ 36
2.2.2.2
Not maximizing the expected utility
................... 38
2.2.2.3
Different histories
............................. 30
2.3
Empirical results
....................................... 40
2.3.1
Monthly data
1970-2008............................... 40
2.3.1.1
Expected utility
.............................. 40
2.3.1.2
Out-of-sample
Sharpe
ratio
........................ 43
2.3.1.3
Different risk aversion
........................... 45
2.3.1.4
Portfolio weights
.............................. 50
2.3.1.5
Wealth allocation
............................. 54
2.3.1.6
CRRA utility function
........................... 54
2.3.2
Monthly data
1970-1989............................... 57
2.3.2.1
Expected utility
.............................. 57
2.3.2.2
Out-of-sample
Sharpe
ratio
........................ 58
2.3.3
Monthly data
1989-2008............................... 59
2.3.3.1
Expected utility
.............................. 59
2.3.3.2
Out-of-sample
Sharpe
ratio
........................ 60
2.3.3.3
Conclusions
................................. 62
Baycsian framework
65
3.1
Introduction
.......................................... 65
3.2
Bayesian approach
...................................... 66
3.3
Implementing the Baycsian solution
............................ 68
3.3.1
Solving an average problem
............................. 68
3.3.2
A remark regarding informed priors
........................ 69
3.3.3
Immediate conclusions for the Bayesian portfolio choice problem
........ 70
3.4
The multivariate integration problem
............................ 71
3.4.1
Solving the multivariate integration problem
................... 71
3.4.2
Quadrature methods with known posterior distribution
............. 74
3.4.2.1
Importance Sampling
........................... 74
3.4.2.2
Adaptive Importance Sampling
...................... 75
3.4.2.3
Multiple Quadrature Integration
..................... 76
3.4.2.4
Subregion Adaptive Integration
..................... 78
3.4.3
Monte Carlo methods with unknown posterior distribution
........... 84
3.4.3.1
Simple importance sampling
....................... 84
3.4.3.2
Mixed integration
............................. 87
3.4.4
Numerical issues in computing the Hesse matrix of the parameters
....... 90
3.4.4.1
Generalized Cholesky decomposition
................... 91
3.4.4.2
Gill-Murray factorization
......................... 91
3.4.4.3
Sclmabel-Eskow Cholesky factorization
................. 92
3.4.5
MCMC approach
................................... 93
3.5
Empirical results
....................................... 93
3.5.1
Monthly data
1970-2008............................... 94
3.5.1.1
Expected utility
.............................. 94
3.5.1.2
Sharpe
ratio
................................ 95
3.5.1.3
Portfolio weights
.............................. 95
3.5.1.4
Wealth allocation
............................. 97
3.5.1.5
CRRA utility function
........................... 97
3.5.2
Monthly data
1970-1989............................... 98
3.5.2.1
Expected utility
.............................. 98
3.5.2.2
Sharpe
ratio
................................ 99
3.5.3
Monthly data
1989-2008............................... 101
3.5.3.1
Expected utility
.............................. 101
3.5.3.2
Sharpe
ratio
................................ 101
3.5.4
Conclusions
...................................... 103
4
Confidence
bands, Shrinkage and Ambiguity Aversion
105
4.1
Shrinkage estimation and robust optimization
....................... 106
4.1.1
Shrinkage estimation
................................. 106
4.1.2
James-Stein Estimator
................................ 107
4.1.3
Frost-Savarino Estimator
.............................. 109
4.1.4
Stein Covariance Estimation
............................ 109
4.1.5
Bayes-Stein Shrinkage
................................ 109
4.1.6
Robust portfolio choice
............................... 110
4.2
Incorporating parameter uncertainty into the utility function
.............. 110
4.2.1
Confidence intervals
.................................
Ill
4.2.1.1
Classical view with respect to confidence intervals
...........
