# Critical Decisions for Asset Allocation via Penalized Quantile Regression

## TL;DR

This paper enhances asset allocation strategies using penalized quantile regression by introducing post-penalization, exploring nonconvex penalties, and optimizing tuning parameter selection, leading to improved performance especially in extreme risk scenarios.

## Contribution

It proposes novel methods including post-penalization and nonconvex penalties for quantile regression in asset allocation, improving upon existing LASSO-based approaches.

## Key findings

- Alternative methods outperform simple LASSO in empirical tests.
- Performance gains are more pronounced in extreme risk scenarios.
- Optimized tuning parameter selection enhances model effectiveness.

## Abstract

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.