Robust mean-variance portfolio through the weighted \(L^{p}\) depth function

  • Giuseppe PandolfoEmail author
  • Carmela Iorio
  • Roberta Siciliano
  • Antonio D’Ambrosio
Original - Survey or Exposition


Portfolios constructed by the classical mean-variance model are very sensitive to outliers. We propose the use of a non-parametric estimation method based on statistical data depth functions. Specifically, we exploit the notion of the weighted \(L^{p}\) depth function to obtain robust estimates of the mean and covariance matrix of the asset returns. This approach has the advantage to be independent of parametric assumptions, and less sensitive to changes in the asset return distribution than traditional techniques. The proposed procedure is evaluated and compared with standard and other robust techniques through simulated and real data. Results indicate effective improvements of the proposed method in terms of out-of-sample performance.


Finance Portfolio selection Outliers Weight function Robust statistics Out-of-sample 



We gratefully acknowledges Valerio Sullo, senior quantitative portfolio manager at Amundi, for gently providing the DAX30 data.


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Authors and Affiliations

  1. 1.Department of Industrial EngineeringUniversity of Naples Federico IINaplesItaly
  2. 2.Department of Economics and StatisticsUniversity of Naples Federico IINaplesItaly

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