# Asset allocation strategies based on penalized quantile regression

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## Abstract

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 benefits by optimizing different risk and performance indicators. In particular, we introduce a risk-adjusted profitability measure, useful in evaluating financial 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 \(\ell _1\)-norm penalty on the assets’ weights.

## Keywords

Quantile regression \(\ell _1\)-Norm penalty Asset allocation## Notes

### Acknowledgements

The authors thank the participants of the “9th Financial Risks International Forum” in Paris, organised by Institut Louis Bachelier, the “9th International Conference on Computational and Financial Econometrics” in London, the “SOFINE-CEQURA Spring Junior Research Workshop” in Nesselwang, the “Financial Econometrics and Empirical Asset Pricing Conference” in Lancaster, the seminar organized by the University of Palermo for the helpful comments and stimulating discussions. M. Caporin acknowledges financial support from the European Union, the Seventh Framework Program FP7/2007–2013 under Grant Agreement SYRTO-SSH-2012-320270, the MIUR PRIN project MISURA-Multivariate Statistical Models for Risk Assessment, the Global Risk Institute in Financial Services and the Louis Bachelier Institute. S. Paterlini acknowledges financial support from ICT COST ACTION 1408-CRONOS.

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