Improved Estimation of the Covariance Matrix of Stock Returns with an Application to Portfolio Selection
What are the article's main points
An article on covariance matrix estimation. The standard covariance estimator $\Sigma$ has $n^2 / 2$ statistics to estimate. It is not biased but has high variance. A single factor model estimator $F$ has just a vector of $\beta$, and has only $2n+1$ variables. It is biased because it imposes a simple structure on the data, but it is expected to have less variance.
The article looks at the possibility of using $\alpha F + (1-\alpha) \Sigma$ as estimator. It shows that $\alpha \rightarrow 0$ as the number of observation increases, and expresses the optimal $alpha$ as a function of the variance and covariance of the estimator $F$ and $\sigma$.