In my understanding, factor analysis is a method developed to avoid the mass estimation of the variance-covariance matrix when doing Markowitz Allocation.
Factor Analysis breakdown the risk factors in stocks into risk factors in portfolio. It apply the basic OLS method to regress out the factors that affact the portfolio return. The more variance the factor estimator could explain, the better factor we have found.
Principle Component Analysis is a way of achieving factor analysis. Instead of find the factor, it find the prouct of factor and the weight of the factor.
We can understand the stock returns as a realization of K factors, but there many be too many factors affecting the return, especially when we face many stocks—their return may be determined by many many factors. So it will be useful to apply the view to the whole portfolio and find out their common factor, rather than look into specific stock.
So, how can we find a set of good factors? PCA provides us with a tool. We can understand PCA as a tool to deduct the dimension of factors. It is a transformation of matrix—it reflects the stock return into fewer but common dimensions, while try to keep the most of variances.
A good set of factor should be able to leave us a diagonal matrix of residuals after the regression—the variation of each stock is orthogonal to each other, that means the comovements (i.e. the common factors are well captured by us).
So here we start an experiment of PCA analysis. The return data is the 5 stocks with biggest capital in SSE (China), and the factor we think of is margin debt growth in SSE. This is a toy model, we want to see what the residual looks like, so don‘t worry too much.
The methods we apply is based on this tutorial: https://www.evernote.com/shard/s155/sh/196f2061-56f6-4a14-9a6c-ddd9efda3856/0b11651f872f2471bd3b365ae9b9f42a.
原文：http://www.cnblogs.com/tiantianlin/p/4973169.html