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 $\backslash$$$77.$ The price of Stock $\backslash ($ A $\backslash )$ next year will be $\backslash (\backslash$$ $66\backslash )$ if the economy is in a recession, $\backslash (\backslash$$ $89\backslash )$ if the economy is normal, and $\backslash (\backslash$$ $99\backslash )$ if the economy is expanding. The probabilities of recession, normal times, and expansion are $\mathrm{.}22\mathrm{.}58,$ and $\mathrm{.}20,$ respectively. Stock A pays no dividends and has a correlation of $72$ with the market portfolio. Stock B has an expected return of $14\mathrm{.}2$ percent, a standard deviation of $34\mathrm{.}2$ percent, a correlation with the market portfolio of $\mathrm{.}26,$ and a correlation with Stock A of $\mathrm{.}38.$ The market portfolio has a standard deviation of $18\mathrm{.}2$ 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$.,32\mathrm{.}161.)$