# In Mean-Variance Analysis, why not the efficient frontier being pushed to the left near the axis?

I took some classes in portfolio theory, and learnt the Markowitz Mean-Variance Analysis. If only two risky assets, the efficient frontier would be a hyperbola passing through the two points; now if added another asset has some correlation with them two, the efficient frontier would be pushed to the left of these three risky assets, generally not passing through them; so, if we keep adding more assets, it seems intuitively that the efficient frontier would be pushed further to the left of the assets points; wouldn't the efficient frontier be like tangent to the y-axis(y axis is for return), causing the standard deviation to be almost zero? I also read Pennacchi's book: Theory of Asset Pricing. it derived the equation for the minimum variance set using linear algebra. And found the position for the global minimum standard deviation point. And it's positive. I understand the equation derivation, but didn't get through the problem as I just thought of. Any help? Much appreciated.