This problem corresponds to problems $10$ and $11$ in Chapter $6$ Problem Set.

Consider historical data showing that the average annual rate of return on the S$\backslash$&P $500$ portfolio over the past $85$ years has averaged roughly $8\backslash \%$ more than the Treasury bill return and that the S$\backslash$&P $500$ standard deviation has been about $\backslash (24\backslash \%\backslash )$ per year. Assume these values are representative of investors' expectations for future performance and that the current T$-$bill rate is $\backslash (3\backslash \%\backslash ).$

$1.$ Calculate the expected return and variance of portfolios invested in T$-$bills and the S$\backslash$&P $500$ index with weights as shown below. Note: Round your "Expected Return" answers to $3$ decimal places and "Variance" answers to $4$ decimal places.

$2.$ Calculate the utility levels of each portfolio for an investor with $\backslash ($ A$=2\backslash ).$ Assume the utility function is $\backslash ($ U$=$E$($r$)-0\mathrm{.}5\backslash$times A $\backslash$sigma$^\{2\}\backslash ).$ Note: Do not round intermediate calculations. Round your answers to $4$ decimal places. Negative amounts should be indicated by a minus sign.