Assume that you decide to form an equal$-$weighted portfolio including only those two stocks.

Stock A

Expected annual rate of return $8\%$

Expected annual standard deviation $24\%$

Stock B

expected annual rate of return $12\%$ expected annual standard deviation $30\%$

Calculate the expected standard deviation of your portfolio, corresponding to each scenario with regard to the correlation coefficient between stock A and stock B$,$ i$.$e$.$ when rho$\_12=-1,-0\mathrm{.}5,0,0\mathrm{.}5,$ or $1.$

If rho $\_12=0\mathrm{.}5,$ what is the standard deviation of the portfolio which invests $1/3$ in stock A$,1/3$ in stock B$,$ and $1/3$ in a risk$-$free asset?

If rho $\_12=0\mathrm{.}5,$ given that $50\%$ of the total investment is financed by borrowing at the risk$-$free rate, what is the standard deviation of the portfolio which invests equally in stock A and B$?$

If rho $\_12=0\mathrm{.}5,$ what combination of stock A and stock B offers the minimum risk?