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. By considering the entire conditional distribution of the dependent variable, we show that it is possible to obtain further benets by optimizing dierent risk and performance indicators. In particular, we introduce a risk-adjusted protability measure, useful in evaluating nancial portfolios from a `cautiously optimistic' perspective, as 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.
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