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

Rate of return if state occurs

State of the economy Probability of state of the economy Stock I Stock II

Recession $0\mathrm{.}150\mathrm{.}11-0\mathrm{.}25$

Normal $0\mathrm{.}550\mathrm{.}180\mathrm{.}11$

Irrational exuberance $0\mathrm{.}300\mathrm{.}080\mathrm{.}31$

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$)$