In a survey of $N=2000$ employees, $1000$ are in the 'Staff' stratum and $1000$ in the 'Management' stratum. A researcher takes a sample of $n=100$ using proportional allocation. If the Staff stratum has a variance $S_1^2 = 100$ and Management has $S_2^2 = 400$, what is the variance of the stratified mean $\bar{y}_{st}$?