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Sparse Portfolio Selection via the sorted $\ell_{1}$-Norm

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  • Philipp J. Kremer
  • Sangkyun Lee
  • Malgorzata Bogdan
  • Sandra Paterlini

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 $\ell_1$-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.

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  • Philipp J. Kremer & Sangkyun Lee & Malgorzata Bogdan & Sandra Paterlini, 2017. "Sparse Portfolio Selection via the sorted $\ell_{1}$-Norm," Papers 1710.02435, arXiv.org.
    • Handle: RePEc:arx:papers:1710.02435
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    References listed on IDEAS

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    Cited by:

    1. Andrew Butler & Roy H. Kwon, 2021. "Data-driven integration of norm-penalized mean-variance portfolios," Papers 2112.07016, arXiv.org, revised Nov 2022.

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