Robust Factor Analysis and Its Applications in the CSI 100 Index

We apply the object-oriented robust factor analysis R package robustfa to the 28 financial indicators of the 100 listed companies in China’s Chinese Securities Index (CSI) 100 index in the first quarter of 2013. First of all, according to the size of the data, we automatically choose a robust estimator, the robust Ogk estimator. By the Mahalanobis distances which are computed by the robust Ogk estimator, greater than the critical value, we find a total of 47 abnormal points. This paper discovers that the results of the sample correlation matrix, the rotated factor loading matrix, the contribution of the factors to the original variables, the contribution rate, the cumulative contribution rate, the screeplot of the eigenvalues of the sample correlation matrix, the scatter plot of the first two factor scores, factor scores, and the sorted scores according to factor scores etc. computed by the classical estimator and the robust Ogk estimator are quite different. Finally, we condense the 28 financial indicators to 5 factors by combining the principal component analysis method and the robust Ogk estimator: Provident fund market value factor, profit factor, market value profit rate factor, value per share factor, and asset liability factor. Finally, we sort the 5 factor scores from high to low of each factor, and also get some special stocks according to the factor scores. The robust factor analysis results provide a good basis for investors to choose the stocks.