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 MarketPeriodU.S$.$ equity $1-$MonthT$-$Bills Excess return StandardDeviation SharpeRatio

$1927-201811\mathrm{.}723\mathrm{.}388\mathrm{.}3420\mathrm{.}360\mathrm{.}41$

$1927-19499\mathrm{.}400\mathrm{.}928\mathrm{.}4926\mathrm{.}830\mathrm{.}32$

$1950-197214\mathrm{.}003\mathrm{.}1410\mathrm{.}8617\mathrm{.}460\mathrm{.}62$

$1973-199513\mathrm{.}387\mathrm{.}266\mathrm{.}1118\mathrm{.}430\mathrm{.}33$

$1996-201810\mathrm{.}102\mathrm{.}217\mathrm{.}8918\mathrm{.}390\mathrm{.}43$

If your risk$-$aversion coefficient is A $=4$ and you believe that the entire $1927-2018$ 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$)0\mathrm{.}5$ times A times sigma$^2$