Assume that the universe of risky assets is composed only of stocks X and Y$.$ The correlation coefficient between the returns of the two stocks is $0\mathrm{.}20.$

Consider the following table to answer the questions below.

Stock X

Stock Y

Expected return

$8\%$

$12\%$

Risk $($standard deviation$)$

$10\%$

$18\%$

Suppose that Natalle, whose degree of risk aversion is $6,$ wants to select the optimal portfollo from the opportunity set.

$1.$ Identify the weight of X in Natalie's optimal portfolio.

$2.$ Identify the weight of Y in Natalie's optimal portfolio.

$3.$ What is the expected return of Natalie's optimal portfolio?

$4.$ What is the risk $($standard deviation$)$ of Natalie's optimal portfolio?

$5.$ What is the value of Natalie's utility?

$6.$ If there exists a risk$-$free asset $($rf$)$ that earns $4\%$ annual return. Identify the weight of X in the optimal risky portfolio $($P$).$

$7.$ Identify the weight of Y in the optimal risky portfolio $($P$).$

$8.$ What is the return of the optimal portfolio of risky assets $($P$)?$

$9.$ What is the risk of returns for the optimal portfolio of risky assets $($P$)?$

$10.$ If Natalie now wants to invest in a complete portfolio. Do you think her utility will be higher, lower, or the same as the utility calculated in part $5$ above?

If higher, write $1$ in the answer box.

If lower, write $2$ in the answer box.

If the same write $3$ in the answer box