Question $13$

$5$ pts

Consider the following four risky assets:

An investor is looking for a portfolio with an expected return of $13\%.$ What weight should she assign to Firm $3$ to achieve a portfolio with $(1)$ the lowest variance possible, and $(2)$ an expected return of exactly $13\%?$ Note the following:

$g=1\mathrm{.}75362=-0\mathrm{.}06611=-0\mathrm{.}04089=-0\mathrm{.}77884$

$h=\{\begin{array}{c}\text{:}[-13\mathrm{.}38079]\\ 1\mathrm{.}47007\\ 1\mathrm{.}68944\\ 10\mathrm{.}22128\end{array}$

Answer in decimal format, rounded to $3$ decimal places. For example, if your answer is $12\mathrm{.}125\%,$ enter $"0\mathrm{.}121".$ If your answer is $12\mathrm{.}188\%,$ enter $"0\mathrm{.}122".$