A benchmark-asset principal component factorization for index tracking on large investment universes

Abstract

This paper proposes an innovative methodology based on a benchmark-asset principal component factorization to determine a tracking portfolio that replicates the performance of a benchmark by investing in a subset of assets of a large investment universe. Our approach exploits the spectral decomposition of each benchmark-asset covariance matrix to formulate the tracking error, which is minimized by analyzing its eigenvalues. We present an in-depth comparison of several competing strategies on real-world data in terms of out-of-sample performance and computational efficiency. The empirical analysis highlights that our approach shows index tracking abilities similar to the optimization-based portfolio selection model but with lower turnover and faster running times of about four orders of magnitude. Furthermore, small replicating portfolios obtained by our method also provide investment performance comparable to the difficult-to-beat equally weighted portfolio.