$1.$ Jordan is attempting to form a portfolio between two risky assets and needs your help. Jordan is considering two potential portfolios:

$($p$1)$ $$50,000$ in Stock A$,$ $$50,000$ in Stock B

$($p$2)$ $$30,000$ in Stock A$,$ $$70,000$ in Stock B

The annualized expected return and volatility of Stock A are $10\%$ and $25\%,$ while for Stock B they are $8\%$ and $15\%.$ The two stocks have a correlation of $0\mathrm{.}5.$ There is a risk$-$free asset earning Rf $=4\%.$

$($a$)$ What is the expected return of each portfolio?

$($b$)$ What is the volatility of each portfolio?

$($c$)$ Suppose that both stocks realize their expected returns over the next

year $(10\%$ and $8\%).$ How much money would Jordan have invested one year from

now with each potential portfolio?

$($d$)$ Assume Jordan is a mean$-$variance investor, which portfolio should Jordan select and why?

$($e$)$ Assume Jordan$$s risk aversion coefficient is A $=3.$ How much should

Jordan allocate to their preferred risky portfolio and how much should they allocate

to the risk$-$free asset?