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My problem is that I want to compute the VAR for several days from now (10,15, maybe even 30). The common idea says that if the return is normally distributed with mean of 0 you can scale up the VAR by multiplying it with SQRT(Time). Obviously I cannot do that for the entire portfolio VAR.

Am I allowed to compute VAR for oil price, scale it up by SQRT(Time) and then introduce that (my 5th quantile of oil) into the portfolio valuation and compute the portfolio once?