Paper: arXiv 2610.04221

Authors: Jun Cai, Zhiqiao Song

Abstract

The enhanced index tracking (EIT) portfolio selection problem aims to construct a portfolio that is expected to outperform a benchmark index. In practice, investors face uncertainty in the joint distribution of asset and index losses, as the true distribution is typically unknown and only partial information is available. Moreover, portfolio selection requires balancing the trade-off between mean loss and downside risk while targeting higher returns. Effectively modeling and managing these factors in EIT portfolio selection is therefore of both practical and research interest. To address these challenges, this paper proposes robust EIT portfolio selection models under distributional uncertainty, guided by Pareto-optimality theory. The models minimize a convex combination of worst-case mean loss and downside risk, subject to a constraint on worst-case mean return. Two uncertainty sets are considered: one assuming a known mean loss vector and covariance matrix, and a more general set with unknown moments. Closed-form solutions are derived for the former, while the latter reduces to tractable convex optimization problems. Empirical results based on real market data show that the proposed models outperform not only the tracked index but also the equally weighted portfolio, robust mean-variance models, and robust variance models in terms of out-of-sample cumulative wealth, as well as Sharpe, Sortino, and Omega ratios. Moreover, portfolios that minimize a convex combination of worst-case mean loss and downside risk consistently outperform those that minimize downside risk alone. We also provide practical guidance for selecting optimal weighting coefficients to effectively balance risk and return.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a robust mathematical framework for EIT under distributional uncertainty, including closed-form solutions and tractable convex optimization problems. It supports its theoretical claims with strong empirical results using real market data and various performance metrics, demonstrating a solid balance between advanced theory and practical application.

Research Flowchart

  flowchart TD
    A[Research Goal: Robust Enhanced Index Tracking under Distributional Uncertainty] --> B{Methodology: Robust Optimization & Pareto-Optimality};
    B --> C[Inputs: Real Market Data (Asset & Index Losses)];
    C --> D{Computational Processes: Closed-form Solutions & Convex Optimization};
    D --> E[Outcomes: Outperformance vs. Benchmarks & Baselines];
    E --> F[Key Findings: Superior Performance of Combined Loss/Risk Models, Practical Guidance for Weight Selection];