How to find the minimum variance portfolio? I am doing some revision questions on my Portfolio Theory module, and have come across the following question:
Consider an investor who has constructed a risky portfolio from N securities. The investment opportunity set is described by the equation:
$$\sigma^2 = 10 - 5{\times}E(r) + 0.5\times(E(r))^2$$
Find the minimum variance portfolio.
I can't find any info in my notes, but my intuition says differentiate, set to zero and rearrange for E(r)?

If you are trying to minimize sigma-squared, then the points where the derivative is zero will be at least local minima or maxima. If this is not intuitive, imagine a parabola and calculate the derivative at various points.
Another step would be to prove that the function is globally concave so that the local minima/maxima are in fact global, but your prof probably won't require that. In comparison with the parabola example, finding where the dy/dx is zero in y = x ^ 3 won't find the global.
I'm not sure what you mean by rearrange for E(r).
