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Feature selection based index tracking: A two-stage approach for optimized sampling

Our paper, written with Mario Brandtner and Christian Pigorsch, has been published open access in Applied Soft Computing.

Background

Behind every exchange-traded fund (ETF) lies a non-trivial problem: how to replicate a benchmark index such as the S&P 500 or the CSI 300 efficiently without holding every constituent.

The established benchmark is mixed-integer programming (MIP), which attains low tracking error but scales poorly in the number of candidate constituents. Deep learning approaches based on autoencoders have more recently been proposed as an alternative, but a systematic evaluation under realistic regulatory regimes (UCITS, the Investment Company Act of 1940) and portfolio constraints (no short selling, weight bounds) was lacking.

Our approach: a two-stage procedure

  1. Recursive feature elimination (RFE) wrapped around supervised learners (ridge, LASSO, elastic net, SVR, XGBoost, random forest, and others) selects the index constituents, with explicit control over portfolio cardinality.

  2. Tracking-error optimization then determines the portfolio weights under all relevant financial constraints.

Findings from 16 years of test data on the S&P 500 and CSI 300

  • The proposed approach matches MIP in tracking error, portfolio concentration, and turnover in a fraction of the computing time (minutes rather than hours).
  • Autoencoders perform consistently worse, with higher tracking error, higher turnover, and more concentrated portfolios. A sensitivity analysis over the autoencoder hyperparameters (summarized with fANOVA and parallel coordinate plots) indicates that this is not an artifact of insufficient tuning.
  • RFE combined with regularized linear methods offers the most favorable trade-off between performance and computational efficiency.

In our setting, autoencoder-based selection was consistently outperformed by simpler, well-specified methods.

The full paper is available here. Open access publication was made possible by the Open Science initiative at Ernst-Abbe-Hochschule Jena.