There are two stocks in the market, stock A and stock $B.$ The price of stock A today is $$88.$ The price of stock A next year will be $$76$ if

the economy is in a recession, $$96$ if the economy is normal, and $$109$ if the economy is expanding. The probabilities of recession,

normal times, and expansion are $0\mathrm{.}2,0\mathrm{.}6,$ and $0\mathrm{.}2,$ respectively. Stock A pays no dividends and has a correlation of $0\mathrm{.}80$ with the

market portfolio. Stock B has an expected return of $16\mathrm{.}0$ percent, a standard deviation of $37$ percent, a correlation with the market

portfolio of $0\mathrm{.}22,$ and a correlation with stock $A$ of $0\mathrm{.}61.$ The market portfolio has a standard deviation of $31$ percent. Assume the CAPM

holds.

a$-1.$ Calculate the expected return of stock $A.($Round the final answer to $2$ decimal places. Do not round the intermediate

calculations.$)$

Expected return

a$-2.$ Calculate the beta of both stock A and stock $B.($Round the final answers to $3$ decimal places. Do not round the intermediate

calculations.$)$

${}_A$

${}_B$

a$-3.$ If you are a typical, risk$-$averse investor with a well$-$diversified portfolio, which stock would you prefer?

Stock B

Stock A

b&c$.$

What are the expected return, standard deviation and beta of a portfolio consisting of $70$ percent of stock A and $30$ percent of stock B$?($Round the beta value to $3$ decimal places and other values to $2$ decimal places. Do not round the intermediate calculations.$)$