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Sparse and Stable Markowitz Portfolios

Author

Listed:
  • Brodie, Joshua
  • Daubechies, Ingrid
  • De Mol, Christine
  • Giannone, Domenico

Abstract

The Markowitz mean-variance optimizing framework has served as the basis for modern portfolio theory for more than 50 years. However, 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. In this paper we address these issues of estimation error by regularizing the Markowitz objective function through the addition of a penalty proportional to the sum of the absolute values of the portfolio weights (l1 penalty). This penalty stabilizes the optimization problem, encourages sparse portfolios, and facilitates treatment of transaction costs in a transparent way. We implement this methodology using the Fama and French 48 industry portfolios as our securities. 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 highly desirable attribute for real life applications. We conclude by discussing a collection of portfolio construction problems which can be naturally translated into optimizations involving l1 penalties and which can thus be tackled by algorithms similar to those discussed here.

Suggested Citation

  • Brodie, Joshua & Daubechies, Ingrid & De Mol, Christine & Giannone, Domenico, 2007. "Sparse and Stable Markowitz Portfolios," CEPR Discussion Papers 6474, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:6474
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    References listed on IDEAS

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    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    2. Brodie, Joshua & Daubechies, Ingrid & De Mol, Christine & Giannone, Domenico, 2007. "Sparse and Stable Markowitz Portfolios," CEPR Discussion Papers 6474, C.E.P.R. Discussion Papers.
    3. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2008. "Forecasting using a large number of predictors: Is Bayesian shrinkage a valid alternative to principal components?," Journal of Econometrics, Elsevier, vol. 146(2), pages 318-328, October.
    4. 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, August.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Penalized Regression; Portfolio Choice; Sparse Portfolio;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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