Network‐based index tracking using asset dependency structures

Index tracking aims to replicate the performance of a selected index by constructing a portfolio. Tracking portfolio decisions rely on minimizing tracking error or the linear relationships among assets, neglecting the impact of complex nonlinear asset dependency structures on portfolio performance. In this paper, the network‐based index tracking model without adaptive adjustment (ITN) and the network‐based index tracking model with adaptive adjustment (ITNA) are proposed by utilizing asset dependency structures. Specifically, we construct networks based on the correlations among assets and express community structure and asset centrality, which reflect the dependency structure, as community structure constraints and centrality constraints, thus forming ITN. This model allows the portfolio to replicate the structure of the index, leading to improved tracking performance. To continuously benefit from asset dependency structures, it is necessary to adjust the portfolio when it significantly diverges from the new dependency structure. A structural consistency constraint, which allows for adjustments to the portfolio in response to variations in the dependency structure, is incorporated into ITN, resulting in ITNA. Empirical tests are conducted using data from six stock market indices. Compared to general index tracking, ITN achieves higher adjusted returns with reasonable tracking error. Additionally, ITNA achieves lower tracking errors and higher adjusted returns in large indices compared to the periodic adjustment strategy.