Show that when =0 the portfolio curve for two assets is convex to the left.

The above is all we are given on the homework.

- In class, we plot this in the first quadrant of the plane with sigma on the horizontal axis, and expected rate of return (rbar) on the vertical axis. Convex to the left means a parabola with the open end on the right. It is a graph we have drawn before... but that's it.

- The professor suggested that we solve this problem by considering sigma as a function of rbar, and show that the second derivative is greater than 0. He also said that rbar is really a function of some alpha, and as alpha increases, rbar increases, so we can instead work with sigma as a function of alpha. So, the second derivative of sigma, in terms of alpha, is positive when rho (correlation) equals zero.

I think I get the general meanings, but I don't know how rho factors into this graph directly! Please help work through this problem!