We discuss how a manipulation of sample eigenvalues affects the actual portfolio risk when a two-step method is used to construct a global minimum variance portfolio (GMVP). For special structures of the true covariance matrix, both a shrinkage on a head eigenvalue and an amplification on a tail eigenvalue are shown to have a marginal effect of reducing the actual risk. In a high-dimensional setting, the marginal effect of amplifying a tail eigenvalue becomes dominant compared with that of shrinking a head eigenvalue. This leads us to propose a new concept called a tail eigenvalues amplification (TEA) method. In the TEA method, the first few eigenvalues are kept unchanged, while the last few eigenvalues are amplified to infinity. This modified covariance matrix is used for constructing a GMVP. Both simulation and empirical results show that the TEA method with the number of eigenvalues to amplify selected using a cross-validation method has an improved actual portfolio risk reduction effect and smaller turnover compared with the “shrinkage towards identity” method. Lastly, when there is a larger gap (in terms of the magnitude) between the off-diagonal elements and the diagonal elements in the true covariance matrix, the TEA method results in a higher percentage actual portfolio risk reduction.