Q$2(60\%)$ Write a Python program that solves $($a$),($b$),$ & $($c$).$

EXERCISE $8\mathrm{.}8$ A portfolio manager is designing a portfolio of stocks in three com$-$

panies: Exxon $($XON$),$ Microsoft $($MSFT$),$ Oracle Systems $($ORCL$),$ plus the S&P$500$

index. Table $8\mathrm{.}16$ summarizes the manager's estimates of the expected annual re$-$

turns, standard deviations, and correlations of the annual returns of the three com$-$

panies' stocks plus the S&P$500$ index.

TABLE $8\mathrm{.}16$

Annual expected

returns, standard

deviations, and

correlations for stocks

in three companies

plus the S&P$500$

index.

Answer the following questions by considering appropriate nonlinear portfolio

optimization models.

$($a$)$ Suppose that the target expected annual return of the portfolio is $30\%.$ What is

the minimum standard deviation of the manager's portfolio? What is the opti$-$

mal asset allocation?

$($b$)$ Suppose that the target standard deviation of the portfolio is $10\%.$ What is the

maximum expected return of the manager's portfolio? What is the optimal asset

allocation?

$($c$)$ Using one of the models in $($a$)$ or $($b$),$ compute and plot the efficient frontier of

this portfolio.