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ETF portfolio construction by feature selection based index tracking

Problem statement

Passive investment vehicles like ETFs require a precise index replication method to minimize tracking error while adhering to regulatory constraints (e.g., UCITS 5/10/40 rule). Traditional approaches, such as mixed-integer programming (MIP), face computational hurdles, while newer machine learning approaches based on autoencoders tend to ignore practical financial constraints.

Approach

We propose a two-stage approach that combines the strengths of machine learning and portfolio optimization:

  1. Feature selection: we select the most relevant index constituents to obtain a small, efficient sample, using recursive feature elimination (RFE) with linear methods (OLS, ridge, LASSO, elastic net, and linear SVR) and tree-based methods (random forest, XGBoost), while controlling the portfolio size explicitly.
  2. Portfolio optimization: we then determine the portfolio weights under financial constraints (no short selling, diversification rules) so as to minimize tracking error.

Contributions

  • A feature selection perspective on the construction of tracking portfolios.
  • Comparable tracking error, diversification, and portfolio turnover to MIP-based optimized sampling at substantially lower computational cost.
  • Lower tracking error and turnover than autoencoder-based selection, with markedly greater diversification.
  • Integration of diversification constraints limiting single-stock and sector concentration, in line with regulatory requirements.

Empirical evaluation

  • Datasets: S&P 500 and CSI 300 (16 years of test data, multiple market regimes).
  • Results: RFE with the linear methods matches MIP in tracking error, turnover, and diversification.
  • Autoencoder-based selection yields higher tracking error and turnover, at higher computational cost and with lower interpretability.
  • Tree-based methods scored worse on the evaluation criteria than the linear methods and were not competitive for constituent selection in our setting.

Implications

  • For research: the results establish a feature selection perspective on financial index tracking and document the limitations of autoencoder-based selection under explicit portfolio constraints.
  • For practice: the framework is scalable and transparent, and is applicable to UCITS-compliant ETFs at reduced computational cost.

Conclusion

The study connects machine learning methods with practical portfolio construction, with an emphasis on parsimony, interpretability, and regulatory compliance.

The paper has been published open access in Applied Soft Computing as Feature selection based index tracking: A two-stage approach for optimized sampling.