The Sample Estimator: Sample Covariance Matrix

For more info about our services contact : help@bestpfe.com

Table of contents

1 Introduction 
1.1 Background
1.2 Current Discussions and Findings
1.3 Practical hindrances and its implication/effect
1.4 Thesis Objective
2 Reviewing Fundamental Concepts 
2.1 Returns
2.2 Net Returns
2.3 Multi-period returns
2.4 Log Returns
2.5 Adjusting for Dividends
2.6 Random Walk Synopsis
2.7 Box-plots
3 Data 
3.1 Descriptive Statistics
4 The Language of Portfolio 
4.1 Risk – Return
4.2 Feasible Portfolio Opportunities
4.3 The Sharpe Ratio
4.4 The Efficient Frontier
4.5 Generating the Efficient Frontier
4.6 Fundamental Limitations of the MVE
4.7 Concept Demonstration: The Efficient Frontier
4.8 Short Selling Scenario
4.9 No Short Selling Scenario
4.10 Tangency Portfolio
5 Estimation Error In Essence 
5.1 Estimation Error
5.2 Finding Estimators To Reduce Estimation Error
5.3 Portfolio Resampling
5.4 Bootstrap Resampling Process – Generating Resampled Efficient Frontier
6 Covariance Estimation 
6.1 Estimation by Shrinkage; Ledoit-Wolf Procedure
6.2 Sharpe’s Single-Index Model
6.3 Shrinkage Estimator of the Ledoit-Wolf Covariance Matrix
6.3.1 The Sample Estimator: Sample Covariance Matrix
6.3.2 The Target Estimator: Single-Index Covariance Matrix Estimator
6.3.3 The Optimal Shrinkage Intensity
Conclusion 
Fulfilment of Thesis Objective
References
A Attributable Factors
A.1 Quadratic Utility Approach
A.2 Rank of a Matrix
A.3 Positive Semi-Definite Matrix
B R Programming Language Codes 57
B.1 Efficient Frontier – Short Selling Allowed
B.2 Efficient Frontier – Short Selling NOT Allowed