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 $$66.$ The price of Stock A next year will be $$55$ if the economy is in a recession, $$78$ if the economy is normal, and $$88$ if the economy is expanding. The probabilities of recession, normal times, and expansion are $\mathrm{.}11,\mathrm{.}69,$ and $\mathrm{.}20,$ respectively. Stock A pays no dividends and has a correlation of $\mathrm{.}61$ with the market portfolio. Stock B has an expected return of $17\mathrm{.}9$ percent, a standard deviation of $33\mathrm{.}1$ percent, a correlation with the market portfolio of $\mathrm{.}15,$ and a correlation with Stock A of $\mathrm{.}27.$ The market portfolio has a standard deviation of $17\mathrm{.}1$ percent. Assume the CAPM holds.

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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$-2.$

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$-3.$

What is the variance of Stock A$?($Do not round intermediate calculations and round your answer to $4$ decimal places, e$.$g$.,\mathrm{.}1616.)$

a$-4.$

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$-5.$

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$-6.$

What is the beta of Stock B$?($Do not round intermediate calculations and round your answer to $3$ decimal places, e$.$g$.,32\mathrm{.}161.)$

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If you are a typical, risk$-$averse investor with a well$-$diversified portfolio, which stock would you prefer?$$

multiple choice

Stock A

Stock B

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b$-1.$

What is the expected return of a portfolio consisting of $75$ percent of Stock A and $25$ percent of Stock B$?($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$-2.$

What is the standard deviation of a portfolio consisting of $75$ percent of Stock A and $25$ percent of Stock B$?($Do not round intermediate calculations and enter your answer$$as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$

What is the beta of the portfolio in part $($b$)?($Do not round intermediate calculations and round your answer to $3$ decimal places, e$.$g$.,32\mathrm{.}161.)$