Optimizing index tracking: A Random Matrix Theory approach to portfolio selection

Abstract

This paper proposes a novel methodology for index tracking that combines Random Matrix Theory with network-based eigenvalue centrality to construct compact and representative portfolios. The approach filters out noise and systemic effects from the asset correlation structure, enabling the identification of stock communities and the selection of their most influential members. A tunable parameter $\lambda$ balances the trade-off between minimizing tracking error and maximizing excess return. Extensive empirical validation across diverse market conditions—classified using a volatility-based regime framework—confirms the robustness and adaptability of the method. This framework offers a scalable and computationally efficient solution for index tracking, suitable for both institutional investors and practical portfolio management.