I am new to PCA and am having trouble understanding some parts of the methodology. In multi-factor models you can run regressions like:
Stock Return = A(1)*Size + A(2)*Market Return + ...
So in this case, you have a clear understanding of what is driving the stocks return. Now, when you have a system of say 100 stocks and extract the 3 most important principal components, is there any way of actually understanding where the risk is coming from? For example, if you ran a regression like:
Stock Return = A(1)*PC1 + A(2)*PC2
While that would tell you the effect of each component, how can that actually help an investor manage their portfolio? Because the PC doesn't really tell you what the actual risk factor is right? Or are you supposed to then run something like:
PC1 = A(1)*Size +...+
To determine what underlies each component?
Please help me with an intuitive answer.