Construction, management, and performance of sparse Markowitz portfolios

We study different implementations of the sparse portfolio construction and rebalancing method introduced by Brodie et al. (Brodie, J., I. Daubechies, C. De Mol, D. Giannone, and I. Loris. 2009. ``Sparse and Stable Markowitz Portfolios.'' PNAS 106 (30): 12267-12272). This technique is based on the use of a l(1)-norm (sum of the absolute values) type penalization on the portfolio weights vector that regularizes the Markowitz portfolio selection problem by automatically eliminating the dynamical redundancies present in the time evolution of asset prices. We make specific recommendations as to the different estimation techniques for the parameters needed in the use of the method and we prove its good performance in realistic situations involving different rebalancing frequencies and transaction costs. Our empirical findings show that the beneficial effects of the use of sparsity constraints are robust with respect to the choice of trend and covariance estimation methods used in its implementation.