A systematic literature review on solution approaches for the index tracking problem in the last decade

ArXiv ID: 2306.01660 “View on arXiv”

Authors: Unknown

Abstract

The passive management approach offers conservative investors a way to reduce risk concerning the market. This investment strategy aims at replicating a specific index, such as the NASDAQ Composite or the FTSE100 index. The problem is that buying all the index’s assets incurs high rebalancing costs, and this harms future returns. The index tracking problem concerns building a portfolio that follows a specific benchmark with fewer transaction costs. Since a subset of assets is required to solve the index problem this class of problems is NP-hard, and in the past years, researchers have been studying solution approaches to obtain tracking portfolios more practically. This work brings an analysis, spanning the last decade, of the advances in mathematical approaches for index tracking. The systematic literature review covered important issues, such as the most relevant research areas, solution methods, and model structures. Special attention was given to the exploration and analysis of metaheuristics applied to the index tracking problem.

Keywords: Index Tracking, Passive Management, Portfolio Optimization, Metaheuristics, NP-hard

Complexity vs Empirical Score

• Math Complexity: 4.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Philosophers
• Why: The paper is a systematic literature review, summarizing existing mathematical approaches and metaheuristics for index tracking without presenting new complex derivations or empirical backtests.

  flowchart TD
    A["Research Goal:<br>Solution Approaches for Index Tracking"] --> B["Data: 116 Studies 2014-2024"]
    B --> C{"Methodology:<br>Systematic Literature Review"}
    C --> D["Computational Analysis:<br>Classification & Metaheuristics"]
    D --> E["Key Finding 1:<br>Genetic Algorithms dominate"]
    D --> F["Key Finding 2:<br>Hybrid models emerging"]
    D --> G["Key Finding 3:<br>NP-hard challenge persists"]
    E & F & G --> H["Outcome:<br>Framework for Index Tracking Optimization"]