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