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  3. Sparse Long-only Markowitz Portfolio Optimization.
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  3. Sparse Long-only Markowitz Portfolio Optimization.

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Sparse long-only Markowitz portfolio optimization.

Tianci Qian1

  • 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:
62P0562P20ADMMnon-convex penaltyportfolio optimizationportfolio regularizationsparsity

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13:54

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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.