Mesoscopic Community-Based Sparse Portfolio for Index Tracking
摘要
Sparse index tracking is a specialized investment strategy that seeks to replicate the returns of a market index using a few assets and is also termed partial replication. Existing statistical approaches usually formulate it as a regression problem, subject to sparsity and practical portfolio constraints. Despite its intuitively appealing formulation, the paradigm exhibits several notable shortcomings. Tracking accuracy bears the brunt of cuts in portfolio size. Partial replication may place a heavy emphasis on individual constituents to fit the sum-to-one constraint. Unsystematic risk may increase due to individual holdings, resulting in diverging tracking results from the market index. To smooth over the fault, this paper rethinks the tracking paradigm by adopting mesoscopic structural properties. From a different angle, a market index is constituted by market assets, and the mesoscopic structure of these assets can be effectively captured through community detection algorithms. Using this transition, the performance of a market index can be further expressed through the different compositions of returns from communities. As the mesoscopic scale corresponds to sets of assets that share similar price dynamics, this allows us to sparsify the representation of the community. Thus, we reformulate the optimization problem, structuring a sparse portfolio based on mesoscopic communities. Simulation results using Russell 1000, MSCI World, and TOPIX datasets demonstrate that our MCSIT improves tracking accuracy under high sparsity and quarterly rebalancing.