II$.$ The single$-$index model for stock i is $r_i-r_f={}_i+{}_i(r_M-r_f)+e_i.$ The single$-$index model for stock

$j$ is $r_j-r_f={}_j+{}_j(r_M-r_f)+e_j.$ The standard deviation of the stock market return is ${}_M=0\mathrm{.}12.$ The

standard deviation of $e_i$ is ${}_e=0\mathrm{.}3.$ The standard deviation of $e_j$ is ${}_{ej}=0\mathrm{.}15.$ The market beta equals

$1\mathrm{.}5$ for stock i and $2$ for stock $j$ or ${}_i=1\mathrm{.}5,{}_j=2.$ The expected stock market return $E(r_M)$ is $12\%$ and

the risk$-$free rate $r_f$ is $5\%.$ Suppose the simple CAPM is valid. $(15$ points$)$

$($a$)$ Calculate the systematic risk, firm$-$specific risk, and total risk of both stocks i and j$.(6$

points$)$

$($b$)$ Which stock has lower total risk and which stock has a lower expected return? $(5$ points$)$

$($c$)$ Does the stock with the lower total risk have a lower expected return? Explain. $(4$ points$)$