portfolio-var

Hi, I have a 2 asset portfolio evenly weighted of stock A and stock B. If I purchase a long put, written on just stock A, with a delta of -0.536, how would I calculate the appropriate option sizing and how much it would minimize my portfolio VaR? Do I use the component VaR? Does the hedge...

Couldn't we combine the portfolio first to get the distribution of portfolio log returns and then calculate the portfolio VaR from there? Why do we need to compute individual VaRs and then combine them together using the var-covariance matrix?