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.

$4-$ Five risky assets: $R_F=4,R^{\text{'}}=[14,11,15,4,22],$ and

$=\left[\begin{array}{ccccc}9& 0& 3& 7& 5\\ 0& 6& -7& 14& 10\\ 3& -7& 12& 6& 5\\ 7& 14& 6& 3& -2\\ 5& 10& 5& -2& 17\end{array}\right]$

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 $4$: Optimal Risky Portfolio

Case $4$: Overall Optimal Portfolio

OR in the order of

Case $4$: Optimal Risky Portfolio

Case $4$: Overall Optimal Portfolio

Please show all steps in your solution and explain them.