$($Qn$.)$ Use the security returns below, to answer the following questions. Assume that each return is equally likely to occur.

Stock A Stock B

$17\mathrm{.}0\%9\mathrm{.}0\%$

$11\mathrm{.}3\%8\mathrm{.}0\%$

$10\mathrm{.}0\%7\mathrm{.}0\%$

$7\mathrm{.}8\%6\mathrm{.}0\%$

$6\mathrm{.}2\%5\mathrm{.}0\%$

$4\mathrm{.}7\%-2\mathrm{.}5\%$

a$.$ What is the correlation between these securities$?$

b$.$ Assuming that an investor can only choose between two securities$,$ A or B$,$ generate a model that will calculate the expected returns and the portfolio standard deviations for each of the following weights in security A: $0\%,10\%,25\%,50\%,75\%,90\%,100\%.$

c$.$ Plot the expected the returns and standard deviations for the portfolios above and tell which ones are efficient $($you can write on your graph $($a scatterplot is fine$)).$

d$.$ Find the expected return and portfolio standard deviation for the minimum variance portfolio.