# How to find the minimum variance portfolio? [migrated]

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)?

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Does anything strike you as odd about the resulting value of sigma squared, when you follow your intuition? Could there be a mistake in the transcription of the question? (I could be wrong, I don't do MPT, it just strikes me as a bit peculiar, that's all) – EnergyNumbers Jan 7 '12 at 7:08