Paper: arXiv 2308.11202

Abstract

Portfolio optimization is a task that investors use to determine the best allocations for their investments, and fund managers implement computational models to help guide their decisions. While one of the most common portfolio optimization models in the industry is the Markowitz Model, practitioners recognize limitations in its framework that lead to suboptimal out-of-sample performance and unrealistic allocations. In this study, I refine the Markowitz Model by incorporating machine learning to improve portfolio performance. By using a hierarchical clustering-based approach, I am able to enhance portfolio performance on a risk-adjusted basis compared to the Markowitz Model, across various market factors.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical techniques like hierarchical clustering, recursive bisection, and quasi-diagonalization of covariance matrices, indicating moderate-to-high complexity. Empirical rigor is strong due to the use of long-term CRSP and Ken French data (1965-2022), multiple look-back windows, and comparative out-of-sample performance metrics against the Markowitz model.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Enhance Markowitz Model<br>using Machine Learning"] --> B["Input: Financial Asset Data<br>Historical Returns & Volatility"]
  
  B --> C["Key Methodology<br>Hierarchical Clustering<br>to group correlated assets"]
  
  C --> D["Computational Process<br>Apply Markowitz Optimization<br>on Clusters vs. Individual Assets"]
  
  D --> E{"Evaluation"}
  E -->|Out-of-Sample| F["Key Finding: Hierarchical Model<br>Superior Risk-Adjusted Returns"]
  E -->|Constraints| G["Key Finding: More Realistic<br>Allocations vs. Standard Markowitz"]
  
  F & G --> H["Outcome<br>Refined Portfolio Optimization Framework"]