Sparse and stable Markowitz portfolios. (English) Zbl 1203.91271

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

Proc. Natl. Acad. Sci. USA 106, No. 30, 12267-12272 (2009).

Summary: 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.

MSC:

91G10

Portfolio theory

Keywords:

penalized regression; portfolio choice; sparsity

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