There are two stocks in the market, stock A and stock $B.$ The price of stock A today is $$67.$ The price of stock A next year will be $$55$ if the economy is in a recession, $$75$ if the economy is normal, and $$87$ 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 $0\mathrm{.}70.$ Stock $B$ has an expected return of $13\%,$ a standard deviation of $34\%,$ a beta of $0\mathrm{.}47,$ 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.$)$

$\backslash$table$[[,$Stock A$],[$Expected return,$\%],[$Standard deviation,$\%]]$

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 $45\%$ of stock A and $55\%$ of stock B$?($Do not round intermediate calculations. Round the final answers to $2$ 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