Based on current dividend yields and expected capital gains, the expected rate of returns, $\backslash (\backslash$beta $\backslash )$ values, and standard deviations of portfolios X and Y are given in the table below. The risk$-$free rate is $\backslash (5\backslash \%\backslash ),$ while the expected return of the market portfolio is $\backslash (40\backslash \%\backslash ).$ The standard deviation of the stock market index is $\backslash (18\backslash \%\backslash ).($a$)$ If you currently hold a market index portfolio, would you add either portfolio to your holdings? Explain your reasoning. $($b$)$ If instead, you could invest only in the risk$-$free asset and one of these alternative portfolios, which would you choose? Justify your answer.