Refer the table below on the average excess return of the U$.$S$.$ equity market and the standard deviation of that excess return. Suppose that the U$.$S$.$ market is your risky portfolio.

Average Annual Returns U$.$S$.$ Equity Market

Period U$.$S$.$ equity $1-$Month T$-$Bills Excess return Standard Deviation Sharpe Ratio

$1927202112\mathrm{.}173\mathrm{.}308\mathrm{.}8720\mathrm{.}250\mathrm{.}44$

$1927195010\mathrm{.}260\mathrm{.}939\mathrm{.}3326\mathrm{.}570\mathrm{.}35$

$1951197410\mathrm{.}213\mathrm{.}596\mathrm{.}6220\mathrm{.}320\mathrm{.}33$

$1975199817\mathrm{.}976\mathrm{.}9810\mathrm{.}9914\mathrm{.}400\mathrm{.}76$

$1999202110\mathrm{.}161\mathrm{.}668\mathrm{.}5018\mathrm{.}850\mathrm{.}45$

Required:

If your risk$-$aversion coefficient is A $=3\mathrm{.}6$ and you believe that the entire $19272021$ period is representative of future expected performance, what fraction of your portfolio should be allocated to T$-$bills and what fraction to equity? Assume your utility function is U $=$ E$($r$)0\mathrm{.}5\backslash$times A$\backslash$sigma $2$squared.

What if you believe that the $19751998$ period is representative?