Caulculation of Cosolidated Standard Deviation

FRM
#1

Hi All,

I found it a bit confused for calculation of the s.d. of a portfolio which is used to arrive the portfolio VaR sometimes.

Given the portfolio consists of security A and B with equal weight, standard deviation of A is S.D.(A), standard deviation of B is S.D.(B) and correlation is 1.

In most cases, the portfolio s.d. is calculated as: {0.5^2*S.D.(A)^2 + 0.5^2*S.D.(B)^2 + 2*0.5*0.5*S.D.(A)*S.D.(B)}^(1/2)

However, sometime, the s.d. is caulcated as: {0.5^2*S.D.(A)^2 + 0.5^2*S.D.(B)^2 - 2*0.5*0.5*S.D.(A)*S.D.(B)}^(1/2)

When should it “+” and when should it “-” for the third term? Could someone please provide some guidance? Thanks.

#2

Use a plus sign when it is Var(aX + bY).

Use a minus sign when it is Var(aX - bY).

#3

^ you probably saw this in the variance of the basis equation.

#4

simpler version: if you have an asset use +

if you have a liability use -

see it from this pov sam…