On the estimation of the global minimum variance portfolio

Expected returns can hardly be estimated from time series data. Therefore, many recent papers suggest investing in the global minimum variance portfolio. The weights of this portfolio depend only on the return variances and covariances, but not on the expected returns. The weights of the global minimum variance portfolio are usually estimated by replacing the true return covariance matrix by its time series estimator. However, little is known about the distributions of the estimated weights and return parameters of this portfolio. Our contribution is to determine these distributions. The knowledge of these distributions allows us to calculate the extent of the estimation risk an investor faces and to answer important questions in asset management.