Sparse and stable Markowitz portfolios

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

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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.

Date: 2007-07, Revised 2008-05
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Citations: View citations in EconPapers (45)

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http://arxiv.org/pdf/0708.0046 Latest version (application/pdf)

Related works:
Working Paper: Sparse and stable Markowitz portfolios (2008)
Working Paper: Sparse and Stable Markowitz Portfolios (2007)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:0708.0046

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