Problem $13-31$ Using CAPM $\backslash (($L O $1,4)\backslash )$ There are two stocks in the market, stock $\backslash ($ A $\backslash )$ and stock $\backslash ($ B $\backslash ).$ The price of stock $\backslash ($ A $\backslash )$ today is $\backslash (\backslash$$ $68\backslash ).$ The price of stock $\backslash ($ A $\backslash )$ next year will be $\backslash (\backslash$$ $56\backslash )$ if the economy is in a recession, $\backslash (\backslash$$ $76\backslash )$ if the economy is normal, and $\backslash (\backslash$$ $88\backslash )$ if the economy is expanding. The probabilities of recession, normal times, and expansion are $\backslash (0\mathrm{.}2,0\mathrm{.}6\backslash ),$ and $0\mathrm{.}2,$ respectively. Stock A pays no dividends and has a beta of $0\mathrm{.}71.$ Stock B has an expected return of $\backslash (13\backslash \%\backslash ),$ a standard deviation of $\backslash (34\backslash \%\backslash ),$ a beta of $0\mathrm{.}48,$ and a correlation with stock $\backslash ($ A $\backslash )$ of $0\mathrm{.}48.$ The market portfolio has a standard deviation of $\backslash (14\backslash \%\backslash ).$ 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$-$diversified portfolio, which stock would you prefer? Stock A Stock B c$.$ What are the expected return and standard deviation of a portfolio consisting of $\backslash (50\backslash \%\backslash )$ of stock $\backslash ($ A $\backslash )$ and $\backslash (50\backslash \%\backslash )$ of stock B$?($Do not round intermediate calculations. Round the final answers to $\backslash (\backslash$mathbf$\{2\}\backslash )$ decimal places.$)$ d$.$ What is the beta of the portfolio in $($c$)?($Do not round intermediate calculations. Round the final answer to $3$ decimal places.$)$ Beta of the portfolio