A novel regression method based on the idea of graphical models is proposed to deal with the portfolio optimisation problem within the Markowitz mean-variance framework,when the number of assets V is larger than the sample size N.Unlike the regularisation methods such as ridge regression,LASSO and LARS,which give biased estimates,the newly proposed method can yield unbiased estimates for important variables,which contributes to improving the portfolios Sharpe ratio by increasing its expected returns and decreasing its risk.Another characteristic of the new approach is that it produces a non-sparse portfolio that is more diversified in terms of stocks and reduces the stockspecific risk.