For me to clear this confusion, can you please briefly conceptually explain how multivariate follows CLT although the variable are dependent (which contradict with concept of CLT, that is independent variables)?
The correct statement should be: The sum of i.i.d multivariate variables, will follow the multivariate normal distribution according to the multivariate CLT.
The CLT is a particular case of multivariate CLT when the dimension of iid multivariate variable is equal to 1. And you can not use the CLT for multivariate variables.
PS: I think this concept is out of scope of CFA program. But if you want to understand more about the multivariate CLT, you should google the three definitions: “multivariate random variable”, “iid” and “multivariate Central Limit Theorem”.