There are two stocks in the market, Stock A and Stock B$.$ The price of Stock A today is $$76.$ The price of Stock A next year will be $$65$ if the economy is in a recession, $$88$ if the economy is normal, and $$98$ if the economy is expanding. The probabilities of recession, normal times, and expansion are $,21,59,$ and $\mathrm{.}20,$ respectively. Stock A pays no dividends and has a correlation of $71$ with the market portfolio. Stock B has an expected return of $14\mathrm{.}1$ percent, a standard deviation of $34\mathrm{.}1$ percent, a correlation with the market portfolio of $\mathrm{.}25,$ and a correlation with Stock A of $37.$ The market portfolio has a standard deviation of $18\mathrm{.}1$ 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$.,32\mathrm{.}161.)$

$\backslash$table$[[$a$-1.$ Recession,$-14\mathrm{.}47,\%$