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 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 answer several important questions in asset management.