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Precision Matrix Estimation for the Global Minimum Variance Portfolio

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Marco Neffelli

    (Alpha Real Capital LLP)

  • Maria Elena Giuli

    (University of Pavia)

  • Marina Resta

    (University of Genova)

Abstract

We use the Minimum Regularised Covariance Determinant Estimator (MRCD) to limit weights’ misspecification within the Global Minimum Variance Portfolio (GMVP) framework. Estimating the precision matrix is a key step that often generates misspecification which translates to resulting portfolio weights, directly affecting the GMVP out-of-sample performance. This effect is exacerbated when data are high-dimensional and non-Normal. To this extent, we propose using the MRCD because is well-designed to deal with high-dimensionality and non-Normality. We perform an extensive Monte Carlo simulation analysis to check the effectiveness of the proposed approach in comparison to the sample estimator. Our analysis demonstrates that the out-of-sample performance of the GMVP benefits from the use of the MRCD estimator: results suggest a reduction in the portfolio turnover at no cost for the portfolio variance and an increase in the portfolio Sharpe ratio.

Suggested Citation

  • Marco Neffelli & Maria Elena Giuli & Marina Resta, 2021. "Precision Matrix Estimation for the Global Minimum Variance Portfolio," Springer Books, in: Marco Corazza & Manfred Gilli & Cira Perna & Claudio Pizzi & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 361-367, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-78965-7_53
    DOI: 10.1007/978-3-030-78965-7_53
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