Research Of Combination Of Equity Investments Under Sparse Principal Component Analysis

Principal component analysis (PCA) is a method widely used in data processing and dimensionality reduction issues.As the principal component analysis are obtained by a linear combination of all the main components of the original variables, it is ofen difficult to explain the cause of the Principal components.This paper presents a new approach named sparsity principal component analysis (SPCA),and applies it to the stock portfolio.There is no scholars who use SPCA to build a portfolio,so this paper extends the study of this part,which builds a portfolios based on SPCA,and carries on the empirical analysis.First,the paper introduces the theory and the basic idea about SPCA,and gives the sparse principal components algorithm based on three different theories.Then,according to the two situations that the number of observations is less than the number of shares and not less than,the paper uses different SPCA algorithms to build a stock portfolio.In order to test the feasibility of the model,in the empirical part,select the871stocks from the Shanghai A-share of52-day-week closing price.According to the official classification,divide them into five sectors:industry,commerce,real estate,public, complex.Then,use the established model to construct investment portfolios and investment ratio in various industries.For comparison with income under SPCA,the paper also builds a portfolio based on PCA,calculates the daily yield, the total rate of return, variance and plots a comparative analysis under two methods in various industries.The results shows that total income rate under SPCA is superior, while the variance that is used to discribe fluctuations is also smaller.Finally,the paper concludes that the earnings of sparse principal components are higher, and the fluctuations are smaller.This result illustrates the effectiveness of the sparsity of principal component analysis in the stock portfolio.