Sparse and stable Markowitz portfolios

TL;DR

This paper introduces a regularized portfolio optimization method that promotes sparsity and stability, improving out-of-sample performance over naive benchmarks by penalizing portfolio weights.

Contribution

It proposes a novel regularization approach within the Markowitz framework that encourages sparse, stable portfolios and accounts for transaction costs, with demonstrated empirical benefits.

Findings

Regularized portfolios outperform naive benchmarks in Sharpe ratio.

Method effectively promotes sparse portfolios with limited short positions.

Empirical results on benchmark datasets show significant out-of-sample improvements.

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.