A Monte Carlo synthetic sample based performance evaluation method for covariance matrix estimators

ABSTRACT

The evaluation of covariance matrix estimators is very important for portfolio analysis and risk management. The Monte Carlo synthetic sample based performance evaluation method proposed by this article can avoid the main shortcomings of statistical and economic methods which are widely used in the existing literature. The proposed method does not need the true covariance and does not need to introduce the performance of the out-of-sample portfolios. It is an intuitive, effective and robust measure for both simulation and empirical analysis.

KEYWORDS:

• Synthetic sample
• performance evaluation
• covariance matrix
• estimators

JEL CLASSIFICATION:

• C13
• C15
• C52
• C83

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}\left(\hat{\mathrm{\Sigma }},\mathrm{\Sigma }\right)=∥\hat{\mathrm{\Sigma }}-\mathrm{\Sigma }∥$, where$∥\bullet ∥$ stands for the Frobenius norm of two matrices.

Additional information

Funding

This work was partially supported by the Chinese Natural Science Foundations [11631013, 11971372 and 11801433]