Q$3.$ Use the monthly return data for IBM, BAC, and MSFT$,$ and the risk$-$free asset$$s return of $3\%$ to do the following:

$1.$ Find the portfolio $($weights of the three assets$)$ with minimum variance for a series of given target expected returns. $(8$ point$)$

$2.$ Find the optimal risky portfolio. $(3$ point$)$

$3.$ Find the Global Minimum$-$Variance Portfolio $($GMVP$).(3$ point$)$

$4.$ We want to form new portfolios using risk$-$free asset and optimal risky portfolio. What are the annual expected return, standard deviation and Sharpe ratio of the new portfolios with different weights of the risk$-$free asset and the optimal risky portfolio? $(4$ points$)$

$5.$ All the portfolios in part $4$ lie on capital allocation line $($CAL$).$ Make a smooth marked scatter plot with the minimum$-$variance frontier, optimal risky portfolio, GMVP and the capital allocation line on the same graph, including legends. $(3$ point$)$