关键词: 分位数回归, Knockoff, Lasso惩罚, 投资组合, CVaR

Abstract: In the current data-driven era, variable selection is commonly encountered in the field of investment portfolio. How to select assets from the numerous options available and allocate the investment proportion plays an important role in stabilizing return and controlling risk. The existing methods of asset selection do not take into account the control of false discovery rate (FDR), which is undoubtedly not conducive to making robust investment decisions. Therefore, a Lasso quantile regression based on Knockoff method is constructed to control FDR and used to solve the CVaR-based portfolio selection model. In the proposed model, Lasso penalty is implemented for variable selection. Knockoff method is designed to control the FDR of variable selection at the given level, which can mimic the correlation structure of the covariates. The model is solved by linear programming under a two-step iterative algorithm. The simulation study is conducted under various scenarios with different error distributions, covariates distributions, and dimensions. The results demonstrate that compared with the existing models, the proposed one can satisfactorily control FDR and presents the best prediction performance. Finally, an empirical study is conducted on SSE 50 stocks, and the rolling modeling technology is used to analyze the decision making of portfolio. It shows that the new model has advantages in return indexes and risk indexes.

Key words: Quantile Regression, Knockoff, Lasso Penalty, Portfolio, CVaR