Efficient Frontiers and CML

[wat]

I must’ve missed out on this in Finance 101, but can someone explain to me the shape of the efficient frontier? I understand that if you only consider risky assets, you end up with something that looks like a truncated y = log(x) graph, or the top half of a parabola that opens to the right, and that when you add a risk-free asset to the mix, you end up with the CML - a straight line that starts at the risk-free rate and goes through M, the optimal risky portfolio.
My question is, why do they get those shapes? In particular, I’m still wondering why adding a risk-free asset creates a linear efficient frontier.

 

[mdecav]

The shape is what it is. Kinda like the Nike symbol upside down.
http://en.wikipedia.org/wiki/Efficient_frontier#The_efficient_frontier
Risky assets only: Markowitz’s efficient frontier (Nike symbol).
Risk-free asset & optimal risky portfolio: Straight line.
If you own 100% of the risk-free asset, you are on the y axis at the risk-free rate.
If you own 100% the market portfolio, you are in the graph somewhere along the efficient frontier that maximizes the angle of the CML from the risk-free asset to the market portfolio.
If you own a portion of both, you’re on the CML somewhere in between both points.
The CML “dominates” the Markowitz efficient frontier either by a higher return for a given risk or a lower risk for given a return objective.