Part $A{?}_{(}()())($Investment Management $-$ algebra $)$

Calculate the optimal risky portfolio for the following cases when short$-$sales are allowed.

Compute its expected return and the standard deviation of its returns.

Three risky assets: $R_F=6,R^{\text{'}}=[11,9,8],$ and

$=\left[\begin{array}{ccc}37& -4& 6\\ -4& 18& 0\\ 6& 0& 15\end{array}\right]$

Part B

Mrs Z$\text{'}$s utility function is given by the following equation:

$U_Z((\frac{?}{\text{b}\text{a}\text{r}}(R)),{}^2)\frac{?}{b}=ar(R)-0\mathrm{.}4{}^2$

For each one of the above cases, find the overall optimal portfolio for Mrs $Z$ and compute its

expected return and the standard deviation of its returns.

Further Guidance

There are two parts in the coursework. In part A$,$ you are asked to solve for the optimal

risky portfolio for $4$ different combinations of assets. Note that in each case, there is

risk$-$free asset available. In part B$,$ you are given the utility function for an individual

and required to find the overall optimal portfolio for each of the four cases in part $A.$

You can present your answer in the order of

Case $3$: Optimal Risky Portfolio

Case $3$: Overall Optimal Portfolio

OR in the order of

Case $3$: Optimal Risky Portfolio

Case $3$: Overall Optimal Portfolio

Please show all steps in your solution and explain them.