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Sparse and stable Markowitz portfolios

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  • Joshua Brodie
  • Ingrid Daubechies
  • Christine De Mol
  • Domenico Giannone
  • Ignace Loris

Abstract

We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the sum of the absolute values of the portfolio weights. This penalty regularizes (stabilizes) the optimization problem, encourages sparse portfolios (i.e. portfolios with only few active positions), and allows to account for transaction costs. Our approach recovers as special cases the no-short-positions portfolios, but does allow for short positions in limited number. We implement this methodology on two benchmark data sets constructed by Fama and French. Using only a modest amount of training data, we construct portfolios whose out-of-sample performance, as measured by Sharpe ratio, is consistently and significantly better than that of the naive evenly-weighted portfolio which constitutes, as shown in recent literature, a very tough benchmark.

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File URL: http://arxiv.org/pdf/0708.0046
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0708.0046.

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Date of creation: Jul 2007
Date of revision: May 2008
Handle: RePEc:arx:papers:0708.0046

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  1. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2006. "Forecasting Using a Large Number of Predictors: Is Bayesian Regression a Valid Alternative to Principal Components?," CEPR Discussion Papers, C.E.P.R. Discussion Papers 5829, C.E.P.R. Discussion Papers.
  2. Ravi Jagannathan & Tongshu Ma, 2002. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," NBER Working Papers 8922, National Bureau of Economic Research, Inc.
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Cited by:
  1. Briec, Walter & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2011. "Portfolio Selection with Skewness: A Comparison and a Generalized Two Fund Separation Result," Working Papers, Hogeschool-Universiteit Brussel, Faculteit Economie en Management 2011/09, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
  2. Imre Kondor, 2014. "Estimation Error of Expected Shortfall," Papers 1402.5534, arXiv.org.
  3. Fan, Jianqing & Liao, Yuan & Shi, Xiaofeng, 2013. "Risks of large portfolios," MPRA Paper 44206, University Library of Munich, Germany.
  4. Oliver Hülsewig & Johannes Mayr & Timo Wollmershäuser, 2008. "Forecasting Euro Area Real GDP: Optimal Pooling of Information," CESifo Working Paper Series 2371, CESifo Group Munich.
  5. Carlos Castro, 2010. "Portfolio choice under local industry and country factors," Financial Markets and Portfolio Management, Springer, Springer, vol. 24(4), pages 353-393, December.
  6. Ignace Loris & Caroline Verhoeven, 2013. "An iterative algorithm for sparse and constrained recovery with applications to divergence-free current reconstructions in magneto-encephalography," Computational Optimization and Applications, Springer, Springer, vol. 54(2), pages 399-416, March.
  7. Bjoern Fastrich & Sandra Paterlini & Peter Winker, 2011. "Cardinality versus q-Norm Constraints for Index Tracking," Center for Economic Research (RECent), University of Modena and Reggio E., Dept. of Economics 056, University of Modena and Reggio E., Dept. of Economics.
  8. Caihua Chen & Xindan Li & Caleb Tolman & Suyang Wang & Yinyu Ye, 2013. "Sparse Portfolio Selection via Quasi-Norm Regularization," Papers 1312.6350, arXiv.org.
  9. Yu-Min Yen, 2010. "A Note on Sparse Minimum Variance Portfolios and Coordinate-Wise Descent Algorithms," Papers 1005.5082, arXiv.org, revised Sep 2013.
  10. Serge Darolles & Christian Gouriéroux & Emmanuelle Jay, 2012. "Robust Portfolio Allocation with Systematic Risk Contribution Restrictions," Working Papers, Centre de Recherche en Economie et Statistique 2012-35, Centre de Recherche en Economie et Statistique.
  11. Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2014. "$L_p$ regularized portfolio optimization," Papers 1404.4040, arXiv.org.
  12. Jun-ya Gotoh & Akiko Takeda, 2011. "On the role of norm constraints in portfolio selection," Computational Management Science, Springer, vol. 8(4), pages 323-353, November.
  13. Mohammed Bouaddi & Abderrahim Taamouti, 2012. "Portfolio risk management in a data-rich environment," Financial Markets and Portfolio Management, Springer, Springer, vol. 26(4), pages 469-494, December.
  14. Enzo Busseti & Fabrizio Lillo, 2012. "Calibration of optimal execution of financial transactions in the presence of transient market impact," Papers 1206.0682, arXiv.org.
  15. Mayr, Johannes, 2010. "Forecasting Macroeconomic Aggregates," Munich Dissertations in Economics 11140, University of Munich, Department of Economics.
  16. Akiko Takeda & Mahesan Niranjan & Jun-ya Gotoh & Yoshinobu Kawahara, 2013. "Simultaneous pursuit of out-of-sample performance and sparsity in index tracking portfolios," Computational Management Science, Springer, vol. 10(1), pages 21-49, February.

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