In addition to the information in Q$\mathrm{.}3,$ assume that the $($annual$)$ risk$-$free $($T$-$bill$)$ rate is

$4\%.$

a$.$ Calculate the expected returns and standard deviations of the following portfolios:

$($i$)75\%$ in the risk$-$free asset, $25\%$ in $B$

$($ii$)25\%$ in the risk$-$free asset, $75\%$ in $B$

$($iii$)50\%$ in the risk$-$free asset, $50\%$ in the portfolio in Q$\mathrm{.}3$a$($ii$)$

b$.$ Calculate the Sharpe ratios of

$($i$)$ asset $A$

$($ii$)$ asset $B$

$($iii$)$ the portfolio in Q$\mathrm{.}3$a$($i$)$

$($iv$)$ the portfolio in Q$\mathrm{.}3$a$($ii$)$

$($v$)$ the portfolio in Q$\mathrm{.}3$a$($iii$)$

$($vi$)$ the portfolio in Q$\mathrm{.}4$a$($iii$)$

c$.$ Find the weights $($T$-$bill, asset A$,$ asset B$)$ for a portfolio with the same expected

return as asset $B,$ using only a combination of the risk$-$free rate and the portfolio

in Q$\mathrm{.}3$a$($ii$)?$ What is the standard deviation of this portfolio? What is the

correlation of this portfolio with the portfolio in Q$\mathrm{.}4$a$($iii$)?$