Penalized Least Squares for Optimal Sparse Portfolio Selection

Markowitz portfolios often result in an unsatisfying out-of-sample performance, due to the presence of estimation errors in inputs parameters, and in extreme and unstable asset weights, especially when the number of securities is large. Recently, it has been shown that imposing a penalty on the 1-norm of the asset weights vector not only regularizes the problem, thereby improving the out-of-sample performance, but also allows to automatically select a subset of assets to invest in. Here, we propose a new, simple type of penalty that explicitly considers financial information and consider several alternative non-convex penalties, that allow to improve on the 1-norm penalization approach. Empirical results on U.S.-stock market data support the validity of the proposed penalized least squares methods in selecting portfolios with superior out-of-sample performance with respect to several state-of-art benchmarks.