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Multi-scale tracking dynamics and optimal index replication

We investigate the index tracking model with the analysis and optimization of tracking dynamic properties. The return deviations between tracking portfolio and the index are first decomposed into several components with different time-scale features. Our model then filters out components at low frequencies. Our approach is implemented to five data sets drawn from major world markets. The results show that our method could control the tracking dynamics and such control could also improve the terminal performance of index tracking.