Variance Properties

[Biju George]

Hi All,

Got a question on the below Variance properties

1)Var (x+y)=Var x +Var y
2)Var xy=Var x+ Var y + 2 covar(xy) corr(xy)

--How do you explain the difference of these two properties
1) If you have a portfolio 10% variance and other with 20 % variance combined variance =30% ?
2)How do you explain the second property in the above example

Thanks in advance

 

[Arka Bose]

Hi,
the first one is where X and Y ar not correlated, i.e x and y are independent variables, however, in 2nd, they are correlated.

 

[Dr. Jayanthi Sankaran]

Hi @RiskGuy,

Also, for the second property, the right formula is:

Var xy = Var x + Var y + 2 Cov(xy)

where Cov(xy) = Corr(xy)*sigma x *sigma y

Thanks!
Jayanthi

 

[Biju George]

Thanks for the comments