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

$$85.$ The price of Stock A next year will be $$74$ if the economy is in a recession, $$97$ if

the economy is normal, and $$107$ if the economy is expanding. The probabilities of

recession, normal times, and expansion are $\mathrm{.}30,\mathrm{.}50,$ and $\mathrm{.}20,$ respectively. Stock A pays

no dividends and has a correlation of $80$ with the market portfolio. Stock B has an

expected return of $15\mathrm{.}0$ percent, a standard deviation of $35\mathrm{.}0$ percent, a correlation with

the market portfolio of $\mathrm{.}34,$ and a correlation with Stock $A$ of $\mathrm{.}46.$ The market portfolio

has a standard deviation of $19\mathrm{.}0$ 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

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

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

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

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

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

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