You$$re considering adding either of two assets to your portfolio. The first has expected returns of $11\%,$ standard deviation of returns of $18\%,$ and a beta of $0\mathrm{.}85.$ The second has a beta of $1\mathrm{.}2,$ standard deviation of returns of $35\%$ and expected returns of $16\%.$ Assume the T$-$Bill rate is $7\%$ and the expected return of the market index is $12\%.$

Suppose you currently hold a market index portfolio. Would you consider adding either or both two assets to your portfolio?

CAPM Formula

Expected Return R$\_$project $=$ R$\_$f$+\backslash$beta $($R$\_$m$-$ R$\_$f $)$

Expected Return R$\_($Asset $1)=0\mathrm{.}07+0\mathrm{.}85(0\mathrm{.}12-0\mathrm{.}07)=0\mathrm{.}1125=11\mathrm{.}35\%$

Expected Return R$\_($Asset $2)=0\mathrm{.}07+1\mathrm{.}2(0\mathrm{.}12-0\mathrm{.}07)=0\mathrm{.}13=13\%$

b$.$ Now suppose you are forced to mix one of the two assets with only T$-$bills. Which asset would you choose to mix with the T$-$Bill and why?

c$.$ If the Covariance of the first asset$$s returns and the market returns is $61$ then what is the standard deviation of expected market returns? Given this result, what is the Covariance of the returns between the second asset and the market?