Accurate measures of the volatility matrix and its inverse play a central role in risk and portfolio management problems. Due to the accumulation of errors in the estimation of expected returns and covariance matrix, the solution to these problems is very sensitive, particularly when the number of assets (p) exceeds the sample size (T). Recent research has focused on developing different methods to estimate high dimensional covariance matrixes under small sample size. The aim of this paper is to examine and compare the minimum variance optimal portfolio constructed using five different estimation methods for the covariance matrix: the sample covariance, Risk-Metrics, factor model, shrinkage and mixed frequency factor model. Using the Monte Carlo simulation we provide evidence that the mixed frequency factor model and the factor model provide a high accuracy when there are portfolios with p closer or larger than T.