硕士论文 Portfolio Optimization 137页│ Master of Science in Applied Economics & Finance
TABLE OF CONTENTS
FIGURES & TABLES ...................................................... 1
1. INTRODUCTION ....................................................2
1.1 BACKGROUND .............................2
1.2 RESEARCH QUESTIONS ................................. 3
1.3 MOTIVATION ............................................... 3
1.4 DELIMITATIONS & ASSUMPTIONS ................. 4
1.5 METHODOLOGY ................................ 5
2. LITERATURE REVIEW ......... 7
3. THEORETICAL FRAMEWORK ............................ 12
3.1 MODERN PORTFOLIO THEORY ..................................... 12
3.1.1 Mean-Variance Portfolio Selection ......................................... 12
3.1.2 Risk & Return ........................................................ 13
3.1.3 Efficient Portfolios ....................................................... 16
3.1.4 Calculating the Efficient Frontier ................................... 19
3.1.5 The Capital Asset Pricing Model ................................. 22
3.1.6 Critique against Modern Portfolio Theory ........................ 24
3.2 THE BLACK-LITTERMAN APPROACH .......................................... 25
3.2.1 A Very Brief Discussion regarding Bayes Theorem ............................. 26
3.2.2 The Original Reference Model ............................................................................................................ 27
3.2.3 The Alternative Reference Model ....................................................................................................... 30
3.2.4 Specifying Investor Views.................................................................................................................... 31
3.2.5 Tau, Measuring Investor Uncertainty ................................................................................................. 33
3.2.6 The Estimation Model ......................................................................................................................... 35
3.2.6.1 The Original Reference Model Revisited .................................................... 35
3.2.6.2 The Alternative Reference Model Revisited .................................................... 37
3.2.6.3 The difference between the two reference models ..................................................................................... 37
3.3 PERFORMANCE EVALUATION ............................................................................................................................. 38
3.3.1 The Sharpe Ratio ................................................................................................................................. 38
3.3.2 The Information Ratio ......................................................................................................................... 39
3.4 STATISTICAL TEST ............................................................................................................................................ 42
3.4.1 The Augmented Dickey-Fuller Test ..................................................................................................... 42
3.5 MARKET ANOMALIES ....................................................................................................................................... 43
3.5.1 The Size Anomaly ................................................................................................................................ 43
3.5.2 The Book-to-Market Anomaly ............................................................................................................ 45
3.5.3 Emerging Markets .............................................................................................................................. 46
4. DATA ............................................................................................................................................................... 48
4.1 SAMPLE DESCRIPTION....................................................................................................................................... 48
4.2 ASSET CLASSES ................................................................................................................................................ 50
4.2.1 MSCI US Large Cap Value ................................................................................................................... 51
4.2.2 MSCI US Large Cap Growth................................................................................................................. 51
4.2.3 MSCI US Small Cap .............................................................................................................................. 51
4.2.4 Stoxx Europe 600 Price Index EUR ...................................................................................................... 51
4.2.5 MSCI Emerging Markets ..................................................................................................................... 52
4.2.6 S&P 500 .............................................................................................................................................. 52
4.2.7 MSCI All Country World Investable Market Index ............................................................................... 52
4.2.7 The Risk Free Asset ............................................................................................................................. 52
4.2.8 Currencies ........................................................................................................................................... 53
4.3 RETURNS ....................................................................................................................................................... 53
5. ANALYSIS ....................................................................................................................................................... 55
5.1 PORTFOLIO DESCRIPTIONS & MODEL SETUP ......................................................................................................... 55
5.1.1 Mean-Variance Portfolios ................................................................................................................... 55
5.1.2 Black-Litterman Portfolios .................................................................................................................. 55
5.2 STATISTICAL TESTS ........................................................................................................................................... 58
5.2.1 The Benchmark Portfolio .................................................................................................................... 58
5.2.2 Portfolio 1 ........................................................................................................................................... 58
5.2.3 Portfolio 2 ........................................................................................................................................... 58
5.3 PERFORMANCE ANALYSIS .................................................................................................................................. 59
5.3.1 Total Excess Returns over rf ................................................................................................................ 59
5.3.2 Sharpe Ratios ...................................................................................................................................... 62
5.3.3 Information Ratios .............................................................................................................................. 63
5.4 ALLOCATION ANALYSIS ..................................................................................................................................... 66
5.4.1 Portfolio Weight Analysis.................................................................................................................... 66
5.4.1.1 Allocation Divergence Analysis ..................................................................................................................... 70
5.4.2 Portfolio Difference Analysis ............................................................................................................... 72
5.5 SENSITIVITY ANALYSIS ....................................................................................................................................... 73
5.5.1 Sensitivity of Sharpe Ratios with respect to δ and τ ........................................................................... 74
5.5.2 Sensitivity of Information Ratios with respect to δ and τ ................................................................... 75
5.5.2 Sensitivity of Sharpe Ratios with respect to Q .................................................................................... 75
5.5.2 Sensitivity of Information Ratios with respect to Q ............................................................................ 76
5.5.3 Sensitivity of portfolio construction with respect to parameter changes ........................................... 76
5.5.3.1 τ = 0.065, δ = 3, qEM = 0.10%, qUSSC= 0.05% .................................................................................................. 76
5.5.3.2 τ = 0.065, δ = 3, qEM = 0.70%, qUSSC= 0.35% .................................................................................................. 77
5.5.3.3 τ = 0.005, δ = 1.7, qEM = 0.10%, qUSSC= 0.05% ............................................................................................... 78
5.5.3.4 τ = 0.065, δ = 1.7, qEM = 0.70%, qUSSC= 0.35% ............................................................................................... 78
6. CONCLUSIONS ............................................................................................................................................... 80
7. PROPOSALS FOR FURTHER RESEARCH .................................................................................................. 83
8. REFERENCES.................................................................................................................................................. 84