Several Methods On Index Replication And Demonstration

The Index Future (IF) will be launched in China soon. There are mainly three functions of IF: hedging, speculating and arbitraging. The spot-future arbitrage and the spread through time arbitrage are two important forms of the IF arbitrage. We have to investigate in index replication because the spot-future arbitrage has to buy or sell spot portfolios. The spot-future arbitrage could be divided into positive arbitrage and reverse arbitrage.In this article, the information of HS300, IF and the IF arbitrage is introduced firstly. Then, we sort the methods of index replication by how to answer the three questions: how many stocks you choose, which stocks you choose, and how to scheme the weights of stocks. We propose four methods to choose stocks: weight, value, industrial stratified weight and industrial stratified value. Next, two common methods, expanding in proportion (EP) and minimizing square sum of residues (MSSR), are introduced specially. On the basis of EP and MSSR, we propose the optimized method subjected to weight restriction (OMWR). The weights of OMWR fluctuate around the weights calculated from EP. In the investigation of the interval of the positive arbitrage, we find out that the positive excess return will improve the return of arbitrage. On the basis of MSSR, we propose a new optimized method (OMOF).Through demonstration of the four methods mentioned above, we find out that:a) No matter we use which of four methods to choose stocks, the tracing error of EP, MSSR and OMWS all increase with time.b) No matter in short term, medium term or long term, the tracing error of OMWR is between EP's and MSSR's or better than both EP's and MSSR's. In fact, OMWR owns the merits of EP and MSSR.c) No matter we use which of four methods to choose stocks, the excess return of MSSR and OMOF decreases with time. This is related to the fact that the in-sample index data fluctuates, but the out-of-sample index data goes down.d) When we use value method and industrial stratified value method to choose stocks, OMOF's excess return is similar to MSSR's. When we use weight method to choose stocks, OMOF's excess return is higher than MSSR's. Furthermore, the difference increases with time. When we use industrial stratified weight method to choose stocks, OMOF's excess return is lower than MSSR's. The difference increase firstly with time, then decrease.