Constructing Optimal Sparse Portfolios Using Regularization Methods

30 Pages Posted: 2 Nov 2012 Last revised: 22 Aug 2014

See all articles by Bjoern Fastrich

Bjoern Fastrich

University of Giessen - Department of Economics

Sandra Paterlini

University of Trento - Department of Economics and Management

Peter Winker

University of Giessen - Department of Economics

Date Written: August 21, 2014

Abstract

The ideas of Markowitz indisputably constitute a milestone in portfolio theory, even though the resulting mean-variance portfolios typically exhibit an unsatisfying out-of-sample performance, especially when the number of securities is large and that of observations is not. The bad performance is caused by estimation errors in the covariance matrix and in the expected return vector that can deposit unhindered in the portfolio weights. Recent studies show that imposing a penalty in form of a l1-norm of the asset weights regularizes the problem, thereby improving the out-of-sample performance of the optimized portfolios. Simultaneously, l1-regularization selects a subset of assets to invest in from a pool of candidates that is often very large. However, l1-regularization might lead to the construction of biased solutions. We propose to tackle this issue by considering several alternative penalties proposed in non-financial contexts. Moreover we propose a simple new type of penalty that explicitly considers financial information. We show empirically that these alternative penalties can lead to the construction of portfolios with superior out-of-sample performance in comparison to the state-of-the-art l1-regularized portfolios and several standard benchmarks, especially in high dimensional problems. The empirical analysis is conducted with various U.S.-stock market datasets.

Keywords: Minimum Variance Portfolio, Statistical Regularization, Non-Convex Penalties

JEL Classification: C15, C61, G11

Suggested Citation

Fastrich, Bjoern and Paterlini, Sandra and Winker, Peter, Constructing Optimal Sparse Portfolios Using Regularization Methods (August 21, 2014). Available at SSRN: https://ssrn.com/abstract=2169062 or http://dx.doi.org/10.2139/ssrn.2169062

Bjoern Fastrich

University of Giessen - Department of Economics ( email )

Licher Str. 64
D-35394, Giessen
Germany

Sandra Paterlini (Contact Author)

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

Via Inama 5
Trento, I-38100
Italy

Peter Winker

University of Giessen - Department of Economics ( email )

Licher Str. 62
D-35394 Giessen, DE
Germany

HOME PAGE: http://wiwi.uni-giessen.de/home/oekonometrie/

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