Consider a two$-$asset portfolio, where the risk $-$free asset offers a return of $5\%$ and the risky asset, A$,$ an expected return of $15\%$ with a standard deviation of $20\%.$

$($a$)$ What would be the expected return and risk of this portfolio if the two assets are combined in equal proportions?

$($b$)$ Suppose the share of the risky asset A in the portfolio is decreased to $30\%.$ What is expected return and risk of the portfolio now?

$($c$)$ Compute the Sharpe ratios in each of $($a$)$ and $($b$),$ draw the Capital allocation line $($CAL$)$ and show the positions of the two portfolios on the CALs. Comment.

$($d$)$ Suppose a second risky asset, B$,$ is added to the portfolio with an expected return of $25\%$ and a standard deviation of returns of $38\%.$ Compute the expected return and standard deviation of this three$-$asset portfolio including assets, A$,$ B and the risk$-$free asset, where all three assets are combined in equal proportions and where the correlation between the risky assets returns is $-0\mathrm{.}5.$