Optimal algorithms and intuitive explanations for Markowitz’s portfolio selection model and Sharpe’s ratio with no short-selling

Most of the previous researches about portfolio analysis focus on short-selling. In fact, no short-selling is also important because short-selling is not allowed in stock markets of some countries. This paper gives the sufficient and necessary conditions and proposes an optimal algorithm for Markowitz’s mean-variance models and Sharpe’s ratio with no short-selling. The optimal algorithm makes it easier to obtain the efficient frontiers with no short-selling.