When Sharpe's Single-Index model was applied to the Korean Stock Market, it's explanatory powers were very low. This implied the existence of the Extra-Market Components in the Korean market. The assumption that the returns of various stocks are related only through common relationships with the market was rejected through the Chi-Square test. Then Three Two-Factor Models were constructed.
Homogeneous Group effects were introduced through the Cluster Analysis technique suggested by King. Pseudo-Industry effects were introduced through Principal Component Analysis. An Interest-Rate factor was introduced as an Extra-Market Component. Canonical Correlation Analysis was used in order that the effects of the Interest-Rate be analyzed further. Additionally, Three Factor Analysis methods (Principal Component, Alpha, and Rao) were applied to the two different samples.
It is interesting that the stock belonging to the "Construction Industry" were clustered into a unique group by the Cluster Analysis and the Pseudo-Industry technique. The Interest-Rate factor did not have any significant explanatory powers, but played important roles in the determination of the characteristics of the groups. The results of the Canonical Correlation Analysis suggested the high possibility that the first factor may not be the market factor. It was found that the structures of the factors extracted by the Factor Analysis methods were not clear in comparison to those of the U.S. Stock Markets. These structures of the factors resulted in the difficulty in finding common factors.
The findings of this article may not be general because of the size of the samples. The samples must be extended time-serially and cross-sectionally to obtain more general findings.
