## VaR

Finance Junkie
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### VaR

Pls explain:

If portfolio A has a VaR of 100 and portfolio B has a VaR of 200, then the VaR of the portfolio C = A + B (perhaps under nonnormal conditions):
a. Will certainly be smaller than or equal to 300
b. Will be exactly equal to 300
c. Can be greater or smaller than 300
d. Will be greater than 300

Pristine Solution: Will certainly be smaller than or equal to 300. You cannot just add tail observations without knowing the distribution, and even then it takes some work.

My Qn: VaR does not follow the subadditivity. So how can we be sure that Portfolio VaR will certainly be smaller than the assets of the portfolio??

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content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

### Re: VaR

Hi Suresh,

The answer would be less than 300 for correlation less than 1. Only if the correlation between the two is equal to 1, then it would equal to 300.

Take a look at the VaR formula for portfolios.

Hope this helps..

Finance Junkie
Posts: 99
Joined: Sat Apr 07, 2012 10:24 am

### Re: VaR

Dear Content Pristine,

No your solution is not helping.

I know the VaR formula for portfolios. What I am asking is that, VaR does not follow the rule of subadditivity(thats why we do stress testing to complement VaR). That means the VaR of a combined portfolio can be larger than the sum of the VaRs of its components.

So in thsi how can we be so sure that VaR is following the rule of subadditivity and it will less than or equal to 300??

content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

### Re: VaR

Unless mentioned, these types of questions refers to historic VaR. Unless mentioned, you do not need to consider the VaR after stress testing.