Linear statistical inference for global and local minimum variance portfolios

Abstract

Traditional portfolio optimization has often been criticized for not taking estimation risk into account. Estimation risk is mainly driven by the parameter uncertainty regarding the expected asset returns rather than their variances and covariances. The global minimum variance portfolio has been advocated by many authors as an appropriate alternative to the tangential portfolio. This is because there are no expectations which have to be estimated and thus the impact of estimation errors can be substantially reduced. However, in many practical situations an investor is not willing to choose the global minimum variance portfolio but he wants to minimize the variance of the portfolio return under specific constraints for the portfolio weights. Such a portfolio is called local minimum variance portfolio. Small-sample hypothesis tests for global and local minimum variance portfolios are derived and the exact distributions of the estimated portfolio weights are calculated in the present work. The first two moments of the estimator for the expected portfolio returns are also provided and the presented instruments are illustrated by an empirical study.