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It is well known that quantile regression model minimizes the portfolioextreme risk, whenever the attention is placed on the estimation of theresponse variable left quantiles. We show that, by considering the entireconditional distribution of the dependent variable, it is possible to optimizedifferent risk and performance indicators. In particular, we introduce arisk-adjusted profitability measure, useful in evaluating financial portfoliosunder a pessimistic perspective, since the reward contribution is net of themost favorable outcomes. Moreover, as we consider large portfolios, we alsocope with the dimensionality issue by introducing an l1-norm penalty on theassets weights.

Asset Allocation Strategies Based on Penalized Quantile Regression