Sparse long-only Markowitz portfolio optimization

This paper introduces a novel regularization framework for the Markowitz mean-variance portfolio optimization under long-only constraints. A sufficient condition that explains the sparsity of long-only optimal portfolios is derived, showing that assets with lower returns, higher volatilities, and greater co-volatilities are more likely to be excluded. Non-convex penalties, including SCAD, TLP, and MCP, are employed to enhance portfolio sparsity while preserving robust out-of-sample performance. An ADMM-type algorithm is developed for efficient portfolio weighting computation, and its effectiveness is demonstrated through both simulations and empirical studies using S&P 500 constituent stocks. The results highlight the ability of non-convex penalties to achieve sparser portfolios with superior Sharpe ratios, reduced turnover, and controlled risks compared to existing methods.