Verfügbarkeit: Optimal portfolio choice under parameter uncertainty

Optimal portfolio choice under parameter uncertainty:

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Bibliographische Detailangaben
Beteilige Person:	Merz, Rolf 1975- (VerfasserIn)
Format:	Hochschulschrift/Dissertation Buch
Sprache:	Englisch
Veröffentlicht:	2011
Schlagwörter:	Portfolio Selection Hochschulschrift
Links:	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
Umfang:	XVII, 235 S. graph. Darst.

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MARC


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Datensatz im Suchindex

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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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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
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