Nonsingular approximations for a singular covariance matrix

2012 ◽  
Author(s):  
Nir Gorelik ◽  
D. Blumberg ◽  
Stanley R. Rotman ◽  
D. Borghys
Keyword(s):  
Covariance Matrix ◽  
Singular Covariance Matrix

scholarly journals An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection

2019 ◽  
Vol 56 (4) ◽  
pp. 773-794 ◽  
Author(s):  
Mårten Gulliksson ◽  
Stepan Mazur
Keyword(s):  
Covariance Matrix ◽  
Portfolio Selection ◽  
Numerical Study ◽  
Asset Returns ◽  
Positive Definite ◽  
Convergence Properties ◽  
Good Convergence ◽  
Optimal Portfolio Selection ◽  
Singular Covariance Matrix ◽  
Better Than

AbstractCovariance matrix of the asset returns plays an important role in the portfolio selection. A number of papers is focused on the case when the covariance matrix is positive definite. In this paper, we consider portfolio selection with a singular covariance matrix. We describe an iterative method based on a second order damped dynamical systems that solves the linear rank-deficient problem approximately. Since the solution is not unique, we suggest one numerical solution that can be chosen from the iterates that balances the size of portfolio and the risk. The numerical study confirms that the method has good convergence properties and gives a solution as good as or better than the solutions that are based on constrained least norm Moore–Penrose, Lasso, and naive equal-weighted approaches. Finally, we complement our result with an empirical study where we analyze a portfolio with actual returns listed in S&P 500 index.

scholarly journals Portfolio Optimization of the Mean-Absolute Deviation Model of Some Stocks using the Singular Covariance Matrix

2019 ◽  
Vol 8 (3) ◽  
pp. 7818-7822
Keyword(s):  
Portfolio Optimization ◽  
Covariance Matrix ◽  
Stock Exchange ◽  
Optimal Portfolio ◽  
Risk Level ◽  
Mean Absolute Deviation ◽  
Investment Portfolio ◽  
Absolute Deviation ◽  
Singular Covariance Matrix ◽  
The Mean

Investing in the stock sector, investors often face risk problems. Usually, forming an investment portfolio is done to minimize risk. In this research, investment portfolio optimization is discussed. The data analyzed are 8 shares traded on the capital market in Indonesia through the Indonesia Stock Exchange (IDX). Optimization is performed using the Mean-Absolute Deviation model with the singular covariance matrix to determine the optimal weights. The results of portfolio optimization Mean-Absolute Deviation model with singular covariance matrix method, was obtained optimal portfolio weights that is of 17.22% for BBCA shares; 26.64% for TKIM shares; 9.96% for BBRI shares; 9.96% for BBNI shares; 8.70% for BMRI shares; 3.75% for ADRO shares; 6.52% for GGRM shares; and 17.25% for UNTR shares. Where the optimal portfolio composition is obtained the expected rate of return (expected return) of 0.18% with a portfolio risk level (standard deviation) of 0.07%.

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