  We extend the analysis of investment strategies derived from penalized
quantile regression models, introducing alternative approaches to improve
state\textendash of\textendash art asset allocation rules. First, we use a
post\textendash penalization procedure to deal with overshrinking and
concentration issues. Second, we investigate whether and to what extent the
performance changes when moving from convex to nonconvex penalty functions.
Third, we compare different methods to select the optimal tuning parameter
which controls the intensity of the penalization. Empirical analyses on
real\textendash world data show that these alternative methods outperform the
simple LASSO. This evidence becomes stronger when focusing on the extreme risk,
which is strictly linked to the quantile regression method.
