Which shrinkage is better? Portfolio selection with a cleaned random matrix

ABSTRACT

Covariance matrix estimation is of great importance in formulating a portfolio. The sample covariance matrix, the most frequently used estimator, is well known to be unstable due to the estimation error, when the sample size is small. A shrinkage approach is one of the popular methods for estimating a stable covariance matrix. This study compares and evaluates performance of the three different shrinkage type covariance matrix estimators for the optimal portfolio selection strategy. To evaluate the performance of the covariance matrix estimators, we consider both the in- and out-of-sample value at risk, conditional value at risk, Sharpe-ratio, adjusted Sharpe-ratio, and a beta of the portfolio selection strategies. Empirical results show that a portfolio using shrinkage covariance matrix estimator with the identity matrix or constant correlation matrix as the shrinkage target tends to have a lower risk. We also find that the random matrix approach has a relatively high out-of-sample return and Sharpe-ratio under the small sample size cases.

KEYWORDS:

• Shrinkage covariance matrix
• random matrix theory
• LASSO
• portfolio selection

JEL CLASSIFICATIONS:

• G11
• G17
• C58
• C63

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Available at: https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

Additional information

Funding

This research was supported by the Chung-Ang University Research Grants in 2021.