There are two stocks in the market, Stock A and Stock B$.$ The price of Stock A today is $$69.$ The price of Stock A next year will be $$58$ if the economy is in a recession, $$81$ if the economy is normal, and $$91$ if the economy is expanding. The probabilities of recession, normal times, and expansion are $14,66,$ and $20,$ respectively. Stock A pays no dividends and has a correlation of $64$ with the market portfolio. Stock $B$ has an expected return of $16\mathrm{.}1$ percent, a standard deviation of $33\mathrm{.}4$ percent, a correlation with the market portfolio of $18,$ and a correlation with Stock A of $30.$ The market portfolio has a standard deviation of $17\mathrm{.}4$ percent. Assume the CAPM holds.

a$-1.$ What is the return for each state of the economy for Stock A$?($A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

a$-$ What is the expected return of Stock A$?($Do not round intermediate calculations

$2.$ and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

a$-$ What is the variance of Stock A$?($Do not round intermediate calculations and round

$3.$ your answer to $4$ decimal places, e$.$g$.,1616.)$

a$-$ What is the standard deviation of Stock A$?($Do not round intermediate calculations

$4.$ and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

a$-$ What is the beta of Stock A$?($Do not round intermediate calculations and round

$5.$ your answer to $3$ decimal places, e$.$g$.,32\mathrm{.}161.)$

a$-$ What is the beta of Stock $B?($Do not round intermediate calculations and round

$6.$ your answer to $3$ decimal places, e$.$g$.,32\mathrm{.}161.)$

Answer is complete but not entirely correct.

$\backslash$table$[[$a$-1.$ Recession,$-15\mathrm{.}94,\%$