A managed portfolio has a standard deviation equal to $25\%$ and a beta of $1\mathrm{.}25$ when the market portfolio's standard deviation is $40\%.$ The adjusted portfolio P$*$ needed to calculate the M$2$ measure will have $\_\_\_\_\_\_\_\_$ invested in the managed portfolio and the rest in T$-$bills.

Multiple Choice

$62\mathrm{.}50\%$

$22\mathrm{.}40\%$

$25\mathrm{.}00\%$

$160\mathrm{.}00\%$