An investor is trying to minimize risk when distributing funds between two investments. The risk function is R⁡(x)=0.0802⁢x^2−0.0722⁢x+0.0361 If x is the portion invested in the first option, how should the investor distribute the funds to minimize risk?

The risk function is a quadratic with a positive leading coefficient, 0.0802, so its minimum occurs at the vertex. For R(x)=ax²+bx+c, the vertex is at x=−b/(2a), giving x=0.0722/(2×0.0802)≈0.45. The remaining portion is 1−0.45=0.55, so the investor should put 0.45 in the first option and 0.55 in the second option.

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