Factor analysis (Factor analytical Sharp)

In my understanding, factor analysis was 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 to 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-a-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 is too many factors affecting the return , especially when we face many stocks-their return is determined by many many factors. So it'll be useful to apply the view to the whole portfolio and find out their common factor, rather than look into spec Ific 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's 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 is able to leave us a diagonal matrix of residuals after the regression-the variation of each The stock is orthogonal to all other, which means the comovements (i.e. the common factors are well captured by us).

So here we start a experiment of PCA analysis. The return data is the 5 stocks with biggest capital in SSE (PRC), and the factor we think of is margin debt growth in S SE. This was a toy model, we want to see what the residual looks like and 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.

Factor analysis (Factor analytical Sharp)