Harold's investments consist entirely of an investment in an index fund. The variance of the return on the fund is $0\mathrm{.}022.$ Harold has decided that he wants to halve his portfolio variance and to achieve this outcome, he will withdraw some of his investment from the fund and invest that amount in the risk$-$free asset.

The percentage that he should withdraw from the index fund is closest to:

$($A$)25\%$

${}_p={}_A^2{}_A^2$

$($B$)29\%$

$($C$)50\%$

$($D$)71\%$