Sparse and stable Markowitz portfolios.

Journal Article (Journal Article)

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 accounting 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 naïve evenly weighted portfolio.

Full Text

Duke Authors

Cited Authors

  • Brodie, J; Daubechies, I; De Mol, C; Giannone, D; Loris, I

Published Date

  • July 2009

Published In

Volume / Issue

  • 106 / 30

Start / End Page

  • 12267 - 12272

PubMed ID

  • 19617537

Pubmed Central ID

  • PMC2718382

Electronic International Standard Serial Number (EISSN)

  • 1091-6490

International Standard Serial Number (ISSN)

  • 0027-8424

Digital Object Identifier (DOI)

  • 10.1073/pnas.0904287106


  • eng