Problem $13-31$ Using CAPM $($LO$1,4)$

$10$ points

References

There are two stocks in the market, stock A and stock $B.$ The price of stock A today is $$74.$ The price of stock A next year will be $$62$ if the economy is in a recession, $$82$ if the economy is normal, and $$94$ if the economy is expanding. The probabilities of recession, normal times, and expansion are $0\mathrm{.}2,0\mathrm{.}6,$ and $0\mathrm{.}2,$ respectively. Stock A pays no dividends and has a beta of $0\mathrm{.}77.$ Stock $B$ has an expected return of $13\%,$ a standard deviation of $34\%,$ a beta of $0\mathrm{.}54,$ and a correlation with stock $A$ of $0\mathrm{.}48.$ The market portfolio has a standard deviation of $14\%.$ Assume the CAPM holds.

a$.$ What are the expected return and standard deviation of stock $A?($Do not round intermediate calculations. Round the final answers to $2$ decimal places.$)$

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

Stock A

Stock B

c$.$ What are the expected return and standard deviation of a portfolio consisting of $55\%$ of stock A and $45\%$ of stock B$?($Do not round intermediate calculations. Round the final answers to $2$ decimal places.$)$

$\backslash$table$[[$Expected return,$\%$