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

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.