Index Portfolio Optimized Replication Analysis Under EWMA Model

The key of index future arbitrage is how to construct stock portfolio to minimizethe tracking error. There are two traditional index replication method, full replicationand optimized replication. Because of transaction costs, it is very difficult to adoptfull replication.The emphasis of this paper is on how to technically construct optimal indexinvestment portfolio under short-term index future arbitrage. Technically, we usingEWMA model to estimate the volatility to improve the traditional quadricprogramming and linear programming. Meanwhile, we restrict the capital andconsider the exchange cost, impact cost, minimum holding level and liquidity risk.We then construct five different methods to choose stocks: weight, value,correlation, industrial stratified weight and industrial stratified value. We choose datafrom Jan.1 2007 to Mar. 31 2007 as in-sample period and Apr. 1 to Apr. 13 2007 asout of sample period to test the tracking error (TE).The main results are as below:1. The 5-days' average TE is much smaller than the 10's.2. EWMA model has effect on industrial stratified value method and little effecton the value method.3. The industrial stratified value method has the minimum TE in our threemodels, while the industrial stratified weight method seems better under the linearprogramming model. We also can see the correlation method always acts the worst.4. If we consider the models and methods together, we will get some interestingresults: The industrial stratified value method using EWMA quadric programmingperforms best under 5-days' average TE test, while the same method using EWMAlinear model seems best under 10-days' test. Thus, we can see our improved modelsusing EWMA can help industrial stratified value method to minimize the TE.