Start with the partial model in the file Ch$03$ P$07$ Build a Model.xlsx$.$ Following is information for the required returns and standard deviations of returns for A$,$ B$,$ and C:

Stock ri $\backslash$sigma i

A $7\mathrm{.}0\%33\mathrm{.}96\%$

B $11\mathrm{.}060\mathrm{.}71$

C $22\mathrm{.}084\mathrm{.}57$

The correlation coefficients for each pair are shown in the following matrix, with each cell in the matrix giving the correlation between the stock in that row and column. For example, $\backslash$rho AB $=0\mathrm{.}1568$ is in the row for A and the column for B$.$ Notice that the diagonal values are equal to $1$ because a variable is always perfectly correlated with itself.

A B C

A $1\mathrm{.}00000\mathrm{.}15680\mathrm{.}1931$

B $0\mathrm{.}15681\mathrm{.}00000\mathrm{.}1673$

C $0\mathrm{.}19310\mathrm{.}16731\mathrm{.}0000$

The data has been collected in the Microsoft Excel file below. Download the spreadsheet and perform the required analysis to answer the questions below. Do not round intermediate calculations. Round your answers to two decimal places.

Download spreadsheet Ch$03$ P$07$ Build a Model$-$c$6$f$650.$xlsx

Suppose a portfolio has $40\%$ invested in A$,20\%$ in B$,$ and $40\%$ in C$.$ What are the expected return and standard deviation of the portfolio?

Expected return: fill in the blank $2$

$13\mathrm{.}80$

$\%$

Standard deviation: fill in the blank $3$

$59\mathrm{.}55$

$\%$

The partial model lists sixty six different combinations of portfolio weights $($only six of them are shown below$).$ For each combination of weights, find the required return and standard deviation.

wA wB wC $\backslash$sigma p

$0\%80\%20\%$ fill in the blank $4$

$\%$ fill in the blank $5$

$\%$

$10\%70\%20\%$ fill in the blank $6$

$\%$ fill in the blank $7$

$\%$

$30\%10\%60\%$ fill in the blank $8$

$\%$ fill in the blank $9$

$\%$

$50\%20\%30\%$ fill in the blank $10$

$\%$ fill in the blank $11$

$\%$

$60\%10\%30\%$ fill in the blank $12$

$\%$ fill in the blank $13$

$\%$

$70\%20\%10\%$ fill in the blank $14$

$\%$ fill in the blank $15$

$\%$

Construct a scatter diagram showing the required returns and standard deviations already calculated. This provides a visual indicator of the feasible set. Choose the correct graph.

The correct graph is

graph C

$.$

A$.$

B$.$

C$.$

D$.$

If you seek a return of $13\mathrm{.}5\%,$ then what is the smallest standard deviation that you must accept?

fill in the blank $17$

$\%$