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Sparse and stable Markowitz portfolios

Author

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

Suggested Citation

  • Giannone, Domenico & De Mol, Christine & Brodie, Joshua & Daubechies, Ingrid & Loris, Ignace, 2008. "Sparse and stable Markowitz portfolios," Working Paper Series 936, European Central Bank.
  • Handle: RePEc:ecb:ecbwps:2008936
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    References listed on IDEAS

    as
    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 5829, C.E.P.R. Discussion Papers.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. 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.
    4. 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.
    5. 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.
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    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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