Portfolio selection with conservative short-selling

Mean-variance analysis is considered the foundation of portfolio selection. Among various attempts to address the limitations of the original model as formulated by Markowitz more than 60 years ago, one simple solution has been to impose constraints on weights in order to reduce efficient portfolios with extreme weights that may be caused by estimation errors in the inputs. Although no short-selling constraints are often considered, the restriction removes opportunities to gain from short-selling and short positions provide various investment opportunities such as long/short strategies. In this paper we propose a portfolio selection model that allows short positions while examining the worst case only for assets that are assigned negative weights. The proposed model constructs portfolios with conservative short positions and the conservative level can be adjusted by the investor.