Another way of formulating the Markowitz' portfolio scheme is via the following

optimization problem.

$mamiz{e}_w,w^{TT}-w^{TT}w$

subject $tow0,w^{TT}1=1$

Here, $>0$ is a trade$-$off parameter which controls how much the investor values the

portfolio variance $($risk$)$ over the portfolio expected return.

$($a$)$ Explain why this problem is QP$?$

$($b$)$ Use the module qpsolvers to find the solution to this problem with $$ and $$ as

given in Problem $1.$ Choose $=\{1,2,$dots,$10\}{10}^{-2}.$

$($c$)$ Plot the elements of $w_{}^{***}$ versus $$ and compare it with the figure in Problem $1$ part

f$.$ Find the value of $$ for which the solution to $(2)$ is as close as possible to the

solution in problem $(1)$ with $=0\mathrm{.}6.$

Observation #$1$: Make sure to write your code in a modular, readable way. Code

organization will be taken into account for the grading. Use meaningful names for

variables, create functions to organize your code as much as possible. In case of doubt

on coding best practices, take a look at the Google's style guide. Note that you don't

have to strictly follow that style, you can develop your own, but make sure it is

understandable and you use it consistently.

Observation #$2$: Submit your code via canvas in zipped file $(.$zip$)$ containing a Jupyter

notebook $(.$ipynb$)$ and also its exported version in the HTML $(.$ html$)$ format.