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Introduction
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Related Experiment Video

Updated: Jun 21, 2026

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Sparse and stable Markowitz portfolios.

Joshua Brodie1, Ingrid Daubechies, Christine De Mol

  • 1Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544-1000, USA.

Proceedings of the National Academy of Sciences of the United States of America
|July 21, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a penalized regression method for portfolio selection, creating sparser portfolios with lower transaction costs. The approach yields significantly better out-of-sample performance than traditional methods.

Related Experiment Videos

Last Updated: Jun 21, 2026

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Area of Science:

  • Quantitative Finance
  • Computational Finance
  • Investment Management

Background:

  • The Markowitz mean-variance framework is a cornerstone of modern portfolio theory.
  • Traditional optimization can lead to overly complex portfolios and high transaction costs.
  • Achieving robust out-of-sample performance remains a challenge in portfolio selection.

Purpose of the Study:

  • To reformulate portfolio selection as a penalized least-squares regression problem.
  • To develop a method that encourages sparse portfolios and accounts for transaction costs.
  • To improve out-of-sample performance compared to standard and naive approaches.

Main Methods:

  • A penalty term proportional to the sum of absolute portfolio weights is added to the objective function.
  • The method regularizes the optimization problem, promoting sparsity.
  • The approach allows for limited short positions, offering flexibility.

Main Results:

  • The penalized regression approach successfully constructs sparse portfolios.
  • The methodology was tested on Fama-French benchmark datasets.
  • Out-of-sample portfolios demonstrated consistently superior Sharpe ratios compared to the naive equally weighted portfolio.

Conclusions:

  • Penalized least-squares regression offers a robust alternative for portfolio optimization.
  • The proposed method balances sparsity, transaction costs, and performance.
  • This technique provides a significant improvement in investment strategy effectiveness.