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Title Page
ABSTRACT
Contents
Chapter 1. Introduction 12
1.1. Research Background 12
1.2. Dissertation Outline 14
Chapter 2. An Alternative Approach for Portfolio Performance Evaluation 16
2.1. Chapter Introduction 16
2.2. Performance Distribution of All Feasible Portfolios 18
2.2.1. Defining a Uniformly Distributed Random Portfolio 18
2.2.2. Probability Distribution of Sharpe Ratio of UDRP 21
2.2.3. UDRP with No-Short Constraint 26
2.3. Is UDRP Representative of All Feasible Portfolios? 30
2.4. Chapter Summary 36
Chapter 3. Performance Evaluation of Benchmark Portfolios 37
3.1. Chapter Introduction 37
3.2. Cap-weighted Portfolios 38
3.3. Equally-weighted Portfolios 39
3.4. Performance Evaluation via UDRP 40
3.5. Chapter Summary 46
Chapter 4. The Importance of Asset Allocation 48
4.1. Chapter Introduction 48
4.2. A Mathematical Justification for Asset Allocation 49
4.2.1. Portfolio Performance Distribution 49
4.2.2. Asset Allocation vs. Security Selection - In an Investor's Point of View 54
4.2.3. Asset Allocation vs. Security Selection - In the Market Point of View 58
4.3. Empirical Analysis 62
4.3.1. Criteria for a Well-designed Asset Universe 62
4.3.2. An Empirical Example - Style Classification in Equity Market 63
4.4. Chapter Summary 65
Chapter 5. The Importance of Asset Class Design 66
5.1. Chapter Introduction 66
5.2. Current Within-Stock Classification - Style and Industry 67
5.3. Optimal Asset Classification 69
5.3.1. Formulation 71
5.4. Cost of Asset Allocation 74
5.4.1. Performance Evaluation of Various Classification Schemes 74
5.4.2. Factor Analysis - Method of Classification, α or β? 78
5.5. Chapter Summary 81
Chapter 6. On the Viability of Robo-Advising for Individual Investors 83
6.1. Chapter Introduction 83
6.2. Construction of Optimal Mean-Variance Portfolio with a Limited Size 85
6.3. Empirical Analysis - The Impact of Portfolio Size on Portfolio Risk 88
6.4. Chapter Summary 93
Chapter 7. Conclusion 94
7.1. Proposition of New Methodologies 94
7.2. Findings on Diversification Strategies 95
7.2.1. Passive Investing and Performance Benchmarking 95
7.2.2. Asset Allocation and Asset Class Design 95
7.2.3. Robo-Advising and Financial Technology (FinTech) 96
Appendix A. Formulas for the Surface Area of the Intersection of Two Hyperspherical Caps 97
References 114
요약문 124
Figure 2.1: Relationship between θi and SR(wi/μ,Σ) in a three-asset market...(이미지참조) 23
Figure 2.2: Wunif outperforms Ws when LΣTWunif lies on the surface of the hyperspherical cap (dark blue)(이미지참조) 24
Figure 2.3: PDF (red) and CDF (blue) of the normalized Sharpe ratio of wunif...(이미지참조) 26
Figure 2.4: Feasible region corresponding to the no-short constraint (dark blue) 28
Figure 2.5: WFR+unif outperforms Ws when LΣTWFR+unif lies on the surface of C(LΣT1,θFR+)∩C(LΣTW*,θs)(이미지참조) 29
Figure 2.6: Comparison between the Sharpe ratio distributions of U.S. equity mutual funds (black bar charts),... 32
Figure 2.7: Comparison between the cumulative Sharpe ratio distributions of... 33
Figure 3.1-1: Historical performance rankings of cap-weighted portfolio among the non-negative UDRP... 43
Figure 3.1-2: Historical performance rankings of cap-weighted portfolio among the non-negative UDRP... 43
Figure 3.2-1: Historical performance rankings of equally-weighted portfolio among the non-negative UDRP... 44
Figure 3.2-2: Historical performance rankings of equally-weighted portfolio among the non-negative UDRP... 44
Figure 4.1: Relative performance level 54
Figure 4.2: Managerial skill √1-I2α-1(N-1/2,1/2)/1-I2α-1(n-1/2,1/2) (line) and asset class well-designedness k(D) (dashed line)(이미지참조) 57
Figure 4.3: Average of ε with respect to к(D) 63
Figure 4.4: Empirical ε and outperformance of style classification 64
Figure 5.1: Graphical representation of the concept of Optimal Asset Classification 70
Figure 5.2: Sharpe ratios of security selection and four classification schemes 75
Figure 5.3: Efficient frontiers of security selection and four classification schemes 76
Figure 5.4: Average correlations of four classification schemes 77
Figure 5.5: Sharpe ratios and average correlations of four classification schemes in the larger universe 79
Figure 5.6: Absolute sum of as of optimal and style asset classes 79
Figure 5.7: Factor loadings of optimal and style asset classes... 80
Figure 5.8: Market betas of the K-means clusters 81
Figure 6.1: Impact of budget on portfolio risk 89
Figure 6.2: Number of stocks in optimal portfolio 91
Figure 6.3: Number of stocks in optimal portfolio (solid line) compared with... 92
Figure A.1: Case 1 in Table A.1 98
Figure A.2: Cases 2 and 3 in Table A.1 100
Figure A.3: Cases 4 and 5 in Table A.1 101
Figure A.4: Case 8 in Table A.1(in R³) 102
Figure A.5: Case 8 in Table A.1 (in R²) 102
Figure A.6: Left part of the intersection in Figure A.5 as... 103
Figure A.7: Cases 6 and 7 in Table A.1 104
Figure A.8: Cases 9 and 10 in Table A.1 105
Figure A.9: Case 11 in Table A.1 106
Figure A.10: Case 12 in Table A.1 106
Figure A.11: Case 13 in Table A.1 107
Figure A.12: Case 14 in Table A.1 107
Figure A.13: Case 15 in Table A.1 108
Figure A.14: Case 16 in Table A.1 108
Figure A.15: Case 17 in Table A.1 109
Figure A.16: Case 18 in Table A.1 109
Figure A.17: Case 19 in Table A.1 110
Figure A.18: Case 20 in Table A.1 110
Figure A.19: Case 21 in Table A.1 111
Figure A.20: Case 22 in Table A.1 111
Figure A.21: Case 23 in Table A.1 112
Figure A.22: Case 24 in Table A.1 112
Figure A.23: Case 25 in Table A.1 113
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