Ill
4.2.1.2
Bayesmn view with respect to confidence intervals
........... 112
4.2.1.3
Likelihood approach for estimating confidence intervals
........ 112
4.2.2
Ambiguity aversion
.................................. 113
4.2.2.1
Joint distributional assumption
...................... 114
4.2.2.2
Asset specific confidence intervals
.................... 114
4.3
Quantifying Parameter Uncertainty: Multivanate Fitting and The Error Matrix
... 115
4.3.1
X 2 minimization and likelihood maximization
................... 116
4.3.2
Estimating the parameter uncertainties involved in a portfolio
.......... 117
4.3.3
The error matrix
................................... 119
4.3.4
Estimating the error matrix
............................. 120
4.3.4.1
Second derivative of the log-likelihood at its maximum
........ 120
4.3.4.2
Non-parabolic log-likelihood approach
.................. 121
4.3.5
Positive definitencss
................................. 122
4.4
Empirical results
....................................... 122
4.4.1
Monthly data
1970-2008............................... 122
4.4.1.1
Expected utility
.............................. 122
4.4.1.2
Sharpe
ratio
................................ 124
4.4.2
Monthly data
1970-1989............................... 126
4.4.2.1
Expected utility
.............................. 126
4.4.2.2
Sharpe
ratio
................................ 128
4.4.3
Monthly data
1989-2008............................... 128
4.4.3.1
Expected utility
.............................. 128
4.4.3.2
Sharpe
ratio
................................ 128
4.4.4
Conclusion
...................................... 132
5
Non-normality
133
5.1
Empirical evidence on non-normality of returns
...................... 133
5.1.1
Fat tails
........................................ 133
5.1.2
Return asymmetry
.................................. 134
5.2
Testing normality with goodness-of-fit tests
........................ 134
5.2.1
The role of the empirical distribution function (EDF)
.............. 135
5.2.2
Choice of goodness-of-fit test
............................ 136
5.2.3
χ2
goodness-of-fit test
................................ 137
5.2.4
EDF statistics
.................................... 139
5.2.4.1
Kolmogorov-Smirnov test
......................... 139
5.2.4.2
Cramér-von Mises
IV 2
........................... 141
5.2.4.3
Anderson-Darling
Ä2
and Watson U2
.................. 141
5.2.4.4
Shapiro/Wilk
W
test
........................... 144
5.2.4.5
D Agostino
s D
test
............................ 145
5.2.4.6
D Agostino/Pearson K2
.......................... 145
5.2.4.7
Test of skewness ( /b{)
.......................... 148
5.2.4.8
Test of kurtosis (62)
............................ 148
5.2.5
Results for the goodncss-of-fit tests
......................... 149
5.3
Normal and Non-normal multivariate return models
................... 149
5.3.1
Lack of multivariate distributions
.......................... 149
5.3.2
A brief discussion on feasible multivariate distributions
............. 151
5.3.2.1
Candidate distributions for modeling fat tails
.............. 151
5.3.2.2
Candidate distributions for modeling skewness
............. 152
5.3.3
Multivariate elliptical distributions
......................... 153
5.3.4
Multivariate normal (MVN) distribution
...................... 153
5.3.5
Multivariate student-i
(MVT)
distribution
..................... 156
5.3.6
Multivariate skew normal (MSN) distribution
................... 157
5.3.7
Multivariate skew
t (MST)
distribution
...................... 158
5.3.8
Estimation and fitting multivariate distributions to data
............. 159
5.3.8.1
Normal Transformation
.......................... 159
5.3.8.2
Maximum Likelihood
........................... 160
5.3.8.3
EM Algorithm
............................... 161
5.3.8.4
Fitting the
MVT,
MSN and MST distribution
............. 162
5.4
Generating multivariate data from normal and non-normal distributions
........ 164
5.4.1
Scheuer-Stoller procedure (MVN random samples)
................ 164
5.4.2
MVT
random samples
................................ 165
5.4.3
Bradley-Fleisher procedure
............................. 165
5.4.3.1
Generation of a multivariate normal random sample using the GLD
distribution
................................. 166
5.4.3.2
Generation of a multivariate non-normal random sample using the
GLD distribution
