A Study On The Index Replication Model

The most commonly-used index replication methods are full replication, opti-mized replication, and sampling replication.This paper is to study and conclude the pros and cons of these replication methods, with the empirical testing of the most representative index of the market-CSI 300 Index. First, this paper summarizes the prior research on index replication models and introduces several commonly-used op-timization and sampling methods. For optimization methods, this paper introduces three methods according to different optimization functions and strategies. For sam-pling methods, it introduces four methods according to different stratified sampling ideas. In the empirical testing phase, for optimized replication and sampling repli-cation, minimizing the tracking error under a quadratic programming framework is defined to be the target function and the sample is stratified by different industry sectors, with the individual stock concentration degree, rebalancing cost, and the minimum stock owned amount as the constraints of optimization. For testing the effectiveness of each index replication method, with the time series data for 5,10,30 business days since effective date of each regular review respectively, as well as the time series data for each period between effective dates of two consecutive regular reviews, the following conclusion can be drawn empirically:with respect to accuracy of replication, full replication is the most accurate method, optimized replication is the next and sampling replication is the poorest; with respect to rebalance cost, full replication is the most cost consuming, optimized replication is the next and sampling replication is the least. The innovation contribution of this paper lies in that, while taking into account of the heteroscedasticity of the stock and index re-turn series, each observed value is assigned a geometrical weight with the improved optimization algorithm based on EWMA model, that is, the later observed value is assigned a larger weight while the earlier observed value is assigned a smaller one. The following conclusion can be finally drawn based on empirical studies:compar-ing with the optimization algorithm based on general model, the tracking error has been better eliminated with the improved optimization algorithm based on EWMA model while the rebalance cost does not show a significant increase, which indicates an effective improvement of index optimized replication made by EWMA model.