Estimating the global Minimum Variance Portfolio

According to standard portfolio theory, the tangency portfolio is the only efficient stock portfolio. However, empirical studies show that an investment in the global minimum variance portfolio often yields better out-of-sample results than does an investment in the tangency portfolio and suggest investing in the global minimum variance portfolio. But little is known about the distributions of the weights and return parameters of this portfolio. Our contribution is to determine these distributions. By doing so, we answer several important questions in asset management.