The main practical problems that are faced by portfolio optimisation under the Markowitz model are (i) its lower out-of-sample performance than the naive 1=n rule, (ii) the resulting asset weights with extreme values, and (iii) the high sensitivity of those asset weights to small changes in the data. In this study, we aim to overcome these problems by using a computation method that shifts the smaller eigenvalues of the covariance matrix to the space that houses the eigenvalue spectrum of a random matrix. We evaluate this new method using a rolling sample approach. We obtain portfolios that show both more stable asset weights and better performance than the 1=n rule. We expect that this new computation method will be extended to several problems in portfolio management, thereby improving their consistency and performance.