Asset Allocation Strategies Based on Penalized Quantile Regression

TL;DR

This paper proposes a novel asset allocation approach using penalized quantile regression to optimize various risk and performance metrics, especially under pessimistic scenarios, while addressing high-dimensional portfolio challenges.

Contribution

It introduces a method that leverages the entire conditional distribution for portfolio optimization and incorporates an l1 penalty for large portfolios.

Findings

Effective in minimizing extreme risk in portfolios.

Provides a new risk-adjusted profitability measure.

Addresses high-dimensional asset allocation problems.

Abstract

It is well known that quantile regression model minimizes the portfolio extreme risk, whenever the attention is placed on the estimation of the response variable left quantiles. We show that, by considering the entire conditional distribution of the dependent variable, it is possible to optimize different risk and performance indicators. In particular, we introduce a risk-adjusted profitability measure, useful in evaluating financial portfolios under a pessimistic perspective, since the reward contribution is net of the most favorable outcomes. Moreover, as we consider large portfolios, we also cope with the dimensionality issue by introducing an l1-norm penalty on the assets weights.