$(20$ points$)$ The table below presents the returns on stocks ABC and XYZ over a five$-$year period.

$\backslash$table$[[$Year$,$ABC,XYZ$],[1,0\mathrm{.}35,0\mathrm{.}13],[2,0\mathrm{.}28,0\mathrm{.}35],[3,-0\mathrm{.}07,-0\mathrm{.}12],[4,-0\mathrm{.}22,-0\mathrm{.}20],[5,0\mathrm{.}48,0\mathrm{.}52]]$

a$.(5$ points$)$ Assume that the average returns from the data equals the expected returns for the respective stocks. If you want to form a portfolio with expected returns of $15\%,$ what proportion of your assets would you invest in each of these stocks?

b$.(5$ points$)$ What is the standard deviation of your portfolio?

c$.(5$ points$)$ Suppose that the risk$-$free rate is $5\%.$ Compute the slopes of the capital allocation lines $($CALs$)$ for ABC and XYZ$.$ Which of these two stocks yields a higher reward$-$to$-$risk ratio?

d$.(5$ points$)$ Your boss claims that you should invest only in the stock with the higher reward$-$to$-$risk ratio, and never invest in the stock with the lower reward$-$to$-$risk ratio. Do you agree? Explain.