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Sparse portfolio selection via the sorted ℓ1-Norm

Kremer, Philipp J. ; Lee, Sangkyun ; Bogdan, Małgorzata LU and Paterlini, Sandra (2020) In Journal of Banking and Finance 110.
Abstract

We introduce a financial portfolio optimization framework that allows to automatically select the relevant assets and estimate their weights by relying on a sorted ℓ1-Norm penalization, henceforth SLOPE. To solve the optimization problem, we develop a new efficient algorithm, based on the Alternating Direction Method of Multipliers. SLOPE is able to group constituents with similar correlation properties, and with the same underlying risk factor exposures. Depending on the choice of the penalty sequence, our approach can span the entire set of optimal portfolios on the risk-diversification frontier, from minimum variance to the equally weighted. Our empirical analysis shows that SLOPE yields optimal portfolios with good... (More)

We introduce a financial portfolio optimization framework that allows to automatically select the relevant assets and estimate their weights by relying on a sorted ℓ1-Norm penalization, henceforth SLOPE. To solve the optimization problem, we develop a new efficient algorithm, based on the Alternating Direction Method of Multipliers. SLOPE is able to group constituents with similar correlation properties, and with the same underlying risk factor exposures. Depending on the choice of the penalty sequence, our approach can span the entire set of optimal portfolios on the risk-diversification frontier, from minimum variance to the equally weighted. 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 sparse equally weighted portfolios, can be developed to exploit the data-driven detected similarities across assets.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Alternating direction method of multipliers, Markowitz model, Portfolio management, Sorted ℓ-Norm regularization
in
Journal of Banking and Finance
volume
110
article number
105687
publisher
Elsevier
external identifiers
  • scopus:85075266091
ISSN
0378-4266
DOI
10.1016/j.jbankfin.2019.105687
language
English
LU publication?
yes
id
8f52fd58-7f3c-4c85-a7de-c07474140d69
date added to LUP
2019-12-04 12:49:44
date last changed
2020-01-13 02:34:24
@article{8f52fd58-7f3c-4c85-a7de-c07474140d69,
  abstract     = {<p>We introduce a financial portfolio optimization framework that allows to automatically select the relevant assets and estimate their weights by relying on a sorted ℓ<sub>1</sub>-Norm penalization, henceforth SLOPE. To solve the optimization problem, we develop a new efficient algorithm, based on the Alternating Direction Method of Multipliers. SLOPE is able to group constituents with similar correlation properties, and with the same underlying risk factor exposures. Depending on the choice of the penalty sequence, our approach can span the entire set of optimal portfolios on the risk-diversification frontier, from minimum variance to the equally weighted. 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 sparse equally weighted portfolios, can be developed to exploit the data-driven detected similarities across assets.</p>},
  author       = {Kremer, Philipp J. and Lee, Sangkyun and Bogdan, Małgorzata and Paterlini, Sandra},
  issn         = {0378-4266},
  language     = {eng},
  publisher    = {Elsevier},
  series       = {Journal of Banking and Finance},
  title        = {Sparse portfolio selection via the sorted ℓ<sub>1</sub>-Norm},
  url          = {http://dx.doi.org/10.1016/j.jbankfin.2019.105687},
  doi          = {10.1016/j.jbankfin.2019.105687},
  volume       = {110},
  year         = {2020},
}