Smoothed Semicovariance Estimation for Portfolio Selection

24 Pages Posted: 23 Mar 2021 Last revised: 26 May 2022

See all articles by Davide Ferrari

Davide Ferrari

Free University of Bozen-Bolzano, Faculty of Economics and Management

Sandra Paterlini

University of Trento - Department of Economics and Management

Andrea Rigamonti

University of Liechtenstein

Alex Weissensteiner

Free University of Bolzano Bozen

Date Written: May 25, 2022

Abstract

Minimizing the semivariance of a portfolio is analytically intractable and numerically challenging due to the endogeneity of the semicovariance matrix. In this paper, we introduce a smoothed estimator for the portfolio semivariance and use it as an objective for portfolio selection. The extent of smoothing is determined by a single tuning constant, which allows our method to span an entire set of optimal portfolios with limit cases represented by the minimum semivariance and the minimum variance portfolios. The methodology is implemented through an interatively reweighted algorithm, which is found to be computationally efficient in large problems with many assets. Our numerical studies confirm the theoretical convergence of the smoothed semivariance estimator to the true semivariance. The resulting minimum smoothed semivariance portfolio performs well in- and out-of-sample compared to other popular selection rules.

Keywords: semivariance, smoothed semicovariance, portfolio optimization, skewness

JEL Classification: G11, D81

Suggested Citation

Ferrari, Davide and Paterlini, Sandra and Rigamonti, Andrea and Weissensteiner, Alex, Smoothed Semicovariance Estimation for Portfolio Selection (May 25, 2022). Available at SSRN: https://ssrn.com/abstract=3786023 or http://dx.doi.org/10.2139/ssrn.3786023

Davide Ferrari

Free University of Bozen-Bolzano, Faculty of Economics and Management ( email )

Sernesiplatz 1
Bozen-Bolzano, BZ 39100
Italy

Sandra Paterlini

University of Trento - Department of Economics and Management ( email )

Via Inama 5
Trento, I-38100
Italy

Andrea Rigamonti (Contact Author)

University of Liechtenstein ( email )

Fuerst Franz Josef-Strasse
Vaduz, 9490
Liechtenstein

Alex Weissensteiner

Free University of Bolzano Bozen ( email )

Universitätsplatz 1
Bolzano, 39100
+39 0471 013496 (Phone)

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