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MINISTRY OF EDUCATION AND TRAINING THE STATE BANK OF VIETNAM
BANKING UNIVERSITY OF HO CHI MINH CITY
DOCTORAL DISSERTATION
NGUYEN MINH NHAT
SHRINKAGE ESTIMATION OF COVARIANCE MATRIX
FOR PORTFOLIO SELECTION ON VIETNAM STOCK MARKET
Ho Chi Minh City - 2020
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MINISTRY OF EDUCATION AND TRAINING THE STATE BANK OF VIETNAM
BANKING UNIVERSITY OF HO CHI MINH CITY
DOCTORAL DISSERTATION
NGUYEN MINH NHAT
SHRINKAGE ESTIMATION OF COVARIANCE MATRIX
FOR PORTFOLIO SELECTION ON VIETNAM STOCK MARKET
Ho Chi Minh City - 2020
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Table of Contents
List of Abbreviations .................................................................................................... iv
List of Figures ............................................................................................................... vi
List of Tables............................................................................................................... viii
CHAPTER 1: INTRODUCTION ................................................................................. 1
1.1 Vietnam stock market overview ............................................................................. 1
1.2 Problem statements ................................................................................................. 6
1.3 Objectives and research questions ........................................................................ 11
1.4 Research Methodology ......................................................................................... 11
1.5 Expected contributions ......................................................................................... 13
1.6 Disposition of the dissertation .............................................................................. 13
CHAPTER 2: LITERATURE REVIEW ................................................................... 16
2.1 Modern Portfolio Theory Framework ................................................................... 16
2.1.1 Concept of risk and return .............................................................................. 17
2.1.2 Assumptions of the modern portfolio theory ................................................... 18
2.1.3 MPT investment process ................................................................................. 19
2.1.4 Critism of the theory ....................................................................................... 20
2.2 Parameter estimation ............................................................................................ 21
2.2.1 Expected returns parameter ........................................................................... 23
2.2.2 The covariance matrix parameter ................................................................... 25
2.3 Portfolio Selection ................................................................................................ 30
2.3.1 Mean-Variance Model .................................................................................... 30
2.3.2 Global Minimum Variance Model (GMV) ...................................................... 32
CHAPTER 3: THEORETICAL FRAMEWORK ..................................................... 34
3.1 Basic preliminaries ............................................................................................... 34
3.1.1 Return ............................................................................................................ 34
3.1.2 Variance ......................................................................................................... 35
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3.2 Portfolio Optimization .......................................................................................... 36
3.3 The estimators of covariance matrix ..................................................................... 37
3.3.1 The sample covariance matrix (SCM) ............................................................. 38
3.3.2 The single index model (SIM) ......................................................................... 39
3.3.3 Constant correlation model (CCM) ................................................................ 41
3.3.4 Shrinkage towards single-index model (SSIM)................................................ 42
3.3.5 Shrinkage towards Constant correlation Model (SCCM) ................................ 44
3.3.6 Shrinkage to identity matrix (STIM) ............................................................... 47
CHAPTER 4: METHODOLOGY .............................................................................. 51
4.1 Input Data ............................................................................................................. 51
4.2 Portfolio performance evaluation methodology .................................................... 55
4.3 Transaction costs .................................................................................................. 59
4.4 Performance metrics ............................................................................................. 60
4.4.1 Sharpe ratio (SR)............................................................................................ 60
4.4.2 Maximum drawdown (MDD) .......................................................................... 61
4.4.3 Portfolio turnover (PT)................................................................................... 61
4.4.4 Winning rate (WR) ......................................................................................... 62
4.4.5 Jensen’s Alpha ............................................................................................... 62
4.4.6 The statistical significance of the differences between two strategies on the
performance measures ............................................................................................ 63
4.5 VN - Index and 1/N portfolios benchmarks .......................................................... 64
CHAPTER 5: EMPIRICAL RESULTS ..................................................................... 66
5.1 VN – Index and 1/N portfolio performance .......................................................... 66
5.1.1 VN – Index performance ................................................................................. 66
5.1.2 1/N portfolio performance .............................................................................. 69
5.2 Portfolio out – of –sample performance ................................................................ 72
5.2.1 Sample covariance matrix (SCM) ................................................................... 72
5.2.2 Single index model (SIM) ............................................................................... 76
5.2.3 Constant correlation model (CCM) ................................................................ 79
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5.2.4 Shrinkage towards single index model (SSIM) ................................................ 82
5.2.5 Shrinkage towards constant correlation model (SCCM) ................................. 90
5.2.6 Shrinkage towards identity matrix (STIM) ...................................................... 95
5.3 Summary performances of covariance matrix estimators on out – of – sample ..... 99
CHAPTER 6: CONCLUSIONS AND FUTURE WORKS ...................................... 105
6.1 Conclusions ........................................................................................................ 105
6.2 Future works ...................................................................................................... 111
REFERENCES ................................................................................................................