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