Paper: arXiv 2407.05912

Abstract

This paper focuses on the application of quantitative portfolio management by using integer programming and clustering techniques. Investors seek to gain the highest profits and lowest risk in capital markets. A data-oriented analysis of US stock universe is used to provide portfolio managers a device to track different Exchange Traded Funds. As an example, reconstructing of NASDAQ 100 index fund is presented.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs substantial mathematical formulations including integer programming, Lagrangian optimization, and quadratic variance minimization. It demonstrates strong empirical rigor by backtesting on real-world data (Yahoo Finance, WRDS Compustat) with specific train-test splits, tracking error calculations, and turnover metrics across multiple rebalancing frequencies.

Research Flowchart

  flowchart TD
  A["Research Goal: <br>Quantitative Portfolio Optimization"] --> B["Input: US Stock Data &<br>NASDAQ 100 Index"]
  B --> C{"Methodology"}
  C --> D["Clustering Algorithm"]
  C --> E["Integer Programming"]
  D --> F
  subgraph F ["Computational Process"]
      direction LR
      F1["Stock Grouping"] --> F2["Selection Logic"] --> F3["Optimization"]
  end
  E --> F
  F --> G["Key Outcomes:<br>Reconstructed Index Fund"]
  G --> H["Conclusion:<br>Effective ETF Tracking Device"]