Additive vs Multiplicative Rate Calcs (VAR)

CFA Level III
#1

Does anyone know why, when converting monthly to yearly VAR, the expected return is adjusted through an additivie calc {monthly E® X 12} vs a multiplicative calc {(1+E®)^12 - 1 }? I would think the annual E® should/would account for compounding…no?

It seems to be a broader inconsistency in the CFA curriculum - would be easier to know if there was some principal or philosophy behind using one over the other, which would make knowing what to do easier to remember/understand than just memorizing something like “if in Fixed Income section, the unhedged return of a foreign bond is the return in local currency plus the return on the currency (R = Rlc + e), but if in the Derivatives section it’s [(1+ Rlc) (1 + Rfx) - 1]” multiplicative. Kind of like BEY calcs in Level I - done differently in different secitons.

For VAR - is there reasoning behind the additive calc or is it just something that needs to be memorized? It seems to be more of a factor here, because using the slightly different calc numbers can yield significantly different VAR answers if using large asset values, which is not uncommon.

Thanks!

#2

looks like this is the convention when annualizing a number. instead of compounding monthly returns you multiply by 12. check out question 12 B from page 113, CFAI Book 5. They give you 12 monthly returns that they compound to find an effective annual return. from that they derive an effective monthly return, which in turn is multiplied by 12 to annualize it. I thought this was weird.