Question

an investor is trying to minimize risk when distributing funds between two investments. the risk function is $r(x) = 0.0802x^2 - 0.0722x + 0.0361$. if $x$ is the portion invested in the first option, how should the investor distribute the funds to minimize risk? first option: 0.98 second option: 0.02 first option: 0.55 second option: 0.45 first option: 0.45 second option: 0.55 first option: 0.02 second option: 0.98

Explanation:

Step1: Identify vertex of quadratic

For quadratic $ax^2+bx+c$, vertex $x=-\frac{b}{2a}$
Here $a=0.0802$, $b=-0.0722$

Step2: Calculate optimal $x$

$$ x = -\frac{-0.0722}{2\times0.0802} = \frac{0.0722}{0.1604} \approx 0.45 $$

Step3: Find second portion

Since total portion is 1, second portion = $1 - 0.45 = 0.55$

Answer:

First option: 0.45
Second option: 0.55