Before revision: We consider the problem of portfolio selection within the classical Markowitz mean-variance optimizing framework, which has served as the basis for modern portfolio theory for more than 50 years. To stabilize the problem, we propose to add to the Markowitz objective function a penalty which is proportional to the sum of the absolute values of the portfolio weights (\ell_1 penalty) .
After revision: We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the Markowitz objective function a penalty which is proportional to the sum of the absolute values of the portfolio weights (\ell_1 penalty) .