Sparse Portfolio Selection via the Sorted L1 - Norm

61 Pages Posted: 9 Oct 2017 Last revised: 2 Jan 2018

See all articles by Philipp Kremer

Philipp Kremer

EBS Universität für Wirtschaft und Recht

Sangkyun Lee

Hanyang University ERICA

Malgorzata Bogdan

University of Wroclaw

Sandra Paterlini

Università degli Studi di Trento - Department of Economics and Management

Date Written: January 2, 2018

Abstract

We introduce a financial portfolio optimization framework that allows us to automatically select the relevant assets and estimate their weights by relying on a sorted L1-Norm penalization, henceforth SLOPE. Our approach is able to group constituents with similar correlation properties, and with the same underlying risk factor exposures. We show that by varying the intensity of the penalty, SLOPE can span the entire set of optimal portfolios on the risk-diversification frontier, from minimum variance to the equally weighted. To solve the optimization problem, we develop a new efficient algorithm, based on the Alternating Direction Method of Multipliers. Our empirical analysis shows that SLOPE yields optimal portfolios with good out-of-sample risk and return performance properties, by reducing the overall turnover through more stable asset weight estimates. Moreover, using the automatic grouping property of SLOPE, new portfolio strategies, such as SLOPE-MV, can be developed to exploit the data-driven detected similarities across assets.

Note: scholarly, OK FOR SMJ DIST, processed -Jessica 10/10/17

Keywords: Portfolio Management, Markowitz Model, Sorted L1-Norm Regularization; Alternating Direction Method of Multipliers

Suggested Citation

Kremer, Philipp and Lee, Sangkyun and Bogdan, Malgorzata and Paterlini, Sandra, Sparse Portfolio Selection via the Sorted L1 - Norm (January 2, 2018). Available at SSRN: https://ssrn.com/abstract=3048879 or http://dx.doi.org/10.2139/ssrn.3048879

Philipp Kremer (Contact Author)

EBS Universität für Wirtschaft und Recht ( email )

Gustav-Stresemann-Ring 3
Wiesbaden, Hessen 65195
Germany

Sangkyun Lee

Hanyang University ERICA ( email )

Seoul
Korea, Republic of (South Korea)

Malgorzata Bogdan

University of Wroclaw ( email )

50-384 Wroclaw
Grunwaldzki 2/4, Lower Silesia Province 50-137
Poland

Sandra Paterlini

Università degli Studi di Trento - Department of Economics and Management ( email )

Via Inama 5
Trento, I-38100
Italy

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