$($Capital asset pricing$$ model$)$Grace Corporation is considering the following investments. The current rate on Treasury bills is $3$ percent and the expected return for the market is $10$ percent.

Stock

Beta

K

$1\mathrm{.}19$

G

$1\mathrm{.}37$

B

$0\mathrm{.}87$

U

$0\mathrm{.}94$

$($Click on the icon in order to copy its contents into a spreadsheet.$)$

a$.$Using the$$ CAPM, what rates of return should Grace require for each individual$$ security?

b$.$How would your evaluation of the expected rates of return for Grace change if the$$ risk$-$free rate were to rise to $4$ percent and the market risk premium were to be only $6\mathrm{.}5$percent$?$

c$.$Which market risk premium scenario$($from part a or b$)$ best fits a recessionary$$ environment? A period of economic$$ expansion? Explain your response.