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Sparse Long-only Markowitz Portfolio Optimization.

Home
Sparse Long-only Markowitz Portfolio Optimization.

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Published on: August 18, 2023

Sparse long-only Markowitz portfolio optimization.

¹School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China.

Journal of Applied Statistics

|June 11, 2026

View abstract on PubMed

Summary

This summary is machine-generated.

This study introduces a new method for optimizing investment portfolios, making them sparser and improving performance using non-convex penalties. This approach enhances risk control and returns for long-only investments.

Keywords:

62P05 62P20 ADMM non-convex penalty portfolio optimization portfolio regularization sparsity

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Published on: August 18, 2023

Area of Science:

Quantitative Finance
Computational Finance

Background:

Markowitz mean-variance optimization is a cornerstone of modern portfolio theory.
Implementing long-only constraints in portfolio optimization presents unique challenges for achieving sparsity.

Purpose of the Study:

To develop a novel regularization framework for Markowitz mean-variance portfolio optimization under long-only constraints.
To investigate the use of non-convex penalties for enhancing portfolio sparsity and out-of-sample performance.

Main Methods:

Derivation of a sufficient condition for portfolio sparsity.
Application of non-convex penalties: SCAD, TLP, and MCP.
Development of an ADMM-type algorithm for efficient computation.
Validation through simulations and empirical analysis of S&P 500 stocks.

Main Results:

Identified factors (low returns, high volatilities, co-volatilities) influencing asset exclusion.
Demonstrated that non-convex penalties lead to sparser portfolios.
Achieved superior Sharpe ratios, reduced turnover, and better risk control compared to existing methods.

Conclusions:

The proposed regularization framework effectively enhances portfolio sparsity under long-only constraints.
Non-convex penalties offer a robust approach to improving portfolio performance and risk management.
The ADMM-type algorithm provides an efficient computational solution for practical implementation.