PCA on the stocks

I have N stocks, and a covariance matrix that indicates the covariance of these N random variables. Now, if I run PCA on the covariance matrix, what can you tell about the principle component?

• If you have a covariance matrix of the returns, the first principle component is comparable to the CAPM or the Single Index Model, ie, there is one common factor that explains a good part of the individual returns Nov 29 '20 at 12:23

If $$N$$ is large, then the first eigendirection or pc is the main factor that moves these assets. So one might say that this "common single factor among all stocks" is the general market risk of the market portfolio ($$\beta$$ in CAPM), i.e. a factor not attributed to individual stocks, rather global macro aspects.