Formula to add two VARS

CFA General
#1

What is the formula to add two vars I know Var A + Var B doesn’t equal the total because of correlation so there must be some formula.

#2

Var(A+B) = Var(A) + Var(B) + 2*COV(A,B) Var(aA + bB) = (a^2)Var(A) + (b^2)Var(B) + 2(ab)COV(A,B) a = weight of asset A b = weight of asset B generally a+b=1

#3

One last useful little thing: COV(A,B) = Corr(A,B) * SD(A) * SD(B)

#4

One “trick” top remember this is to relate it to the formula for (A+B)^2 (A+B)^2 = A*^2 + B^2 + 2AB vs Var(A+B) = Var(A) + Var(B) + 2*COV(A,B)

#5

Yep, that’s how I remember it.

#6

because Var is not a linear operator like Expected value. If you have a constant inside the brackets you can square it to take it out. [list] [*]Cov(X,X)=Var(X) [*]Var(aX) = a^2Var(X) [*]Var(a) = 0 (variance of a constant is 0) [/list] In your example, Var(A)+Var(B) = Var(A+B) when the A,B is 0 correlation.

#7

you sure you’re not talking about VaR? :slight_smile:

#8

isnt VaR non additive?

#9

Var = Variance VaR = Value at Risk