Estimation error in the average correlation of security returns and shrinkage estimation of covariance and correlation matrices

The correlation matrix of security returns is an important input component for mean-variance portfolio analysis. This study uses the average of sample correlations to estimate the correlation matrix and derives an expression of its estimation error in terms of sampling variance. This study then considers the impact of such estimation error on shrinkage estimation, where a weighted average is sought between the sample covariance matrix and an average correlation target, and between the sample correlation matrix and the target. An illustrative example using monthly returns of the current Dow Jones stocks is provided.