$4$ Manager A follows the stocks in a broad market index and has made independent forecasts for $225$ of them. Manager A$\text{'}$s information coefficient $($IC$)$ is $0\mathrm{.}12.$

Manager B has made independent forecasts for $49$ stocks. Manager B$\text{'}$s IC is $0\mathrm{.}25.$

$($i$)$ Approximate the information ratio for each manager.

$($ii$)$ Which manager has the best performance as measured by the information ratio?