A large CVaR-based portfolio selection model with weight constraints

Although the traditional CVaR-based portfolio methods are successfully used in practice, the size of a portfolio with thousands of assets makes optimizing them difficult, if not impossible to solve. In this article we introduce a large CVaR-based portfolio selection method by imposing weight constraints on the standard CVaR-based portfolio selection model, which effectively avoids extreme positions often emerging in traditional methods. We propose to solve the large CVaR-based portfolio model with weight constraints using penalized quantile regression techniques, which overcomes the difficulties of large scale optimization in traditional methods. We illustrate the method via empirical analysis of optimal portfolios on Shanghai and Shenzhen 300 (HS300) index and Shanghai Stock Exchange Composite (SSEC) index of China. The empirical results show that our method is efficient to solve a large portfolio selection and performs well in dispersing tail risk of a portfolio by only using a small amount of financial assets.