Sally is evaluating two portfolios which consist of four assets but with different proportions. She is interested in using beta to compare the risk of the portfolio. Given below is the information on each of the portfolios:

$($a$)$ Calculate the betas for portfolios X and Y $.(6$m$)$

$($b$)$ Compare the risk of each portfolio to the market portfolio as well as to each other. Assume the market beta is $1\mathrm{.}0.(4$m$)$

$($c$)$ Determine which portfolio is riskier. Explain. $(4$m$)$

$($d$)$ Calculate the required return for each portfolio based on the capital asset pricing model $($CAPM$),$ assuming the risk$-$free rate is $2\%$ and the market return is $9\%.(6$m$)$