Hi all, got a question on VaR subadditivity here. Is the subadditivity of VaR dependent on level of confidence? Or will the criteria of normal distribution be sufficient? My friend and I are confused and we much appreciate any help. Pls see the reference paper attached. Especially on page 14 , first paragraph and paragraph after remark 4. It says VaR computed under a distribution for which all prices are jointly normal distributed, do satisfy subadditivity as long as probability of excedence are smaller than 0.5. The paper then go on to show an example where using a 90% confidence limit, VaR is not subadditive. But most will think that as long as the normal distribution assumption holds, VaR is intuitively subadditive, isn't that true? Consider a 2 asset portfolio, if correlation is perfectly +1, then VaR (portfolio) = VaR(asset 1) + VaR(asset 2). And any other correlation will mean VaR (portfolio) < VaR(asset 1) + VaR(asset 2), thus this formula only ask for normality and level of confidence has no effect. Is this a true statement.When does the above statement breakdown? What are the qualifications? Any comments welcomed!IF you have better reference paper to direct me to, much appreciated !!Thanks for enlightening me!!

From what I recall if you are trying to calculate VAR of 2 assets than for subadditivty to exist you need the payoffs from the assets to have an elliptical distribution....There was a post about this somewhere in the forum.As an example consider the VAr of a bunch of digital options