It is well known that the quantile regression model, used as an asset allocation tool, minimizes the portfolio extreme risk whenever the attention is placed on the lower quantiles of the response variable. We show that, by considering the entire conditional distribution of the dependent variable, it is possible to obtain further benefits by optimizing different risk and performance indicators. In particular, we introduce a risk-adjusted profitability measure, useful in evaluating financial

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... olios under a "cautiously optimistic" 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 1 -norm penalty on the assets weights.