Index-tracking Research Based On The ISPCA

With the rapid development and increasing maturity of Chinese stock market,different types of stock index have been raised and the corresponding construction methods have also been improved.Nowadays,more and more individual investors and investment institutions are trying to make investment decisions based on stock indexes.Regarding the constantly changing conditions of the stock market,considering research significance and economic value,it is important to find out a stock index with satisfied performance to construct an ideal stock portfolio that can track the underlying stock index.When making the investment choice of stock portfolio,traditional stock index tracing methods usually copy the proportion of constituent stocks,or construct stock portfolio based on their market value.However,these methods only consider the current time information and data from the stock market,the historical information is not taken into account.In this paper,we divided the yield rate of selected stock index and constituent stocks into training set and test set and adopted the integrated sparse principal component and sparse principal component to extract the informative principal component of the constituent stocks.We selected several most influential stocks in the principal component,based on which we computed the optimal tracing error and the proportion of each stock to compare the performance.Results showed that,in the training set,the tracing error decreased with the number of selected stocks increased,the decrease became slower overtime.The sparse principal component analysis showed satisfied and comparable performance as the available products in the market based on Shanghai and Shenzhen 300 index.For the test set,integrated sparse principal component analysis outperformed the sparse principal component analysis,the tracing performance approximated to some of the products in the market but with a much smaller stock holding,which had certain amount of interpretability and sparsity and could be used as investment guidance for medium and small investors.