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Sparse and stable Markowitz portfolios

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

Abstract

We consider the problem of portfolio selection within the classical Markowitz meanvariance optimizing framework, which has served as the basis for modern portfolio theory for more than 50 years. Efforts to translate this theoretical foundation into a viable portfolio construction algorithm have been plagued by technical difficulties stemming from the instability of the original optimization problem with respect to the available data. Often, instabilities of this type disappear when a regularizing constraint or penalty term is incorporated in the optimization procedure. This approach seems not to have been used in portfolio design until very recently. To provide such a stabilization, we propose to add to the Markowitz objective function a penalty which is proportional to the sum of the absolute values of the portfolio weights. This penalty stabilizes the optimization problem, automatically encourages sparse portfolios, and facilitates an effective treatment of transaction costs. We implement our methodology using as our securities two sets of portfolios constructed by Fama and French: the 48 industry portfolios and 100 portfolios formed on size and book-to-market. 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 naïve portfolio comprising equal investments in each available asset. In addition to their excellent performance, these portfolios have only a small number of active positions, a desirable feature for small investors, for whom the fixed overhead portion of the transaction cost is not negligible. JEL Classification: G11, C00

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Bibliographic Info

Paper provided by European Central Bank in its series Working Paper Series with number 0936.

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Date of creation: Sep 2008
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Handle: RePEc:ecb:ecbwps:20080936

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Keywords: Penalized Regression; Portfolio Choice; Sparse Portfolio;

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References

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  1. Christine De Mol & Domenico Giannone & Lucrezia Reichlin, 2008. "Forecasting using a large number of predictors: is Bayesian shrinkage a valid alternative to principal components?," ULB Institutional Repository 2013/6411, ULB -- Universite Libre de Bruxelles.
  2. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1684, 08.
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Cited by:
  1. Jianqing Fan & Yuan Liao & Xiaofeng Shi, 2013. "Risks of Large Portfolios," Papers 1302.0926, arXiv.org.
  2. Serge Darolles & Christian Gouriéroux & Emmanuelle Jay, 2012. "Robust Portfolio Allocation with Systematic Risk Contribution Restrictions," Working Papers 2012-35, Centre de Recherche en Economie et Statistique.
  3. Bjoern Fastrich & Sandra Paterlini & Peter Winker, 2011. "Cardinality versus q-Norm Constraints for Index Tracking," Center for Economic Research (RECent) 056, University of Modena and Reggio E., Dept. of Economics.
  4. Mayr, Johannes, 2010. "Forecasting Macroeconomic Aggregates," Munich Dissertations in Economics 11140, University of Munich, Department of Economics.
  5. Carlos Castro, 2010. "Portfolio choice under local industry and country factors," Financial Markets and Portfolio Management, Springer, vol. 24(4), pages 353-393, December.
  6. Oliver Hülsewig & Johannes Mayr & Timo Wollmershäuser, 2008. "Forecasting Euro Area Real GDP: Optimal Pooling of Information," CESifo Working Paper Series 2371, CESifo Group Munich.
  7. Yu-Min Yen, 2010. "A Note on Sparse Minimum Variance Portfolios and Coordinate-Wise Descent Algorithms," Papers 1005.5082, arXiv.org, revised Sep 2013.
  8. Enzo Busseti & Fabrizio Lillo, 2012. "Calibration of optimal execution of financial transactions in the presence of transient market impact," Papers 1206.0682, arXiv.org.
  9. 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.
  10. Briec, Walter & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2011. "Portfolio Selection with Skewness: A Comparison and a Generalized Two Fund Separation Result," Working Papers 2011/09, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.

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