come on ,with your passation.

CAPM is based on the analysis of Mea-Variance Model. In MV Model he efficient frontier is a line which can maximize the ultility of investors and minimize the risks of the portfolio. To get Efficient Frontier mathematically, we can minimize the deviation of portfolio subject to maximize the utility function of investor. Put it in an intuitive way, the EF is just the parabola of effient sets allowing risk free borrowing and lending. If we assume that there are risk free borrowing and lending and existence of risk free asset, we therefore can draw a tangent line with the parabolic line. That line is the line we call EF. For the assumption of facing the same EF and Market portforlio( market portfolio can be obtained by "two fund theorem"), we employ the "two fund separation" to draw a line, the Capital Market Line. This line is the same with the EF we described early. However, there are still some misleading if the interest rates of borrowing and lending are different. So we can adjust the EF in MV model, EF can be devided by three parts straight-line, parabola and then straight line again.

We have different EF to reflect different assumptions indeed, such only with risk free borrowing but withour lending whatever. If there is not a risk free asset, the EF can be above half part of opportunity sets frontier, that is a half of parabola.

I hope my argument is useful and helpful for you, mate.

I strongly recommand you to cover the book INVESTMENTS BY SHARPE. It is really superb for our module cos you know this smart guy is the inventor of CAPM. Cheers!