## Improved Estimation of the Covariance Matrix of Stock Returns with an Application to Portfolio Selection

A 2000 article by O Ledoit, M Wolf that can be found here and here.

### 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 $\sigma$.