Problem $4(26$ marks$)$:

Consider the following information about stocks I and Il$.$

Rate of return if state occurs

State of the economy

Probability of state of the economy

Stock I

Stock $11$

Recession

$0\mathrm{.}15$

$0\mathrm{.}11$

$-0\mathrm{.}25$

Normal

$0\mathrm{.}55$

$0\mathrm{.}18$

$0\mathrm{.}11$

Irrational exuberance

$0\mathrm{.}30$

$0\mathrm{.}08$

$0\mathrm{.}31$

a$)$ Compute the expected return, variance, and standard deviation of stock I. $(7$ marks$)$

b$)$ Compute the expected return, variance, and standard deviation of stock II$.(7$ marks$)$

c$)$ Stock I has a beta of $1\mathrm{.}5,$ and stock II has a beta of $0\mathrm{.}8.$ If the market risk premium is $7\mathrm{.}5$ percent, and the risk$-$free rate is $4$ percent, is stock I correctly priced according to the CAPM? Stock II$?$ If these stocks are not correctly priced, what are your investment recommendations? $(12$ marks$)$