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

$$67.$ The price of Stock A next year will be $$56$ if the economy is in a recession, $$79$ if

the economy is normal, and $$89$ if the economy is expanding. The probabilities of

recession, normal times, and expansion are $\mathrm{.}12,\mathrm{.}68,$ and $\mathrm{.}20,$ respectively. Stock A pays

no dividends and has a correlation of $\mathrm{.}62$ with the market portfolio. Stock $B$ has an

expected return of $17\mathrm{.}3$ percent, a standard deviation of $33\mathrm{.}2$ percent, a correlation with

the market portfolio of $\mathrm{.}16,$ and a correlation with Stock A of $.28.$ The market portfolio has

a standard deviation of $17\mathrm{.}2$ 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

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$.,\mathrm{.}1616.)$

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

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

would you prefer?

Stock $A$

Stock B

b$-$ What is the expected return of a portfolio consisting of $70$ percent of Stock A and $30$

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$-$ What is the standard deviation of a portfolio consisting of $70$ percent of Stock A and

$30$ 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$.,32\mathrm{.}161.)$