On the mean-square error performance of adaptive minimum variance beamformers based on the sample covariance matrix

1994 ◽  
Vol 42 (2) ◽  
pp. 445-448 ◽  
Author(s):  
J.L. Krolik ◽  
D.N. Swingler
Keyword(s):  
Covariance Matrix ◽  
Mean Square Error ◽  
Minimum Variance ◽  
Sample Covariance Matrix ◽  
Mean Square ◽  
Error Performance ◽  
Sample Covariance ◽  
The Mean ◽  
Mean Square Error Performance

scholarly journals Shrinking the Variance-Covariance Matrix: Simpler is Better

2016 ◽  
Vol 21 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Muhammad Husnain ◽  
Arshad Hassan ◽  
Eric Lamarque
Keyword(s):  
Root Mean Square Error ◽  
Covariance Matrix ◽  
Mean Square Error ◽  
Minimum Variance ◽  
Factor Models ◽  
The Philippines ◽  
Risk Profile ◽  
Additional Benefit ◽  
Mean Square ◽  
Weighted Portfolio

This study focuses on the estimation of the covariance matrix as an input to portfolio optimization. We compare 12 covariance estimators across four categories – conventional methods, factor models, portfolios of estimators and the shrinkage approach – applied to five emerging Asian economies (India, Indonesia, Pakistan, the Philippines and Thailand). We find that, in terms of the root mean square error and risk profile of minimum variance portfolios, investors gain no additional benefit from using the more complex shrinkage covariance estimators over the simpler, equally weighted portfolio of estimators in the sample countries.

scholarly journals Target Matrix Estimators in Risk-Based Portfolios

2018 ◽  
Author(s):  
Marco Neffelli
Keyword(s):  
Covariance Matrix ◽  
Moving Average ◽  
Estimation Error ◽  
Minimum Variance ◽  
Sample Covariance Matrix ◽  
Sample Mean ◽  
Index Model ◽  
Single Index Model ◽  
Sample Covariance ◽  
Risk Contribution

Portfolio weights solely based on risk avoid estimation error from the sample mean, but they are still affected from the misspecification in the sample covariance matrix. To solve this problem, we shrink the covariance matrix towards the Identity, the Variance Identity, the Single-index model, the Common Covariance, the Constant Correlation and the Exponential Weighted Moving Average target matrices. By an extensive Monte Carlo simulation, we offer a comparative study of these target estimators, testing their ability in reproducing the true portfolio weights. We control for the dataset dimensionality and the shrinkage intensity in the Minimum Variance, Inverse Volatility, Equal-risk-contribution and Maximum Diversification portfolios. We find out that the Identity and Variance Identity have very good statistical properties, being well-conditioned also in high-dimensional dataset. In addition, the these two models are the best target towards to shrink: they minimise the misspecification in risk-based portfolio weights, generating estimates very close to the population values. Overall, shrinking the sample covariance matrix helps reducing weights misspecification, especially in the Minimum Variance and the Maximum Diversification portfolios. The Inverse Volatility and the Equal-Risk-Contribution portfolios are less sensitive to covariance misspecification, hence they benefit less from shrinkage.

scholarly journals Target Matrix Estimators in Risk-Based Portfolios

Risks ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 125 ◽  
Author(s):  
Marco Neffelli
Keyword(s):  
Covariance Matrix ◽  
Moving Average ◽  
Minimum Variance ◽  
Sample Covariance Matrix ◽  
Estimation Errors ◽  
Sample Mean ◽  
Index Model ◽  
Single Index Model ◽  
Sample Covariance ◽  
Risk Contribution

Portfolio weights solely based on risk avoid estimation errors from the sample mean, but they are still affected from the misspecification in the sample covariance matrix. To solve this problem, we shrink the covariance matrix towards the Identity, the Variance Identity, the Single-index model, the Common Covariance, the Constant Correlation, and the Exponential Weighted Moving Average target matrices. Using an extensive Monte Carlo simulation, we offer a comparative study of these target estimators, testing their ability in reproducing the true portfolio weights. We control for the dataset dimensionality and the shrinkage intensity in the Minimum Variance (MV), Inverse Volatility (IV), Equal-Risk-Contribution (ERC), and Maximum Diversification (MD) portfolios. We find out that the Identity and Variance Identity have very good statistical properties, also being well conditioned in high-dimensional datasets. In addition, these two models are the best target towards which to shrink: they minimise the misspecification in risk-based portfolio weights, generating estimates very close to the population values. Overall, shrinking the sample covariance matrix helps to reduce weight misspecification, especially in the Minimum Variance and the Maximum Diversification portfolios. The Inverse Volatility and the Equal-Risk-Contribution portfolios are less sensitive to covariance misspecification and so benefit less from shrinkage.

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