Exercise $1$

Using the data on these $6$ companies, compute the weights of two tangency portfolios and use these two portfolios to generate the mean$-$variance efficient frontier. Plot the frontier in the usual mean$-$standard deviation space.

$($For consistency, choose the following $"c"$ values: $c=0\%$ and $c=\mathrm{.}25\%($monthly$).)$

Hint: First compute the means and variance$-$covariance matrix for the six companies

Also Plot the tangent to the mean$-$variance frontier for the risk free rate of $.25\%$

Exercise $2$:

Using the data on these six companies compute the return matrix and variance covariance matrix and then use solver to compute the return and variance of efficient frontier without shortsale.

Hint: Compute the min. variance for Rp ranging from $.2\%$ to $1\%$ with increments of $\mathrm{.}1\%.$

$\backslash$table$[[$Month$,$PFE,BAC,$\frac{?}{\text{b}\text{a}\text{r}}(AA),\frac{?}{\text{b}\text{a}\text{r}}(GE),VZ,$MO$],[-0\mathrm{.}01319,-0\mathrm{.}01014,0\mathrm{.}044681,-0\mathrm{.}10153,-0\mathrm{.}06079,-0\mathrm{.}11195],[,2,0\mathrm{.}006038,-0\mathrm{.}01965,0\mathrm{.}028513,0\mathrm{.}096027,0\mathrm{.}093528,0\mathrm{.}010677],[,3,-0\mathrm{.}04502,0\mathrm{.}024432,0\mathrm{.}007159,-0\mathrm{.}00076,-0\mathrm{.}05386,-0\mathrm{.}01307],[,4,0\mathrm{.}021315,0\mathrm{.}003882,-0\mathrm{.}00612,0\mathrm{.}03426,-0\mathrm{.}04508,0\mathrm{.}019859],[,5,0\mathrm{.}028419,0\mathrm{.}007735,0\mathrm{.}033082,0\mathrm{.}033861,-0\mathrm{.}06099,-0\mathrm{.}01173],[,6,-0\mathrm{.}00561,-0\mathrm{.}04413,-0\mathrm{.}02607,-0\mathrm{.}01147,-0\mathrm{.}03579,-0\mathrm{.}02346],[,7,-0\mathrm{.}04407,-0\mathrm{.}00433,0\mathrm{.}035571,-0\mathrm{.}03916,0\mathrm{.}073479,246],[,8,-0\mathrm{.}00161,-0\mathrm{.}0258,0\mathrm{.}055854,132,-0\mathrm{.}03957,441],[,9,-0\mathrm{.}02161,0\mathrm{.}008331,0\mathrm{.}05389,-0\mathrm{.}02002,-0\mathrm{.}08847,-0\mathrm{.}00061],[,10,0\mathrm{.}038955,0\mathrm{.}007128,0\mathrm{.}018179,-0\mathrm{.}12936,-0\mathrm{.}00532,-0\mathrm{.}02371],[,11,0\mathrm{.}060585,0\mathrm{.}053377,-0\mathrm{.}03011,-0\mathrm{.}0161,0\mathrm{.}134623,0\mathrm{.}014916],[,12,0\mathrm{.}005666,-0\mathrm{.}01176,0\mathrm{.}037505,0\mathrm{.}1,0\mathrm{.}078803,-0\mathrm{.}05816],[,13,-0\mathrm{.}0416,-0\mathrm{.}06562,185,0\mathrm{.}101201,269,1575],[,14,0\mathrm{.}036627,0\mathrm{.}011298,608,0\mathrm{.}029206,-0\mathrm{.}06444,0\mathrm{.}06],[,15,0\mathrm{.}004144,0\mathrm{.}058108,-0\mathrm{.}00334,-0\mathrm{.}04849,0\mathrm{.}042292,0\mathrm{.}010683],[,16,0\mathrm{.}096179,-0\mathrm{.}00546,0\mathrm{.}032458,0\mathrm{.}016453,0\mathrm{.}105366,-0\mathrm{.}01835],[,17,-0\mathrm{.}02043,-0\mathrm{.}00954,-0\mathrm{.}01107,-0\mathrm{.}05646,-0\mathrm{.}05654,-0\mathrm{.}0551],[,18,-0\mathrm{.}0062,-0\mathrm{.}03065,0\mathrm{.}025985,-0\mathrm{.}00803,0\mathrm{.}020177,0\mathrm{.}073054],[z,19,0\mathrm{.}07131,-0\mathrm{.}00819,0\mathrm{.}089064,7371,448,.],[33,20,0\mathrm{.}009703,0\mathrm{.}041909,0\mathrm{.}044517,0\mathrm{.}069642,-0\mathrm{.}0404,0\mathrm{.}040213],[34,21,0\mathrm{.}0408,0\mathrm{.}043746,-0\mathrm{.}07327,0\mathrm{.}029028,-0\mathrm{.}01924,0\mathrm{.}055429],[35,22,0\mathrm{.}0056,-0\mathrm{.}00538,0\mathrm{.}062443,-0\mathrm{.}0603,0\mathrm{.}031027,0\mathrm{.}007406],[36,23,010024,0\mathrm{.}004842,0\mathrm{.}035411,0\mathrm{.}040525,0\mathrm{.}083362,-0\mathrm{.}01727],[7,24,-,0\mathrm{.}062642,0\mathrm{.}029331,-0\mathrm{.}05784,-0\mathrm{.}03722,0\mathrm{.}065827]]$