Question $1(5$ points$)$

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A portfolio manager is using utility function U$($X$)=$ X $-($$/2)$X$^2$$^2$ to optimize allocation to a tech stock ETF, where $=0\mathrm{.}12(12\%$ expected return$),$ $^2=0\mathrm{.}09(30\%$ volatility$),$ and $=2($risk aversion$).$ What is the optimal allocation X$*$ to the ETF?$$

Question $1$ options:

$1\mathrm{.}33$ or $133\%$

$0\mathrm{.}45$ or $45\%$

$0\mathrm{.}89$ or $89\%$

$0\mathrm{.}67$ or $67\%$