Question $1(10$ marks$)$

$($a$)$ You are given the following table that shows the probabilities of occurrence of $3$ states and expected rate of returns on stocks W and X :

$\backslash$table$[[$State$,$Probability,$\backslash$table$[[$Expected Returns on$],[$Stock W$]],\backslash$table$[[$Expected Returns on$],[$Stock X$]]],[$Boom$,0\mathrm{.}3,0\mathrm{.}20,-0\mathrm{.}10],[$Neutral$,0\mathrm{.}5,0\mathrm{.}10,0\mathrm{.}10],[$Recession$,0\mathrm{.}2,-0\mathrm{.}05,0\mathrm{.}15]]$

Calculate the expected rates of returns and standard deviations of stocks W and X$.(6$ marks$)$

$($b$)$ Your colleague has given you his forecasts of stocks Y and Z as follows:

$\backslash$table$[[$State$,$Probability,$\backslash$table$[[$Expected Returns on$],[$Stock Y$]],\backslash$table$[[$Expected Returns on$],[$Stock Z$]]],[$Boom$,0\mathrm{.}5,0\mathrm{.}12,-0\mathrm{.}10],[$Bust$,0\mathrm{.}5,-0\mathrm{.}03,0\mathrm{.}20]]$

He would like to invest $40\%$ of his money in stock Y and $60\%$ of his money in stock Z to construct a portfolio.

Calculate the portfolio expected returns and its standard deviation $(4$ marks$)$

Question $2(10$ marks$)$

Suppose you consider buying a share of Stock J at a price of $$41.$ The stock is expected to pay a dividend of $$5$ next year and its price is expected to be $$39$ next year.

$($a$)$ Calculate the expected returns of Stock J in this year. $(2$ marks$)$

According to the data on Yahoo Finance, the yield on short$-$term government securities is $3\%$ and the expected return of market portfolio is $10\%.$ The beta of stock J is $0\mathrm{.}85.$

$($b$)$ According to the CAPM, what is the fair returns of Stock J$?(2$ marks$)$

$($c$)$ Compare the returns found in $($a$)$ and $($b$),$ is Stock J currently overpriced or underpriced? $(2$ marks$)$

$($d$)$ Draw the security market line $($SML$)$ on a well$-$labelled diagram and plot Stock J$.$ Is Stock J above or below the SML$?(4$ marks$)$