Markowitz Portfolio Construction at Seventy

ArXiv ID: 2401.05080 “View on arXiv”

Authors: Unknown

Abstract

More than seventy years ago Harry Markowitz formulated portfolio construction as an optimization problem that trades off expected return and risk, defined as the standard deviation of the portfolio returns. Since then the method has been extended to include many practical constraints and objective terms, such as transaction cost or leverage limits. Despite several criticisms of Markowitz’s method, for example its sensitivity to poor forecasts of the return statistics, it has become the dominant quantitative method for portfolio construction in practice. In this article we describe an extension of Markowitz’s method that addresses many practical effects and gracefully handles the uncertainty inherent in return statistics forecasting. Like Markowitz’s original formulation, the extension is also a convex optimization problem, which can be solved with high reliability and speed.

Keywords: Markowitz Portfolio Theory, Convex Optimization, Risk-Return Trade-off, Portfolio Construction, Forecasting, Multi-Asset

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper features advanced convex optimization theory and robust formulations (high math), while providing extensive numerical experiments and back-testing frameworks (high rigor).

  flowchart TD
    A["Research Goal: Extend Markowitz portfolio construction<br>to handle practical constraints & statistical uncertainty"] --> B["Key Methodology: Convex Optimization Framework"]
    B --> C["Inputs: Asset Return Forecasts<br>& Covariance Matrices"]
    C --> D["Computational Process:<br>Convex Optimization with Constraints"]
    D --> E["Key Outcomes:<br>Robust, Fast, & Practical Portfolio Solution"]