How can we calculate standard deviation for a large (around 200 stocks) equity portfolio?

start with calculating the daily return for your portfolio as follows:

((Stock1 exposure / Total portfolio) * Stock1 return) + ((Stock2 exposure / Total portfolio) * Stock2 return) +................ + ((Stock200 exposure / Total portfolio) * Stock200 return)

this will give your daily return

and out of the results you can calculate the SD for your portfolio returns.