Quantile– based portfolios: post– model– selection estimation with alternative specifications

We extend the analysis of investment strategies derived from penalized quantile regression models, introducing alternative approaches to improve state– of– art asset allocation rules. We make use of the post– model– selection estimation, which builds on two important choices: the specification of the penalty function and the selection of the optimal tuning parameter. Therefore, we first investigate whether and to what extent the performance of a given portfolio changes when moving from convex to nonconvex penalty functions. Second, we compare different methods to select the optimal tuning parameter, which controls the intensity of the penalization. Empirical analyses on real– world data show that these alternative methods outperform the standard LASSO, providing improvements in terms of risk, risk– adjusted return and portfolio concentration. This evidence becomes stronger when focusing on extreme risk, which is strictly linked to quantile regression.