I am trying to connect some dots in my understanding between 2 concepts.
Utility function: I can see there there are different utility functions and I can draw them at different levels until I find one that is touching the efficient frontier, call it point A. That will define a portfolio that is optimal for a given utility function.
CAPM line: if I introduce a risk free asset to my portfolio I can draw a straight line between the return of that asset and touch the efficient frontier. Then, this line will have a well known equation and will define an attainable optimal portfolio I can achieve, call it B, and also the one I can get if I lend/borrow using risk free asset.
How those points A and B related. Are they the same in a particular case?