............................. 168
5.5
Empirical results
....................................... 170
5.5.1
Monthly data
1970-2008............................... 170
5.5.1.1
Parameter estimates
............................ 170
5.5.1.2
Portfolio weights and portfolio statistics
................. 172
5.5.2
Monthly data
1970-1989............................... 173
5.5.2.1
Parameter estimates
............................ 173
5.5.2.2
Portfolio weights and portfolio statistics
................. 173
5.5.3
Monthly data
1989-2008............................... 177
5.5.3.1
Parameter estimates
............................ 177
5.5.4
Portfolio weights and portfolio statistics
...................... 177
5.5.5
Conclusion
...................................... 178
6
Higher moments
181
6.1
Introduction
.......................................... 181
6.2
Economic importance of higher moments
.......................... 182
6.3
CRRA utility function with higher moments
........................ 183
6.4
Extended resampling procedure
............................... 184
6.5
Empirical results
....................................... 186
6.5.1
Expected utility
................................... 186
6.5.2
Sharpe
ratio
...................................... 186
6.5.3
Conclusion
...................................... 186
7
Concluding remarks
191
Appendix
A Decision with Estimation Uncertainty
193
A.I Optimal portfolio choice under a non-informative prior
.................. 193
A.
2
Michauďs resampled
efficiency approach
.......................... 195
A.3 Optimal two-fund rule
....................................
19G
A.
4
Mixture Densities Parameters via the EM Algorithm
................... 198
В
GLD distribution
203
D.I RS parametrization
...................................... 203
B.2 FMKL parametrization
................................... 204
B.2.1 Estimation methods for fitting the GLD distribution to data
.......... 204
B.2.
2
Moment-matching method
.............................. 205
B.2.
2.1
Moment-matching method with RS parametrization
.......... 205
B.2.
2.2
Moment-matching method with FMKL parametrization
........ 207
B.2.3 Fitting the GLD distribution using the (Q3,Q4) method
............. 208
B.2.
4
Fitting the GLD distribution using the Starship method
............. 210
Abbreviations
211
Glossary
213
Operators
217
Bibliography
219
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| author_GND | (DE-588)143914855 |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T23:21:56Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022471334 |
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| owner_facet | DE-355 DE-BY-UBR DE-384 DE-188 DE-739 DE-703 |
| physical | XVII, 235 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| record_format | marc |
| spelling | Merz, Rolf 1975- Verfasser (DE-588)143914855 aut Optimal portfolio choice under parameter uncertainty submitted by Rolf Merz 2011 XVII, 235 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier St. Gallen, Univ., Diss., 2010 Portfolio Selection (DE-588)4046834-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Portfolio Selection (DE-588)4046834-3 s DE-188 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022471334&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Merz, Rolf 1975- Optimal portfolio choice under parameter uncertainty Portfolio Selection (DE-588)4046834-3 gnd |
| subject_GND | (DE-588)4046834-3 (DE-588)4113937-9 |
| title | Optimal portfolio choice under parameter uncertainty |
| title_auth | Optimal portfolio choice under parameter uncertainty |
| title_exact_search | Optimal portfolio choice under parameter uncertainty |
| title_full | Optimal portfolio choice under parameter uncertainty submitted by Rolf Merz |
| title_fullStr | Optimal portfolio choice under parameter uncertainty submitted by Rolf Merz |
| title_full_unstemmed | Optimal portfolio choice under parameter uncertainty submitted by Rolf Merz |
| title_short | Optimal portfolio choice under parameter uncertainty |
| title_sort | optimal portfolio choice under parameter uncertainty |
| topic | Portfolio Selection (DE-588)4046834-3 gnd |
| topic_facet | Portfolio Selection Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022471334&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT merzrolf optimalportfoliochoiceunderparameteruncertainty |