$23.$ The table below presents the variance $-$ covariance matrix and the mean returns for six different stocks of financial institutions, based on their monthly data.

A

B

$$

D

FRE

WM

STT

$1$

$2$

FRE

$0\mathrm{.}0052$

$3$

WM

$4$

STT

$5$

JPM

$6$

GS

$7$

C

F G $0\mathrm{.}00330\mathrm{.}00150\mathrm{.}00390\mathrm{.}00680\mathrm{.}00100\mathrm{.}00330\mathrm{.}01200\mathrm{.}00340\mathrm{.}00720\mathrm{.}00630\mathrm{.}00150\mathrm{.}00150\mathrm{.}00340\mathrm{.}00460\mathrm{.}00580\mathrm{.}00390\mathrm{.}00150\mathrm{.}00390\mathrm{.}00720\mathrm{.}00580\mathrm{.}03790\mathrm{.}00730\mathrm{.}00230\mathrm{.}00680\mathrm{.}00630\mathrm{.}00390\mathrm{.}00730\mathrm{.}03890\mathrm{.}00230\mathrm{.}00100\mathrm{.}00150\mathrm{.}00150\mathrm{.}00230\mathrm{.}00230\mathrm{.}0018$

E

H

I Mean

JPM

GS

returns

$0\mathrm{.}24\%$

$-0\mathrm{.}89\%$

$0\mathrm{.}48\%$

$0\mathrm{.}44\%$

$-1\mathrm{.}46\%$

$1\mathrm{.}04\%$

a$.$ Calculate the Global Minimum Variance Portfolio $($GMVP$).$

b$.$ Calculate the efficient portfolio, assuming the monthly risk free rate is

$0\mathrm{.}45\%.$

c$.$ Draw the efficient frontier with the expected return on the vertical axis, the standard deviation on the horizontal axis, and use convex

combinations between the GMVP and the efficient portfolio from $($a$)$ and $($b$),$ correspondingly $($notice that the whole efficient frontier can be drawn from any two points on it$,$ therefore since we know how to find the GMVP and the efficient portfolio it is enough to depict the complete efficient frontier$).$