A portfolio is composed of two stocks, A and B$.$ Stock A has a standard deviation of

return of $30\%,$ while stock B has a standard deviation of return of $21\%.$ Stock A

comprises $60\%$ of the portfolio, while stock B comprises $40\%$ of the portfolio.

a$.$ If the variance of return on the portfolio is $0\mathrm{.}055,$ what is the correlation coefficient

between the returns on A and $B?$

b$.$ Does the portfolio weight minimize the portfolio variance? If not, please calculate the

minimum variance portfolio weights of A and B $?$ What is the expected return of this

minimum variance portfolio?

$($Hint: You are asked to use the formula to calculate the minimum$-$variance portfolio.

$\{$:$w_A=\frac{{}_B^2-{}_A*{}_B*{}_{AB}}{{}_A^2+{}_B^2--{}_A*{}_B*{}_{AB}})$