Problem $11-37$ Standard Deviation and Beta

There are two stocks in the market, Stock A and Stock B$.$ The price of Stock A today is $$81.$ The price of Stock A next year will be $$70$ if the economy is in a recession, $$93$ if the economy is normal, and $$103$ if the economy is expanding. The probabilities of recession, normal times, and expansion are $\mathrm{.}26,\mathrm{.}54,$ and $\mathrm{.}20,$ respectively. Stock A pays no dividends and has a correlation of $\mathrm{.}76$ with the market portfolio. Stock $B$ has an expected return of $14\mathrm{.}6$ percent, a standard deviation of $34\mathrm{.}6$ percent, a correlation with the market portfolio of $\mathrm{.}30,$ and a correlation with Stock A of $\mathrm{.}42.$ The market portfolio has a standard deviation of $18\mathrm{.}6$ 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$.,\mathrm{.}1616.)$

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$.,32\mathrm{.}161.)$