With the efficiency improvements of the stock market in China,above 70% individual stock risk can be eliminated with diversification,so diversification improve portfolio obviously.With main component analysis,we demonstrate the composite stock index and the composite A-index are good indexes in that they can reflect market behavior.But they are not good indexes to tell us the returns of investment strategies.According to APT model,with main component analysis,cluster analysis,regression analysis,and optimization,above 20 stocks are selected to form a portfolio that can have the same return as the Shanghai composite A-index in a not long time.So by investing a few stocks,a return of index is obtained.

运用主成分分析法分析我国上海和深圳两个交易所几个市场指数对市场变化的反应情况,结果表明两个股票市场的综合指数和A股指数可以反应市场的变化,而其他指数不能反映各自代表的股票市场变化.由于这4个指数都不是一个好的投资组合,要得到与指数一致的投资收益需要构造指数投资组合.本文利用多因子定价模型,结合统计分析和优化方法,从每个股票市场上选取20余支股票,经过适当的组合就可以得到与指数一致的收益.