A Benchmark-Asset Principal Component Factorization for Index Tracking on Large Investment Universes

A novel index-tracking methodology combining benchmark-asset selection with PCA to efficiently replicate large equity indices. Applied to the S&P 500 and Euro Stoxx 50, the method achieves near-perfect tracking with dramatically reduced portfolio cardinality, outperforming classical optimisation methods on both in-sample and out-of-sample tracking error — critical for transaction-cost minimisation and regulatory compliance.